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Physical and System-Level Design

MEMS Design and Analysis Tutorials, Vol. 1

CoventorWareTM 2008

. coventor .com

Version 2008

Coventor, Inc.This manual and its accompanying materials are licensed to the user for the period set forth in the applicable license agreement, subject to termination of the license by Coventor, Inc. at any time. The manual at all times remains the property of Coventor, Inc., or third parties from whom Coventor, Inc. has obtained a licensing right. The information contained in this manual including but not limited to the ideas, concepts and know-how, is proprietary, confidential and trade secret to Coventor, Inc. or such third parties and the information contained therein shall be maintained as proprietary, confidential, and trade secret to Coventor, Inc. or to such third parties. The information in this manual shall not be copied or reproduced in any form whatsoever, nor is any information in this manual to be disclosed to anyone other than an authorized representative of the user’s employer who is contractually obligated not to disclose same, without express prior written consent of Coventor, Inc. The user of this manual and the computer program(s) referred to herein retains full control over and is solely responsible for the mechanical design of the user’s equipment, machinery, systems, and products. COVENTOR, INC. MAKES NO WARRANTIES OF ANY KIND, INCLUDING THE WARRANTY OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE WITH RESPECT TO THE EQUIPMENT, MACHIN-ERY, SYSTEMS, AND PRODUCTS, DERIVED OR RESULTING HEREUNDER, AND THE USER ASSUMES ALL RISKS AND LIABILITY FOR RESULTS OBTAINED BY THE MANUFACTURING, USE OR IMPLEMENTATION OF THE COM-PUTER PROGRAMS(S) DESCRIBED HEREIN, WHETHER USED SINGLY OR IN COMBINATION WITH OTHER DESIGNS OR PRODUCTS. Coventor shall not be liable for any incidental, indirect, special, consequential, or punitive damages. Coventor makes no warranty that the equipment, machinery, systems, and products derived or resulting hereunder will not infringe the claims of domestic or foreign patents and further does not warrant against infringement by reason of the user, thereof in combi-nation with other designs, products, or materials or in the operation of any process. User shall protect, indemnify and hold harm-less Coventor of and from any loss, cost, damage (including attorney’s fees) or expense arising from any claim that is any way associated with the computer programs(s) described in this manual. Data presented in examples do not necessarily reflect actual test results and should not be used as design criteria.By acceptance of this manual, the user agrees to the above conditions and further agrees that this manual will not be exported (or re-exported from a country of installation), directly or indirectly, separately or as part of a system, without user or user’s employer, at its own cost, first obtaining all licenses from the United States Department of Commerce and any other appropriate agency of the United States Government as may be required by law.© Coventor, Inc., 2008.All rights reserved. No part of this work may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic or mechanical, including photocopying and recording, or by any information storage or retrieval system without prior permission in writing from Coventor, Inc. Information in this document is subject to change without notice.CoventorWare includes software developed by the University of California, Berkeley and its contributors.CoventorWare is enhanced with Visualization Software from Tecplot, Inc. of Bellevue, Washington, USA.CoventorWare and the associated documentation incorporate portions of ABAQUS/CAE and its associated documentation under license from ABAQUS, Inc. ABAQUS is a registered trademark of ABAQUS, Inc.Coventor, CoventorWare, Bubble-DropSim, CoSolve-EM, CoventorWare ANALYZER, CoventorWare ARCHITECT, Coventor-Ware DESIGNER, FlowMM, CoventorWare INTEGRATOR, MemElectro, MemCFD, DampingMM, MemFSI, MemHenry, MemMech, NetFlow, ReactSim, SwitchSim, and WHAT’S NEXT, AND NEXT, AND NEXT are registered trademarks of Coven-tor, Inc. Cary, NC.DXF is a trademark of Autodesk, Inc.Excel is a registered trademark of Microsoft CorporationFLEXlm is a registered trademark of Globetrotter Software, Inc.I-deas is a trademark of UGS. Permalloy is a registered trademark of B&D Industrial & Mining Services, Inc.SABER is a registered trademark of American Airlines, Inc., licensed to Synopsys, Inc.SaberDesigner, SaberGuide, CosmosScope, SaberSimulator, and SaberSketch are trademarks of Synopsys, Inc. Tecplot is a registered trademark of Tecplot, Inc.Cadence, Verilog and Verilog-XL are registered trademarks of Cadence Design Systems, Inc.Excel, and Windows XP are registered trademarks of Microsoft Corporation.X Window System is a trademark of Massachusetts Institute of Technology.MUMPs is a registered trademark of MEMSCAP, Inc.VdmTools is proprietary and copyrighted software of Visual Kinematics, Inc.All other trademarks or registered trademarks belong to their respective holders.Contact us at www.coventor.comDoc Ver 2008 Rev A Compatible with CoventorWare version 2008

ii March 3, 2008 Coventor, Inc.

Table of Contents Version 2008M

Table of Contents

Section 1: Introduction

1.1: Overview.................................................................................................. T1-1

1.2: Using CoventorWare .............................................................................. T1-1

1.3: Tutorials .................................................................................................. T1-2 1.3.1: Volume 1...................................................................................................................T1-2 1.3.2: Volume 2...................................................................................................................T1-4 1.3.3: Tutorial Installation Files ...........................................................................................T1-7 1.3.4: Tutorial Conventions .................................................................................................T1-7 1.3.5: Helpful Hints..............................................................................................................T1-7

Save Project Settings Often .....................................................................................T1-7

Material Properties Database Values .......................................................................T1-7

Matching Tutorial Results .........................................................................................T1-7

Setting Unused Boundary Condition Lines ..............................................................T1-8

Viewing Results from Previous Solver Runs ...........................................................T1-8

Defragment Hard Drive.............................................................................................T1-8

Section 2: Beam Design

2.1: Beam Design in Analyzer....................................................................... T2-2 2.1.1: Demonstrated Techniques........................................................................................T2-3 2.1.2: References................................................................................................................T2-3 2.1.3: Tutorial Initialization ..................................................................................................T2-4 2.1.4: Material Properties Database Setup .........................................................................T2-7 2.1.5: Process Editor.........................................................................................................T2-11 2.1.6: Layout Viewing and Editing.....................................................................................T2-14 2.1.7: Building the Solid Model .........................................................................................T2-18 2.1.8: Naming Entities.......................................................................................................T2-19 2.1.9: Meshing ..................................................................................................................T2-24

Choosing an Adequate Mesh .................................................................................T2-26 2.1.10: MemElectro...........................................................................................................T2-28 2.1.11: MemMech .............................................................................................................T2-33

MemMech BCs Window .........................................................................................T2-34 2.1.12: CoSolveEM ...........................................................................................................T2-39

MemMech Setup for CoSolveEM ...........................................................................T2-39

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Table of Contents Version 2008

2.1.13: MemMech Coupled Electrostatic Analysis ........................................................... T2-45 2.1.14: Parametric Study.................................................................................................. T2-50

MemMech BCs for Parametric Study .................................................................... T2-50

2.2: Modal and Harmonic Analysis in Analyzer......................................... T2-61 2.2.1: Modal Analysis ....................................................................................................... T2-61

Parametric Study Using MemElectro..................................................................... T2-65 2.2.2: Electrostatic Spring Softening ................................................................................ T2-68

MemMech .............................................................................................................. T2-68 CoSolve ................................................................................................................. T2-69

2.2.3: Harmonic Analysis ................................................................................................. T2-70

Initialization ............................................................................................................ T2-70 MemMech .............................................................................................................. T2-71 Queries .................................................................................................................. T2-77

Reference .............................................................................................................. T2-79

2.3: Contact, Pull-in, and Lift-off in Analyzer............................................. T2-81 2.3.1: Demonstrated Techniques ..................................................................................... T2-81 2.3.2: Reduce Beam Mesh Density.................................................................................. T2-81

Remesh Existing Model ......................................................................................... T2-82 Run MemElectro for Electrostatic Results ............................................................. T2-84 Run MemMech for Mechanical Results ................................................................. T2-85

2.3.3: Pressure and Contact Surfaces ............................................................................. T2-86

MemMech Settings for Parametric Study .............................................................. T2-86

Perform a Parametric Study with Contact Surface ................................................ T2-87 2.3.4: Beam Pull-in Voltage.............................................................................................. T2-90

Prepare MemMech for CoSolve ........................................................................... T2-90 Run CoSolve to Determine Pull-in Voltage............................................................ T2-91

2.3.5: Beam Lift-Off Voltage............................................................................................. T2-94 Prepare MemMech for CoSolve ............................................................................ T2-95 Run CoSolve to Determine Lift-Off Voltage ........................................................... T2-95

2.3.6: Design Optimization ............................................................................................... T2-98

Prepare MemMech for Parametric Study .............................................................. T2-98

2.4: Transient Mechanical Analysis in Analyzer ..................................... T2-105 2.4.1: Demonstrated Techniques ................................................................................... T2-105 2.4.2: Model Creation.................................................................................................... T2-105 2.4.3: MemMech Transient Simulation Setup and Solution ........................................... T2-110 2.4.4: Run a Query in a Region of Interest..................................................................... T2-113

2.5: Temperature Sensitivity Analysis in Analyzer ................................. T2-115 2.5.1: Demonstrated Techniques ................................................................................... T2-115

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2.5.2: Introduction ...........................................................................................................T2-115 2.5.3: Construction..........................................................................................................T2-115 2.5.4: Thermal Conduction - MemMech..........................................................................T2-116

Parametric Study of Thermal Conduction.............................................................T2-120 2.5.5: Film Convection - MemMech ................................................................................T2-124

Parametric Study of Film Convection ...................................................................T2-126

Section 3: Mirror Design

3.1: Introduction............................................................................................. T3-1 3.1.1: Model ........................................................................................................................T3-1

3.2: Mirror Design with Analyzer .................................................................. T3-2 3.2.1: Initialization ...............................................................................................................T3-2 3.2.2: Layout Viewing..........................................................................................................T3-3 3.2.3: Process Editor...........................................................................................................T3-5 3.2.4: Building a Solid Model ..............................................................................................T3-7 3.2.5: Meshing ....................................................................................................................T3-8

Uniform Mesh ...........................................................................................................T3-8

Multi-Volume Mesh.................................................................................................T3-14 3.2.6: MemMech Modal Analysis ......................................................................................T3-20

Monolithic Control Model ........................................................................................T3-20

Linked Model ..........................................................................................................T3-22 3.2.7: CoSolveEM - Single Run ........................................................................................T3-23

Monolith Model .......................................................................................................T3-23

Multi-Mesh Model ...................................................................................................T3-29 3.2.8: CoSolveEM - Multiple Run Capability .....................................................................T3-30

3.3: Mirror Design with Integrator .............................................................. T3-37 3.3.1: Introduction .............................................................................................................T3-37

System Modeling Theory........................................................................................T3-38

Demonstrated Techniques .....................................................................................T3-40

Tutorial Files ...........................................................................................................T3-40 3.3.2: Macromodel Generation .........................................................................................T3-41

Initialization.............................................................................................................T3-41

Electrical Spring......................................................................................................T3-41

MemElectro ............................................................................................................T3-42 Mechanical Spring ..................................................................................................T3-48 InertiaMM................................................................................................................T3-54 DampingMM ...........................................................................................................T3-57

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3.3.3: System Model of the Mirror: Schematic Creation................................................... T3-65

Schematic Assembly ............................................................................................. T3-65 3.3.4: FEM Performance Analysis.................................................................................... T3-75 3.3.5: System Model Performance Analysis .................................................................... T3-77 3.3.6: Summary................................................................................................................ T3-84 3.3.7: References............................................................................................................. T3-84

Section 4: Gyroscope Design

4.1: Introduction............................................................................................. T4-1 4.1.1: Tutorial Requirements.............................................................................................. T4-1 4.1.2: Gyroscope Operation ............................................................................................... T4-2 4.1.3: Gyroscope Design Parameters ................................................................................ T4-3

4.2: Schematic Creation ................................................................................ T4-5 4.2.1: Schematic Creation Guidelines................................................................................ T4-5

Components ............................................................................................................ T4-5

Connectivity ............................................................................................................. T4-5

Knots........................................................................................................................ T4-6 4.2.2: Initialization .............................................................................................................. T4-6 4.2.3: Set Design Variables.............................................................................................. T4-10 4.2.4: Place and Connect Parametric Component Symbols ............................................ T4-11 4.2.5: Assign Properties to Placed Symbols .................................................................... T4-16

Set Beam Component Properties .......................................................................... T4-16 Set Rigid Plate Component Properties .................................................................. T4-20 Set Electrode Component Properties .................................................................... T4-23 Set Straight Comb Component Properties ............................................................ T4-24

4.2.6: Add Additional Components................................................................................... T4-25

Mechanical Stimuli Components ........................................................................... T4-25 Electrical Stimuli Components ............................................................................... T4-26 Mechports_Bus_Connector ................................................................................... T4-29

4.2.7: Final Schematic...................................................................................................... T4-30

4.3: Schematic Layout Verification............................................................. T4-31

4.4: Architect Analysis................................................................................. T4-32 4.4.1: DC Operating Point Analysis.................................................................................. T4-33 4.4.2: DC Transfer (Sweep) Analysis............................................................................... T4-34

Pull-in Voltage........................................................................................................ T4-34

Impact of Driving Bias Voltage on Levitation ......................................................... T4-38 4.4.3: Small Signal AC Analysis....................................................................................... T4-40

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Resonance Frequencies.........................................................................................T4-40 Resonance Frequencies: Impact of Length_Beam1 Parameter.............................T4-45 Resonance Frequencies: Impact of Length_Beam2 Parameter.............................T4-51

4.4.4: Sensitivity and Monte Carlo Analysis......................................................................T4-53 4.4.5: Transient Analysis ..................................................................................................T4-60

Setting Up the Time-Varying Sources ....................................................................T4-60

Transient Analysis for the Mismatched Frequency Design ....................................T4-60

Matching Resonance Frequencies for Driving and Detection Mode ......................T4-67 4.4.6: AC Analysis: Determining the Detection Amplitude ................................................T4-69 4.4.7: Impact of Plate Curvature .......................................................................................T4-70

4.5: FEM and Architect Comparison .......................................................... T4-73 4.5.1: Mesh Creation.........................................................................................................T4-74

Meshing ..................................................................................................................T4-77 4.5.2: FEM Simulation.......................................................................................................T4-79

Modal Analysis .......................................................................................................T4-79

Pull-in Analysis .......................................................................................................T4-81 4.5.3: FEM and Architect Results .....................................................................................T4-86

4.6: Mesh Convergence Study.................................................................... T4-87 4.6.1: General Mesh Convergence Strategy.....................................................................T4-87

Gyroscope Mesh Series .........................................................................................T4-87

Symmetry Features ................................................................................................T4-88 4.6.2: Manhattan Mesh .....................................................................................................T4-89

Convergence ..........................................................................................................T4-91

Interpretation of Convergence ................................................................................T4-93

Comparison with Architect ......................................................................................T4-95

MemElectro Mesh...................................................................................................T4-96 4.6.3: Extruded Meshing ...................................................................................................T4-96

Extruded Algorithms ...............................................................................................T4-98 4.6.4: Tetrahedral Meshing ...............................................................................................T4-99 4.6.5: Conclusions and Recommendations ....................................................................T4-101

4.7: DampingMM Macromodel Extraction ............................................... T4-103 4.7.1: Introduction ...........................................................................................................T4-103 4.7.2: Squeezed- and Slide-Film Macromodel Extraction...............................................T4-104

Initialization...........................................................................................................T4-104

Examine Model .....................................................................................................T4-105

DampingMM Setup and Solution..........................................................................T4-106

Squeezed-Film Translational Damping ................................................................T4-108

Squeezed-Film Rotational Damping.....................................................................T4-115

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Slide-Film Damping ............................................................................................. T4-120 4.7.3: Comparison of Extracted and Parametric Plate Dampers ................................... T4-124 4.7.4: Stokes Flow Damping ........................................................................................ T4-129

Examine Model .................................................................................................... T4-129

Stokes Setup and Solution .................................................................................. T4-130 4.7.5: Slide-Film Damping Effects on Gyroscope Driving Mode .................................... T4-135

4.8: Design Modification Using Integrator ............................................... T4-141 4.8.1: Macromodel Creation........................................................................................... T4-142 4.8.2: Schematic Construction ....................................................................................... T4-145 4.8.3: System Analysis................................................................................................... T4-147

DC Operating Point.............................................................................................. T4-147 DC Transfer (Sweep) Analysis ........................................................................... T4-148

4.9: Package Design Tutorial .................................................................... T4-151 4.9.1: Introduction .......................................................................................................... T4-151

Demonstrated Techniques................................................................................... T4-151 4.9.2: Package Thermomechanical Analysis ................................................................. T4-152

Initialization .......................................................................................................... T4-153

Examine Model .................................................................................................... T4-153

Mesh Creation ..................................................................................................... T4-155

MemMech Setup and Computation ..................................................................... T4-156 4.9.3: Package Analysis with Variable Temperature...................................................... T4-163

MemMech Setup and Computation ..................................................................... T4-163 4.9.4: Package Analysis with Lid.................................................................................... T4-168

Numerical Results................................................................................................ T4-168

Graphical Results ................................................................................................ T4-169

Visualizer Results ................................................................................................ T4-171 4.9.5: Package Deformations in Architect ...................................................................... T4-172

Initialization .......................................................................................................... T4-172 Impact of Temperature on Resonant Frequencies .............................................. T4-175 Impact of Device Position on Performance.......................................................... T4-177

Section 5: RF Switch Design

5.1: Introduction............................................................................................. T5-1 5.1.1: Demonstrated Techniques ....................................................................................... T5-1

5.2: RF Switch Design in Architect............................................................... T5-2 5.2.1: RF Switch Schematic ............................................................................................... T5-3

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5.2.2: Solid Model ...............................................................................................................T5-5 5.2.3: RF Switch Electromechanical Analysis.....................................................................T5-6

Closing the Switch ....................................................................................................T5-6

Frequency Response .............................................................................................T5-17

Modeling Switching Time........................................................................................T5-22 5.2.4: RF Electrical Analysis .............................................................................................T5-25

Schematic Construction for RF Electrical Analysis.................................................T5-29

Modeling Contact Resistance.................................................................................T5-29

Two-Port S-Parameters..........................................................................................T5-33

Adding Transmission Lines to a Design .................................................................T5-37

Adjusting Actuation Voltage to Meet a Specification ..............................................T5-43

Adding Custom Microstrip Discontinuity Models (optional) ....................................T5-44

Plotting Results on a Smith Chart...........................................................................T5-48 Exporting RF Data in Touchstone Format ..............................................................T5-51

5.2.5: FEM and Architect Comparison ..............................................................................T5-53

Mesh Creation ........................................................................................................T5-53 FEM Simulation ......................................................................................................T5-56

5.3: Drop Test of RF Switch in a HyCap Package..................................... T5-65 5.3.1: Introduction .............................................................................................................T5-65

Hycap Packaging....................................................................................................T5-66

Tutorial Requirements ............................................................................................T5-66 5.3.2: Initialization .............................................................................................................T5-66 5.3.3: Packaged RF Switch Design ..................................................................................T5-67

Process...................................................................................................................T5-67

Layout.....................................................................................................................T5-69

3-D Model ...............................................................................................................T5-71

Calculating the Mass of the Packaged Switch........................................................T5-74 5.3.4: Stiffness ..................................................................................................................T5-75

Adding the Floor to the Model ................................................................................T5-75

Run MemMech to Calculate Displacement ............................................................T5-78 5.3.5: Drop Test ................................................................................................................T5-82

Architect Schematic................................................................................................T5-82

Stress Detailed with MemMech ..............................................................................T5-87

5.4: References ............................................................................................ T5-91

MEMS Design and Analysis Index ...................................................... IX-1

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Notes

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Section 1: Introduction Overview Version 2008M

Section 1: Introduction

1.1: OverviewThe MEMS Design and Analysis Tutorials, Vol. 1 and Vol. 2 provide numerous practical examples that demonstrate many of the capabilities of CoventorWare. Each example has been carefully constructed to illustrate a variety of soft-ware features. By completing the examples, you will gain a thorough, practical understanding for designing MEMS (Micro Electro Mechanical Systems).

All the tutorials share a common set of characteristics. Each tutorialtakes you through the software functions, dialogs, and settingsexplains the tutorial proceduresallows you to make meaningful changes and provide input during the processprovides you with an opportunity to complete some sequences with limited guidanceshows you resultant values, windows, and screens that are createdprovides cross-references to other sections providing more in-depth knowledge

The tutorials are organized with clearly marked steps that detail user input and responses, along with brief explana-tions of the procedures. Additional detail is provided within the tutorial, along with typical screen illustrations of the dialogs that appear.

The tutorials accommodate a variety of user backgrounds. The first beam tutorial details almost every step required to process an entire design through CoventorWare. Other tutorials intentionally provide fewer details to allow you to learn by thinking and acting on your own.

The tutorials accommodate the two major operating system platforms supported for CoventorWare: Windows XP and RedHat Enterprise Linux. Your system hardware should provide reasonable performance for graphics and design pro-cessing. The software must be installed on your system with all required files, including the files needed to run the tutorials. For more information on system requirements, see the Installation Instructions.

1.2: Using CoventorWareTo understand the overall structure of the CoventorWare suite of tools, please see Using CoventorWare, accessed from the Function Manager’s Help menu. This document gives the following information:

overview of CoventorWare components (see page U1-1)

document conventions, including icons and page numbering (see page U1-6)

software conventions, including directory structure and units of physical quantities (see page U1-8)

licensing (see page U1-10)

overview of the Function Manager, which is the main navigation window (see page U1-11)

window overview, including explanations of the project browser, Database Browser, Job Queue, and export capability (page U1-22)

common button functions (see page U1-34)

file organization (see page U1-35)

file and database conversions (see page U1-39)

design considerations, including guidelines and considerations that will help ensure that your designs progress smoothly and without difficulty (see page U1-42)

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Section 1: Introduction Tutorials Version 2008

techniques for enhancing productivity (see page U1-44)

interfacing with third-party software (see page U1-49)

1.3: TutorialsThe MEMS design tutorials are contained in two volumes. They are divided into two volumes simply to keep the pdf file size from getting too big. Smaller pdfs load and open faster in Acrobat Reader. The tutorials in each volume are outlined below.

1.3.1: Volume 1


The Beam Design section includes a basic tutorial that provides a thorough explanation of how to design and simulate a simple beam using Designer and Analyzer. This basic tutorial covers every step in detail and displays virtually every basic screen. The tutorial establishes user familiarity with the various screens, screen fields, and settings. It includes the following techniques:

how to build and mesh a model for Analyzer simulationhow to run MemElectro to calculate capacitance and chargehow to run MemMech to calculate deformations and stresshow to simulate modal analysis with MemMechhow to compute the capacitance of a modal shape using MemElectrohow to simulate harmonic analysis with MemMechhow to simulate electrostatic spring softening with CoSolvehow to remesh a model for faster simulationhow to simulate contact with MemMechhow to simulate pull-in with CoSolvehow to simulate lift-off with CoSolvehow to solve thermal conduction problems with MemMechhow to solve film convection problems with MemMechhow to perform a temperature sensitivity study with MemMechhow to partition a modelhow to simulate transient mechanical analysis with MemMech

This section starts on page T2-1.


The Mirror Design tutorial shows how to design a mirror that rotates around a support. It includes the following tech-niques:

how to use the Process Editor to create a processhow to partition a model to refine the mesh applied to parts of a modelhow to use the automatic linking feature of CoventorWarehow to use CoSolve to actuate the mirrorhow to extract macromodels from the design components using Integratorhow to assemble and simulate the mirror macromodels in Architect Saber

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Section 1: Introduction Tutorials Version 2008M

how to compare FEM and Architect results

This tutorial begins on page T3-1.


The Gyroscope Design tutorial shows how to design and simulate a Z-plane gyroscope that is composed of a perfo-rated rectangular plate suspended by four L-Shaped flexures, two comb drives, and three electrodes. The tutorial includes the following techniques:

how to assemble the gyroscope in Architecthow to verify an Architect schematic using Scene3Dhow to perform pull-in, resonance frequency, transient, and vary analyses in Architect Saberhow to create a 3-D mesh of the gyroscopehow to perform modal and pull-in analysis in Analyzerhow to perform a mesh studyhow to use DampingMM to generate damping values for use in the gyroscope designhow to extract a double-ended spring using Integrator’s SpringMM modulehow to incorporate a macromodel into a schematic that uses parametric library models.how to account for packaging effects using Analyzer FE results in an Architect schematic.

This tutorial starts on page T4-1.


This section shows how to simulate a cantilever beam resistive switch. The tutorial provides several prebuilt Archi-tect schematics that represent the switch at different stages of development, and it outlines several Architect simula-tions that demonstrate device behavior. It also includes an FEM verification of the switch design. The tutorial demonstrates the following techniques:

how to extract a 3-D model from an Architect schematichow to use Architect to simulate the closing of the switch, contact force, resonant frequencies, and switching timeshow to connect the electromechanical switch to electrical componentshow to estimate RF characteristics such as insertion loss and isolation by using S-parameter extraction on the electrical circuithow to create and add transmission lines to a designhow to adjust actuation voltage to meet a specificationhow to add custom microstrip discontinuity models to a designhow to plot results on a Smith charthow to export RF data to Touchstone formathow to mesh and simulate the switch in Analyzerhow to calculate the mass of the packaged RF switch using Integrator’s InertiaMM module how to apply a transform operation on a solid modelhow to calculate the stiffness of the package hitting the floor using Analyzer’s MemMech modulehow to enter the stiffness and the mass into the drop test schematic for the RF switch and observe the drop test performance of the switchhow to calculate the stress suffered by the mechanical beam using the maximum displacement (calculated in a previous step) as an initial boundary condition




1.3.2: Volume 2

Section 6: Latching Magnetic Relay Design in Architect

This tutorial shows how to design and simulate a latching magnetic relay in Architect using magnetic and electrome-chanical parametric components. The device modeled is a cantilever beam placed 12 µm above a planar coil. The coil acts as a temporary magnetic field that acts on the movable actuator (the cantilever). The tutorial demonstrates the following techniques:

how to add material to the Material Properties Databasehow to verify a schematic using Scene3Dhow to extract a 3-D model from an Architect schematichow to simulate the cantilever beam movement over timehow to view the magnetic response.

The tutorial begins on page T6-1.

Section 7: 2-D Optical Scanner Design in Architect

This tutorial shows how to design and simulate a 2-D optical scanner in Architect. The device modeled is a mirror suspended above four electrodes. The tutorial demonstrates the following techniques:

how to assemble the scanner in Architecthow to link the optical model of the system to the electromechanical modelhow to verify a schematic using Scene3Dhow to simulate the effects of scanning mirror distortion and correction using non-differential and differential voltageshow to export results from Saberhow to import results to Excelhow to plot results in Excel.


Section 8: Layout Creation in Designer

This tutorial shows how to use the Designer software suite to create the layout for a mirror array. It demonstrates the following techniques:

how to create basic objects in the Layout Editorhow to correct errors in the Layout Editorhow to reference the contents of one cell into anotherhow to create an array referencehow to modify existing objectshow to creating a clipping pathhow to build a solid model from a 2-D layout and process filehow to build only a portion of a layout using a clipping path.




Section 9: FBAR Design

The FBAR Design tutorial demonstrates how to design and simulate a Film Bulk Acoustic Resonator (FBAR) using CoventorWare. It includes the following techniques:

how to create a process and layout for the FBARhow to use the Partition tool to create unique faceshow to run a DC analysis in MemMechhow to generate PZE real and imaginary chargeshow to conduct a frequency analysis on a closed and open circuithow to view mode shapes in the Visualizer and to identify the breathing modehow to compare simulation results with analytical resultshow to calculate the Q factor in a resonatorhow to run a piezoelectric harmonic analysis to estimate the displacement and impedance variation with sig-nal frequency


Section 10: Simulation of Buckled Structures

This tutorial shows how to use Analyzer and Architect to simulate a buckled beam. It demonstrates the following techniques:

how to use Analyzer to simulate biasing toward the post-buckled statehow to establish the post-buckled statehow to simulate the switching to another stable statehow to use Architect to establish the post-buckled statehow to use Architect to simulate the switching to another stable state

The tutorial also has a section that compares the Analyzer, Architect, and analytical results and shows how the analyt-ical results were calculated. This tutorial starts on page T10-1.

Section 11: PZR Analysis

This section has two tutorial exercises that demonstrate piezoresistive analysis using Analyzer and Architect. The first tutorial design is composed of a piezoresistor model and a cantilevered beam. In a two-step solution, the software solves the beam mechanical problem and then applies the beam stress results to solve for the resultant piezoresistive change. The tutorial includes the following techniques:

how to configure MemMech to calculate beam stresshow to use MemMech stress results in MemPZR to calculate the resulting piezoresistor currenthow to use the parametric study function to calculate stress along the model length by measuring piezoresis-tor currenthow to use the parametric study function to vary conductivity.


The second tutorial design is a silicon diaphragm. The tutorial uses a hybrid approach that is a combination of dia-phragm FEM analysis using Analyzer’s MemMech and MemPZR solvers and piezoresistive sensor modeling using Architect. The tutorial demonstrates the following:

how to create a process for a silicon diaphragmhow to use plane and block partitioning in the Preprocessorhow to use the mapped mesher



how to run a MemMech parametric study to model diaphragm deformation under variable pressure how to construct a PZR schematic in Architecthow to perform PZR design studies in Architect based on MemMech results stored in the databasehow to extract a layout how to perform MemPZR/Architect bottom-up verification

This PZR tutorial starts on page T11-31.

Section 12: Thermal Transient Analysis in Analyzer

This tutorial shows how to simulate thermal transient analysis using Analyzer’s MemMech solver. The tutorial device is a chemical reaction chamber composed of an outer casing made of a polymer material, with the interior chamber filled with water. An aluminum heater inside the chamber provides a heat source when BCs are applied. The tutorial demonstrates the following techniques:

how to view hidden parts and faces in the Preprocessorhow to set up a thermal transient problem in MemMechhow to view hidden parts in the Visualizerhow to create a slice plane in the Visualizerhow to use the parametric study function to vary heat generationhow to perform a query on a result database.


Section 13: Electro-thermomechanical Analysis in Analyzer

This tutorial demonstrates how to compute the thermal field and the electrical potential resulting from an imposed voltage and/or current flow through a resistive material using Analyzer’s MemMech solver. The tutorials set up a thermal actuator that moves in relationship to the current passed through the device. The actuator’s geometry is designed to take advantage of thermal heating effects and produce a significant amount of mechanical deflection. The tutorial includes the following techniques:

how to configure MemMech to calculate electrical and mechanical resultshow to set up a parametric study to plot the actuator deflection as a function of varying voltagehow to set up a parametric study to plot the actuator deflection as a function of varying actuator thickness.


Section 14: Resistance and Inductance Analysis in Analyzer

These tutorial exercises explore the design of an inductive proximity sensor using Analyzer’s MemHenry solver. The tutorial model is a pancake spiral inductor, and its proximity to a nearby metal plane is measured by the self-induc-tance of the spiral. The tutorial includes the following techniques:

how to solve for frequency-dependent resistance and inductancehow to rotate a device in the Visualizer using angleshow to view vectors in the Visualizerhow to suppress a part from calculationshow to remove skin effect refinement from calculationshow to vary the position of the part and observe the effect on resistance, inductance, and current density




Section 15: Spring Extraction with Integrator

This tutorial outlines a sequence of steps for defining the parameters for a spring constant extraction and applying the mathematical spring model to a new design problem. The tutorial includes the following techniques:

how to configure MemMech and SpringMM to extract spring constantshow to plot a spring constant polynomialhow to use the spring constants as a boundary condition in MemMech.


1.3.3: Tutorial Installation FilesThe files required for running the tutorials are in your installation directory. When you choose a tutorial project, the files needed to run that tutorial are automatically copied to your work directory. Process files and mask files are installed in the appropriate tutorial_project\Devices directory. For some tutorials, prebuilt models are included in the project database. Because schematic creation can be time consuming, for the Architect tutorials prebuilt schematics are provided for users who would like to skip the schematic creation steps.

1.3.4: Tutorial ConventionsThe tutorials are designed to allow both advanced and mainstream users to pace comfortably through the procedures. The Advanced User Procedure column includes concise, but complete steps for the tutorial sequences. All users should first attempt to complete the tutorials by reading only this column (and any accompanying graphics), if possi-ble. The short explanations provide complete summaries and allow users to think more about the problem setup and results, rather than on the mechanics of clicking buttons and setting fields. For users unfamiliar with concepts or with the software interface, the Detailed User Procedure column offers much more explanation on exactly how to accom-plish the objectives of the Advanced User Procedure column. For many of the lettered steps, there are summary notes (indicated with an arrow directly under the step), which explain why specific settings are used or why certain results are displayed.

1.3.5: Helpful HintsThe tutorials in this documentation set are intended to show you how to use CoventorWare and to demonstrate Cov-entorWare capabilities. The tutorial designs are simplified versions of real designs. This section offers some helpful hints for these tutorials.

Save Project Settings OftenThe settings file created at the beginning of each tutorial preserves input parameters such as boundary conditions, file paths, and other parameters. Be sure to save this file periodically after making changes (this action is prompted before running any solver). You also can create intermediate versions of settings files not specifically called out in the tutori-als if you want to go back to an earlier stage in the tutorial sequence.

Material Properties Database ValuesUsing the default Material Properties Database (MPD) values instead of those specified in the tutorial may result in different numerical results from those published in this document.

Matching Tutorial ResultsIf you set the MPD parameters as shown in the tutorial, your numerical results should match those in the tutorials. A small amount of variation in results can be accounted for by differences in operating systems or machine configura-tions. But if your numbers are significantly different, you may have used a wrong file, used incorrect boundary condi-tions, or not completed the correct sequence in the tutorial. If your input sequence was in error, you may get a result window that includes an error button with additional diagnostics.



Setting Unused Boundary Condition Lines In some of the complex boundary condition dialogs shown in the tutorials, only one or two of the setting lines are active. The other lines contain the setting “none” in the first column of the line. This setting instructs the software to ignore the entire line. When boundary conditions are set for these dialogs, as long as “none” appears in the first col-umn of an inactive line, the rest of that line’s settings do not need to match those shown in the tutorial dialogs.

Viewing Results from Previous Solver Runs Any other results created while running this software may be viewed without rerunning the solver. Set the Analysis field on the Analyzer tab for the desired run, then select the View Result icon to the right of the field. The software will then bypass the setup screens and proceed to the output display windows.

Defragment Hard DriveIf CoventorWare takes an unusually long time to open a project and the Function Manager appears locked up, your hard drive may need defragmenting. Project databases can get very large; and the database file may get fragmented because it starts as a small file and grows incrementally as more data is added. If this happens, run Disk Defragmenter (accessed from Start > Programs >Accessories > System Tools). You can also copy the CPDB and GBAK files, delete the originals, and work with the copies to ensure that these files are also defragmented.


Section 2: Beam Design Version 2008M


In MEMS design, the beam structure has many applications, including sensors, accelerometers, and RF switches. This section investigates two beam structures: the tethered beam, with both ends fixed, and the cantilever beam, with one end fixed and the other end free. It also investigates several types of analyses, including

mechanical deformation and stressescapacitance and chargemodal analysisharmonic analysiselectrostatic spring softeningcontactpull-inlift-offtemperature sensitivitytransient mechanical analysis

The table below summarizes the tutorial sections and the models used for each.

Table T2-1 Tutorial Summary

Tutorial Description Models needed Page

Beam Design in Analyzer

This basic tutorial provides a thorough explanation of how to design a simple beam with rigid conformal supports using Designer and Analyzer. The tutorial establishes user familiarity with the various screens, screen fields, and settings.

tethered beam T2-2

Modal and Harmonic Analysis in Analyzer

This tutorial shows how to partition the tethered beam to isolate the area of interest. It uses the partitioned beam for modal, harmonic, and electrostatic spring softening analyses.

beam partitioned to remove tethers

T2-61

Contact, Pull-in, and Lift-off in Analyzer

This tutorial shows how to coarsen the original tethered beam design and use it for contact, pull-in, and lift-off analyses.

tethered beam with coarsened mesh

T2-81

Transient Mechanical Analysis in Analyzer

This tutorial shows how to simulate transient mechanical analysis using MemMech. A simple beam is fixed at one end to simulate a cantilever beam.

cantilever beam made of one material

T2-105

Temperature Sensitivity Analysis in Analyzer

This tutorial shows how to simulate thermal conduction and convection problems with MemMech. It also shows how use the Queries feature to extract and graph thermal data and how to use the parametric study function to run a sensitivity analysis.

bimetal cantilever beam

T2-115


Section 2: Beam Design Beam Design in Analyzer Version 2008

2.1: Beam Design in AnalyzerThis tutorial provides a solution for an electrostatically actuated fixed-fixed beam with conformal supports, based on a generalized surface-micromachining process. It gives the user basic experience with the CoventorWare simulation environment.

Figure T2-1 shows a simple 2-D sketch of the basic model and the problems to be solved.

A parametric study using MemMech will be performed to investigate the sensitivity of the beam's mechanical response to a fixed pressure load as a function of varying residual (internal) stress.

This tutorial introduces basic applications of the modules mentioned above in the context of a simple problem. Dur-ing the tutorial, the user is encouraged to think about more complex issues that may be important for this type of structure. For example, how important are the effects of the conformal supports? How does beam geometry (thick-ness, width, length, and gap) affect the behavior, and what are the sensitivities to fabrication errors in geometry? Is a given mesh dense enough? For most design cases, asking the right questions initially is a critical step in getting an answer that is both correct and useful.

Figure T2-1 Beam Tutorial Model

ground plane

aluminum beam

ground plane

++++++++++++++------------------------

voltage potentialpressure load

This introductory tutorial investigates four different problems:

apply voltage; calculate capacitance between beam and ground

mechanical solution (MemMech):apply pressure load; calculate beam displacement and stress

coupled solution (CoSolve):apply voltage; calculate capacitance, beam displacement, and stress

parametric study: apply pressure load; vary internal stress; calculate set of beam mechanical solutions

electrostatic solution (MemElectro):


Section 2: Beam Design Beam Design in Analyzer Version 2008M

2.1.1: Demonstrated TechniquesThis tutorial covers these techniques:

using the basic features of CoventorWare

entering materials into the Material Properties Database (page T2-7)

creating and editing a process flow (page T2-11)

using the 2-D layout tool (page T2-14)

building a 3-D solid model of a beam from a 2-D layout using the solid model tool (page T2-18)

creating a finite element model and mesh using the meshing tool (page T2-24)

assigning names and materials to model components (page T2-19)

running the MemElectro module to calculate capacitance and charge (page T2-28)

running the MemMech module to calculate deformations and stresses (page T2-33)

running the CoSolve module to produce a coupled electromechanical solution (page T2-39)

how to use MemMech to perform fully coupled electrostatic analysis (page T2-45)

running a parametric study, varying model parameters (page T2-50)

2.1.2: ReferencesThis beam design is a comprehensive exercise that takes you through many of the software screens. Users will likely run this tutorial before reading much of the background and reference material found in these manuals. If you decide to skip the reading and proceed, here are references to specific places in the manuals that may answer questions or solve problems you may have while running the tutorials.

Using CoventorWare (page U1-1)This introductory section briefly covers all the major design steps. It also explains CoventorWare software and documentation conventions, directory structure, and major menu and dialog functions. Fluidics Channel Tutorial (page M3-2)A basic fluid channel is used to demonstrate elementary concepts to users interested in fluidics design. The tuto-rial, found in Microfluidics Design and Analysis Tutorials, is very similar to this Beam Design and provides addi-tional practice on using the various software packages within CoventorWare. DESIGNER Tutorial (page T8-1)This tutorial covers the 2-D layout creation in detail. It shows how to create basic objects, how to correct mis-takes, how to reference other cells, and how to create an array. The tutorial is found in MEMS Design and Analy-sis Tutorials, Vol. 2.



2.1.3: Tutorial InitializationThe initialization procedure sets up the directories you will use for your files, starts the software, and creates a set-tings file used to store all your input and configuration parameters for the software. The first time you run the soft-ware, you will have to set a work directory, a temp directory, and a shared directory (default location). These directories will not have to be set again.

The directory creation and file storage are automated for you. After you start the software, you need to copy the tuto-rial directory to your work directory. When the tutorial directory is created, all the files you need for the tutorial are copied to the appropriate directory, and the software will default to that directory. File and directory setup has been simplified from previous versions. All files needed for the tutorials are located in your installation directory. After you import the tutorial directory (the BeamDesign directory), you will have a beam.cat file and a beam_init.proc file installed in your BeamDesign\Devices directory.

This first tutorial explains procedures and file organization structure. For complete information on CoventorWare file organization, see page U1-35 of Using CoventorWare.

Advanced User Procedure Detailed User Procedure

1. Start CoventorWare. a. Windows User: On your desktop, double click on the CoventorWare shortcut icon or select Coventor > CoventorWare 2008 from the Start menu.

b. Linux User: From your Linux shell, type coventorware.

2. Set your directory and licence file preferences in the User Settings dialog.

a. If this is the first time you have run the software, the User Settings dialog will open. See Figure T2-2.

b. Set the Work Directory: user’s root directory\Design_Files. c. Press Enter on the keyboard and the rest of the directories will be filled in

automatically:d. Scratch Directory: user’s root directory\Design_Files\Tempe. Shared Directory: user’s root directory\Design_Files\Shared

The Work directory will contain all project directories. It is also the default location for the Shared, Temp, and Logs directories.

The Temp directory stores all the temporary files created by the solvers.

The Shared directory contains the mpd file, which is the Material Properties Database file that contains all the materials and their assigned properties used in creating a MEMS design.

f. Type in the locations of your license files. You only need to set the fields for which you have a license. For example, if you do not have an ARCHITECT/Saber license, leave that field blank.

The license fields default to the settings specified at installation.g. Click on OK.

The Function Manager and the Project Browser become active.



Figure T2-2 User Settings Dialog

After you set your user settings, the Function Manager, shown in Figure T2-3, and the Project Browser dialog, shown in Figure T2-4, open. The Function Manager has tabs that access various tools needed for a MEMS design. This win-dow is the means of navigation throughout the tutorial. When you finish one step in your design, the software returns control to this window.

Figure T2-3 Function Manager

Before you can begin to build your design, you must create a new project directory and new project settings. Use the Project Browser dialog to access the Tutorials projects directory, which contains the files needed to run the tutorials.

If you have an individual license, the hostname value would be the name of your machine. If you have a floating license, your hostname value would be the name of the machine where the floating license resides. Put the name of that machine after the @ symbol. Do not enter “hostname”.



Figure T2-4 Project Browser Dialog

The Project Browser dialog has icons along the top that allow the user to import projects from previous versions of the software, import tutorial projects, delete projects, and create new projects. The user can also delete and create new settings files. When a project is selected or created in the Projects pane of the Project Browser dialog, a default set-tings file and any other settings files associated with that project are displayed in the Settings pane.

The software uses settings files to track file paths, finite-element meshes, material properties, locations of solved model files, and other simulation parameters. Create multiple settings files when you vary designs, meshes, or bound-ary conditions within a single project; this will preserve each variation in an individual file for later comparison. A default settings file based on the project directory name is automatically created for you. Use the File menu in the Function Manager to manage projects and settings.


3. Import the BeamDesign project directory and create a settings file.

a. In the Project Browser dialog (see Figure T2-4), click on the Import

Tutorials icon.

b. In the Import Tutorials dialog that opens, select BeamDesign.c. Click on OK.d. Verify that the software has created a default settings file that has the

same name as the project directory name. The BeamDesign.mps settings file should appear in the Setting file field.

e. Click on Open.

When you select the BeamDesign directory, the software copies this directory to your work directory. All the files needed for the tutorial are stored in this directory, and the software will default to the appropriate directory when looking for a file.

For more details on file organization, refer to the File Organization section in Using CoventorWare, starting on page U1-35.

When naming files or directories or designating path names, do not use spaces.



These steps complete the initialization procedure. Now, a project directory and settings file exist and will be modified in the next sections of the tutorial. In this tutorial, our procedure will

check and modify the Material Properties Databaseview and modify the process flowview and modify the 2-D mask designbuild a 3-D solid modelmesh the modelname faces and conductorssimulate electrostatic and mechanical stimulus

The order of these steps can be varied and still allow for a smooth work flow. Experienced users may wish to change this procedure.

2.1.4: Material Properties Database SetupThe Function Manager provides access to the Material Properties Database in the top portion of the window, above the tabs. Material Properties Database access and setup is the first field in the Function Manager because the process is dependent on the materials in the Material Properties Database, and in turn, the rest of the design creation is depen-dent on the process file. In other words, the Material Properties Database is the basic foundation of your design. This database stores properties for materials used for MEMS design. Materials or parameters can be added or modified at any time from this or from other dialogs in the software. The user designates the file path for the mpd file in the Users Settings dialog the first time CoventorWare is run. This setting can be changed from the Tools > User Settings menu.

In this tutorial, the Material Properties Database is checked and validated before a process file is created because the materials used in the process file must exist and have the correct values. The process file takes the materials and their values from the Material Properties Database. In the next step, properties for both Silicon and Aluminum Film will be checked. These materials are used to construct the beam.

Saving SettingsIn CoventorWare, any settings established in setup dialogs are saved to local memory when Open is clicked. However, the new or modified dialog contents are not written to the settings file. Before exiting the software, always click on the File > Save Settings button to save the file’s contents to disk. Also, save after modifications as often as possible to preserve data in the event of a system crash.

The materials and their properties provided in the default Materials Properties Database (MPD) are there to serve as examples and to make the tutorials easier to use. CoventorWare does not supply material properties for design use. Users should enter their own materials and properties and save them into their custom MPD file for use in their design work.


1. Access the Material Properties Database. a. In the Function Manager, click on the Start MPD Editor icon.

There is no need to set the Materials field for the mpd file because the software defaults to the path set in the User Settings dialog the first time it is run.



2. Select ALUMINUM(FILM), which will be the beam material, and verify its material properties. If it is not in the MPD, add it and use the properties shown in Table T2-2. Modify the Material Properties Database if necessary.

a. In the Edit Materials dialog that opens, click on the drop-down arrow beside the Materials field.

The Material Properties Database always initially displays the material at the beginning of the alphabet. If the default mpd file is specified, AIR is displayed.

b. Select the material named ALUMINUM(FILM), if it appears in the drop-down menu.

c. If the material exists, check the property values against those in Table T2-2. Only these values must match for the tutorials. Ignore the other settings.

In this step you are verifying that ALUMINUM(FILM) exists in your Material Properties Database and has the correct material properties.

If ALUMINUM(FILM) is not on the list:d. Click on New Material.e. In the dialog that opens, enter ALUMINUM(FILM).

Material names can have no more than 32 characters.f. Click on OK.

You created the material, but it does not have valid properties yet.

If you just created ALUMINUM(FILM), or if its existing properties are incorrect:g. Set the properties for the materials shown in Table T2-2.

After creating a new material, the user has to assign valid properties to that material. These are the only properties needed for this tutorial.

3. Select SILICON, the substrate material, and verify its material properties. If it is not in the MPD, add it and use the properties shown in Table T2-2. Modify the Material Properties Database if necessary.

a. Select SILICON from the Materials drop-down menu.b. If SILICON is not on the list, or if the existing properties are incorrect,

repeat the parts of the procedure shown above as applicable.

In this step you are verifying that SILICON exists in your Material Properties Database and that it has the correct properties assigned to it.

4. Close the Materials Editor. a. When finished in the Edit Materials dialog, click on Close.

Clicking on Close writes the changes in the new materials to the mpd file.

Control returns to the Function Manager.

The sequence on page T2-7 sets material properties for the beam design. From the MPD Editor icon, permanent changes may be made to the database that will be valid for all future projects. The Material Properties Database also can be accessed from within the Preprocessor. In the Preprocessor, click on the desired part in the canvas; then select Edit > Properties. An icon in this dialog accesses the Materials Editor. Changes made from within the Preprocessor only apply to the displayed model and are not permanently stored to the database. Refer to the CoventorWare Designer Reference (page U2-1) for complete details.

When entering values for the Material Properties Database, do not type in any spaces between numbers or exponents.




Table T2-2 Material Properties for Tutorial

The final Material Properties Database setup for each material is shown in Figure T2-5 and Figure T2-6. Refer to the CoventorWare Designer Reference (page U2-1) for more details.

Figure T2-5 Materials Properties for Aluminum(FILM)

Property Data Type Sub prop Aluminum(FILM) Silicon Units

Elastic Constants Elastic-Iso E 7.70e+04 1.69e+05 MPa

Poisson 3.00e-01 3.00e-01

Density Constant-Scalar 2.30e-15 2.50e-15 kg/µm3

Stress AnIso Sx 0 0 MPa

Sy 0 0

Sz 0 0

TCE Constant-Scalar 2.31e-05 2.5e-06 1/K

Thermal Cond Constant-Scalar 2.40e+08 1.48e+08 pW/µm · K

Specific Heat Constant-Scalar 9.03e+14 7.12e+14 pJ/kg · K



Figure T2-6 Materials Properties for Silicon

In the Edit Materials dialog, the column of buttons to the right display properties that have only a single entry. For all other cases, the buttons retain the Edit label. For example, the single SILICON Density value of 2.5e-15 is displayed on the button, while the Young’s Modulus and Poisson’s Ratio Elastic Constants are displayed only when you click on the Edit button and open the dialog for setting these parameters.

The value for the Dielectric Constant within the Materials Property dialog determines whether the material is declared as a Conductor (low values) or Dielectric (high values) in the Properties dialog within the Preprocessor.



2.1.5: Process EditorThe Process Editor supplies the information needed to construct the 3-D solid model of the device from the 2-D masks viewed in the Layout Editor. Material layers are constructed in a deposit and etch sequence that emulates the actual fabrication process. The process parameters that can be adjusted include:

material thickness (during deposition)deposition type (stacked, conformal, or planar)sidewall angles (profiles of the angular slope allowed during an etch operation)a mask perimeter offset (the ability to change the mask dimensions through an undersized or oversized oper-ation to accommodate foundry processing requirements)mask polarity (positive or negative tone to determine whether light or dark areas of the mask are etched)

Refer to the Process Modeling section of the CoventorWare DESIGNER Reference, beginning on page U3-1, for an in-depth discussion on these topics.

Figure T2-7 is a cross-section diagram of the beam structure used in this tutorial.

Figure T2-7 Beam Cross-Section Diagram

In this figure, a ground plane is overlaid with a nitride layer for isolation of the beam. A delete layer of BPSG (boron phospho-silicate glass) is deposited on the nitride layer. It is etched to define the areas where the beam will be anchored to the nitride layer. The BPSG thickness sets the separation between the nitride layer and the thin aluminum beam to be built on top. After the entire wafer is deposited with aluminum, a selective etch defines the actual beam dimensions. Note that the aluminum beam conforms to the deposited BPSG, with equal thickness on the top and on the sidewalls of the BPSG.

The BPSG is called a delete layer because it is etched away when the MEMS process is complete. After the delete layer is removed, the final MEMS design looks as shown in Figure T2-8.

Figure T2-8 Beam Cross-Section with Sacrifice Layer Etched

When the BPSG is removed, the fixed-fixed beam is held to the nitride by its conformal supports in the region where the BPSG holes were created. The free section of the beam in the middle is now free to deflect when an external force, such as a pressure or electrostatic load, is applied.

In photolithography, the term polarity is used to indicate whether drawn features, such as an enclosed polygon, appear light or dark on the mask plate. In actual fabrication, the polarity of a mask determines whether a defined shape is retained or etched away. This depends on the type of photoresist used, as well as the process by which the material is deposited. In the Process Editor, however, positive polarity always means features are preserved, and negative means features are etched away.

ground plane

nitrideBPSG

aluminum



The process steps define the structure of Figure T2-7 and provide instructions for the actual fabrication of the model.

The Process Editor is accessed from an icon in the top half of the Function Manager. The initial process flow does not show the deposit and etch steps required to form the aluminum beam. In the steps below, the process file will be mod-ified so an appropriate model can be built.

Figure T2-9 Process Editor

The GND layer in CoventorWareAll design structures must include a GND or base layer. This layer defines the boundaries of the model’s active area and is not associated with an electrical ground or a deposition layer that is connected to ground.


1. Open the beam_init.proc file in the Process Editor.

a. In the Function Manager, click on the drop-down arrow to the right of the Process field.

b. Select the beam_init.proc file located in the BeamDesign\Devices directory.

c. Click on the Process Editor icon.

The software defaults to the BeamDesign\Devices directory. The user can browse to choose other directories and files.

The Process Editor defines a series of simple deposit and etch steps to model the actual MEMS process.

The Process Editor displays the beam_init.proc file.

Process Description Process Library

Step Parameters



The Process Description identifies all the steps used in creating the beam design. The Process Library provides the modeling step options. The Step Parameters pane allows the user to set parameters for a selected step in the Process Description. The Substrate in the Process Description pane corresponds to the ground plane, the next Stack Material corresponds to the Silicon Nitride layer, and the next Stack Material and Straight Cut steps correspond to the defined BPSG material on which the aluminum beam is placed. Finally, the BPSG delete step is shown at the end.

The beam process is now complete. The finished Process Description pane of the Process Editor should look as shown below.

Figure T2-10 Process Editor After Edits


2. Edit the process flow. Add a Conformal Shell and Straight Cut step with the attributes shown below.

a. In the Process Description pane, highlight Step 3 (Straight Cut) by clicking on the fourth row.

Selecting a row in the Process Description pane allows you to choose whether to insert above or below the highlighted step.

b. On the right-hand side of the Process Editor, in the Process Library pane, double-click on Modeling Actions to expand the folder. Right-click on Conformal Shell and select Insert Below Current Step.

c. Right-click on Straight Cut and insert it below the current step.

Clicking on the different options in the Modeling Steps folder inserts new deposit and etch steps. The Process Library can be docked outside the Process Editor by dragging the gray bars at the top of the Process Library pane outside the Process Editor.

d. Highlight Step 4 (Conformal Shell) in the Process Description pane, and enter the following attributes into the Step Parameter fields:

LayerName: enter beam (or another descriptive name)Material: select ALUMINUM(FILM)Thickness Nominal Value: enter 0.5Display Color: select red

The color designations for the deposits should correspond to the layer colors that appear in the solid model.

e. Select Step 5 (Straight Cut) and enter the following attributes:Select Cut Last Layer CompletelySelect Front SideMask: enter beamPhotoresist: select +

Step 5 creates a positive tone beam mask etch, with no oversize/undersize or sidewall angles. All but the narrow beam is etched away.



2.1.6: Layout Viewing and EditingAfter defining material properties and the deposit and etch sequence, the next step in creating a MEMS design is cre-ating the 2-D layout. The 2-D Layout Editor is used to create, import, view, and edit 2-D mask information. For users with alternative software, the Layout Editor can import CIF and GDSII format files and convert them to a Coventor-Ware-compatible format. The Layout functions are accessed by selecting the Designer tab from the Function Man-ager. From this window, the user selects a cat file. The cat file is the storage location for the 2-D layout created or edited in the Layout Editor. This cat file can include any number of individual cell layouts. The 2-D layout informa-tion can be used to create foundry masks for building the MEMS device and is used as the source for rendering a 3-D model for meshing and solving.

In the next sequence, the 2-D mask layout will be viewed in the Layout Editor. It may appear to be a dummy step because no changes are made to the design. Note, however, that this tutorial is a simplified example. A design may be built or modified, or imported from another layout database. Thus, consider the next step as part of the methodology for creating a real layout.

For practice and guidance in creating a 2-D layout, see the tutorial starting on page T8-1. For Layout Editor reference documentation, see the CoventorWare DESIGNER Reference. You can access a PDF of this manual from the Func-tion Manager Help > Contents option.

Adjusting Windows for Full Field ViewingAs an alternative to using the horizontal scroll bar in the window above, the window can be stretched horizontally to see all the fields. The column widths can also be adjusted with the mouse. Many dialogs in the software allow horizontal and vertical adjustment, as well as resizing of individual fields or columns.

Creating a New Process FlowThe method described in Step 2 is commonly used for creating new process flows from existing file descriptions. A new process file can be started in several ways:

Select File > New from the Process Editor menu bar. Initially, only a base layer appears. Proceed with developing a flow.Specify the create a new process option in the Process file field, and click on the Process Editor icon. When the Process Editor opens, the base layer appears.


3. Save the file as beam.proc. a. From the menu at the top of the Process Editor, select on File > Save As.b. Type the new file name beam.proc in the File name field.c. Click on Save.d. From the File menu, select Exit.

By default, the file is saved in the BeamDesign\Devices directory.

The file path in the Process field is updated automatically to the new beam.proc file.



Figure T2-11 2-D Layout Editor with Beam Design Displayed


1. Open the beam.cat file in the Layout Editor.

a. From the Function Manager, click on the tab labeled Designer.

The Designer tab gives the user access to the Layout Editor, the Solid Modeler, and the Preprocessor (for viewing the 3-D model and meshing).

b. Click on the icon to the right of the Layout field.

The software defaults to the BeamDesign\Devices directory.c. Select the beam.cat file in the BeamDesign\Devices directory.d. Click on Open.

e. Click on the Layout Editor icon.

The Layout Editor main window opens, displaying the beam design. A Terminal opens directly below the editor window.



The Layer Browser dialog is a key element in the 2-D Layout Editor. It displays and controls various attributes, including the following:

Layer Name - Displays the mask layer nameColor - Displays/controls the layer colorFill - Displays/controls the layer fill pattern (solid, dots, hatched, etc.)V - Controls the visibility of the layerS - Controls the selectability of the layer (for edit operations)Layer Polarity on Mask - Controls whether a layer is added or subtracted from the layout.Mask Name - Allows several layers to be assigned to the same maskDark/Light Mask Field - Controls how the shape drawn by the mask appearsMagnifier - Opens Layer dialog for editing and exporting layer properties

The 2-D Layout Editor will open .cat files generated in older versions of the software, but will not convert them to the current version until the file is saved.


2. Use the Grid tool to set the Working Grid to 5.0 and the Display Grid to 1.0.

a. From the top menu bar, select Tools > Options > Grid.b. In the grid dialog, set the Working Grid to 5.0,5.0 so that the cursor now

snaps to the nearest 5-micron grid point. c. In the grid dialog, set the Display Grid multiple to 1.d. Click on Apply.e. Click on Close.

The Display Grid setting displays a grid dot every 5 microns (not every 1 micron). The multiple value is multiplied by the Working Grid value to derive the display distance. For example, a Display Grid multiple of 5 for the same Working Grid of 5 sets the grid dots at 25-micron intervals.

3. Use the Ruler tool to measure the beam. a. From the top menu bar, select Tools > Ruler.b. Click on the top and then the bottom of the red aluminum beam. The

Terminal responds with "Distance = 100.0 microns."c. Along the top of the Layout Editor window, click on the Refresh icon

, which causes the screen to refresh and clears the ruler.

4. Access the Layer Browser.a. Click on the Layer Browser icon.

The Layer Browser dialog shown below opens.

Layer information can be directly edited from within this dialog.



The Layout Editor represents the BPSG as the solid yellow color and the aluminum beam in red. The next steps are a simple exercise with the Layer Browser that changes the appearance of the layers displayed.


5. Use the Visibility feature to identify each layer.

a. In the Layer Browser dialog, at the top of the Visibility column, click on V to turn visibility off for all layers.

b. One by one, click on the boxes in the V column next to the following layers: GND, anchor, and beam.

This action toggles the visibility on for each layer and allows the layers to be identified as they appear on the screen. Clicking on V again would also restore the original settings.

6. Set the anchor layer fill to none. a. For the anchor layer, select the none Fill pattern.

In the main window, the yellow squares of the anchor layer are now outlines. The modified view, including grid dots, is shown below.

b. In the Layer Browser dialog, select File > Close.

7. Exit the Layout Editor a. From the Layout Editor File menu, select Save.

The file is written to the BeamDesign\Devices directory.b. Select File > Exit.

The Layout Editor section is complete. In the next tutorial sequence you will use the 2-D layout to build your solid model.

anchor mask

beam mask

GND mask



2.1.7: Building the Solid ModelNow that the process and layout files are complete, a 3-D model can be built using the thickness and etch profile information from the process file and the 2-D layout mask information. To create the solid model, from the Designer tab, click on the arrow beside the Model/Mesh field and select the create new model option. Then click on the Build a New 3D Model icon. This will start the building process. When the software completes the solid model, the Prepro-cessor will automatically open.

Figure T2-12 Preprocessor Rendering of the Beam Model

The Solid Model Tool and Older Process Editor FilesIf CoventorWare is used with Process Editor files created in an earlier versions, the solid model tool will not read the older format directly. The Process Editor must be opened, the older file read in and resaved. The conversion is automatic.


1. Build the solid model of the beam. a. Click on the down arrow Model/Mesh field and select create a new model.

b. Click on the Build a New 3D Model icon.

c. In the Input dialog that opens, enter beam.d. Click on OK.e. Wait for the build to finish; the Preprocessor will automatically open.

A 3-D model is built using the mask and supplied process information. The model appears as shown in Figure T2-12. Note that the figure shows the model with a white background and no shadow effect. These features are controlled from the Tools > Options > View menu. See page D4-34 for more details.

Canvas

GeometryBrowser



The rendered 3-D beam is created from the 2-D layout drawing, with the red aluminum beam elevated and anchored by supports to an underlying layer. The process file information allows the depth of the beam to be extruded.

Viewing control icons along the top of the window allow for rotation, zooming, and other view perspectives. These features are detailed later in this and other tutorials.

2.1.8: Naming EntitiesThe next step in the design process is to add the desired layers to the Mesh folder and assign electrical characteristics and unique names. The entities are named before meshing because the names are actually attached to the solid model. If you assign the names at this point, the names will perpetuate throughout all meshes created with these layers. The names will remain even if you remesh.

Naming the faces is an important step because only those faces assigned user names appear in the solver boundary condition dialogs.


1. Hide the Nitride layer. a. In the Geometry Browser on the left side of the Preprocessor, right click on the Nitride layer and select Hide Selection.

The Nitride layer will not be part of the meshed model, so hiding this layer in the Solid Model folder makes it easier to work with the layers that will be meshed.

To view any entity that you have hidden, right click on its name in the Geometry Browser and select Show Selection.

2. Add the Substrate and Beam layers to Mesh folder.

a. Hold down the Ctrl key and click on the Substrate layer and the Beam layer.

b. Right click on the layers and select Add to Mesh Model.

Adding the layers to the Mesh Model folder makes them available for meshing.

You are selecting only the layers of interest to be meshed. Only the ground and beam layers are used by the solvers, so the other layers are not added to the mesh folder.

The Geometry Browser now appears as shown below.




3. Apply the Substrate properties shown below.

a. If necessary, double click on the Substrate layer to expand the Geometry Browser.

b. Click on Part_0(Substrate) to select.c. Select Edit >Properties.d. In the Name field, enter ground.e. In the Analysis options select these options:

ConductorSolidSuppress, except for MemElectro

The Suppress option removes this part from any mechanical simulation.

f. Click on OK.

The Part Properties dialog has an icon that accesses the Materials Properties Database (MPD) Editor. The user can make changes to material property values from this dialog, but these changes will not be written to the MPD file. The changes will be stored in the project’s database.

Any changes entered in the Preprocessor's MPD editor are immediately saved to the currently open model/mesh document, without waiting for the user to issue an explicit 'Save' request.




4. Apply the Beam properties shown below. a. If necessary, double click on the Beam layer to expand the Geometry Browser.

b. Right click on the beam part and select Properties.c. Verify these settings:

Name = beam.ConductorSolid.

d. Click on OK.

The beam part has the necessary material assignments. It will remain a movable part and therefore be a part of the mechanical simulation.


5. Set the Z scale for easier face identification.

a. In the Preprocessor menu bar, find the Z Scale field, and select or enter a number between 3 and 10.

b. Click on the Face Selection Mode icon.

You are expanding the viewing height for easier face naming. The Z Scale distorts the height of the model. Choose a number that allows easy selection and identification of the sides and anchors of the beam.



6. Name the top surface of the beam top. (See Figure T2-13).

a. In the canvas area of the window, left click on the top surface of the beam. (See Figure T2-13).

Note that the Geometry Browser for beam region automatically expands to the Part and Face level, and the corresponding Face number for the top beam surface is highlighted.

b. Right click and select Set Name.c. In the Set Face Name dialog that opens, enter top in the Name field.d. Click on OK.

A change is made to a default face name assigned by the software. The name top is appended to the corresponding face in the Geometry Browser. The canvas area does not change.

7. Name the top surface of the substrate ground.

a. Repeat the above procedure for the ground surface, changing the face name to ground.

8. Name the side surfaces of the beam side1 and side2.

a. Repeat for the visible side surface, changing the face name to side1.

The beam is thin, so side1 would be difficult to select if the Z scale had not been distorted in the previous step.

b. Click on top and then on the Hide Selection icon.

This hides the top surface, revealing the inside view of the other side and beam bottom.

You can also right click on an entity and select Hide Selection.c. Identify the opposite side and name it side2.

9. Name the bottom of the beam bottom. a. Identify the bottom of the beam and name it bottom.

10. Name the bottom anchor faces anchor1 and anchor2.

a. Hide the top face of the anchor and select the bottom anchor face (face touching the ground surface). Name it anchor1.

You need to name these faces because they will be used to fix the anchors of the beam during the MemMech simulation. Only faces that must be identified for solver boundary condition setup must be named by the user. These named faces appear in the pull-down patch menus in the boundary conditions (BC) setup dialogs.

b. Select the Rotate Model icon , and rotate the model so that the other anchor is accessible.

When you use the rotate tool, the Face Selection Mode is no longer active. To continue selecting faces, click on the Face Selection Mode icon. Or to rotate a model while keeping the face selection mode active, use the Ctrl + Right Click and drag option.

c. Reselect the Face Selection Mode icon.d. Hide the top face of the anchor and name the bottom anchor face

anchor2.

To display all the faces you have hidden without selecting them one by one, right click on the region that contains the beam and select Show Selection.

e. Select File > Save.




Figure T2-13 Face Assignments


11. Rename the conductors beam and ground. a. In the Geometry Browser, double click on the Conductors folder to expand the tree.

b. Right click on the Conductor entity that corresponds to the ground part and select Set Name.

c. In the dialog that opens, enter ground.d. Select the other Conductor.e. Rename it beam.

Conductor names are displayed in BC setup dialogs and in results windows. Assigning more meaningful names makes it easier to identify the conductors in these dialogs.

Z scale = 5

ground

top side1

anchor2

anchor1(top face hidden)

bottom and side2faces not shown

(top face hidden)



2.1.9: MeshingThe next step in the design process is meshing. The model must now be meshed so the geometry of the structure can be reduced to a group of simpler finite element bricks and presented to the solver for finite element analysis. You will select the meshing method, and then create a mesh for the beam and the substrate. The mesh, part, and face informa-tion are stored in the project database. This database information is used in solver simulation. Figure T2-14 shows the process flow for executing this type of sequence.The flow chart illustrates the general ways in which designs can be built and simulated.

Figure T2-14 Meshing in CoventorWare

In this mesh sequence, you will assign different meshes to different regions: the beam will have a Manhattan mesh, and the ground will have a surface mesh.

Optional: Import Mesh from

2-D model creation (Layout Editor)

Designer tab

Process Editor

Analyzer tab

CoventorWare Solvers

3-D model creation

Can create different finite element

Optional: Export 3-D to external program

Meshing (from within the Preprocessor)

external program

Material Properties Database

mesh for different layers



Figure T2-15 Mesher Settings


1. Assign a Manhattan mesh type to the Substrate layer. Use the Parabolic element type and element sizes of 2,2,and 10 in the X, Y, and Z directions respectively.

a. From the Geometry Browser, click on the region containing the Substrate layer.

b. Right click and select Mesher Settings.c. Select the Manhattan mesh type.

The Manhattan mesh option creates brick elements. This type of meshing is used for models with orthogonal geometry, i.e all the model faces are planar and join at 90 degree angles.

The Parabolic element order, the default setting, creates a hexahedron with node solutions at 27 points (8 vertices, 12 midpoints between vertices, 6 hexahedral face centers, and 1 center).

d. For the Element Size, enter the following:For X direction: 2For Y direction: 2For Z direction: 10

e. Check that the dialog parameters match those shown below.f. Click on OK.

For more explanation of Manhattan Mesher Settings, see page R2-16.



Figure T2-16 Meshed Beam and Substrate

Choosing an Adequate MeshIn this tutorial, the mesh settings for the model are provided, but when meshing your own design, it is important to conduct a mesh study to verify that you have used a sufficiently refined mesh to accurately model your device. Com-puter resources required to run your simulation increase as the mesh is refined; therefore, it is important to optimize your mesh so that you can obtain acceptable results in an acceptable amount of time. The numerical solution provided by your model will tend toward a unique value as you increase the mesh density. The mesh is said to be converged when further mesh refinement produces a negligible change in the solution.You can be confident that your model is producing a mathematically accurate solution if the two meshes give essentially the same result.

To conduct a mesh convergence study, create multiple models that have different element sizes. You may want to vary the mesh in only one direction of interest. For example, if your device will experience a lot of stress in the Z direction, you may want to vary the mesh only in that direction.We chose to vary the mesh in each direction as follows:

first model with element size = xsecond model with element size = x/2third model with element size = x/4


2. Assign a Manhattan bricks mesh type to the Beam layer. Use element sizes of 2,2,and 10 in the X, Y, and Z directions respectively.

a. Click on the region containing the beam layer.b. Apply the same mesher settings you applied to the substrate.

The beam is 100 µm by 10 µm, so 250 bricks will be created for the beam layer in the XY plane, plus another 20 bricks in the XY plane for the anchor supports.

The beam is only 0.5 microns in height, so the mesher will create a single layer of bricks.

c. Check that the dialog parameters match those shown in Figure T2-15.d. Click on OK.

3. Create the mesh.a. Click on the Generate Mesh icon .

This action creates a mesh on all the regions in the Mesh Model folder. See the resulting meshes in Figure T2-16.



Run the same analysis on each mesh and compare results. For this particular device, models with mesh densities of x/2 and x/4, yielded results that were less than one percent in variation from the tutorial mesh, but took a significantly larger amount of simulation time. The mechanical results from each mesh are listed below:

Table T2-3 Mechanical Results of Mesh Convergence Study

Refining the mesh any further than what is specified in the tutorial leads to negligible differences in results, but increases simulation time.

Note that for this example, the point of interest was the mechanical displacement. You could also run the same exam-ple with MemElectro to check for convergence of the electrostatic results. Convergence in one type of simulation does not imply convergence in all types of simulations. When conducting a mesh study, consider which type of phys-ical phenomenon you would like to investigate, then choose your module accordingly.

For more information on mesh convergence studies, see page R3-5 and page R4-12.

To see a Quality Query, right-click on a region and select Quality Query. Figure T2-17 shows the results of a Quality Query performed on the substrate region of the beam model.

Figure T2-17 Quality Query on Substrate Region

The meshing step is complete, except for saving the file.

Mesh model Mesh Size in X, Y, Z direction

Max. Node Displacement % Difference

Tutorial mesh 2.0, 2.0, 10 1.510403E-01 NA

Tutorial mesh/2 1.0, 1.0. 5.0 1.516704E-01 0.42%

Tutorial mesh/4 0.5, 0.5, 2.5 1.519611E-01 0.61%

Save the FileAfter renaming entities in the Preprocessor, it is critical to save the changes using the File > Save option. After performing the naming sequence a few times, it can be very easy to forget this step.



2.1.10: MemElectroThe MemElectro solver produces an electrostatic solution by solving for the charge and capacitance interaction between the beam and ground components of the created model. MemElectro uses the Boundary Element Method (BEM). During the calculation, MemElectro computes the charge on each surface panel and presents a final solution with charge distribution calculated for all the panels in the model.

This process is started from the Analyzer tab, used for accessing the core solvers used in this tutorial. The MemElec-tro, MemMech, and CoSolveEM modules are all used for this tutorial.


4. Save the model and close the Preprocessor. a. Click on File > Save.b. Click on File > Exit.

The necessary model preparation steps have been completed. You will now begin running simulations.


1. Set up the Analyzer tab to point to the MemElectro solver for the beam model.

a. From the Function Manager, click on the Analyzer tab.b. Click on the arrow to the right of the Solver field, and from the drop-

down menu, select MemElectro.c. Click on the arrow beside the Model/Mesh field. Select the beam model.

The Model/Mesh field defaults to the model created in previous steps. The Browse icon to the right of this field allows the user to select other models.

d. In the Analysis field, make sure create a new analysis is displayed.

You do not have to specify an analysis results directory in the Analyzer tab. You will specify a directory before the simulation begins.

e. Click on the Solver Setup icon.

Clicking on Solver Setup opens the MemElectro Settings dialog, which configures the solver for the type of problem presented to it.

Solver Setup icon



The number of solver categories and solver types that a user can access is dependent on the specific licensed configuration of CoventorWare.

The Solver Setup icon also has two other options: Load Setup from Previous Analysis and View Results. Both options become active when an analysis results directory from a previous run is selected in the Analysis field. The Load Setup from Previous Analysis option loads the boundary conditions used in the selected analysis. The View Results option opens the Analysis Results window, which allows the user to view the table and graphical results of a previously run solution without running through the complete solver setup and execution sequence. For consistency, the name Solver Setup will be used for this icon, even when a different option is selected.


2. Verify the default MemElectro settings. a. In the MemElectro Settings dialog, verify the default settings shown in the screen shots below.

The Settings setup dialogs allow parameters to be specified to run the electrostatic solver. These default settings are correct for this tutorial. The Settings dialogs only need to change from their default settings for very complex models requiring changes to achieve convergence or optimize speed.

b. Click on Next.

Clicking on Next opens the solver BCs dialog, where simulation conditions are set.



During the solver setup, if existing analysis results will be overwritten, a warning message appears:


3. In the ConductorBCs dialog, apply a voltage of 0 to the ground and a voltage of 1 to the beam.

a. In the MemElectro BCs dialog, click on ConductorBCs.b. Modify the dialog so the conductor ground has a 0.0 volt stimulus

applied and the conductor beam has a 1.0 volt stimulus applied.c. Click on OK.

A voltage difference is required between the beam and the ground to compute a charge for the structure.


4. Start the simulation. a. In the MemElectro BCs dialog, click on Run to start the simulation.b. In the Run Analysis dialog that opens, enter electro_run1, and click on

OK.

The Run Analysis dialog allows the user to name or select a result analysis, which will be written to the project database. If an analysis is selected from the Analyzer tab, that analysis is displayed, but the user can opt to select another analysis.

The user also has the option to run the analysis at a later time using the Add to Job Queue and hold or Save for Batch Run options. See for more information.

c. In the Confirm dialog click on Yes.

When the simulation starts, the Job Queue dialog opens. It can be used to monitor simulation progress and to access simulation results.



This dialog appears for all of the solvers when an overwrite is about to occur. Confirm by clicking on OK.

Activity during the computation appears in the normally minimized log window on the screen.


5. When the simulation is finished, open the Analysis results for the electro_run1 simulation.

a. When the Job Queue dialog indicates that the simulation is finished (green check mark appears by the electro_run1 job), click on the View

Results icon.

The Analysis Results window opens with access through a drop-down menu for capacitance, voltage, and charge results. This window also has access to 3-D visualization results and Query analysis.


6. View the electrostatic results. a. Click on the arrow beside the Tables field and select Capacitance Matrix (pF) from the drop down menu.

b. Click on the View Table icon.

c. Verify the results shown below, then click on OK.

The Capacitance Matrix dialog shows the capacitance values for the beam problem.

d. Select Voltage and Charge on Conductors from the Tables drop-down menu and click on the View Table icon.

e. Verify the results shown below, then click on OK.

The Voltage and Charge on Conductors dialog shows the corresponding charge for the voltages applied, using the capacitance solution in the Q=CV calculation.

View numerical results

Start a query

View results in 3-D

Select numerical results



The Capacitance Matrix dialog shows several values of capacitance, with all units in picofarads. Values where the names match (i.e. beam-to-beam capacitance) represent the self-capacitance due to stored charge on the device. Note that the rows and columns of this matrix add up to zero. By CoventorWare’s convention, self-capacitance terms (located on the diagonal of the capacitive matrix) should be positive. Mutual-capacitance terms (off-diagonal ele-ments) should be negative. A Capacitance Matrix dialog that deviates from this rule is an indication that the mesh needs to be refined.

Refer to the CoventorWare ANALYZER Reference (page R3-7) for an explanation of the derivation of this capacitance matrix.

Figure T2-18 Modified Surface Charge View


7. Use the Visualizer to view the 3-D charge results. a. Click on the View 3D Results icon.

Note that with this MemElectro simulation, the Charge Density values are already loaded and displayed in the Visualizer.

b. Select Coventor > Geometry Scaling.c. In the Scaling panel that opens, change the Z Scale field to 5. Click on

Apply, then on Close.

Changing the Z Scale field distorts the view for an enhanced view.

The image appears as in Figure T2-18.

8. Close the Visualizer, and the MemElectro results dialog.

a. From the Visualizer menu bar, select File > Exit.b. From the Analysis Results dialog, click on Close.

This completes the MemElectro step.

Control returns to the Function Manager Analyzer tab.



2.1.11: MemMechMemMech computes the mechanical solution for the beam problem. The solver uses the finite element method to solve for mechanical stress and displacement at each node on each brick created for the model. For the simple tutorial problem, the calculation is fast.


1. Set up Analyzer tab to point to the MemMech solver for the beam model.

a. Click on the arrow to the right of the Solver (effects) field, and from the drop-down menu, select MemMech.

b. Select the beam model.c. Click on the Solver Setup icon.

MemMech uses the model file information stored in the project database to compute a mechanical solution.

2. Verify the default settings in the MemMech Settings dialog.

a. Check that the defaults settings are as shown below.

This Settings dialog displays the current settings for the mechanical solver. Other settings allow for modal and harmonic analysis and are covered in later tutorials and in the CoventorWare ANALYZER Reference.

b. If you are using external ABAQUS, click on the Advanced button and select Yes for Use external Abaqus? (ABAQUS users, see page R4-62 of the Analyzer Reference).

c. In the MemMech Settings dialog, click on Next.



MemMech BCs WindowThe hierarchical MemMech BCs window provides access to dialogs that set the boundary conditions for the Mem-Mech solver. Usually, only one or two dialogs need to be set for any given problem.

In the next step, boundary conditions will be assigned for the model through the MemMech SurfaceBCs dialog, illus-trated in Figure T2-19. The left section of the SurfaceBCs boundary conditions dialog allows specification of which surfaces of the beam model receive a mechanical stimulus. Surfaces are specified by using the face names created in the Preprocessor (only user-named faces appear in the pull-down menus). These faces correspond to patch names in the boundary condition dialogs and can be controlled in a variety of ways, including applying loads or specifying that patches remain stationary in the X, Y, or Z axes. Boolean capability allows a selection of the union or intersection of patches when applying forces.

With the LoadPatch type already selected, the right section of the SurfaceBCs dialog allows the user to apply a pres-sure load to the patch surface in a variety of ways, including a scalar load in a direction normal to the patch or a vector load in any direction. Value dialogs are used to enter these values.

Before executing the next sequence of steps, note that the Surface BCs dialog specifies AND and OR functions; these apply to unions and intersections correspondingly akin to similar logical values. The distinction is further defined within the Step table.

Figure T2-19 MemMech SurfaceBCs Setup



The remaining sections of the boundary conditions set up are inactive. Quickly review the screens to become familiar with them and to verify that no conditions are set. For further information on the functionality of the other boundary conditions in MemMech, refer to the CoventorWare ANALYZER Reference.


3. In the SurfaceBCs dialog, fix the anchor faces.

a. Click on SurfaceBCs from the MemMech BCs window.b. Modify Set 1 as described below:

For FixType, select fixAll.For Patch1, select anchor1.For and1, select or.For Patch2, select anchor2.The rest of the Set 1 line does not change.

A Set describes a particular set of conditions. It associates patches with a specified action.

During the model calculations, the patches assigned are assumed to be stationary in the X,Y, and Z directions.

The patches named anchor1 and anchor 2 are designated as fixed, so they do not move during the calculations.

In this context, or is used as an additive quantity (the union of two entities). It says that in addition to anchor1, the entire next patch specified also has the same Fix Type applied. Do not use and here; the anchor1/anchor2 surfaces have no common intersection.

4. Apply a 0.001 MPa load to the top patch. a. Modify Set 2 as described below:For FixType, select LoadPatch.For Patch1, select top.Do not change any of the Boolean settings.For LoadValue type, select Scalar.For LoadValue, enter 0.001.

The load is applied to the entire top surface, and only the top surface.

The load is applied in the -Z direction, with a magnitude of 0.001 MegaPascals.

None of Sets 3-8 are used. The none setting (set by default) tells the software to ignore the entire line. Note that if the first column of a row is set to none then the entire line is ignored.

b. The Surface BCs dialog should now be set as shown in Figure T2-19. Click on OK.


5. Start the MemMech simulation. a. Click on Run.b. Save the analysis results as mech_run1.c. Click on Yes to save project settings.

When you save the settings at this point, all the file pointers and BC dialogs that you have set are preserved.

The mechanical solver starts. Simulation time varies according to the user’s computer configuration.




6. Verify the mechDomain results. a. When the simulation is finished, click on the View Results icon in the Job Queue dialog.

b. Select mechDomain from the Tables drop-down menu.c. Click on the View Table icon to review the mechanical results.

The mechDomain dialog shows the maximum and minimum of both the magnitude of the displacement vector over the entire solution domain, as well as the maximum and minimum of each of the components.

d. Click on OK.


7. Verify the rxnForces results. a. Select rxnForces from the Tables drop-down menu, then click on the View Table icon.

The rxnForces dialog shows the reaction forces that develop at the fixed ends when a pressure load is exerted downward.

b. Click on OK.



Figure T2-20 Beam Surface Stress View in Visualizer


8. View the 3-D mechanical results. a. Click on the View 3D Results icon.

For mechanical simulations, the default view does not show parts that were designated Suppress, except for MemElectro in the preprocessor. To show the substrate, select Coventor > Parts Visibility and move ground from the Hidden list to the Visible list with the Show button.

b. From the Visualizer menu bar, select Plot > Contour/Multi-coloring.c. In the dialog that opens, select Mises Stress from the drop-down menu.d. Click on Close.e. Select Coventor > Geometry Scaling.f. In the dialog that opens, set Scale Z to 5.g. Select Deform Using Displacements, and set the Exaggeration to 15.h. Click on Apply; click on Close.

Deform Using Displacements and Exaggeration settings display beam deflection.

Note that the Deform Using Displacements setting shows the physical deformed shape, deformed with the displacement vector. It does not depend on the selected contour.

The display shows a color map of surface stress along the beam surface, illustrated in Figure T2-20.

Maximum deflection is at the beam center, but maximum surface stress is at the fixed anchors.

i. Select View > Fit to Full Size.j. Adjust Rotation and Scale for best viewing.

9. Exit the Visualizer, and close the Analysis Results window.

a. From the Visualizer menu bar, select File > Exit.b. Click on Close to close the Analysis Results window.



To see the relative effects of the applied pressure, perform the following exercise:

The illustration in Figure T2-20 shows colors of the frame background, color map legend, and 3-D axis symbol reversed from the default display. To change the background to white and the legend and 3D axis symbol to black, run the White Background macro, accessed from Tools > Quick Macro Panel.

The Visualizer has many different functions for analysis and display. The on-line help, accessed from the Help menu, covers all of these modes in detail. Visualizer functionality that is specific to CoventorWare is detailed in the CoventorWare ANALYZER Reference (starting on page R9-1).


10. Rerun the MemMech simulation with a surface load of 0.005.

a. Go back to the MemMech Surface BCs dialog and change the Scalar force to 0.005.

b. Rerun the simulation and save the new analysis to mech_run2.

This setting allows you to observe the relative displacement effect with an increased pressure.

11. Observe and compare the new results with the results from mech_run1.

a. When the simulation is finished, make sure that mech_run2 is selected in the Job Queue window, and click on the View Results icon.

b. In the Analysis Results window, select mechDomain.c. Compare the results shown below with those from the original exercise.

The increased scalar force increases deflection, but the relationship is not linear.

d. Click on Close in Analysis Results window.



2.1.12: CoSolveEMThe CoSolveEM tool couples the electrostatic and mechanical solvers. In an iterative process, the electrostatic results are input to the mechanical solver, and the results are fed back until convergence is reached.

MemMech Setup for CoSolveEMBefore beginning with the CoSolve setup, go to the MemMech setup and change the surface boundary conditions. When MemMech was run, a 0.005 MegaPascal pressure load was applied when the boundary conditions were set. For the CoSolve run, remove the pressure and observe the mechanical deflection that takes place due solely to the electrostatic charge attracting the beam. The following steps are similar to the MemMech portion of this tutorial.


1. Set the MemMech SurfaceBCs LoadValue to 0.

a. Verify that the MemMech solver is still selected.b. Click on the drop-down arrow beside the Solver Setup icon and select

Solver Setup.c. Click on Next.d. In the dialog that opens, click on SurfaceBCs.e. Change the Set2 LoadValue to 0.0. The dialog appears as shown below.

External pressure loads must be removed for this problem.f. Click on OK in the SurfaceBCs dialog.g. Click on Close in the MemMech BCs window.

Clicking on Close will not initiate the solver. MemMech is accessed to set relevant boundary conditions.




2. Set up the Analyzer tab to point to the CoSolve solver for the beam model.

a. From the Analyzer tab, set the Solver field to CoSolveEM. b. From the Model/Mesh drop-down menu, select the beam model.c. Click on Solver Setup.

The setup is nearly the same as for MemElectro and MemMech.

CoSolve sets parameters, changes settings for electrical and mechanical stimuli, and performs a coupled solution using electrostatic and mechanical solvers.

3. Configure the CoSolve solver to run with Single Step and the Relaxation settings.

a. In the CoSolveEM Settings dialog, set the Independent Variable to Voltage.

The Settings dialog controls convergence settings, CoSolve tool parameters, and the type of iterative analysis performed.

b. Set the Analysis Options field to Single Step.c. Set the Iteration Method to Relaxation.

The Iteration Method allows the solver to iterate until the solutions converge (using relaxation or Newton techniques) or perform a single combined electrostatic and mechanical solution step. Other convergence parameters can be set from the Advanced Settings dialog. For more details on these settings, see page R5-6.

d. Click on Next.e. Click on OK in the warning dialog.



The window shows the beam displacement in the X,Y, and Z directions after iterating until convergence is reached. In 3-D space, there may be a range of nodal displacements. The Max and Min columns show the limit values for this set.


4. Apply a voltage of 20 volts to the beam. a. In the CoSolveEM BCs window click on ConductorBCs.b. Change the voltage for the beam to 20 volts.c. Click on OK.

The voltage is increased to increase the electrostatic charge that develops. Without an applied pressure load, the beam deflection will come solely from this charge.

5. Start the CoSolve simulation. a. In the CoSolve BCs window, click on Run.b. Save the analysis as cs_run1.c. In the Save Settings dialog click on Yes.


6. View the numerical displacement results. a. When the simulation is finished, in the Job Queue dialog click on the View Results icon.

b. Select Displacement from the Tables drop-down menu, and click on the View Table icon.

c. Click on OK.

This action displays the computed mechanical displacement of the beam.




7. View the Capacitance results. a. Select Capacitance to view the electrostatic portion of the results.

This window summarizes the capacitance matrix electrostatic results. b. Click on OK.


8. View the Voltage results on Conductors. a. Select Voltage to view the voltage for the conductors.

This window summarizes beam and ground voltage results.b. Click on OK.


9. View the Charge results on Conductors. a. Select Charge to view the charge for the conductors.

This window summarizes beam and ground charge results.b. Click on OK.



Figure T2-21 CoSolve Surface Visualization of Results


10. View the Reaction Force results. a. Select Reaction Force to view the reaction forces portion of the solution.

This window lists the forces at the fixed anchors.b. Click on OK.


11. View the 3-D charge results. a. Start the Visualizer by clicking on the View 3D Results icon. b. In the MemElectro Results frame, select Coventor > Geometry Scaling,

and set the Z Scale to 5.

CoSolve produces both electrostatic and mechanical solutions, showing both charge and deflection in the same run.When CoSolve results are loaded into the Visualizer, the MemElectro and MemMech results are displayed in separate frames.

c. Select Plot > Contour/Multi-coloring, and display the Charge Density results.

d. Select View > Fit to Full Size. The results are shown in Figure T2-21.

Observe that the charge value is about the same as when MemElectro was run.



Figure T2-22 CoSolve Mechanical Results


12. View the 3-D mechanical results. a. Select Frame > Push Current Frame Back.

The MemMech results are displayed in a separate frame, this action brings the frame forward.

For mechanical simulations, the default view does not show parts that were designated Suppress, except for MemElectro in the preprocessor. To show the substrate, select Coventor > Parts Visibility and move ground from the Hidden list to the Visible list with the Show button.

b. Select Plot > Contour/Multi-coloring, then select Mises Stress.c. Set the Geometry Scaling dialog as follows:

Scale Z = 5Select Deform Using DisplacementsExaggeration = 50.

d. Select View > Fit to Full Size.

The results are shown in Figure T2-22.

The mechanical deflection is much less because the beam bends from the electrostatic charge only without any external pressure applied.

e. Close the Visualizer and the Analysis Results window.



2.1.13: MemMech Coupled Electrostatic AnalysisMemMech provides a capability for performing fully coupled electrostatic analysis. This capability will be demon-strated here, and the results are compared with those obtained from the CoSolveEM simulation in the previous sec-tion.

Because the substrate is much thicker than the beam, the deformation of the substrate will be small compared to that of the beam. For this reason, the substrate will be meshed with just a single element.

Figure T2-23 Region 1 Mesher Settings and Resulting Mesh

For more information on coupled mechanical-electrostatic analysis, see page R4-49 of the Analyzer Reference.


1. Remesh the beam’s substrate region using mapped bricks, linear element order, and an element size of 130. Unsuppress the substrate.

a. From the Function Manager/Analyzer tab, click on the Start Preprocessor icon beside the Model/Mesh field to open the beam model.

b. In the Geometry Browser, right click on Region 1 (the substrate layer) and select Mesher Settings.

c. Change the Mesh Type to Mapped Bricks, the Element Order to Linear, and the Element Size to 130.0. Click on OK.

d. Right click on Region 1 and select Properties. In the dialog that opens, un-check the Suppress, except for MemElectro option.

e. From the Preprocessor icon menu, click on Generate Mesh. The model should appear as shown below.

f. Select File > Save As and save the model as beam_coupled.g. Select File > Exit to close the Preprocessor.




2. Configure the MemMech solver to use the beam_coupled model and use its default solver settings.

a. From the Analyzer tab, select MemMech from the Solver drop-down menu and make sure the beam_coupled model is selected in the Model/Mesh field.

b. From the Analysis field drop-down menu, select create a new analysis, and then click on the Solver Setup icon.

c. In the MemMech Settings dialog, make sure these options are set:Physics: MechanicalLinear or Nonlinear?: NonlinearTime Dependence: SteadyStateAdditional Analysis: None

d. Click on Next.

3. In the SurfaceBCs dialog, fix the anchor1, anchor2, and ground patches. Apply a 20 volt potential between the ground and bottom patches.

a. Click on SurfaceBCs.b. Apply a fixAll FixType to anchor1 or anchor2 or ground (see below).c. Apply a Potential FixType to ground with a LoadValue of 0.0.d. Apply a Potential FixType to bottom with a LoadValue of 20.0.e. Click on OK.


4. Designate the bottom and ground as the electrostatic surfaces.

a. Click on ElectroStaticBCs.b. For Set1, set Surface_1 to bottom and Surface_2 to ground.

MemMech creates a set of finite elements between the surfaces to model the electrostatic forces. Surface_1 controls the definition of the mesh. For each solid element face on Surface_1, an electrostatic element is created that spans the space between Surface_1 and Surface_2.

c. Click on OK.



This window shows the maximum (or minimum) beam displacements in the X, Y, and Z directions for the converged solution. Note that the Minimum value of Node Z Displacement of -0.055 microns compares closely with the value obtained from CoSolveEM for the same model (-0.059; see page T2-41).


5. Run the analysis and view the results. a. In the MemMech BCs window, click on Run.b. Save the analysis as electrostatic_mech.c. In the Save Settings dialog click on Yes.d. When the simulation is finished, click on the View Results icon in the Job

Queue dialog.e. Select mechDomain from the Tables drop-down menu and click on the

View Table icon.


6. View the 3-D mechanical results. a. Start the Visualizer by clicking on the View 3D Results icon.b. Select Coventor > Parts Visibility, and hide the ground part.

Hiding the substrate makes it easier to view the beam results.c. Select Plot > Contour/Multi-coloring, then select Mises Stress.d. Select Coventor > Geometry Scaling and set the following parameters:

Scale Z = 5.0Select Deform Using Displacements.Exaggeration = 50.

e. Select View > Fit to Full Size.

The results are shown in Figure T2-24. As expected, this result is very similar to the CoSolveEM results shown in Figure T2-22 on page T2-44.



Figure T2-24 MemMech Coupled Electrostatic-Elastic Results

For some MEMS devices such as switches, it is important to know the time required to move parts of the device from one position to another. This information can be obtained by performing a transient analysis in MemMech. To dem-onstrate this capability we will calculate the transient response of the beam to the same electrical potential loading considered above.


1. Configure the MemMech solver to use the beam_coupled model and transient solver settings.

a. From the Analyzer tab, select MemMech from the Solver drop-down menu and make sure the beam_coupled model is selected in the Model/Mesh field.

b. From the Analysis field drop-down menu, select create a new analysis, and then click on the Solver Setup icon.

c. Set the MemMech Settings dialog as shown below.d. Click on Next.



Figure T2-25 Transient Results of Beam Loaded with Electrical Potential


2. Verify the SurfaceBCs and ElectroStaticBCs dialogs.

a. In the SurfaceBCs dialog, verify that the entries in the table are unchanged from the previous analysis.

b. Verify that the ElectroStaticBCs dialog is unchanged from the previous analysis.

3. Run the analysis and view the results. a. In the MemMech BCs window, click on Run.b. Save the analysis as electrostatic_trans_mech.c. In the Save Settings dialog click on Yes.d. When the simulation is finished, in the Job Queue dialog, click on the

View Results icon.

This analysis may take as long as 1/2 an hour to complete.e. Select dyna from the Graphs drop-down menu and click on the View

Graph icon.f. Click on Mapping Style.g. In the dialog that opens, click on the Max_Displacement Map Name to

select it. h. Click on and hold Map Show to select Show Selected Only, then close the

Mapping Style dialog.

Note that the maximum absolute displacement at approximately 1.5 µs is 0.096 µm. This is nearly twice the value of 0.055 µm obtained in the static analysis.

The published graph format was created using a Visualizer macro. See the Visualizer section in the CoventorWare ANALYZER Reference, page R9-34, for details.



2.1.14: Parametric StudyThe next major sequence in the tutorial uses the Parametric Study function to demonstrate how a parameter can be varied automatically to analyze device sensitivity to manufacturing and design variations. The Parametric Study func-tion, accessed from the BCs window of each solver, has the capability to define variables that vary one or more mechanical properties, dimensions, input boundary conditions, or some other parameter. After the variable has been defined, the solver starts a batch run of simulations to be solved in sequence by one of the solvers, resulting in a series of output files. The file information can be viewed in table or plot format or displayed in the 3-D visualizer.

MemMech BCs for Parametric StudyIn this parametric study, the initial stress is changed while applying a constant pressure load. The simulation uses MemMech to compute the actual series of results. In preparation, the mechanical surface boundary condition in MemMech needs to be restored to the 0.001 MegaPascal pressure load value applied from the MemMech run (this was removed when CoSolve was run).

Because MemMech is the solver to be used for the study, the Settings dialog needs to be set up properly with the cor-rect path and parameter settings, as if MemMech was rerun for a single point solution. However, because no changes were made to these MemMech dialogs since the initial setup, do not recheck them for this tutorial.


1. Open the beam model into the Preprocessor and save as beam_stress.

a. From the Analyzer tab, select the beam model from the Model/Mesh field.

b. Click on the Start Preprocessor icon. c. In the Preprocessor, select File > Save As, and save the model

as beam_stress.

2. Change the initial stress material property of ALUMINUM(FILM) to 10, 10, 0.

a. Click on the Part Selection icon; then click on the beam.b. Select Edit > Properties (or right click and select Properties).c. In the Properties dialog, click on the MPD Editor icon.d. Change the ALUMINUM(FILM) Stress values to 10, 10, 0 for

Sx, Sy, and Sz, respectively.

You are applying stress to the beam so that you can apply a trajectory to those values.

e. When finished, click on OK. f. Save changes and exit the Preprocessor.

In the step above, you were instructed to save the model under a different name, and then change the new model’s material properties. If you were to change material properties, and then rename the model, the material properties would be associated with the original beam model as well as the new beam_stress model. Any changes entered in the Preprocessor's MPD editor are immediately saved to the currently open model/mesh document, without waiting for the user to issue an explicit Save request.



Figure T2-26 Parametric Study Setup Window for MemMech


3. Reapply the 0.001 pressure load to the top patch.

a. From the Analyzer tab, select MemMech as the solver.b. Select the beam_stress model.c. For the Analysis field, select create a new analysis.d. Click on the Solver Setup icon.e. In the Settings dialog that opens, click on Next.f. In the MemMech BCs window, click on SurfaceBCs.g. Change the second line as shown below.h. Click on OK.

The change reapplies the pressure load for the parametric study.

If changes were previously made within the MemMech setup, check the other boundary condition dialogs to verify that no conditions are active.


4. Access the MemMech Parametric Study Function.

a. In the MemMech BCs window, click on Parametric Study. The window shown in Figure T2-26 opens.

Note that the BCs buttons in this window will vary according to which solver is being used for the parametric study.



The buttons in the window above set all the properties required to complete a simulation run. The individual dialogs set parameter conditions that allow the simulation to be run over a series of steps, varying mechanical, dimensional, material, or other properties in each step. After the dialogs are set, the Run button starts the solver.


5. Set up a Delta trajectory of 5 steps that increment with a step size of 1.

a. Click on Trajectories.

The TrajectoryType section allows for definition of how a certain parameter varies during the simulation iteration.

b. Set the t1 TrajectoryType to Delta.

The default Delta category defines values as increments between steps.c. Click on Edit. Set the increment values as shown below.

The parametric study runs 5 sets of computations using a variable t1 that changes in 1 unit increments.

d. Click on OK.e. In the Label column, delete t1 and type stress multiple.

The Label column uses a user-defined label as the abscissa annotation.f. Click on OK.


6. Apply the t1 trajectory to the Stress property, and then assign the trajectory to the beam’s material.

a. Click on MaterialProperties. b. Set the MaterialProp1 Property to Stress.c. Set the Trajectory to t1.

The solver assigns the t1 trajectory to Stress, varying it from 1 to 5 times its original value in increments of 1. The original value is derived from the Material Properties Database.

d. Set the ScaleFactor to 1.0.e. Set the Material to ALUMINUM(FILM).

The Stress is assigned to ALUMINUM(FILM), which is the material for the beam.

The pressure load of 0.001 MegaPascals is applied for each of the 5 iterative steps.

f. Click on OK.



The settings required for this tutorial run are complete. You may want to check other dialogs to become familiar with them for use with other tutorials. The dimension dialog can be used to scale, offset, or rotate model parts. An example is given elsewhere in this book (see page T2-100). The mechBCs dialog can be used to vary one or more boundary conditions set up for the mechanical solver, such as pressure load. Examples are given elsewhere in this book (see page T2-120 and page T2-126).

7. Start the simulation. a. In the Parametric Study window, click on Run. b. In the Run Analysis window, enter mech_para.

Saving the results to a new directory preserves the simulation results from the previous simulation.

c. Click on OK.d. Click on Yes to save the project settings.

For some parametric study computations that use the CoSolve or MemMech solvers, the output results can include a solution for moments. For such cases, Moments Table and Moments Graph buttons appear in the results window. In this tutorial, the moment values are zero because fixing the beam ends do not allow a rotational degree of freedom.





8. Open the Job Queue dialog to monitor the progress of the simulation.

a. In the Job Queue dialog, click on the Progress tab.

This dialog allows the user to see how many trajectory steps have been completed. It also allows the user to manage simulations that have been added to the job queue. For more information on this dialog, see page U1-31 of Using CoventorWare.


9. View the steps results. a. When the simulation is finished, click on View Results icon in the Job Queue dialog.

b. Select steps from the Tables drop-down menu. c. View the step values.

This window shows the step values derived from the Delta settings.d. Click on OK.




10. View the numerical and graphical mechDomain results.

a. Select mechDomain from the Tables drop-down menu. The numerical and graphical results are displayed in Figure T2-27.

b. View the table results; click on Close.c. Select mechDomain from the Graphs drop-down menu, then click on the

View Graph icon.d. In the left panel of the Visualizer, click on Mapping Style.e. In the dialog that opens, click on Node Displacement_Maximum Map

Name to select.f. Click on and hold Map Show to select Show Selected Only, then close the

Mapping Style dialog.g. View the graphical results, setting the view parameters for the best

display.

The graph on the left is for the tutorial five-step run, while the graph on the right increases resolution by plotting stress variation over 20 steps (too long a run for tutorial purposes). In both graphs, the Y axis values represent displacement.

Even though the initial residual stress increases, the displacement continues to increase. Because the beam is not constrained along the Y axis, as the stress increases, the anchors begin to be displaced. This movement can be seen in the Visualizer.

h. Close the Visualizer.



Figure T2-27 Parametric Study mechDomain Numerical and Graphical Results

fiv5-step run 20-step run

Note: window split for easier viewing



Figure T2-28 Displacement in the Y Direction


11. View the displacement results in the Visualizer.

a. Click on the arrow beside the Load Result view and select All results.b. Click on the View 3D Results icon.

This action loads all the results in the simulation run. c. Select Coventor > Part Visibility and move the ground part to the Visible

column.d. Select Plot > Contour/Multi-coloring, and select Displacement Y from

the drop-down menu.e. Select Coventor > Geometry Scaling.f. Set the Z scale to 5.g. Check Deform Using Displacements.h. Set Exaggeration to 10.i. Click on Apply and Close.

This sets the display for viewing displacement with deformation enabled.

12. View the results for each trajectory step. a. Select Coventor > Result Selection.b. Use the Next button to view the displacement for each trajectory

step.The fifth trajectory step is shown in Figure T2-28.

The Visualizer displays the beam deflection in the Y direction. Even though residual stress is increased in each trajectory step, the anchors of the beam begin to buckle, increasing overall displacement of the beam.

13. Exit the Visualizer. a. Select File > Exit.

step 5



Figure T2-29 Numerical and Graphical Reaction Force Results


14. View the numerical and graphical Reaction Force results.

a. Select rxnForces from the Tables drop-down menu. b. View the table results; click on Close.c. Select rxnForces from the Graphs drop-down menu.d. View the graphical results, setting the view parameters for the best

display.

The numerical and graphical results are displayed in Figure T2-29. The Y axis values represent reaction forces.

The published graph format was created using a Visualizer macro. See the Visualizer section in the CoventorWare ANALYZER Reference, page R9-34, for details.

e. Click on Close.f. Click on Close in the Analysis and Job Queue windows.

15. Exit CoventorWare. a. From the Function Manager, select File > Exit.b. Save your project settings.

The beam design is relatively simple. But with design projects that have complex designs, large meshes, or numerous simulations, the project database can get very large. The database file may get fragmented because it starts as a small file and grows incrementally as more data is added. If this happens, run Disk Defragmenter (accessed from Start > Programs >Accessories > System Tools). You can also copy the CPDB and GBAK files, delete the originals, and work with the copies to ensure that these files are also defragmented.



Now that the tutorial is complete, if you review any steps, keep in mind the following:Be sure to save the project from the Function Manager main menu before exiting.All results are saved in the project database file for later viewing.All solver tabular and Visualizer results can be reviewed from each solver by setting the Analysis field on the Analyzer tab to the saved analysis results and selecting View Analysis Results from the Solver Setup drop-down menu. Other tutorials in this book further extend the beam analysis by covering topics such as pull-in analysis, modal and harmonic analysis, rigid surface effects, scale and offset, and accuracy and run time changes caused by the use of an alternate meshing technique. Contact mechanics problems are covered in detail in the tutorial exercise beginning on page T2-86.



Notes


Section 2: Beam Design Modal and Harmonic Analysis in Analyzer Version 2008M

2.2: Modal and Harmonic Analysis in AnalyzerThis tutorial covers these techniques:

how to run modal analysis as part of a MemMech computation (page T2-62)

how to visualize modal vibrations in the Visualizer (page T2-63)

how to use a modal output result to calculate capacitance as a function of modal amplitude (page T2-65)

how to simulate electrostatic spring softening with CoSolve and observe mode frequency shifts (page T2-68)

how to run harmonic analysis as part of a MemMech computation (page T2-70)

how to analyze the harmonic response of a MEMS structure (page T2-72)

how to use the Queries feature to extract total displacement for a harmonic analysis (page T2-77)

This tutorial requires the MemMech, MemElectro, and parametric study functions.

2.2.1: Modal AnalysisA modal analysis calculation computes the natural resonant frequencies of a mechanical structure at equilibrium. At these resonant frequencies, an undamped (lossless) mechanical structure responds to a bounded excitation with an unbounded response. In other words, its system transfer function becomes infinite at the resonant frequency. These frequencies and their associated mode shapes are of particular interest in design because they closely resemble the corresponding characteristics of an underdamped mechanical system, and they indicate when the system will have its maximum response to an intended or unintended (noise) input.

The resonant frequencies are computed as the eigenvalues of the undamped, homogeneous equation of motion for the system. In addition, the resulting eigenvectors, or mode shapes, are computed. These mode shapes represent the over-all deformation of the mechanical structure oscillating at the associated modal frequency. The modal frequencies and shapes of a finite-element model can be calculated and visualized in CoventorWare through MemMech and the 3-D viewer. Because the modal analysis is performed on an undamped system, the amplitudes of these mode shapes do not indicate the actual amplitudes of the structure’s motion and are thus normalized to a maximum deflection of 1 micron. Combined with amplitude scaling and automated by the parametric study function, this information can be used to calculate capacitance versus mode shape amplitude. You can then apply these results in developing system macromodels.

In this next procedure, modal analysis is performed on the pressure-loaded beam. MemMech solves an eigenvalue problem to find the natural frequencies and mode shapes of the structure. The solution includes the mode shapes and modal displacements, as well as the deformation and stress values due to the pressure load. The numerical table results will include the load-dependent displacements and reaction forces, as well as the modal frequencies and gen-eralized mass. In the Visualizer, you can see the deformations, stresses, and modal displacements for each mode shape. In this example, the residual stress specified for the beam material will cause a shift in the natural frequency compared to the same beam without any residual stress. The applied pressure load also causes a resonant frequency shift.

Coventor, Inc. February 8, 2008 T2-61

Section 2: Beam Design Modal and Harmonic Analysis in Analyzer Version 2008


1. Start CoventorWare and create a new settings file in your BeamDesign directory.

a. Start CoventorWare.b. In the Project Browser that opens, select the BeamDesign

directory.c. Create a new settings file named modal.mps.

To create a new settings file from the Project Browser dialog, select the name of the project to which the new file will be assigned. Then, edit the file path that appears in the Settings file field by changing the name of the currently selected file to the desired name for the new file. Click on Open and the new file will be created for you.

2. Set up a MemMech simulation with the beam model as the input mesh.

a. Set the Analyzer tab for a MemMech simulation.b. In the Model/Mesh field select the beam model from the drop-

down menu.c. Click on the Solver Setup icon.

3. In the Settings dialog, setup a Mechanical/Modal analysis with 3 modes.

a. In the Settings dialog, set the Physics field to Mechanical.b. Set the Additional Analysis field to Modal.c. Set Number of Modes to 3. d. Click on Next.

4. Set up the SurfaceBCs dialog:Fix the ends of the beam.Apply a 0.001 MPa pressure load to the top patch.

a. Set the SurfaceBCs dialog Set 1:FixType: fixAllApply to: anchor1 or anchor2

b. Set SurfaceBCs dialog Set2:FixType: LoadPatchPatch1: topLoadValue: Scalar 0.001

c. Click on OK.

5. Start the simulation. a. Click on Run to begin the mechanical and modal computation.b. Save the analysis as mech_modal.

6. Verify simulation results as shown in Figure T2-30. a. When the simulation is finished, in the Job Queue dialog click on the View Results icon.

b. In the Analysis results window, select the mechDomain table results; verify with the results shown below.

c. Verify the rxnForces results.d. Verify the modeDomain results.

The modeDomain window lists each of the modes requested for calculation on a separate line in order of increasing frequency. For each mode, the mode Frequency, Generalized Mass, and Damping parameters are calculated. Because no material damping was set, the Damping column is empty.

T2-62 February 8, 2008 Coventor, Inc.


Figure T2-30 MemMech Modal Analysis Results


7. View the modal results in the Visualizer as shown in Figure T2-31. The illustrations show the three modes that correspond to the three files; frequencies from the mode table have been added to the Visualizer displays.

a. Select All Results and start the Visualizer.b. From the Coventor > Part Visibility menu, display the ground

as a reference point.c. Select Coventor > Geometry Scaling, and set the Z Scale to 10.d. Select View > Data Fit.e. Use View > Zoom to zoom in on the beam.f. Select Coventor > Mode Shapes then check Deform using

Modal Displacement, and click on Apply.

Selecting Deform using Modal Displacement allows the modal shape for each mode to be viewed.

g. Click on Next to cycle through the mode files. The modes are shown in Figure T2-31.



Figure T2-31 Visualizer Modes


8. View the vibrations of the mode shapes. a. Select 1 from the Mode No. menu.b. Click on Play to view the vibrations of that mode.

c. Click on Stop.d. Select and view Modes 2 and 3.e. Exit the Visualizer.f. Close the Analysis Results window.

Mode 1freq = 4.25e05

freq = 1.19e06

Mode 3freq = 2.31e06

Mode 2



Parametric Study Using MemElectroThe next sequence in the tutorial shows the user how to compute capacitance of the modal shape versus its amplitude. The MemElectro Parametric Study function is used, with a MemMech result file as the input.


1. Access the MemElectro solver; for input mesh select beam_mode_001 in the BeamDesign mech_modal analysis.

a. From the Analyzer tab, select MemElectro. Select the beam model.

b. For the rest of the MemElectro Settings dialog, verify the default settings as shown on page T2-29.

For brevity, this tutorial does not include a MemElectro simulation, but it is good practice to actually run the MemElectro solver in order to get a sense of how long each simulation will take and if the capacitance matrix is symmetrical and close to analytical results.


2. In the ConductorBCs dialog, apply a voltage of 0 to the ground and a voltage of 1 to the beam.

a. In the MemElectro ConductorBCs dialog, set the voltage of ground to 0.

b. Set the voltage of the beam to 1.

3. Set up a parametric study using MemElectro: Set a trajectory to vary beam displacement amplitude between -2 and 2 with a Delta increment of 1.

a. From the MemElectro BCs window, click on Parametric Study.

b. Click on Trajectories.c. Set the Trajectory Type to Delta.d. Set the Edit dialog:

Start to: -2Delta: 1Stop: 2

e. Change the label to amplitude.

Setting the trajectory allows the solver to create five solution steps, varying the beam displacement amplitude 2 microns above and below its base position. The bottom of the beam is 2.2 microns above ground; any larger swing would cause the beam to contact or penetrate the ground surface.

4. From the dimension dialog, apply a t1 trajectory to beam using the Mode Transform type (factor of 1).

a. Click on Dimensions.b. Set the Trajectory on the first line to t1.c. Set the Transform type to Mode.d. In the Mode Edit dialog that opens, set the ModeScale to 1, and

for the ModalResultMesh, select the beam_mode_001 result.

The Transform pull-down menu includes a special Mode function. The ModeScale sets the scale factor for the trajectory values used for the beam vibration swing. In this tutorial, the solver computes capacitance for each of the trajectory steps specified.

e. Click on List and set the Part to beam.



Figure T2-32 Parametric Study Capacitance Results

5. Start the simulation; save the results to electro_para. a. Click on Run.b. In the Run Analysis dialog, enter electro_para.c. In the Job Queue dialog, click on the Progress tab to view the

progress of the simulation.

6. Verify the table and graph results shown in Figure T2-32.

a. When the simulation is finished, in the Job Queue dialog click on the View Results icon.

b. Select Capacitance Matrix (pF) from the Tables drop-down menu to view numerical results.

c. Select Capacitance Matrix (pF) from the Graphs menu.d. In the Visualizer left panel, click on Mapping Style.e. Click on the ground_beam map, then hold down Map Show

and select Show Selected Only.

The total capacitance varies over the simulation as beam distance from ground changes. In this simulation, the beam shape changes with modal amplitude, affecting its capacitance values.




The capacitance simulation in the parametric study can be rerun for Mode 2 and Mode 3. You can go back to Step 1 on page T2-65 and point the Mode Edit dialog to the appropriate modal result and repeat the preceding documented sequence. As expected, capacitance as a function of deflection for both the asymmetric second mode and the torsional third mode produce symmetrical capacitance graphs, as shown below.

Figure T2-33 Capacitance Results for Modes 2 and 3


7. View the capacitance charge results in the 3-D viewer.

a. Load all results and start the 3-D viewer.b. View the Charge Density contour.c. In the Geometry Scaling dialog, set Z Scale to 10.d. Select View > Data Fit and Coventor > Result Selection to

view the charge results for each trajectory step.

The viewer displays the individual Mode 1 solver results. Viewing the capacitance charges illustrates the major difference between this setup and the display previously set up using Modes. The individual result groups created by the parametric study for each incremental mode step allow for viewing of the capacitance and charge distribution results for each Mode 1 result, which was not possible with the results created by MemMech and viewed with the 3-D viewer.

Mode 2 Mode 3



2.2.2: Electrostatic Spring SofteningElectrostatic spring softening is encountered in simulations of devices that have both an AC voltage and DC bias applied. Examples of such devices include RF filters, microrelays, gyros, and accelerometers. When an oscillating mechanical structure is subject to a constant electric field, the resonant frequency shifts compared to the resonant fre-quency observed without the DC field. For devices exhibiting pull-in behavior, the resonant frequency drop goes to zero at the pull-in voltage. The "softening" of the resonant frequency is often associated with points of developing instability. The capacitor’s downward force opposes the spring’s upward force, and they are in equilibrium. Stability is determined by how these forces vary with gap. When the increase in downward force for a small decrease in gap is larger than the increase in spring’s upward force, pull-in occurs. But even before pull-in, the nonlinear electrostatic force is reducing the net restoring force.1 This spring softening effect can be seen in the following simulation.

This simulation of a shift in resonant frequency due to applied electrostatic forces can be performed as a CoSolve post-analysis function. If you completed Tutorial 2.1 and Tutorial 2.2.1, you have observed how CoSolve can be used for a coupled electromechanical analysis on the beam, and how MemMech can be used to perform a modal analysis of the beam. This tutorial builds on your existing knowledge of the simple beam design.

In this sequence, you will perform an analysis on what is known as the beam’s normal mode. The normal mode is identified when a movable conductor moves along a line perpendicular to both the movable and fixed conductors. In Tutorial 2.2, you reviewed the mode shapes displayed in Figure T2-31 (page T2-64) and set the Visualizer to simulate the modal vibration frequencies (page T2-64). From this information, you can determine that the first mode is the beam’s normal mode.

In general, when performing a spring softening analysis, you should run a MemMech modal analysis first to identify the mode number corresponding to the normal mode. However, because you already performed the modal analysis and generated the modal frequency you will use for comparison in Tutorial 2.2, you do not need to run MemMech again in this segment.

In this tutorial you will use MemMech to fix the beam ends, use CoSolve to apply a DC voltage, compute the shifted modal frequency for the normal mode, and compare the results with those you obtained in Tutorial 2.2.

MemMechBecause CoSolve uses MemMech during the computation, you must be sure to set some of the dialogs properly.



a. Start CoventorWare.b. Select the BeamDesign project directory.c. Create a new settings file named modesoften.mps.

2. Access the MemMech solver with the beam model as the input mesh.

a. From the Analyzer tab, select MemMech as the solver.b. Set the Model/Mesh file path to the beam model and the Analysis

field to create a new analysis.c. In the MemMech Settings, set the Additional Analysis field to

Modal. All other MemMech settings remain at the default settings.

3. Set the SurfaceBCs dialog so that the ends are fixed.

a. In the SurfaceBCs dialog apply the fixAll FixType to end1 or end2.

No loads are assigned. For frequency analysis, if any LoadValue is entered, it is ignored by the solver.

b. Check that no other boundary conditions are set.c. Click on Close in the MemMechBCs window.



CoSolveCoSolve computes the shift in mode frequency due to electrostatic spring softening.


1. Set up a CoSolve simulation with the beam model as the input mesh.

a. From the Analyzer tab, select CoSolveEM as the solver type. b. Set the Model/Mesh file path to the beam model.

2. Set the CoSolve Settings dialog to Relaxation, Electrostatic Spring Softening, Mode_Number=1.

a. Set the CoSolve Settings dialog as follows:Set the CoSolve Steps to Single.Set the Iteration Method to Relaxation.Set the Additional Analysis to Electrostatic Spring Softening.For the Mode Number, accept the default setting of 1.

CoSolve will only simulate electrostatic spring softening for single mode in one simulation. For this simulation, we will use the first mode (shown in Figure T2-31 on page T2-64). For computing electrostatic spring softening on more than one mode, change the mode number and repeat the simulation.

b. Click on Next.

3. In the CoSolve ConductorBCs dialog, apply a 10 volt voltage to the beam, and start the simulation.

a. From the CoSolve BCs window, click on ConductorBCs. b. Verify that the ground is fixed and the voltage is 0.c. Verify that the beam is fixed, and set the voltage to 10 volts.d. Click on OK.e. Click on Run.f. Save the analysis as soften_run1.

4. Review the modeDomain results. Observe the frequency value and compare to that from the original MemMech modal analysis.

a. When the simulation is finished, click on the View Results icon in the Job Queue dialog.

b. In the Results window, select the modeDomain table results. Compare the frequency with that from the Tutorial 2.2 modal table, copied below for easy reference. The comparison is valid for Mode 1 only. You will observe a shift in frequency.

c. You can review the other result windows, but the mode frequency change is the most relevant part of the tutorial.

d. Close all remaining CoventorWare windows.

Original MemMech modal run. Only Mode 1 is used for comparison.

Shifted frequency CoSolve spring softening run.



2.2.3: Harmonic Analysis In this tutorial, the structural response of the same fixed-fixed beam is examined when subjected to a harmonic exci-tation. There are two methods for running a harmonic analysis: mode-based harmonic analysis or direct integration harmonics (see page R4-25 of the Analyzer Reference). In this tutorial we will use mode-based harmonic analysis in which the harmonic response is reconstructed from eigenvalues and a modal damping factor.

In a harmonic analysis a load with a prescribed sinusoidal frequency is applied to the model. For this simulation we apply a harmonic pressure load between the frequencies of 300 kHz and 6 MHz to the top surface of the beam. In this range the response is domination by the first six modes, so only these modes are use to construct the response. The seventh mode has a frequency of 6.36 MhZ, above 6 MHz.

Figure T2-34 Harmonic Analysis

InitializationBefore proceeding, be sure that you have set up a project directory and installed the files needed for this tutorial. The tutorial starts by starting the software.



a. Start CoventorWare.b. In the Project Browser dialog that opens, select the

BeamDesign directory.c. Create a new settings file named harmonic.mps.

1 kPa

Harmonic load used in Harmonic Analysis

ground plane

constant pressure load

ground plane

harmonic pressure load

1 kPa load used in first beam design tutorial and in modal analysis



MemMech


1. Set up a MemMech simulation with the beam model as the input mesh.

a. From the Analyzer tab select the MemMech solver.b. Set the Model/Mesh file path to the beam model.

2. In the MemMech Settings dialog, specify six modes to be computed by the MemMech solver, and set up a harmonic analysis for a range of 3e5 Hz to 3e6 Hz with 4 intermediate frequencies.

a. In the MemMech Settings dialog, set Additional Analysis to Modal Harmonic.

b. Set the Specify modes by option to Number of Modes and the Number of Modes to 6.

c. Set the Harmonic Analysis:Minimum Freq: 3e5 Maximum Freq: 3e6 No. of Frequencies: 10

The ten intermediate frequencies are generated for each interval between natural frequencies, or between the lowest or highest harmonic frequency and its closest natural frequency. Make sure the Modal Damping Coefficient is set to 0.1.

The Modal_Damping value is expressed as a fraction of critical damping. See page R4-27 for more details.

d. Click on Next.

3. In the SurfaceBCs dialog, fix the ends of the beam. Do not apply a scalar load.

a. In the MemMech BCs dialog, click on SurfaceBCs.b. For Set1:

fixType: fixAllApply to anchor1 or anchor2

c. Click on OK.

4. In the HarmonicSurfBCs dialog, set up a 1 kPA load on the top patch.

a. Click on Harmonic_SurfaceBCs.b. For Set1:

FixType: LoadPatchPatch1 topLoadValue: Scalar 0.001

This setup applies a 1kPa load, but this is not a constant pressure load. The load is applied as a sinusoid frequency as set in the MemMech Settings dialog.

c. Click on OK.

5. Start the simulation. a. Click on Run.b. Save the Analysis as mech_harmonic.



Figure T2-35 Modal Shapes for Each Mode

6. View the resulting mode shapes in the Visualizer. a. Select the mech_harmonic results and open the Analysis Results window.

b. Load all results and start the Visualizer.c. Select Coventor > Geometry Scaling, and set the Z Scale to 10.d. If necessary, select View > Data Fit.e. Select Plot > Contour/Multi-coloring, and select Modal

Displacement Mag.f. Select Coventor > Mode Shapes and select on Deform Using

Modal Displacement. Click on Apply.g. Click on Next to view each mode, as shown in Figure T2-35.

The first three mode shapes look exactly the same as on page T2-64.


7. View the modeDomain numerical results. a. From the Tables drop-down menu, select modeDomain.

The modeDomain window lists each of the modes requested for calculation on a separate line in order of increasing frequency. Because no material damping has been input, the Damping column is empty.


Mode 2

Mode 3

Mode 1

Mode 4

Mode 5 Mode 6



In the MemMech Settings dialog, ten frequencies were requested for the 300kHz to 6 MHz harmonic frequency range. This means that ten intermediate frequencies were created between (and including) each of the following ranges:

the lowest harmonic frequency of 300KHz and the lowest mode natural frequency of 454 kHzthe lowest mode frequency of 454 kHz and the next one at 1.2 MHz


8. View harmonic_Disp Table results. a. Select the harmonic_Disp table.

The window lists the maximum x, y, and z components of displacement for each requested frequency in the harmonic frequency range. Because the analysis includes modal damping, the response is complex. For each x, y, and z component, the magnitude and phase angle of the complex displacement are shown in the table. An explanation for how the frequencies in the table are derived is included below.



the 1.2 MHz mode frequency and the next one at 2.33 MHzthe 2.33 MHz mode frequency and the next one at 2.46 MHZthe 2.46 MHz mode frequency and the next one at 3.92 MHzthe 3.92 MHz mode frequency and the next one at 4.75 MHzThe 4.75 MHz mode frequency and the maximum simulation frequency of 6 MHz.

This is illustrated in the figure below, for a simulation with five steps:

When performing a modal harmonic analysis, it can sometimes be useful to understand how individual mode shapes contribute to the harmonic response. We can determine this by viewing the generalized_Disp result table.


9. View the harmonic_Disp graphical results. a. Select the harmonic_Disp graph.b. In the left pane of the Visualizer, click on Mapping Style.c. In the dialog that opens, click on MaxZ_Mag to select.d. Click and hold Map Show, then select Show Selected Only from

the drop-down menu.e. View the MaxZ_Mag plot in the main Visualizer window. f. In the Mapping Style dialog, click on MaxZ_Phase, then select

Map Show > Show Selected Only.




10. View generalized_Disp Table results. a. Select the generalized_Disp table.

The window lists the real component of the generalized displacement for each excitation frequency. As can be clearly seen, only modes 1 and 4 contribute to the response. The reason for this can be seen by looking at the mode shapes in Figure T2-35 and the equation for the modal force, (2). The applied force F is the uniform pressure. From equation (2), the product of this force with modes 2, 3, 5, and 6 is zero.


11. View the harmonic_Disp graphical results. a. Select the harmonic_Disp graph.b. In the left pane of the Visualizer, click on Mapping Style.c. In the dialog that opens, use the Ctrl key to select Mode1 and

Mode4.d. Click and hold Map Show, then select Show Selected Only from

the drop-down menu.

To better see the response, we remove modes 2, 3, 5, and 6.e. In the Visualizer window, select Plot > Axis. f. Click on the Y1 button, and from the Range tab, select the Use Log

Scale option.



The harmonic simulation was run with a number of ten frequencies to minimize simulation time. For simulation plots with higher resolution you can run the simulation with more frequencies. As a comparison, shown below is the Gen-eralized Displacement curve for a simulation with fifty frequencies. Because it has more simulation points, the graph has a higher resolution. But on a Windows XP machine with dual 3 GHz processors and 2 GB of RAM, the simula-tion time for fifty frequencies is 15 minutes, as opposed to three minutes for the simulation with ten frequencies.

Figure T2-36 Results with Fifty Frequencies



QueriesNow that you have verified the numerical and Visualizer results, you can display even more data with the use of the Queries function.

The Queries button is accessible from the Analyzer Results window. It allows calculation of additional data that is not available from the tables, graphs, or Visualizer display. For harmonic analysis, a special Harmonic Response field is available within the Queries function. This field allows you to calculate and view the total displacement values at spe-cific points in the model. In the Query for this tutorial, you will select a patch. The software finds the node closest to the geometric center of that patch and extracts the displacement data for that point. If you query a region specified by coordinates, the software will find a node closest to those coordinates and calculate the harmonic response for that point.


12. Perform a query on the top patch using the HarmonicResponse field option.

a. In the Analysis Results window, click on Custom Query.b. In the hierarchical window, click on On a Patch.c. Set the QueryLabel to HarmonicResponse.d. For Query1, select the top patch.e. Select HarmonicResponse from the Field pull-down menu.f. Click on OK in the Query on a Patch dialog.g. In the hierarchical Query window, click on Execute.

This sequence extracts the displacement data for the top patch.


13. View the numerical results of the query. a. In the results window, select the HarmonicResponse table.b. Review the results. The window displays the magnitude and

phase angle for the complex displacement for each harmonic frequency.

The Uz_mag and Uz_phase values are the only non-trivial results. The other values are mostly noise.




14. View the graphical results of the query. a. Select the HarmonicResponse graph.b. Set the graph window to display individual curves for displacement

magnitude and phase angle in the Z direction. The graphs show a distinct peak at the Mode 1 natural frequency. If you look back at the table results for the generalized coefficients of displacement, you will see that the Mode 1 values are significantly larger than the other mode values. When the coefficients are multiplied and summed over all modes to create the values shown in the graph, the Mode 1 numbers still dominate when viewing the graph shapes.



Reference1. Stephen D. Senturia. Microsystem Design. Boston: Kluwer Academic Publishers, 2001. 168-169.



Notes


Section 2: Beam Design Contact, Pull-in, and Lift-off in Analyzer Version 2008

2.3: Contact, Pull-in, and Lift-off in Analyzer


Remeshing an existing model to reduce computation time (page T2-81)

Analyzing trade-offs for computation time vs. accuracy in a simulation (page T2-84, page T2-85)

Creating a contact surface to limit mechanical deflection (page T2-86)

Performing a pull-in analysis (page T2-90)

Performing a lift-off analysis (page T2-94)

Using a parametric study to vary model characteristics and change the pull-in voltage (page T2-98)

Creating nested trajectory steps by running a parametric study through CoSolve (page T2-98)

2.3.2: Reduce Beam Mesh DensityThe beam structure created in the first tutorial exercise demonstrated many CoventorWare features using a straightfor-ward design with readily observable results. In the tutorial exercises that follow, you will be conducting complex analyses that would be best simulated with a simplified mesh.

The first exercise in this tutorial shows how the geometry of the model can be changed to optimize results. In this exercise the user remeshes the original mesh to reduce the number of elements. Remeshing the model preserves the user-assigned face and conductor names. Then, running MemElectro and MemMech will allow comparisons of the accuracy and computation time results with those from the original beam design.

Subsequent exercises explore several mechanical and electromechanical analysis techniques, including contact, pull-in, and lift-off.

If you have not reviewed the information in the first beam tutorial for some time, go back and review the beam 2-D layout design, Process Editor file, and solid model 3-D view before continuing.


Section 2: Beam Design Version 2008

Figure T2-37 Tutorial Step Sequence

Remesh Existing ModelThis exercise reduces the mesh density of the beam model. The result is reduced computation time with sufficient accuracy to run the many iterative simulations in this tutorial.


1. Initialize the software. a. Start CoventorWare and choose the BeamDesign project and BeamDesign.mps settings file.

b. Select the Function Manager Designer tab and set the Model/Mesh field to beam.

c. Click on the Start Preprocessor icon.

ground plane

pressure load

ground plane

++++++++++++++------------------------

voltage potential

Reduce beam mesh density and then investigate how this change affects solution accuracy and computation time. (page T2-81)

Apply a pressure load ramp to the beam using the parametric study function. With a rigid plane set up to simulate a contact surface, observe how the pressure load ramp causes the beam to flatten at this surface.(page T2-86)

Perform an electromechanical pull-in analysis on the beam and observe how an applied voltage ramp causes the beam to deflect and then pull in or snap to the ground surface. (page T2-90)

Perform a lift-off analysis to determine at what point release would occur in a descending voltage trajectory.(page T2-94)

Perform a parametric study to investigate how to optimize the beam’s geometry (beam thickness) to reduce the high voltage required for pull-in. (page T2-98)



Figure T2-38 Simplified Model

Table T2-4 Mesh Comparison

2. Delete the original mesh. a. Save the model as beam_reduced_mesh.b. Select Region 1 and Region 2 (use the Ctrl key), then click on the Delete

Mesh icon.

Note that the face and conductor names are preserved when the mesh is deleted.

3. Remesh the ground and beam regions so that so the beam has 20 x 2 brick elements along its 80 µm length (excluding the anchors), one layer deep.

a. For the ground and beam regions, select a Manhattan bricks mesh type and a Parabolic Element Order. Set the X, Y, and Z Element Sizes to 4, 4, and 10.

The original mesh used 2 x 2 x 10 µm bricks. The change represents a reduced element density ratio of 5:1.

b. Click on the Generate Mesh icon. The resulting mesh is shown below.


4. Compare the mesh statistics with the mesh statistics for the original beam model.

a. Compare the mesh report from the original beam; see below for a comparison of the old and new meshes.

This information can be found in the Mesh Report. Select Mesh > Mesher Log and scroll to the bottom to find the mesh statistics.

b. Exit the Preprocessor.

Original Mesh New Mesh

Number of Vertices 19710 5010

Number of Edges 8284 2124

Number of Faces 6424 1594

Number of Volume Elements 1570 380




Run MemElectro for Electrostatic ResultsThe MemElectro step produces capacitance and charge electrostatic results for the simplified beam model.

Figure T2-39 Capacitance and Charge Comparison

The computation should run much faster for this tutorial than for Tutorial 1. The new results are shown side by side with the results for beam. The capacitance matrices for the original and simplified model differ by about 7.5%. But a query on the charges on the bottom patch of the beam gives the following results:

The values differ by about 0.7%. The trade-off for simplification and reduced compute time is some inaccuracy in the solution.


1. Set the Analyzer tab for a MemElectro simulation.

a. From the Analyzer tab, set up a MemElectro simulation with the beam_reduced_mesh model.

2. Create a 1 volt difference between beam and ground.

a. In the MemElectro Conductor BCs dialog, apply 1 volt to the beam.

3. Start the simulation. a. Click on Run.b. Save the analysis as electro_reduced_mesh.

4. Compare results with those from Tutorial 1.

a. Compare the Capacitance (pF) and Voltage and Charge on Conductors results with those from Tutorial 1. See Figure T2-39.

original model reduced mesh model

original model reduced mesh model



Run MemMech for Mechanical ResultsThe MemMech step produces mechanical results for the simplified beam model.

Figure T2-40 MechDomain Comparison Results

The MemMech solver should complete in less time with this simplified beam model. In addition to demonstrating how to modify model meshes and the computation trade-offs for simplified designs, the new beam_reduced_mesh model can be used as a substitute for the more complex beam. The advantages of reduced compute time are seen in the remaining sections of this tutorial, all of which iterate MemElectro and/or MemMech many times.


1. Set the Function Manager for a MemMech simulation.

a. Set the Analyzer tab for a MemMech simulation, with the Model/Mesh field path set to the beam_reduced_mesh model.

2. Set the SurfaceBCs dialog so the beam ends are fixed in all degrees of freedom, with a 0.001 MPa scalar pressure load applied to the top surface.

a. Set the SurfaceBCs dialog Set1 for:fixType set to: fixAllfixType applied to patches: anchor1 or anchor2

b. Set the SurfaceBCs dialog Set2 for:fixType set to: LoadPatchPatch1 set to: topLoadValue set to: Scalar 0.001

The setup is identical to the BCs applied in Tutorial 1 (see page T2-34).

3. Start the simulation. a. Click on Run. b. Save the Analysis as mech_reduced_mesh.

4. Compare results with those from Tutorial 1.

a. Verify the mechDomain results shown in Figure T2-40.

The results differ on average by about 1.3%.

reduced mesh modeloriginal model



2.3.3: Pressure and Contact SurfacesIn this tutorial segment, MemMech and the parametric study function are used to set up a contact surface and to apply a pressure load range to the beam. The results are used to graph the beam deflection after it reaches that contact plane.

The process highlights a new feature: the ability to create and model a rigid contact surface for analyzing structural behavior.

MemMech Settings for Parametric StudyFrom MemMech, a rigid contact surface will be set up that prevents the beam from deflecting beyond the ground plane. Then the pressure load ramp is modeled by the parametric study settings.

Figure T2-41 ContactBCs Dialog Setup



a. Save the settings as contact.mps.b. In the Function Manager, select the MemMech solver.

2. Change the SurfaceBCs to apply a pressure load of 0.01, and tag the line as a variable so a trajectory can be applied.

a. In the SurfaceBCs dialog, change the second line to a 0.01 Scalar Load value and attach the MechBC1 variable.

3. Set a contact ZPlane surface 0.1µm above ground with the bottom of the beam chosen as the contact patch.

a. In the ContactBCs dialog, in the first row, choose a Zplane Surface. See Figure T2-41.

b. Click on Edit; set the Z field to 0.1.You are setting up a rigid surface that is a mathematical definition of a ground plane. The offset is 0.1µm above ground and accounts for a possible presence of a thin dielectric stop layer. This offset will also be important for subsequent CoSolve runs.

c. Choose bottom as the toPatch setting.

The bottom patch of the beam is set as a movable surface that contacts the Zplane. The other settings on this line are not used; refer to the CoventorWare ANALYZER Reference (see page R4-82) for more details.



Perform a Parametric Study with Contact SurfaceTo set up the rest of the problem, use the Parametric Study function.

For the parametric study you will need to determine the correct pressure load range to allow the beam to deflect sev-eral µm. This will be done through a test simulation, identical to the actual run but with no contact boundary condi-tions set. The test simulation result is shown in Figure T2-42, where you can observe the characteristics of a parametric ramp with no contact surface. In the Figure T2-42 example, the response is a slightly nonlinear curve that increases in deformation as the pressure increases. Note the sketch in Figure T2-42, which shows that the bottom of the beam is offset 2.2 µm from the ground plane. After accounting for the 0.1 µm offset set up for the contact surface, the graph shows that a pressure of 0.06 MPa produces a MinZ deflection of approximately 2.1 µm. Based on the test simulation, a pressure load range of 0.01 to 0.15 MPa should produce the desired results.

Figure T2-42 Test Simulation of Deflection as a Function of Pressure

Clear the MaterialProperties dialogWhen you started this tutorial, you used an existing settings file from Tutorial 2.1. In that settings file, the Parametric Study MaterialProperties dialog was set. You must clear that dialog for this simulation to run properly.


1. After determining the correct pressure range to allow the beam to contact the ground plane, set up the Parametric Study.

a. In the MemMech BCs window, click on Parametric Study.

pressure load

ground plane

2.2µ



Figure T2-43 MechDomain Results


2. Set a trajectory to vary the pressure load from 0.01 to 0.15 MPa in 0.01 MPa steps.

a. In the Parametric Study window, click on Trajectories. b. Verify that the t1 TrajectoryType is set to Delta.c. In the Edit dialog, set:

Start to: 1Delta to: 1Stop to: 15

In MemMech, a factor of 0.01 MPa was used, so the load ramp ranges from 0.01 to 0.15 MPa in 0.01 MPa steps.

d. In the label column for t1, enter pressure load.

3. Equate the MemMech variable line to the trajectory ramp in the mechBCs dialog.

a. Click on mechBCs and set the MechBC1 line with a t1 trajectory.b. If you have not already done so, click on the MaterialProperties button and

clear any trajectory setting that may appear in this dialog.

4. Start the simulation. a. In the Parametric Study window, click on Run. b. Save the analysis as mech_contact.c. In the Job Queue dialog that opens, click on the Progress tab to view the

simulation progression.

MemMech performs sixteen sets of computations in about ten minutes.

5. Verify the mechDomain table and graph results, noting the maximum beam deflection.

a. Open the Analysis Results dialog, and select mechDomain from the Tables drop-down menu to review the results as shown in Figure T2-43.

b. Select mechDomain from the Graphs drop-down menu.c. In the left pane of the Visualizer, click on Mapping Style. d. Select Node Z Displacement Minimum. Click and hold Map Show to select

Show Selected Only.

The beam deflection is held to a maximum of -2.1µm once a pressure load of 0.06 MPa or more is applied.

Image edited for clarity



Figure T2-44 Contact Force Results


6. Verify the Contact Force table and graph results, noting the increase in force once contact is made.

a. Select conForces from the Tables drop-down menu.

New tables appear when a contact surface is set.b. Select conForces from the Graphs drop-down menu.c. Select and show only the bottom ConForce curve.d. Review the results as shown in Figure T2-44.

The table and graph show the increasing force that is applied to the Rigid Plane as the beam bends with increasing pressure. The bottom ConArea table column shows how the beam increasingly flattens out with increased pressure.

7. View the solver pressure load ramp results in the 3-D viewer, noting the increased beam flattening with increased pressure.

a. Select All results from the Load Result drop-down menu.b. Click on the View 3D Results icon.c. Select Coventor > Parts Visibility and show the ground.d. Select Plot > Contour/Multi-coloring, then select Mises Stress.e. Select Coventor > Geometry Scaling, then set the Z Scale to 10 and check

Deform Using Displacements. Click Apply.f. Select View > Data Fit.g. Use the Coventor > Result Selection option to cycle through the solver

pressure load ramp results. See Figure T2-45.

A small deflection change is visible with each increasing step, until the beam reaches the contact surface. When the beam contacts the Rigid Plane, the beam flattening becomes pronounced.



Figure T2-45 Visualizer Results for Contact Example

2.3.4: Beam Pull-in VoltageIn this tutorial segment, CoSolve is used to apply a voltage ramp trajectory to the beam and calculate the beam’s elec-tromechanical response. In this tutorial, unlike the sequence in Pressure and Contact Surfaces, no pressure load is applied. The beam’s mechanical deflection results solely from the electrostatic force caused by the voltage difference between the beam and the underlying ground plane.

This tutorial sequence illustrates the software’s capability to treat the highly non-linear electromechanical phenome-non called pull-in. When subjected to an increasing electrostatic force, the beam deforms until a critical voltage, the pull-in voltage, is reached. At this point, the growth of the electrostatic force becomes dominant over the linearly increasing mechanical restoring force, and the beam quickly snaps, or pulls in, to the ground plane. The beam response is highly non-linear at this point and may require numerous CoSolve iterations to find a stable solution. CoSolve solver parameters will be adjusted and status indicators will be monitored in order for CoSolve to converge to a quick, accurate, and stable solution.

Prepare MemMech for CoSolve


1. Create a new settings file. a. Save the settings as pull_in.mps.b. In the Function Manager, set the Solver to MemMech and the model to

beam_reduced_mesh.c. Set the Analysis field to create a new analysis.

2. Set the Surface BCs so no load is applied.

a. Leave the fixall fixType applied to anchor1 or anchor2.b. Set the SurfaceBCs Set2 Scalar LoadValue to 0.c. Remove the Set2 MechBC1 variable tag.

Only the CoSolve voltage setup will be used to cause mechanical deformation.

3. Remove the contact surface from the problem.

a. In the ContactBCs dialog, remove the Set1 settings.

Pull-in calculations are always performed with no contact boundary conditions.

b. In the MemMech BCs window, click on Close.

0.15 MPa pressure applied: beam flattens at Rigid Plane surface. Gap is the 0.1µm offset used in the example setup.Note: To see the model in the same view as shown above, select View > Rotate, and click on the YZ button in the bottom of the window.



Run CoSolve to Determine Pull-in VoltageThe rest of the problem setup uses CoSolve, which generates a voltage ramp trajectory within the module without using the parametric study function.

Figure T2-46 CoSolve Settings Dialogs


1. Set the Function Manager for a CoSolve simulation.

a. Set the Solver to CoSolveEM.b. Verify that the Mode/Mesh path is still the beam_reduced_mesh model.c. Set the Analysis field to create a new analysis.

2. Set the Settings dialog to perform a pull-in/relaxation analysis.

a. Set the Settings dialog as shown in Figure T2-46:Analysis Options = Detect Pull-InIteration Method = Relaxation

b. Click on the Advanced button and set the Maximum number of steps to 36.

The Tolerance setting determines how many iterations CoSolve must perform before the delta between calculations is less than this amount. The Maximum number of steps sets an upper limit on the number of iterations. CoSolve adds 1 to this number as the upper iteration limit.


3. Perform a trajectory analysis: Set the trajectory dialog for a 50 - 80 volt ramp in 10 volt increments.

a. In the CoSolveEM BCs window, click on trajectory.b. Verify that the t1 TrajectoryType is set to Delta.c. In the Edit Delta dialog, set Start to 50, Delta to 10, and Stop to 80.

A voltage ramp is set up for this simulation. The ramp ranges from 50 to 80 volts in 10 volt steps. For this problem, we already know the approximate range of the pull-in voltage. If the beam electrostatic characteristics were unknown, a greater range and coarser step size for the ramp could be chosen to find a pull-in voltage. Note, however, that a very coarse step can require CoSolve to perform many more iterations to reach convergence.

d. In the label column for t1, enter voltage.

4. Equate the Voltage1 variable to the t1 trajectory, set a pull-in tolerance of 0.5 volts.

a. Click on Voltages.b. In the dialog that opens, assign the Voltage1 variable to the defined t1

trajectory.c. Verify these defaults: Factor as the type; Scale Factor of 1.0; PullIn of 0.5.



The PullIn setting is the tolerance for the final calculated pull-in voltage. CoSolve starts by iterating the calculations, using the linearly increasing voltage ramp that was defined. When CoSolve produces a divergent result for a specified voltage (such as at 70 V after a convergent solution at 60 V), it then reduces the voltage change to be half the differ-ence between these two bounding voltages (such as 65 V). It repeats the calculations, increasing the voltage change by half after a convergent solution and reducing the voltage change by half after a divergent result. It stops when the difference in voltage between the last convergent solution and last divergent result is less than the PullIn setting (in this case, 0.5 V).

5. Set a voltage ramp for the beam using 1 volt as the scale factor.

a. Click on ConductorBCs.b. Choose a Voltage1 tag for the beam Variable setting.

Voltage1 is a variable tag (just like a parametric study variable) that will be set to a voltage ramp using the CoSolve trajectory function. The voltage setting of 1 is a factor to be multiplied by the trajectory values.

6. Start the simulation. a. Click on Run.

The solver iteration begins. CoSolve performs many calculation steps: one set of MemElectro and MemMech solutions for each iteration of each trajectory step. While the model is simple, the run time will be around 30 minutes.

b. Save the analysis as pullin.c. In the Job Queue dialog that opens, click on the Progress tab to view

simulation progression.

While this CoSolve run using the reduced-mesh beam takes about 1 hour of computation time, the original beam from Tutorial 1 would have required more than four hours for the same pull-in calculation.


7. Verify the Summary, Displacement, and PullIn numerical results.

a. Open the Analysis pull-in results window, and verify the Summary table shown in Figure T2-47.

The t1 column shows the voltage steps executed during the simulation. The Iterations column shows the number of iterations CoSolve requires for convergence (to the 0.001 tolerance in the Settings dialog) for each step. At step_3, CoSolve produces a divergent result. CoSolve then cuts the next attempted voltage step in half (to 65 V) and calculates the result. The convergent solution caused CoSolve to increase the voltage by half. CoSolve continues the calculations until the difference between the last convergent and divergent results is less than 0.5 volts. The Pullin results indicate that the actual pull-in voltage is about 66.25 volts (the last convergent solution).

b. Verify the Displacement table and graph shown in Figure T2-47.

The table shows the iterations CoSolve completed successfully. The last number is the beam deflection at the pull-in voltage.

c. Verify the PullIn range shown in Figure T2-47.

The window shows the voltage required for pull-in. Because CoSolve seeks a solution within the 0.5 volt tolerance, the voltage is expressed as a range between the final two computation values.

d. Click on Close in the Analysis Results window.




Figure T2-47 Pull-In Simulation Results

If this CoSolve simulation was run with a Maximum number of steps setting of 12 (the default value) in the Settings dialog, the hierarchical results window would have included an extra Warnings button. The Warnings window indicates that some of the CoSolve iterations require more than the Maximum number of steps setting in order to achieve convergence. However, the results may still be close to the value achieved with a higher convergence setting.



2.3.5: Beam Lift-Off VoltageIn the Beam Pull-in Voltage section of this tutorial, the characteristics of the beam were studied under the load of a linearly increasing voltage ramp, which forced the beam to deform and come in contact with the ground. In this tuto-rial, the opposite effect will be simulated by applying a linearly decreasing voltage ramp and solving for the voltage at which the beam is released from contact with ground. Figure T2-48 illustrates the relationship between the pull-in and lift-off phenomena.

Figure T2-48 Pull-In and Lift-Off in a Fixed-Fixed Beam

The CoSolve Detect Lift-Off option will make finding the solution easy by automatically simulating the behavior of the beam and detecting the voltage at which lift-off occurs. For this exercise, a single, decreasing voltage trajectory will be specified. The beginning voltage value of the trajectory will exceed the pull-in conditions found previously. During simulation, CoSolve will reduce the voltage by fixed steps until a divergent solution (voltage lower than lift-off conditions) is found. Then, CoSolve will increase and decrease the voltage, reducing the size of each successive step by half to find more precise lift-off conditions.

pull-in

contact surface

lift-off

displacement

voltage

beam displacement line for decreasing voltage

beam displacementline for increasing voltage



Prepare MemMech for CoSolveCoSolve uses the MemMech solver in its iterative calculation sequence. Therefore, the MemMech Settings and boundary condition dialogs must be set up before starting CoSolve.

Run CoSolve to Determine Lift-Off VoltageThe rest of the setup for the problem is accessed from CoSolve. CoSolve generates a decreasing voltage ramp trajec-tory within the module without using the Parametric Study function.



a. Save your project settings as lift_off.mps.b. In the Function Manager, set the solver to MemMech.c. Check to be sure the Model/Mesh is still beam_reduced_mesh.d. In the Analysis field, select create a new analysis.

2. Set up a contact plane with a 0.1 µm offset from the ground.

a. Verify that the SurfaceBCs Set 2 has a LoadValue of 0 and a Fixed Variable.b. In the ContactBCs dialog, restore the contact surface settings previously set.

Select a ZPlane with a 0.1 Z value and bottom as the toPatch (see the figure on page T2-86).

Lift-off calculations are performed with contact boundary conditions.

A rigid surface is set up with an offset that is 0.1 µm above the ground plane. This offset is necessary for the CoSolve run. See the note below.

For electrostatic analysis (CoSolve) CoventorWare does not allow you to set up a contact problem that allows two conducting volumes to touch. In this application, a rigid plane is used as the contact surface for the beam and is placed above the ground plane.


1. Set the Function Manager for a CoSolve simulation.

a. Select the CoSolveEM solver.b. For the Analysis field, select create a new analysis.

2. Set the CoSolve Settings for Lift-Off. a. Set the Analysis Options field to Detect Lift-Off.b. Click on Advanced and set the Maximum number of steps to 48.c. Click on Next.

3. Set a lift-off trajectory to range from 80 to 0 volts in -20 volt increments.

a. In the hierarchical window, click on trajectory.b. Set the t1 TrajectoryType to Delta.c. In the Edit Delta dialog, set Start to 80, Delta to -20, and Stop to 0.

For this tutorial, a wide ranging voltage ramp is used, but a narrower one could be set if the approximate lift-off voltage is known.

d. Set the trajectory Label to voltage.

4. Set a voltage variable and a 19 Volt PullIn voltage.

a. In the hierarchical window, click on Voltages.b. Verify that the t1 trajectory is assigned to the Voltage1 variable with a 19 Volt

PullIn setting.

The Voltage1 variable is set to a 80-0 volt ramp.



Figure T2-49 Liftoff, Displacement, and Summary Results

5. Set a voltage ramp for the lift-off calculation.

a. In the hierarchical window, click on ConductorBCs.b. Choose a Voltage1 tag for the beam Variable setting and set its voltage to 1.

You need a voltage difference between beam and ground for the lift-off analysis to work.

6. Start the simulation. a. In the hierarchical window, click on Run. b. Save the analysis as cs_liftoff.c. In the Job Queue dialog, click on the Progress tab to view the simulation

progression.


7. Verify the lift-off results. a. When the simulation is finished, click on the View Results icon in the Job Queue dialog.

b. In the CoSolve Simulation Results window that opens, Select the LiftOff Table. See Figure T2-49.

8. Verify the Displacement table and graph results.

a. Select the Displacement Table and Displacement Graph to view the results shown in Figure T2-49.

The edited Displacements table shows that 5 steps were required to produce the lift-off effect.

To adjust the Displacement graph to show only the MinZ results, click on Mapping Style, and in the dialog that opens, click to select the MinZ Map Name, then click on Map Show to select Show Selected Only.

9. Verify the Summary table results. a. Select the Summary Table to view the results illustrated in Figure T2-49.

This dialog shows that lift-off occurred at 20 V. The beam was pulled down again when the voltage was increased to 30 V.


table edited for clarity



Figure T2-50 Displacement at Lift-Off Trajectory Voltages


10. Verify the 3-D release motion for the 5-step beam solution.

a. Load all the step results and start the 3-D viewer.b. Select Plot > Contour/Multi-coloring, and select Displacement Mag.c. In the Geometry Scaling dialog, set the Z Scale to 5, and check Deform Using

Displacements. Click Apply.d. Select View > Rotate, and click on YZ.e. Use the Zoom icon to get a better view of the area where the beam and

ground are in contact.f. Use the Result Selection dialog to cycle through the 5 steps and view the

release action of the beam.

Figure T2-50 shows progression through the voltage trajectory and the resulting lift-off.

A small change is visible with each step, until the beam reaches release voltage.

Hysteresis as an Alternative Solution MethodThe Detect Lift-Off option was added in CoventorWare 2008 as an alternative to the time-consuming process of generating and interpolating hysteresis curves by trial and error. If, however, you wish to generate such a curve to observe the full range of behavior of a model under both increasing and decreasing voltage trajectories, set up the simulation with rising and falling voltages in the trajectory dialog.

Step 1: 80 volts

Step 3: 40 volts Step 4: 20 volts

Release

Step 2: 60 volts

Step 5: 30 volts



2.3.6: Design OptimizationThe analysis of the beam as originally designed has been completed, subjecting it to a pressure load and an applied voltage to determine its mechanical and electromechanical response. The results show that a high voltage (about 80 V) must be applied in order for pull-in to be reached. In a real design, these characteristics may be unacceptable for manufacturing because voltages that high in a mask-processed or micro-machined chip may be difficult to achieve or may cause breakdown problems with diffused junctions, oxides, surface films, or other materials. This tutorial uses a parametric study to investigate how varying the beam thickness changes the pull-in voltage in order to achieve a more workable design.

Prepare MemMech for Parametric Study

CoSolve Setup for Parametric Study

A few changes are required in the original CoSolve setup; then the parametric study settings are made. Remember that the parametric study iterates through individual CoSolve runs, and that CoSolve requires a MemMech setup for the mechanical boundary conditions.


1. Set the Function Manager to run MemMech.

a. Save the settings file as para_study.mps.b. Set the solver to MemMech and select create a new analysis.c. Verify that the Model/Mesh field is still set to the beam_reduced_mesh

model.

2. Remove any contact surface boundary conditions.

a. Set the Contact BCs dialog so that no ContactBCs are applied.b. In the hierarchical window, click on Close.

In this Problem Analysis, you will be running CoSolve trajectories to determine pull-in. The beam ends need to be fixed, but no load is applied, and no contact surface is present.


1. Set the Function Manager to run CoSolve.

a. In the Function Manager, select the CoSolveEM solver and select create a new analysis.

2. Configure CoSolve to simulate for pullin.

a. In the Settings dialog, set Analysis Options field to Detect Pull-In.



Figure T2-51 CoSolve Settings for Parametric Study


3. Set a t2 trajectory to range between 20 and 120 volts in 10 volt steps.

a. In the CoSolveBCs window, click on the trajectory button.b. Remove the t1 setting from the previous run (set it to None).

The CoSolve trajectory number must be higher than the trajectory number set for the Parametric Study, so you will use the t2 trajectory for CoSolve and the t1 trajectory for the Parametric Study. See page R5-10 for more details.

c. Set a t2 Delta trajectory is set with a Start of 20 and a Delta of 10. Change the Stop to 120.

The range of the voltage ramp is extended because the solver iterations should allow the pull-in voltage to drop with each successive run. In a real design, if it is difficult to predict the effect that the solver changes will have on pull-in, use trial and error until an acceptable range is found.

4. Set a voltage variable and a 0.25 volt PullIn voltage.

a. In the CoSolveBCs window, click on Voltages.b. Check that the Voltage1 line is assigned a t2 Trajectory Factor, with a Scale

of 1 and a PullIn of 0.25.


5. Set the trajectory for 3 beam thicknesses scaled at 80%, 60%, and 40% of the original value.

a. Click on Parametric Study.b. In the Parametric Study window, click on the Trajectories button. c. Set the t1 TrajectoryType to Enumerate. d. In the Edit Enumerate dialog that automatically opens, set a Count of 3 with

increment values of 0.8, 0.6, and 0.4.e. Click on OK.f. Set the label for t1 to thickness.

A trajectory is set up that reduces the beam thickness. After a few more setups, the process will be understood more clearly.



Figure T2-52 Dimension Dialog Setup

In this tutorial, the beam is originally modeled as a 0.5 µm thick aluminum strip offset from ground by 2.2 µm. In the scale setup, the beam dimension is scaled in the positive Z direction (up) starting at the beam bottom. A scale factor of 1 is used, which is multiplied by factors from the trajectory, resulting in beam thicknesses of 0.4, 0.3, and 0.2 µm. The origin of scaling is specified in the Z direction at the bottom of the beam (Z=2.2 µm) to avoid scaling the position of the beam.

6. Use a ScaleDir dimension option. To avoid scaling the distance between the beam and ground, set the scaling origin to be the bottom of the beam (2.2 µm above the ground plane) and only in the positive Z direction.

a. Click on the Dimensions button.b. Set the Trajectory column to t1.c. Select ScaleDir from the Transform pull-down menu and set the Edit dialog

as shown in Figure T2-52.

The ScaleDir option allows the user to scale the model using direction coordinates. Setting the Dir_Z setting to 1 in the Edit dialog scales the model only in the positive Z direction above designated origin (Z=2.2). With these settings, only the beam itself is scaled, not the gap between the beam and ground or the beam supports or anchors.

d. Click on the Part List button and select beam from the list.

7. Start the simulation. a. Clear any settings in the mechBCs dialog.b. In the Parametric Study window, click on Run.

This simulation may take three hours or more, depending on your hardware configuration. To avoid running the simulation, click on Close, and review the following pages of results. The result windows indicate why the simulation takes so long to complete.

c. Save the analysis as thickness_para_study.


ground plane

2.2µm

0.5µm Z



Figure T2-53 Parametric Study 3-D Results


8. Verify the 3-D results, viewing the result files at 60 volts.

a. Open the thickness_para_study results.b. For result files, choose All Trajectory Steps and Voltage Step No. 7 (voltage = 60

volts), then start the 3-D viewer.c. Select Frame > Push Current Frame Back.d. Select Plot > Contour/Multi-coloring and select Displacement Z.e. In the Geometry Scaling dialog, set the Z Scale to 10; check Deform Using

Displacements.f. Select View > Rotate, and click on YZ.g. Select View > Fit to Full Size.h. Cycle through the steps and view the variation in beam thickness and deflection.

See Figure T2-53.

As many as 12 CoSolve trajectory steps are required to complete each thickness pull-in calculation, but not every thickness requires that many steps.

The 60-volt trajectory point is near pull-in for the 0.2 µm thickness and produces a more dramatic difference in distance to ground among the three files.

0.3µm

0.2µm

0.4µmthickness

thickness

thickness



Figure T2-54 Parametric Study Pull In Results

Figure T2-55 Summary Table Results


9. Verify the parametric study pull in results.

a. Review the PullIn table results illustrated in Figure T2-54.

The pull-in results show that the pull-in voltage decreases as beam thickness is decreased.


10. Verify the Summary results. a. Review the large Summary table of results as shown in Figure T2-55, and see a detailed explanation on the page that follows.



Table T2-5 provides the following information:

The summary table in Figure T2-55 shows how many iterations were required to complete the simulation. Table T2-5 shows that a complete simulation requires 363 separate sets of MemElectro and MemMech calculations. This large number of calculations explains why the process took nearly three hours to com-plete. The simulation ran with two nested trajectories: a complete set of CoSolve voltage ramp trajectories running for each of the parametric study thickness trajectories.

The summary table also shows that a single step required as many as 31 iterations to complete. The cho-sen Maximum number of steps limit of 48 was therefore sufficient for this simulation. For the purpose of this tutorial, the optimal Maximum number of steps setting was supplied to the user, but in real-world cir-cumstances, the user may have to run a series of simulations using larger maximum steps settings to achieve convergence.

Table T2-5 Summary MemElectro/MemMech Iterations

Also consider that for this simulation the very small thicknesses required to reduce the pull-in voltage may not be achievable with a conventional MEMS process. Even so, the reduction of the voltage down to about 53 volts may still be too high to be practical. If this were a real design, more parametric studies would be needed so that other parame-ters (such as beam width, beam material type, and beam offset from the ground plane) could be varied to achieve the desired results.

Parametric Study thickness

(µm)

Number of CoSolve trajectory steps

Total number of iterations for CoSolve to achieve

PullIn tolerance

0.4 12 131

0.3 11 121

0.2 11 111



Notes


Section 2: Beam Design Transient Mechanical Analysis in Analyzer Version 2008M

2.4: Transient Mechanical Analysis in AnalyzerThis tutorial explores how to run a transient mechanical analysis on a simple cantilevered beam, using a pulsed force as a boundary condition.

The setup is shown in Figure T2-56. This simple beam produces the desired response to the input force and enables the computation to be performed in a short time.

Figure T2-56 Transient Mechanical Analysis Setup


how to partition and simplify a modelhow to configure MemMech to run a transient analysishow to simulate a cantilever beam using a simple beamhow to apply a pressure load to the tip of a beamhow to export results for graphing in other programs

2.4.2: Model CreationThis tutorial starts with the creation of the simple model. This model will be similar to the one you created in Tutorial 2.1, except you will use the partition tool to remove the anchors. Simplifying the model by removing the anchors reduces the computation time and the results obtained are not greatly different from the model with anchors. If you wish to skip the model creation steps, the tutorial project directory, which you imported in Tutorial 2.1.3, has a preb-uilt simple model in the gbak file.

Refer to the basic beam creation steps in Tutorial 2.1 for practice on creating layout, process, and mesh attributes for the model.



a. Start CoventorWare.b. In the Project Browser that opens, select the BeamDesign directory.c. Create a trans_mechanical.mps.

2. Rebuild the model using the beam.proc and the beam.cat file.

a. From the Designer tab, select the beam.proc in the Process field.b. Select the beam.cat file in the Layout field.c. In the Model/Mesh field, select create new model.d. Click on the Build a New 3D Model icon.e. Name the model simple.

Beam fixed at one end

Force pulse applied


Section 2: Beam Design Transient Mechanical Analysis in Analyzer Version 2008

Figure T2-57 Partition Plane for Beam Anchor

3. Use the Solid Model\Partition tool to remove the front beam anchor.

a. From the Solid Model folder, hide the Substrate and Nitride layers.b. Set the Z Scale to 5.c. Use the Rotate and Zoom tools to view the front tether as shown in

Figure T2-57.

d. Click the Vertex selection mode icon.

e. Hold the Ctrl key and select the three vertices as shown in Figure T2-57 to create the partition plane.

f. Select Solid Model > Insert > Plane > Use Selected Vertices.g. In the Geometry Browser, hold the Ctrl key and click on the beam

layer and the partition Plane to select.h. Select Solid Model > Partition.i. Hide the newly created layer that represents the anchor of the

beam.


Vertices



Figure T2-58 Partitioned Model with Anchor Layers Hidden


4. Rotate the model and partition the other anchor. a. Use the Rotate and Pan icons to focus on the other anchor.b. Select the vertices that correspond to the vertices selected for the

other anchor and partition them similarly.c. Select the original beam layer and the new partition plane, then

select Partition.d. Hide the newly created anchor layer. The resulting model is

shown below.

You may hide the planes if you find them distracting.


5. Add the substrate layer and the visible part of the beam layer to the Mesh Model folder. Rename the substrate part ground, designate it as a conductor, and suppress it except for MemElectro.

a. Right click on the Substrate and select Show Selection.b. Drag the beam part of the beam layer and the substrate layer to

the Mesh Model folder.c. In the Mesh Model folder, right click on the substrate part and

select Properties.d. In the Properties dialog, name the substrate ground.e. Designate it as a conductor.f. Check the Suppress except for MemElectro option.

6. Make sure the beam part is designated as a conductor and that it has the beam name.

a. Select the beam part of the beam layer, then right click and select Properties.

b. Name it beam.c. Designate it as a conductor.



Figure T2-59 Face Name Assignments


7. Name the faces as shown in the figure below. a. Select the Face selection mode icon.b. Right click on each face and select Set Name. Name the faces

required for setting up boundary conditions for the simple beam. top surface topbottom surface bottomvisible end end1hidden end end2visible side side1hidden side side2ground top surface ground


8. Create and view a mesh for the ground plane substrate. The ground plane is 130 µm x 40 µm x 10 µm thick. Create the mesh using Manhattan parabolic elements and size it so the ground has 4 x 10 elements along the X and Y axes.

a. Right click on the region containing the ground layer, and select Mesher Settings.

b. In the Mesher Settings dialog, select a Manhattan bricks Mesh Type and a Parabolic Element Order. Set the X, Y, and Z Element Sizes to 10, 12, and 5.

bottom

end2

end1

side1

side2

top patch is hidden

ground



Figure T2-60 Tutorial Model

9. Create and view a mesh for the aluminum beam. The beam is 100 µm x 10 µm x 0.5 µm thick, including 10 µm x 10 µm x 2 µm anchor supports. Create the mesh using 27 node bricks, and size it so the beam itself has 10 x 1 brick elements along its 80 µm length, one layer deep.

a. For the beam region, select a Manhattan bricks mesh type and a Parabolic Element Order. Set the X, Y, and Z Element Sizes to 10, 8, and 5.

The original beam mesh used 2 x 2 x 10 µm bricks. The change represents a reduced element density ratio of 20:1. The thin aluminum beam brick depth is 0.5 µm because the beam thickness limits the depth size.

b. Click on the Generate Mesh icon. The resulting mesh is shown below.




2.4.3: MemMech Transient Simulation Setup and SolutionIn this tutorial, set up all parameters through the MemMech module.

Figure T2-61 Transient Mechanical Settings


1. Configure the MemMech solver to run with the simple model. Set the MemMech Settings dialog for Mechanical physics. Set up for a Transient simulation that runs for 20 µs, with a 1e-12s solver timestep and a 1 µs output file timestep.

a. In the Function Manager Analyzer tab, set the Solver to MemMech.b. Set the Model/Mesh field to simple.c. Set the Analysis field to create a new analysis.d. Click on the Solver Setup icon.e. In the MemMech Settings dialog, choose Mechanical physics.f. Set the Time Dependence to Transient.g. Set the Stop Time to 2.0e-5 s and the Output Timestep to 2.0e-7 s.

For this setting, 100 result sets are produced.h. Then set the Timestep Method to Variable and the Solver Timestep

to 1.0e-7 s. See Figure T2-61.

The Timestep chosen is the initial timestep used in the analysis. It will be automatically adjusted during the analysis to achieve the required accuracy. The required accuracy is determined by the Residual Tolerance parameter described below.

i. Set the Residual Tolerance to 10.

This parameter has dimensions of force (mN) and is often set to approximate the expected reaction force value for the problem. One common strategy for setting this parameter is to use a relatively large value for preliminary runs and then decrease its value in later runs and verify that the results do not change significantly.



Figure T2-62 Surface, Volume, and Transient Boundary Conditions


2. Set the SurfaceBCs dialog for the beam so one end has a transient force applied. Do this by fixing end1 and applying a vector force of 0.01 µN pointing toward ground at the top/end2 corner. Make this force a Transient1 variable.

a. Set the SurfaceBCs dialog as shown in Figure T2-62.

The settings fix one end of the beam and apply a load to the tip of the other, effectively turning it into a cantilevered beam model.

The Transient1 variable applies a temporary force on the beam end.

3. Apply material damping to the beam, using the values shown below.

a. In the VolumeBCs dialog, apply a MaterialDamping BCType to the beam, and apply the MaterialDamping LoadType shown below.

4. In the transients dialog, set up a Curve transient to apply a 1 µs pulse force.

a. In the transients dialog, set the first line as Transient1, using a Curve transient with the Edit Curve values shown in Figure T2-62.

The Curve setting applies a 1 µs pulse force to the beam tip. This is 5% of the total time allowed for simulation.

5. Start the simulation, and save the analysis as trans_mech.

a. Click on Run.b. Save the analysis as trans_mech.

The simulation may take as long as 20 minutes.



Figure T2-63 Numerical Transient Results


6. Verify the numerical results for the dyna table, as shown in Figure T2-63.


b. In the Analysis trans_mech window, open the dyna table, and verify the results shown in Figure T2-63.

The dyna window shows that the simulation created 100 output steps. The first 25 steps are shown below.

Note that the table shows several local peak displacement entries (3.4 µs, 5.2 µs, 10.8 µs. etc.).



2.4.4: Run a Query in a Region of InterestBecause of the large volume of data generated in the transient simulation, it may be easier to look at results at a point of interest. In this section, you will run a query on such a point to extract the relevant data.


1. Use the In a Region Query function to extract the Displacement_Z values at the center of the edge that connects the top and end2 faces.

a. In the Analysis Results window, click on Custom Query.b. In the hierarchical window, click on In a Region.c. Set the Query In A Region dialog as shown below.

The point defined in the Query dialog is the center of the edge that connects the top and end2 faces. This edge is where the load was applied.

d. Click on Execute.


2. Verify the numerical and the graphical results of the query, as shown in Figure T2-64.

a. In the Analysis Results window, select the Displacement Z table. The first 25 results are shown in Figure T2-64.

b. Select the Displacement Z graph.

From the plot it can be seen that the primary period of the response is approximately 14.3 µs, corresponding to a frequency of 70000 Hz. As expected, this is close to the first natural frequency of the beam, 74400 Hz.



Figure T2-64 Query Results


Section 2: Beam Design Temperature Sensitivity Analysis in Analyzer Version 2008M

2.5: Temperature Sensitivity Analysis in Analyzer

2.5.1: Demonstrated TechniquesThis tutorial covers the following techniques:

how to solve thermal conduction problems using MemMech (page T2-116)

how to use the Queries feature to extract and graph thermal data from a parametric study (page T2-122)

how to solve film convection problems using MemMech (page T2-124)

how to use the parametric study function to run a sensitivity analysis (page T2-126)

how to set the Visualizer to set Active Fields for display (page T2-118)

how to use the Visualizer Probe feature (page T2-128)

2.5.2: IntroductionCoventorWare has the ability to solve problems related to temperature variation. Users can set temperature-related boundary conditions, and the solver can compute temperatures at a surface or through a volume. Additional features such as solutions for temperature gradients and convection supplement the analysis. Examples in this tutorial illus-trate the many capabilities of this CoventorWare feature.

2.5.3: ConstructionThis tutorial uses a technique suited to illustrating temperature effects—a model composed of strips of two different materials, aluminum and silicon. With different TCE (temperature coefficient of expansion) values set up in the Material Property Database, the combined model undergoes mechanical displacement as temperature changes. With the Visualizer, you also will be able to see temperature gradients through the model.

Figure T2-65 Bimetal Cantilever Beam Tutorial Model

In model setup and simulation, the bottom of the support structure is fixed. Various temperatures are applied to the material surfaces or volumes, and a solution for mechanical displacement and temperature variation across the vol-ume is created. In addition to observing static temperature variations, the tutorial also illustrates how an air flow applied across a material surface can remove heat through convection.

support

m2: aluminum

m1: silicon


Section 2: Beam Design Temperature Sensitivity Analysis in Analyzer Version 2008

2.5.4: Thermal Conduction - MemMechBecause the other tutorials in this manual have prepared you for layout, process, and meshing tasks, this tutorial starts with a model that already has been created for you. You can proceed directly to the dialogs that set up and observe the results of the solvers. In the tutorial you have access to all the necessary dialogs through the MemMech and paramet-ric study functions.

Figure T2-66 Mesh and Face Assignments


1. Start CoventorWare.2. Import the Temperature tutorial directory

and save the settings file as therm_cond.mps.

a. Start CoventorWare.b. Click on the Import Tutorial icon.c. In the Import Tutorial dialog that opens, select the Temperature directory.d. Save the settings file as therm_cond.mps.

3. Verify mesh and face name assignments shown in Figure T2-66.

a. From the Analyzer tab, click on the drop-down arrow in the Model/Mesh field, and select the bimetal model.

b. Click on the Start Preprocessor icon.c. In the Preprocessor, expand the Geometry Browser Mesh Model to verify

the face assignments shown below.



Table T2-6 Settings for Tutorial


4. Verify the material properties assigned to the aluminum and silicon materials.

a. Click on the m1 part and then right click to select Properties.b. In the Part Properties dialog, click on the MPD icon.c. Verify the SILICON material properties shown below. Make changes if

necessary.As with all tutorials, it is important that your Material Property Database entries match those used in the tutorial. Of particular importance are the TCE values.

d. Select the m2 part and verify the aluminum material properties.e. Save the model and exit the Preprocessor.

Property Sub prop Silicon Aluminum(film)

Elastic Constants E 1.69e+05 7.70e+04

ν 3.00e-01 3.00e-01

Density 2.50e-15 2.30e-15

Stress Sx 0 0

Sy 0 0

Sz 0 0

TCE 2.50e-06 2.31e-05

Thermal Cond 1.48e+08 2.40e+08

Specific Heat 7.12e+14 9.03e+14


5. Set up a MemMech analysis on the bimetal model.

a. From the Analyzer tab, select the MemMech solver.b. Select the bimetal model as the Model/Mesh input.

6. In the Settings dialog, set up a thermo-mechanical analysis.

a. In the MemMech Settings dialog set the Physics option to Thermomechanical.

The thermomechanical solver computes mechanical displacement and temperature variation.

7. Set the SurfaceBCs dialog so that the bottom patch of the cantilever beam is fixed, and apply a temperature of 320 K to the top patch of the aluminum material.

a. Set the SurfaceBCs dialog Set1:FixType: fixAllPatch1: fix_bot

b. Set the SurfaceBCs dialog Set2:FixType: TemperaturePatch1: m2_topLoadValue: Scalar 320



Figure T2-67 Mechanical Results

8. Set the VolumeBCs dialog so that a fixed temperature of 293 is applied to the m1 volume.

a. Set the VolumeBCs Set1:BCType: T-FixedPart: m1LoadValue: Scalar 293m1 is the silicon material underneath the aluminum.

9. Start the simulation. a. In the MemMech BCs window, click on Run.b. Save the Analysis Results as conduction.

With these settings, you can expect to see a temperature gradient between the top surface at 320 K and the bottom volume set at 293 K. The material differences should cause bending of the strip at the higher temperature.


10. Verify the mechDomain and rxnForces results.


b. Select the mechDomain and rxnForces tables for viewing.c. Observe the results as shown in Figure T2-67.

11. View the temperature and displacement results in the Visualizer.

a. Start the Visualizer.b. Select Coventor > Part Visibility and Show the gnd.c. Select Coventor > Geometry Scaling.d. Check Deform Using Displacements.

Note that the Deform Using Displacements setting shows the physical deformed shape, deformed with the displacement vector. It does not depend on the selected contour.

e. Select Plot > Contour/Multi-coloring. f. From the Current Contour Variable drop-down menu select Mises Stress.

The results are seen in Figure T2-68.g. Select Temperature as the Contour Variable. The results are seen in

Figure T2-69.




Figure T2-68 Mises Stress Results

Figure T2-69 Temperature Results

For these displays, the ground plane appears to be at 0 Kelvin. Actually, the ground plane is not part of the thermal solution because it is not a movable volume. It is set to an initial value of 0 and is not changed during the simulation.



Parametric Study of Thermal ConductionIn the next sequence, you will vary temperature using the parametric study function. In preparation, you need to assign a variable in the MemMech SurfaceBCs dialog for which a trajectory can be applied. The previous MemMech run used a fixed face temperature for the solver. In this example, you will apply a temperature on the m2 top face that varies with the trajectory setting you will apply in the Parametric Study dialogs.


1. Set the MemMech SurfaceBCs dialog so the temperature is tagged as a variable.

a. In the MemMech SurfaceBCs dialog, set the Variable for Set2 in the second line to MechBC1.

You are tagging the temperature boundary condition to be a variable in the parametric study. The temperature range will be set in the Parametric Study Trajectories dialog.

2. Set up a parametric study with a trajectory with a temperature range of 100-350 K in 50 K increments.

a. Click on Parametric Study.b. Click on Trajectories.c. Set the t1 TrajectoryType to Enumerate.d. In the Edit Enumerate dialog set the Count to 6, and set the range from

100-350 K, using 50 K increments.e. Set the label name to temperature.

3. From the mechBCs dialog, set the MechBC1 variable to use a t1 absolute trajectory.

a. Click on mechBCs.b. Set the MechBC1 trajectory to t1.c. Set the Type to Absolute.

4. Start the simulation. a. In the MemMech BCs window, click on Run.b. Save the Analysis Results to conduction_para.

5. View the displacement results a. When the simulation is finished, click on the View Results icon.b. View the mechDomain table; compare with Figure T2-70.c. View the mechDomain graph; display the Node Z Displacement

Maximum and Node Z Displacement Minimum values:In the panel to the left of the canvas, click on Mapping Style.Use the Ctrl key to select Node Z Displacement Maximum and Node Z Displacement Minimum.Click MapShow, then select Show Selected Only.



Figure T2-70 Displacement Results

Because the temperature settings were above and below the 293 K set for the bottom volume, the bimetal strip bends both ways. The composite effect shown in the graph combines the MaxZ and MinZ values, which reflect direction as well as magnitude. The result is a nearly linear change in absolute displacement over the parametric study tempera-ture range.


6. View the temperature results in the Visualizer.

a. Load all the results and start the Visualizer.b. Set the Geometry Scaling dialog to enable Deform Using Displacements

with an Exaggeration of 2.c. Set the Plot > Contour/Multi-coloring to Displacement Z.d. Select Coventor > Part Visibility and move the gnd part to the Hidden

Parts column if it is not already hidden.e. Review the six solutions:

Select Coventor >Result Selection.Click on Next to cycle through the results, or click on Play to animate the results. At temperatures below 293 K, the bimetal strip bends upward. Above 293 K, the strip bends down. See Figure T2-71 for an illustration.



Figure T2-71 Displacement at Different Temperatures


7. Use the Query function to extract the average, maximum, and minimum temperature values for the m2_e1 patch.

d. In the Analysis results window, click on Custom Query.e. In the hierarchical window, click on On a Patch.f. Set the Query on Patch dialog as shown below.a. Click on Execute.

Thermomech solution at 100K Thermomech solution at 350K

m2_e1





8. Verify the numerical and graphical results of the query as shown in Figure T2-72.

a. In the Analysis Results window, select the m2_e1 table.b. Select the m2_e1 graph. Note the following:

The maximum temperature is the trajectory set for the aluminum top surface. The m2_e1 patch touches this top surface.The minimum temperature is the 293 K set for the silicon part. The m2_e1 patch touches this part.The average temperature is the average of the two extremes.



2.5.5: Film Convection - MemMechIn addition to performing a static temperature simulation, CoventorWare can simulate temperature effects using con-vection. An air flow applied over the surface or volume of a part is modeled as a film convection effect. The air flow temperature may be set as a boundary condition, allowing the air to convect heat away from the model.

Figure T2-73 Surface BCs for Film Convection


1. Set up a new MemMech simulation. a. From the Function Manager menu bar, select File > Save As and save the settings file to film_conv.mps.

b. Review the MemMech Settings dialog. The parameters should be the same as in the previous part of the tutorial.

c. Click on Next.

2. Set the SurfaceBCs dialog:Fix the fix_bot patch.Apply a surface temperature of 310 K to the end of the silicon strip.Apply an air flow to the top surface of the aluminum and the bottom surface of the silicon to convect heat away from the 310 K silicon surface using the Convection-Radiation function.

a. Set the SurfaceBCs dialog as shown in Figure T2-73. See Figure T2-74 and its accompanying text to understand the boundary conditions set.

Note that the Set2 Temperature FixType is now applied to m1_e1 and the LoadValue has been reduced from 320 to 310, and that its Variable has been reset to Fixed.

3. Remove the Volume BCs previously set. a. Click on VolumeBCs. b. Set the BCType on the first line to none so no boundary

condition is set.

4. Start the simulation. a. Click on Run.b. Save the Analysis results as mech_film.



Figure T2-74 Boundary Conditions for the Bimetal Strip

The air flow and temperature are set by choosing Convection-Radiation as a LoadValue for the FilmConvection boundary condition. In the Value edit dialog, four parameters can be entered:

Convection_Coefficient: the convection coefficient h. If the convection coefficient is not known, enter a value of 0 and specify an ambient air flow temperature and velocity. See page R4-73 to review the equations that explain the relationships.Emissivity: If radiation heat transfer is applied as a boundary condition, a value for emissivity is entered in this field. In this example, there is no radiation assumed, so the value entered is 0.Ambient_Temp: the temperature of the air flow in K. A room air temperature of 293 K is applied in this example.Ambient_Flow: the velocity of the air flow in µm/sec.

Figure T2-75 Film Convection Results


5. View the mechanical displacement numerical results. The results are shown in Figure T2-75.

a. When the simulation is finished, click on the View Results icon.b. In the results window that appears, select mechDomain from the Tables

drop-down menu.

6. View the temperature results in the Visualizer.

a. Start the Visualizer.b. Set the Visualizer for temperature viewing. c. Change the Z Scale to 2, and deform using displacements. The results

show bending due to the 310 K applied at the bimetal strip end. The areas that are farther away from the heat source show considerable convection.

Air convection at 293 K and 1e6 µm/sec flow on top and bottom surfaces of the bimetal strip

Volume m2

air over top surface of m2

air under bottom surface of m1

Volume m1Apply 310 K to this face (m1_e1).



Parametric Study of Film ConvectionIn the next sequence, you will use the parametric study function to vary air flow. In preparation, the boundary condi-tions must be changed to include a variable for which a trajectory can be applied. While the MemMech Settings dia-log also must be configured, it should already be set if you are completing this tutorial sequentially.


1. Set the MemMech SurfaceBCs dialog so that both the Convection-Radiation line and the air flow parameter are tagged as variables for the parametric study. Change the Ambient flow to 1e05.

a. From the MemMech SurfaceBCs dialog, choose MechBC1 from the Variable column for the Convection-Radiation line.

b. Edit the Convection-Radiation Edit dialog:Change the Ambient_Flow value to 1e05.Change the Ambient_Flow from Fixed to Variable. Both the Convection-Radiation line and the air flow parameter must be tagged as variables for the parametric study.

2. Set a parametric study trajectory to vary air flow from 1e05 to 5e06.

a. Click on Parametric Study.b. Click on Trajectories.c. Set the t1 trajectory type to Enumerate.d. Edit the trajectory:

Set the Count to 6.Enter the trajectory values of 1-50 in multiples of 10.Change the label name to convection flow.

The trajectory is set to vary air flow from 1e05 to 5e06 (prescaled in the SurfaceBCs Value dialog to 1e05 and multiplied by the trajectory of 1-50 units).

3. In the mechBCs dialog, set the trajectory to t1 and the Type to Factor.

a. Click on mechBCs.b. Set the MechBC1 variable line to t1.c. Set the Trajectory Type to Factor.

4. In the material dialog, vary the Thermal Conductivity property of the silicon material. Set the trajectory to use the sensitivity analysis with a scale factor of 5.

a. Click on MaterialProperties.b. Set the Property to ThermalCond (Thermal Conductivity).c. Set the Trajectory to sens.d. Set the ScaleFactor to 5.e. Set the Material to SILICON.

Setting the trajectory to sens sets up the parameter for a sensitivity analysis.The ScaleFactor field sets the ±percentage variation of the material. Thermal Conductivity is varied ±5% for each of the trajectory points specified in the Enumerate dialog.

5. Start the simulation. a. Click on Run.b. Save the analysis results as film_para.

You are setting up the parametric study to run a convection solution in ten steps. With the sensitivity option enabled in the material dialog, the solver actually runs eighteen different simulations and produces eighteen results.

Because so many steps are run, expect a long computation cycle. If you wish to reduce the time, you can cut down on the number of Enumerate steps or decide to run the simulation without the sensitivity analysis.




6. View the mechDomain results. a. Open the film_para results.b. Select the perturbation table for viewing.

Because the sensitivity analysis was set, the results window includes perturbation.The perturbation results show the original material property setting for Thermal Conductivity and the ±5% variation used in the simulation.

c. Select the mechDomain table; view results. The table below has been edited so that only the minimum Z values are shown.

d. Select the mechDomain graph; view results.The Min_Z results are plotted in the window below.

The data and graph show that the convection change results in a nonlinear increase in displacement. The divergence of the plots between 30 and 50 demonstrates a greater sensitivity to the thermal conductivity.

result window edited for easier viewing



Figure T2-76 Convection Solution at Maximum Ambient Flow Setting

While this feature is very useful, the Queries function views the temperature change in a region over the entire set of simulations and notes any change in temperature due to the sensitivity analysis.



a. In the Analysis Results window, for Trajectory Step No. select All, and for Sensitivity Step No. select 1; start the Visualizer.

b. Show gnd, then set the Visualizer for temperature and displacement viewing (Plot > Contour/Multi-coloring) as in the previous sequences.

c. Use the Coventor > Result Selection option to review the six solutions. Use the Play button to see an animated viewing. The Visualizer shows the convection variations, as illustrated in Figure T2-76.

Note that the Visualizer reads only the main results, not those that contain the sensitivity calculations.

8. Use the Visualizer Probe tool to probe points on the surface of the parts to display temperature readings.

a. Click on the Probe icon.

With this Probe feature, you can probe the model to display temperature, stress, or any parameter that the Visualizer is capable of viewing.

b. Click the model to display the temperature at different points. Use the Scroll Down button to locate Temperature data.

You can use the Ctrl key to snap to the nearest grid point.




The data and graph show that the convection change results in a nonlinear decrease in temperature.

Advanced Procedure Detailed User Procedure

9. Use the Query function to extract the maximum temperature values for the m2_e2 patch.

a. Click on Custom Query.b. Click on On a Patch.c. Set the Query dialog:

Set the label to m2_e2.Set the Patch to m2_e2. (This patch is the back end of the top aluminum part.)Set the Field to MaxTemperature. This extracts the maximum temperature on the m2_e2 patch for each of the ten convection runs.Clear any other Patches.

d. Click on Execute.

10. View the table and graph query results. a. Select the m2_e2 table.b. Select the m2_e2 graph. Show the three MaxTemperature plots.c. Verify the results shown in Figure T2-77.



Notes


Section 3: Mirror Design Introduction Version 2008M


3.1: IntroductionThis part demonstrates how CoventorWare can be used to design and simulate a tethered mirror that has two actuating electrodes under the mirror ends. The tutorials demonstrate Analyzer, Integrator, and Architect capabilities. The tuto-rials include

Mirror Design with Analyzer: This tutorial demonstrates several Analyzer techniques, including partition-ing a solid model, using MemMech links and ties, and using CoSolveEM to actuate the mirror. This section starts on page T3-2.Mirror Design with Integrator: This tutorial demonstrates how to create macromodels that represent the mirror design created in the previous tutorial. The tutorial shows how the mirror can be partitioned and then simulated in Analyzer’s SpringMM and InertiaMM modules. The mirror parts are converted to macromodels and then assembled in Saber for system simulation. This section also compares the FEM and Saber results. This tutorial begins on page T3-37.

3.1.1: ModelAll the tutorials in this section use the same mirror design, which consists of a thin, multi-sided aluminum plate that rotates about an axis. At this axis is a support rod, integral to the aluminum plate, which undergoes rotational forces and stress as the plate rotates. The aluminum plate rotation is controlled by applying alternate voltages to electrodes that are located under the mirror ends. The electrostatic force created by the voltage difference between the mirror and electrodes causes the mirror movement. Adjusting the voltage at the electrodes can change the mirror angle, mak-ing the structure suitable for a variety of precisely controlled optical applications. The model is shown in Figure T3-1.

Figure T3-1 Mirror Model

support rod

electrode2

aluminum mirror

electrode1


Section 3: Mirror Design Mirror Design with Analyzer Version 2008

3.2: Mirror Design with AnalyzerThis tutorial covers these techniques:

how to create a process flow sequence from a cross-section of a processed wafer (page T3-5)how to create an extruded mesh on a monolithic volume (page T3-8)how to use the partition tool to create separate layers for the mirror beams (page T3-15)how to mesh different layers of the same design with different mesh types (page T3-17)how to assemble and simulate MEMS components using a joining technique (links and ties) (page T3-22)how to analyze mirror charge and displacement characteristics by running CoSolveEM (page T3-23)how to use and synchronize multiple trajectories in the same simulation (page T3-30)how to observe mirror deflection and stresses in the Visualizer (page T3-35)

3.2.1: InitializationIn this tutorial sequence, you will start CoventorWare, import the required project directory, and create a settings file.


1. Import the MirrorDesign project directory, and create a settings file.

a. Start CoventorWare.

If this is the first time you have run the software, you will have to configure the User Settings dialog. For more details, see the first Beam Design tutorial, beginning on page T2-4.

b. In the Project Browser dialog that opens, click on the Import Tutorials icon.

c. From the list of tutorial projects, select MirrorDesign.d. Click on OK.

In this step you are copying the project directory to your directory. You now have the mirror.cat file in the MirrorDesign\Devices directory. The software will now store all created files in the MirrorDesign directory and will set all the correct file paths for you.

e. In the Settings file field at the bottom of the dialog, highlight the default MirrorDesign.mps filename, and type mirror_a.mps.

f. Click on Open.

The software creates a default settings file based on the project directory name. You are changing the name to reflect the tutorial sequence because this tutorial will require more than one setting file. The file paths and boundary conditions for this part of the tutorial are stored in mirror_a.mps.


Section 3: Mirror Design Mirror Design with Analyzer Version 2008M

3.2.2: Layout ViewingIn the typical design flow, the user creates a process file, and then creates a 2-D layout. In this tutorial sequence, the user will view the 2-D model of the mirror layout to decide which process steps would be needed to create the 3-D model.

Figure T3-2 2-D Layout View of Mirror

This X-Y view of the mirror shows the large movable mirror component attached to a long narrow rod. The rod is connected to the device surface through the two conformal supports shown as yellow squares in the layout. The mir-ror component rotates about its center, with the rod fixed at the support ends. The rod torsion allows for the move-ment of the mirror; conducting plates under each of the mirror halves control movement. Compare this layout with the 3-D view shown in Figure T3-1 on page T3-1. The cross-section diagram of the process is presented in Figure T3-3 on page T3-5. Two different cross-section views are shown, with arrows in the illustration above indicating the ori-entations.


1. Open the mirror.cat file in the Layout Editor.

a. Click on the Function Manager’s Designer tab.b. Click on the drop-down arrow beside the Layout file field.c. Select the mirror.cat file. d. Click on the Layout Editor icon.

Because mirror.cat contains only a single cell, mirror_demo opens automatically.

The 2-D view of the mirror is shown in Figure T3-2.

cross-section A view orientation

cross-section B view orientation



Table T3-1 Object and Layer Information

This information enables the user to create the process flow for the design. To create the process flow, access the Pro-cess Editor from the top of the Function Manager after exiting the Layout Editor.


2. View the object information for each object on the Layout Editor canvas. a. Click on the Repeat Mode icon.

b. From the top menu bar, select Object, then select Info.

The Object menu provides information about the mask layers.c. Click anywhere along the outline of each of the four types of objects seen

on the layout.d. Observe the results in the terminal window.

Refer to Table T3-1. From the Terminal window response and observation of the layout, verify all the entries in the table. The layer names used in the layout are identified and additional information about the way the polygons are drawn is presented.

When finished, compare Table T3-1 with Figure T3-3 to gain a better understanding of the mask and process relationship.

Outline color What it is Object Mask name

Number of points to create object

Number of instances of each object

Cyan Base silicon layer Rectangle GND 2 1

Green Electrodes to control mirror movement

Rectangle electrode 2 2

Yellow Rod supports Rectangle rod_support 2 2

Red Torsional rod Rectangle mirror 2 1

Red Aluminum mirror Polygon mirror 21 1


3. Save the file, and exit the Layout Editor. a. From the Layout Editor File menu, select Save.b. Select File > Exit.

The 2-D layout is now ready to be used in the solid model step. But first, a process file must be created.



3.2.3: Process EditorThis section describes defining and modifying the process flow. In the CoventorWare 2008 flow, defining the process flow comes first. But this tutorial deviates from this typical flow to make the user think about what kind of process file would be needed for a particular design. The tutorial asks you to think, "If I had this type of design in mind, what type of process would I need?" Figure T3-3 shows the necessary process steps for the mirror design. Note that the cross-section A and B views were first explained on page T3-3.

Figure T3-3 Process Steps for Mirror Design

cross-section A view cross-section B viewBase GNDSilicon:8 microns

Deposit PlanarSiN: 0.5 microns

Polysilicon: 0.5 micronsDeposit Planar

Etch electrode +

Polyimide: 2.0 micronsDeposit Planar

Etch rod_support -

Aluminum (Film): 0.5 micronsDeposit

Conformal

Etch mirror +

PolyimideSacrifice



The GND layer in CoventorWareAll design structures must include a GND or base layer. This layer defines the boundaries of the model’s active area, and is not associated with an electrical ground or a deposition layer that is connected to ground.


1. Using Figure T3-3 on page T3-5 as a guide, create the steps from the process and mask flow information that has already been presented.

a. From the top of the Function Manager, click on the arrow beside the Process field, and select create a new process from the drop-down menu.

b. Click on the Process Editor icon.

The 2-D layout is now ready to be used in the solid model step. But first, a process file must be created.

c. Using Figure T3-3 on page T3-5 as a guide, create the steps from the process and mask flow information that has already been presented, rather than copying the information from the illustration shown below.

Use the Planar Fill, Straight Cut, Conformal Shell, and Delete modeling actions to add the necessary process procedures.In the Process Description pane, select each step you added, and set the material, color, and mask polarity in the Step Parameters fields below. Type the layer and mask names in the appropriate fields. See page T2-13 for more details.

2. Save the file as mirror.proc. a. From the Process Editor File menu, select Save As, and save the file as mirror.proc.

The process flow is saved in the MirrorDesign\Devices directory, and the process file field is updated to show the mirror.proc file path. This file will be combined with the mirror.cat file to create the solid model.

b. Select File > Close.



3.2.4: Building a Solid ModelNow that the layout and process files are complete, a 3-D model can be built using the 2-D layout mask information and the thickness and etch profile information from the process file.

The rendered 3-D model is created from the 2-D layout drawing. The process file information allows the depth of the mirror to be extruded. The next step is to prepare the model for meshing; this includes designating part properties and naming faces.

The model creation steps that follow are very complex. If you would like to bypass the model creation steps, the tutorial directory contains the two models files used for simulation: monolith_prebuilt and multi_mesh_prebuilt. You will be able to select these models from the Model/Mesh field in the Designer and Analyzer tabs. If you choose to use the prebuilt models rather than create your own, go to page T3-20 to begin the model simulations.


1. Build a solid model using mirror.cat and mirror.proc.

a. From the Designer tab, make sure the mirror.proc and the mirror.cat files are displayed in their respective fields.

b. From the Model/Mesh file field, select create a new model from the drop-down menu, and click on the Start Preprocessor icon.

c. In the dialog that opens enter mirror.d. When finished, the Preprocessor opens.e. In the Geometry Browser, right click on the Substrate layer and select

Hide Selection. f. Hide the Nitride layer.

The Substrate and Nitride layers are hidden because they will not affect the electrostatic and mechanical simulations, and therefore will not be meshed.



3.2.5: MeshingMeshing reduces the geometry of a structure to a group of simpler finite element bricks that can be presented to the solver for finite element analysis. In this section you will mesh the solid model you just created twice: you will first create a model that has a uniform mesh on the mirror. Then you will create a second model will be partitioned so that a finer mesh can be applied to the tethers. This second model will be used to demonstrate the usefulness of Coventor-Ware’s link capability. The uniformly meshed model will be used for comparison.

Uniform MeshThe monolithic model created in this section will have a uniform Extruded mesh on the mirror. The electrodes will have a separate Manhattan mesh.

Figure T3-4 Properties Dialog for Part_0(electrode)


1. Rename the model monolith. a. From the Preprocessor menu bar, select File > Save As.b. Save the model as monolith.

2. Add the mirror and electrode layers to the Mesh folder.

a. In the Geometry Browser to the left of the canvas, hold down the Ctrl key and click on the electrode and mirror layers, then right click to select Add to Mesh Model.

3. Rename the electrode parts electrode1 and electrode2. Check Suppress, except for MemElectro for both parts.

a. In the Geometry Browser, under the expanded Mesh Model, double click on the electrode layer to display its parts.

b. Right click on Part_0(electrode), and select Properties.c. In the dialog that opens, in the Name field enter elect1.

Part properties can be assigned from the Solid Model folder or from the Mesh Model folder.

d. Select the Suppress, except for MemElectro option.

This option removes the part from the input into the FEM solvers, so that, for example, in CoSolveEM the part would still go through electrostatic solver, but not through MemMech.

e. Click on OK.f. For Part_1(electrode), assign a name of elect2 and select the Suppress,

except for MemElectro option.



Table T3-2 Material Properties for Aluminum (Film)

Next, you will assign face names to the model. Face names are assigned from the Mesh folder, but before meshing.


4. Rename the mirror part mirror. Make sure that it is assigned the Conductor and Solid options.

a. Expand the mirror layer if necessary.b. Right click on mirror part, and select Properties.c. Check that the Conductor and Solid Analysis Options are selected.

5. Verify the mirror’s material properties, as shown below.

a. Click on the Material Properties Editor icon to the right of the material field.

b. Verify the ALUMINUM(FILM) values shown in Edit Materials dialog. They should match the values shown in the table below. If needed make necessary changes.

When the model is created, material properties are automatically assigned to the parts based on the material name that was assigned to each part in the Process Editor. The material properties are taken from the user’s Material Properties Database (MPD).

Any changes made to the material properties from the Parts Properties dialog are only saved to the active model; the changes are not saved to the user’s MPD.

In the previous step, the electrodes’ POLYSILICON material was not verified because it is not part of any mechanical solution; its properties can be ignored.

c. Click on Close in the Edit Material dialog.d. Click on OK in the Properties dialog.

Property Data Type Sub prop Aluminum (film) Units

Elastic Constants Elastic-Iso E 7.70e+04 MPa

Poisson 3.00e-01

Density Constant-Scalar 2.30e-15 kg/µm3

Stress AnIso Sx 0 MPa

Sy 0 MPa

Sz 0 MPa

TCE Constant-Scalar 2.31e-05 1/K

Thermal Cond Constant-Scalar 2.40e+08 pW/µm · K

Specific Heat Constant-Scalar 9.03e+14 pJ/kg · K



Figure T3-5 Face Assignments for Mirror Model


6. Rename the mirror faces using Figure T3-5 as a guide.

a. In the Z-Scale field in the upper left corner of the Preprocessor, enter 3.

b. Select the Face selection mode icon.

Face names assigned in the Preprocessor correspond to patch names in the boundary condition dialogs.

Face names can be assigned before the mesh is created. These names will be preserved even if the model is remeshed.

c. Right click on each face in the Canvas, and select Set Name. Set the face names as listed below, using Figure T3-5 as a guide:

mirror top surface topbottom of support end1 fix_end1elect1 top surface elect1elect2 top surface elect2bottom of support end2 fix_end2

d. Use the Rotate and Pan icons to change the view, or use the mouse/key shortcuts to rotate, pan, or zoom without losing the mode selection tool.

Rotate: Ctrl, right click, dragPan: Alt, right click, dragZoom: Shift, right click, drag

e. From the Preprocessor File menu select Save, which saves the new face names to the model file.

top

fix_end1

elect1

elect2

fix_end2




7. Rename the conductors electrode1, electrode2, and mirror.

a. Expand the Conductor browser if necessary.b. Right click on each conductor, and assign the names electrode1,

electrode2, and mirror, as appropriate.

When you click on a conductor in the Geometry Browser, the corresponding conductor is highlighted on the canvas.

You are providing meaningful names to the conductors for easier identification in the solver boundary condition dialogs.

8. Assign a Manhattan bricks mesh to the electrodes. Define the element sizes as 2.5, 2.5, and 0.5 in the X, Y, and Z directions respectively.

a. From the Mesh Model folder, click to select the region containing the electrode layer, and then right click to select Mesher Settings.

b. For the Mesh Type, select Manhattan bricks.c. Set the element size/number as follows:

X-direction: 2.5 Y-direction: 2.5 Z-direction: 0.5

d. Verify that the Bias types are set to None.e. Click on OK.

In this step, only the electrodes will be meshed. The ground layer does not need to be meshed because does not affect the tutorial simulations. The mirror layer is meshed separately using the Extruded mesh option.

Because the electrodes have Manhattan geometry, it is best to use the Manhattan mesh type.

Parabolic elements give more accurate results than linear elements and is the default Element Order.




9. Assign an Extruded bricks mesh with the Pave algorithm to the mirror. Define an element size of 3.0 in the X-Y directions, 0.5 in the Z direction.

a. Click to select the region containing the mirror layer, then right click to select Mesher Settings.

b. For the Mesh Type, select Extruded bricks.c. Select the Pave, QMorph Algorithm.

The Extruded/Pave combination produces hexahedral elements, which in general generate accurate results for all solvers. Note that because the mesh is generated from the boundaries inward, the mesh sometimes looks irregular in the interior of the domain where the meshing fronts collide.

d. Choose the Parabolic element order if it is not already selected.e. For the Planar directions, set the Element size to 3.0.f. For the Extrude direction, set the Element size to 0.5.

The value entered in the Element size field specifies the mesh edge length of the model faces. The model edges and model faces will be meshed such that each mesh edge length is equal to this value.

g. Click on OK.



Figure T3-6 Mirror and Electrode Meshes


10. Generate the mesh.a. Click on the Generate Mesh icon.

Clicking on the Generate Mesh icon creates a mesh for any region that has had a mesh specified for it and that has the Generate mesh option checked in the Mesh Settings dialog.

As an alternative to clicking on the Create Mesh icon, you can also use Ctrl + G.

b. Rotate the model so you can view both the mirror and electrode mesh. The meshes appear as shown in Figure T3-6.


11. View the mesh quality statistics. a. Select Mesh Model from the Geometry Browser. b. From the Preprocessor menu bar, select Tools > Quality Query.c. Review the statistics, as shown in Figure T3-7.You can toggle between

Volume Mesh and Surface Mesh summaries. Verify that the volume mesh model results are similar to those shown below. If they are, the model database should contain the same information as in the tutorial; the solver results should be similar.

d. Click on OK.e. In the Preprocessor select File > Save.f. Select File > Close.

Z scale =1



Figure T3-7 Mesh Quality Report

Multi-Volume MeshIn this section you will create the multi-volume mesh. For simplification purposes, the mirror model created in the previous section was meshed with a single mesh. To do an in-depth study of the torsional movement of the tethers, you would need to create a finer mesh in the tethers, which are subject to higher stresses than the rest of the mirror. At least four elements in the cross-section of the tether are recommended. To create this finer mesh, you would have to partition the solid model so that the tethers are on different layers, assign a finer mesh to those layers, and then use CoventorWare’s links and ties capability to join the parts of the mirror.

The links and ties capability in CoventorWare allows multiple volumes with dissimilar mesh definitions to be mechanically joined into one part. The volumes are joined by specifying the connecting patches. The joining flexibil-ity allows independent volume transformation and scaling, and enables a parametric study of structural variations due to geometry.

In order to link the separate volumes together, a patch on one volume is chosen and linked to a patch on another vol-ume. An accompanying specification of radius extending from the center of the patch defines the area where mechan-ical computations are transferred to the joining parts. The computed deformations are transferred between patches when a force is applied to the device, even when the two patches are not coincident. When the volumes are linked (using the RigidLink option), the patches are rigid but are allowed to translate in all six degrees of freedom. When the same volumes are tied (using the TiedLink option), patches are allowed to translate and deform, resulting in a more accurate solution that better resembles a fully merged mesh. As expected, the greater versatility of ties requires more computational power, while links are recommended when modeling accuracy is not as critical. Both techniques are demonstrated in this tutorial. An additional ThermalLink option, which allows transfer of thermal characteristics, is not covered.

More information on this topic can be found in the CoventorWare ANALYZER Reference, starting on page R4-28.



Partition the Solid Model

Before meshing, the tethers must be partitioned so that they are on separate layers than the main body of the mirror. The Partition tool will not be active if any layers are in the Mesh folder.

Figure T3-8 First Partition Step


1. Create a new model from the original mirror model; save it as multi_mesh.

a. Select File > Open.b. Select the original mirror model.c. Select File > Save As; save the model as multi_mesh.

2. Partition the front tether from the main body of the mirror.

a. Use the Zoom icon to get a good view of the entire tether.

b. Use the Ctrl key and the Vertex selection mode to select (4, -0.2, 3.5) and (18, 0.2, 0.5) (see below). Select Solid Model > Insert > Block > Use Selected Vertices.

c. In the Geometry Browser, Ctrl click on the mirror layer and the newly created Block to select.

d. Select Solid Model > Partition.

Figure T3-8 shows the vertices selected to create the partition box, the result of inserting that box, and the result of the partition.

e. Rotate the model to view the other tether. Repeat the process using coordinates (-4, 0.2, 3.5) and (-18, -0.2, 0.5).

(box is hidden)



Name Entities

Figure T3-9 Part Names


1. Turn off the Automatically merge touching layers option.

a. From the Preprocessor menu, select Mesh > Automatically merge touching layers to deselect this option.

This setting will prevent the newly created layers from merging when they are added to the Mesh Model folder. Each layer will be in its own region, and you will be able to apply different mesh settings to each region.

Note that this setting will be turned off for the current Preprocessor session, but when you exit and then reopen it, the setting will be turned on again.

2. Add the mirror, electrode, and tethers layers to the Mesh Model folder.

a. Right click on the mirror, electrode, and tether layers and select Add to Mesh Model.

Note that when you added these layers to the Mesh Model folder, four regions are created: one for the electrodes, one for the mirror body, and one for each tether.

3. Name the mirror parts as shown below. a. In the Geometry Browser, right click on each of the design parts and select Set Name.

b. Assign part names as shown below.

4. Make sure the electrode parts are fixed. a. Right click on each of the electrode parts and select Properties.b. In the Properties dialog for each electrode, make sure that

Suppress, except for MemElectro is checked. The Conductor and Solid options should also be selected.

c. For the mirror and tethers, make sure the Conductor option is selected.

mirror

elect1

elect2 tether1

tether2



Create a Mesh for the Model

In this sequence, you will mesh the mirror, tethers, and electrodes with different mesh dimensions.


5. Rename the mirror and electrode faces as shown in Figure T3-5 on page T3-10.

a. Select the Face selection mode icon.

b. Name the faces as shown in Figure T3-5 on page T3-10.

Note the additional faces on the mirror and tethers that will be used to link the tethers to the mirror will be named using the Automate MemMech Links feature in a later step.


1. Create a mesh for the electrodes using a Manhattan mesh with element sizes 2.5, 2.5, and 0.5.

a. In the Mesh Model tree, right click on the region that contains the electrodes, and select Mesher Settings.

b. In the dialog that opens, select the Manhattan bricks mesh type.c. Select the Parabolic element order.d. Set the X, Y, and Z element sizes to 2.5, 2.5, and 0.5, respectively.

2. Mesh the mirror with an extruded mesh using the Pave, QMorph algorithm, a Planar element size of 3, and an Extrude element size of 0.5

a. Right click on the region that contains the mirror.b. In the dialog that opens, select the Extruded bricks mesh type.c. Select the Pave, QMorph algorithm.d. Select the Parabolic element order.e. Set the Planar element size to 3.0.f. Set the Extrude element size to 0.5.

These settings are the same as the settings for the previous mirror tutorial. See page T3-8 for a more detailed explanation of the mesher options.

3. Mesh the tethers with an extrude mesh using the Pave, QMorph algorithm, a Planar element size of 3, and an Extrude element size of 0.25.

a. To each of the regions that contain the tethers, apply these mesher settings:

Extruded bricksPave, QMorph algorithmParabolic element orderPlanar element size to 3.0Extrude element size: 0.25

The extrude element size will ensure that four elements are created in the cross-section of the tethers.

4. Create the mesh. a. Click on the Generate Mesh icon. The resulting mesh is shown in Figure T3-10. Compare it to the monolithic mesh on page T3-13.

b. Select Tools > Quality Query and compare with Figure T3-11; also compare with the quality report for the monolithic model shown on page T3-14.



Figure T3-10 Mesh for Multimesh Model

Figure T3-11 Mesh Quality Report

Close up of tether mesh



Automate MemMech Links

Figure T3-12 Name Assignment with Automate MemMech Links


1. Apply the Automate MemMech Links feature to the mirror and tether meshed regions.

a. In the Mesh Model tree, use the Ctrl key to select the regions that contain the mirror and tethers.

b. Select Mesh > Automate MemMech Links.

This option only becomes active when the selected regions have been meshed and are touching.

c. Expand the Geometry Tree to view the assigned face names, as shown in Figure T3-12.

When two or more regions share faces, this option automatically names the matching faces. The names will be appended with a master or slave designation, with the face with the larger area designated as the master. For more information, see page R4-32.

The COV_master_0 and _1 faces are on the mirror sides where the tethers touch the mirror. The COV_slave_0 and _1 faces are on the tethers.


2. Give the conductors more appropriate names. a. Right click on each of the conductors and rename them so they correspond to the part names shown in Figure T3-9 on page T3-16.

3. Save the model and exit the Preprocessor. a. Select File > Save.b. Select File > Exit.



3.2.6: MemMech Modal AnalysisThe tutorial starts here for advanced CoventorWare users that do not want to create the model files. In this section you will run a modal analysis on both the monolithic model and the multi-mesh model, and then compare results. The multi-mesh model will require the use of links. Modal analysis is chosen for the initial simulation because it is rela-tively fast.

Monolithic Control Model


1. Set the Analyzer tab for a MemMech simulation.

a. From the Analyzer tab, set the Solver field to MemMech. b. Select the monolith model.c. Click on the Solver Setup icon.

2. Set the MemMech Settings dialog to perform a modal analysis that extracts the first four modes.

a. In the MemMech Settings dialog, set the Physics to Modal (non-equilibrium).

There is no initial stress in the model, and we will not apply any load, so there is no need to run a mechanical analysis.

b. Set the Modes to 4.c. Click on Next.



Figure T3-13 Modal Results for Monolithic Model


3. In the SurfaceBCs dialog, fix the anchor faces.

a. In the MemMech BCs window, click on SurfaceBCs.b. Set the dialog to the values shown below.c. Click on OK.d. In the MemMech BCs window, click on Run.e. Save the analysis as modal_monolith.


4. View the numerical modeDomain results. a. When the simulation is finished (noted by the green checkmark by the modal_monolith job in the Job Queue dialog), click on the View Results icon.

b. In the Analysis Results window, select modeDomain from the View Table drop-down menu.

c. Verify the results shown below.



Linked Model


1. Configure MemMech to run with the multi_mesh model.

a. From the Analyzer tab, select the MemMech solver and the multi_mesh model.

b. From the Analysis field drop-down, select create a new analysis. c. Click on the Solver Setup icon.

2. In the LinkageBCs dialog, link the tethers to the mirror using the TiedLink option.

a. Click on Next.

The MemMech Settings dialog does not need to be changed.

Because the relevant faces names in the monolith and multi_mesh model are the same, the SurfaceBCs dialog does not need to be changed.

b. In the MemMech BCs window, click on LinkageBCs.c. In the Update Table dialog that opens, click on OK.d. Verify that the dialog appears as shown below.

Because we used the Automate MemMech Links option in the Preprocessor, the software will automatically populate the LinkageBCs dialog with the master/slave pairs created. Note that if you change the name of the automatically assigned faces, the LinkageBCs will not prompt you to add the pairs.

The TiedLink option is automatically selected because it is more accurate. The RigidLink option saves computation time at the expense of accuracy. For more information on CoventorWare’s link capability, see page R4-28.

3. Start the simulation. a. In the MemMechBCs window, click on Run.b. Save the analysis as modal_multi.



Figure T3-14 Linked Results

3.2.7: CoSolveEM - Single RunIn this section, the CoSolveEM solver produces an electrostatic and mechanical solution for the mirror. The actual MEMS mirror tilts about the thin rod in response to different voltages applied at the electrodes. All the movement results from the charge developed by the voltage applied to the electrode. For the solution, use CoSolveEM in the One Step mode. CoSolveEM will first calculate the electrostatic charges with the same solver used for MemElectro. Then it will apply these results as electrostatic pressure in calculating the mechanical solution with the same solver used for MemMech. Finally, MemElectro will run again to compute capacitance values. Unlike the full iterative CoSolveEM that continues until convergence is reached, the One Step mode stops after these calculations. The result is an approximate electrostatic and mechanical solution that saves time for the purposes of this tutorial.

Monolith ModelYou will first run CoSolveEM with the monolith model, and then run with the linked model to compare results.


4. View the numerical modeDomain results. a. When the simulation is finished, from the Job Queue dialog, make sure the modal_multi is selected, and click on the View Results icon.

b. In the Analysis Results window, select modeDomain from the View Table drop-down menu.

c. Verify the results shown below.

Compare the linked results with the monolithic results on page T3-21. The results are different because the linked model has more elements in the tethers, making it less stiff. The differences between results become even more significant when using an iterative tool such as CoSolveEM; as you will investigate in the next section.


1. Set up the Analyzer tab to point to the MemElectro solver for the monolith model.

a. From the Analyzer tab, choose the MemElectro solver.b. Select the monolith model from the Model/Mesh drop-down menu.c. Click on the Solver Setup icon.d. Check that the Settings dialog has the default settings.

Set the MemElectro Settings dialog to be the same as in Tutorial 1. See page T2-28.

CoSolveEM uses both MemElectro and MemMech to perform the calculation. These individual solvers must also be configured properly.

e. Click on Next.



2. Apply a fixed voltage of 5.0 to electrode1, and a fixed voltage of 10 to electrode2.

a. Click on ConductorBCs.b. Apply the voltages as shown below.c. Click on OK.d. In the MemElectroBCs window, click on Close.


3. Set up the Analyzer tab to point to the MemMech solver for the monolith model. Configure MemMech to run a Mechanical analysis.

a. From the Analyzer tab, choose the MemMech solver.b. Select the monolith model from the Model/Mesh drop-down menu.c. Set the Analysis field to create a new analysis.d. Click on the Solver Setup icon.e. Set the Physics to Mechanical.

In this simulation, we will actuate the mirror using a voltage on the electrodes, so there will be mechanical displacement.

f. Set the Additional Analysis field to None.

4. Check that the anchor faces are still fixed. Remove any links that are set.

a. Check that the SurfaceBCs dialog still has the anchor faces fixed (see page T3-21).

b. In the LinkageBCs dialog, remove any links by setting the LinkType to none.

c. In the MemMech BCs window, click on Close.

MemMech boundary conditions are set, but the solver is not activated; the simulation will be run using CoSolveEM.





5. Configure CoSolveEM to run Single Run analysis with the One Step iteration method.

a. From the Analyzer tab, choose CoSolveEM as the solver type.b. Select the monolith model.c. Click on the Solver Setup icon.d. In the CoSolveEM Settings dialog, verify the following settings:

CoSolve Steps = Single Iteration Method = One Iteration

e. Click on Next.


6. Verify the voltage assignments made in MemElectro.

a. In the CoSolveEM BCs window, click on ConductorBCs.b. Verify that the values are identical to those set up from the MemElectro

BCs window(page T3-24).c. Click on OK.

7. Start the simulation. a. Click on Run.b. Save the analysis as monolith_single.c. Click on Yes to save the settings file.



Figure T3-15 CoSolveEM Numerical Results


8. From the simulation results window, review results for Displacement, Reaction Forces, Capacitance, and Charge, illustrated in Figure T3-15.

a. When the simulation is finished, click on the View Results icon.b. In the Analysis results window, select Displacement from the Tables

drop-down menu.c. Verify that the values are identical to those shown below.d. Verify the Reaction Force, Capacitance, and Charge results shown

below.

The numbers show small charges and some deflection, but do not indicate which way the mirror tilts.



Figure T3-16 Charge Results for the CoSolveEM Run


9. View the charge distribution in the Visualizer.

a. From the Results window, click on the View 3D Results icon.

For a CoSolveEM simulation, the Visualizer has two frames: one for MemElectro results and one for MemMech results. The MemElectro results are displayed in the top frame.

b. Select Coventor > Geometry Scaling.c. Set Z scale for the best view (try Z = 3); then click on Apply and Close.

The view is illustrated in Figure T3-16.

This step allows you to view the charge distribution under the mirror with the Visualizer by optimizing the view.

d. Select Coventor > Part Visibility. In the dialog that opens, move the elect1 and elect2 parts to the Visible column.

e. Select Plot > Contour/Multi-coloring and select Charge Density.

f. In the left panel of the Visualizer, click on the Probe icon.

g. Click on the different parts to view the charges, which appear in the Probe dialog. Note that you may have to use the Scroll Down button to view the desired results.

Note: The image above has been edited for clarity; the charge results are actually displayed in theProbe window.

1.68E-04-7.3E-05



Figure T3-17 Stress Results for the CoSolveEM Run


10. View the stress results in the Visualizer. a. To see the MemMech results, select Frame > Push Current Frame Back.b. Select Plot > Contour/Multi-coloring and select Mises Stress. Click on

Close in the Contour Details dialog.c. Select Coventor > Part Visibility and Show elect1 and elect2.d. In the Geometry Scaling dialog:

Adjust the Z scale for the best view (try Z = 3). Click on Deform Using Displacements to see the mirror deflection. Adjust the Exaggeration for the best view (try Exaggeration = 20). Click on Apply and Close.The view appears similar to the one illustrated in Figure T3-17.

The mirror tilts toward the electrode with the higher charge. Maximum stress is along the narrow mirror rod about which the mirror twists. The Visualizer can display surface and internal stresses in a variety of modes and formats. Refer to the CoventorWare ANALYZER Reference (page R9-1) for an explanation of the Visualization functions.

e. Select View > 3DRotate; the rotation mode is now active. Use the mouse to rotate the model.

f. When finished, select File > Exit.g. Click on Close in the Analysis Results window.



Multi-Mesh Model

Figure T3-18 CoSolveEM Results for Multi-Mesh Model


1. Reset the MemElectro, MemMech, and CoSolveEM solvers to run with the multi-mesh model.

a. From the Analyzer tab, select the MemElectro solver, and set the Model/Mesh field to the multi_mesh model.

b. Select the MemMech solver and the multi_mesh model.c. From the MemMech LinkageBCs dialog, reset the links between the

tethers and mirror, as shown on page T3-22.d. From the Analyzer tab, select the CoSolveEM solver and the multi_mesh

model.e. Set the Analysis field to create a new analysis.

2. Start the simulation. a. From the CoSolveEM BCs window, click on Run.b. Save the analysis as multi_single.c. Click on Yes to save the settings file.


3. From the simulation results window, review results for Displacement, Reaction Force, and Capacitance, and Charge, illustrated in Figure T3-18.

a. When the simulation is finished, click on the View Results icon.b. In the Analysis results window, select Displacement from the Tables

drop-down menu.c. Compare the results to those shown below.d. Verify the Reaction Force, Capacitance, and Charge results shown

below.e. Compare the results with the monolith model results (see page T3-26).



3.2.8: CoSolveEM - Multiple Run CapabilityIn this sequence, the boundary conditions will be set through CoSolveEM so that the mirror is able to move in differ-ent directions at different angles in a sequence of software runs. The goal is to create an animated display in the Visu-alizer so that the mirror tilts back and forth between the two electrodes.

Before starting this sequence, give some thought on how to formulate an approach that allows the software to produce this result. A sequence of runs is required, so is it necessary to use the Parametric Study function? To get the mirror to tilt, how are a set of voltages applied to the electrodes? If a single trajectory is used, how would the mirror tilt back and forth?

CoSolveEM has the capability to produce multiple runs when voltages are to be varied, without needing to use the Parametric Study function. In addition, this CoSolveEM feature can use more than one trajectory. With this informa-tion in mind, start the tutorial, and try to anticipate how some of the setups will turn out before actually reading the corresponding step sequence.

Because this simulation can take some time, you will only run it with the multi_mesh model.


1. Create a new .mps file to store a new solver setup.

a. From the menu bar, click on File > Save As.b. In the navigation dialog that opens, in the Settings File field, highlight the

current filename and enter mirror_b.mps. This new file name is saved in the project directory.

c. Click on Save to accept the file.

Saving the settings file name under a different name preserves the original setup and create a new settings file for any new settings.

2. Configure CoSolveEM to run with a Trajectory analysis and the One Step iteration method.

a. From the Analyzer tab, make sure CoSolveEM is still the active solver and the multi_mesh model is still selected.

b. Set the Analysis field to create new analysis, then click on Solver Setup.c. In the CoSolveEM Settings dialog, set the following fields:

CoSolve Steps = TrajectoryIteration Method = Relaxation

Setting CoSolveEM to Trajectory mode enables new dialogs. The CoSolveEM BCs window will have trajectory and voltages buttons, as well as the ConductorBCs and DielectricBCs buttons that appear when the Settings dialog is set to Single Run.

d. Click on Next.



Figure T3-19 Trajectory Setup in CoSolveEM


3. Assign a voltage variable and a 1 volt voltage to each electrode.

a. In the CoSolveEM BCs window click on ConductorBCs.b. Assign a voltageBC variable (Voltage1 and Voltage2) to each electrode.c. Set the two electrodes to 1 volt values.d. Click on OK.

In this setup, voltage variables are assigned. The variable values will be multiplied by the unit voltages in the calculations.


4. Create two trajectories that apply alternate voltages of 10 and 20 volts on the two electrodes.

a. Click on trajectory. The dialogs are illustrated in Figure T3-19.b. Select the Enumerate type for both trajectories.c. Set 4 enumerate values for each trajectory.d. Assign a label for each trajectory.e. Click on OK.

This setup defines trajectories for the simulation. In another dialog, the voltage variables previously assigned will be equated to these trajectories.

The assigned values apply alternate voltages of 10 and 20 volts to the two electrodes, causing the mirror to tilt back and forth.

Note that with multiple trajectory assignments, the number of time steps must be identical. The software reads the trajectory values as two different conditions applied at the same time for each of four steps.

images edited for clarity




5. Set the Voltages dialog as shown below. a. Click on Voltages.b. Assign a t1 trajectory to Voltage1 and a t2 trajectory to Voltage2.

The voltage variables take on the 4 step trajectory values. The unit voltages set in the surfaces dialog cause the trajectory values to be multiplied by 1.

c. Verify Factor as the types and 1.0 as the Scale Factors.d. Set the PullIn of both sets to 0.

The PullIn setting is often used when creating a voltage ramp to determine the point that a model displacement changes significantly when “pulling in” to a surface due to charge attraction. The PullIn setting allows CoSolveEM to recalculate values if the large displacement swing causes an unstable solution. This iterative seek routine continues until a stable solution is reached. An example that uses pull in is shown in Tutorial 3 (see page T2-90).

If a pull-in calculation is not being performed, and if a set of enumerating values is applied that causes the voltage to increase and decrease during the same simulation (as is the case with our example), CoSolveEM may think that a solution has reached the pull-in criteria before the simulation is complete and may end the simulation before completing all trajectory points. In such cases, the PullIn should be set to 0 to avoid the premature termination.

e. Click on OK.

6. Start the simulation. a. Click on Run in the CoSolveEM BCs window (but first see note below).

The simulation may take up to 30 minutes on a fast machine. This is why only four trajectory points are used.

b. Save the Analysis Name as cs_multiple.c. Click on Yes to save settings.




7. Open the Job Queue dialog to monitor the progress of the simulation.

a. Click on the Job Queue icon to monitor the progress of the simulation.

The Job Queue dialog can also be opened from the Function Manager’s Tools menu.

b. In the Job Queue dialog, click on the Progress tab.

This dialog allows the user to see how many trajectory steps have been completed. It also allows the user to manage simulations that have been added to the job queue. For more information on this dialog, see page U1-31 of Using CoventorWare.




8. Verify the numerical displacement results. a. When the simulation is finished, click on the View Results icon.b. Select Displacement from the Table drop-down menu.c. Verify the MaxZ results as shown below.d. Click on OK.

The 3-D display of the simulation results conveys the most meaning for this simulation. The specific numerical results are not of interest here.

The displacement results for the monolith model are provided for comparison.

Results for monolith model (for comparison)



Figure T3-20 Visualizer View of the CoSolveEM Trajectory Run



a. Load All results and click on the View 3D Results icon.

The All results function allows all files created by the solvers to be viewed.

b. Select Frame > Push Current Frame Back.c. Select Coventor > Part Visibility, and make the electrodes visible.d. Set the Contour Variable to Mises Stress.e. Open the Geometry Scaling dialog and set the following parameters:

Z Scale = 3Deform Using Displacements = checkedExaggeration = 3Click on Apply and Close.

f. Select Coventor > Result Selection, and click on Next to load the results one at a time, or click on Play to see an animated display.

This setup allows viewing of the movement of the mirror.Two frames of this animation are illustrated in Figure T3-20.

g. Click on Stop when finished.

For a system-modeling approach using a mirror design, see the macromodeling Mirror Tutorial, beginning on page T3-37. In this tutorial, the user constructs and simulates the design in Saber. The system-modeling approach is then compared to results obtained using FEM analysis of the tutorial model.

electrode1 = 20 volts electrode2 = 20 volts



Notes


Section 3: Mirror Design Mirror Design with Integrator Version 2008

3.3: Mirror Design with Integrator

3.3.1: IntroductionCoventorWare offers macromodel creation through several macromodeling tools. These tools automatically generate macromodels with up to six degrees of freedom to represent sub-components of a system. These sub-components can then be connected within the Saber or Cadence environments to specify the force-balance relationships of the system. The Saber or Cadence simulator can then set up and solve the appropriate ordinary differential equations to determine the dynamics of the device operation. This tutorial shows how to create and use macromodels in the Saber simulator. For more information on how to create and use macromodels for the Cadence simulator, please see the IntegratorCa-dence.pdf in /Coventor/CoventorWare2008/docs/aux_docs.

The approach for creating each macromodel sub-component involves exploring the device operation space (coupled multi-degrees of freedom), modeling device data through multi-degree polynomial curve fitting, and using the poly-nomial coefficients and other simulation data to generate the ordinary differential equations that constitute the macro-model (also called reduced-order model). The essential macromodel components are electrical springs (electrostatic actuators), mechanical springs, mechanical dampers, and inertia (masses). The automatic extraction of macromodels reduces the system model creation time from weeks to hours.

The macromodeling solvers are accessed from the Solver (effects) drop-down menu on the Analyzer tab. If the MEMS domain is selected, the SpringMM, DampingMM, and InertiaMM solvers appear in the menu (see Figure T3-21). If the Microfluidics domain is selected, the FlowMM solver appears in the menu.

Figure T3-21 Macromodeling Solvers

Each macromodeling solver includes setup dialogs, a simulation start procedure, and displayed output results. Specif-ically, the solvers perform the following functions:

SpringMM: Includes model extraction for mechanical, electrostatic, and electromechanical springs. Refer-ence section information for this function begins on page N2-4.DampingMM: Allows the calculation of damping coefficients and the creation of a damping system model. Tutorials and a reference section for this function begin on page N4-17.InertiaMM: Computes the mass and moments of inertia of movable mechanical structures and their cen-troids. Reference section information for this function begins on page N3-1.



FlowMM: Generates macromodels of flow devices and is used to determine the resistance and inertance of a two-port device of arbitrary geometry. The resistance is found by calculating the flow rate for different pres-sure drops across the device, and the inertance is found by calculating the time-constant for flow to reach steady state. A tutorial and a reference section for this function begin on page N5-1.

System Modeling TheoryPerforming finite element (FE) analysis involves solving partial differential equations for the degrees of freedom defined by the partitioning of a solid into finite elements. The computation time required increases with the number of finite elements required to represent the device with a specified accuracy. The number of elements increases rap-idly with the complexity and size of the modeled device. Simulation times for dynamic analyses or sensitivity curve plots can be quite long for even moderately complex devices. This problem can be remedied by simplifying the model. One method of simplification uses a macromodeling or reduced-order modeling approach. This technique is an established engineering method and has been developed specifically for MEMS devices by research collaborations between Coventor, Inc. and others [1,2].

An integral part of the process of creating a macromodel requires the designer to divide the structure into several sub-components, which may or may not be coupled to each other. For example, Figure T3-22 shows the pertinent compo-nents of the mirror design used in this tutorial.

Figure T3-22 Mirror with Macromodels Labeled

In a macromodeling approach, the mirror is represented as a movable mass attached to two massless tethers. The elec-trostatics between the mass and the electrodes below the mass are represented by variable capacitors. The partitioning of the full model is not a trivial process, requiring engineering intuition and experience.

After the model is partitioned, substructures are identified. These structures form the reduced-order elements in the model of the device. The accuracy of the simulations that use the extracted models depends on the validity of the cho-sen representation. Each component of this macromodel can be treated individually, so finite-element analysis can be performed only on the components. Because each component has a mesh that is much smaller than that of the full device, it will require less time to simulate.

For example, a variable capacitance-actuator (or sensor) is a typical MEMS structure. Upon applying a voltage between two or more conductors (mass, comb fingers, etc.) of such a device, an electrostatic attractive force devel-ops. A description of the procedure and technique for calculating the capacitance and the charge distribution is dis-cussed in the following tutorial. The result of this calculation is typically a capacitance versus position table.

The next step is fitting this array of simulated capacitance points to a polynomial surface. The electrostatic actuating force (F) can then be easily estimated in terms of voltage (V) and capacitance (C). For instance, for a model which only moves in the z direction:

The SpringMM solver performs the electrostatic force calculation above.

cap tethermodels stiffness of a

massmodels the mass

models the capacitance single tether

F V2

2------dC z( )

dz-------------=



Similar approaches are used to create models for the forces of mechanical deformation, damping, and inertia. These sub-components can then be connected within a system-modeling environment’s schematic editor to specify the force-balance relationships. The system simulator can then set up and solve the appropriate ordinary differential equations to determine the dynamics of the device operation.

For instance, applying engineering intuition to the mirror shown above, we realize the motion of the device is well represented by two degrees of freedom: the displacement in z of the mirror center and the rotation about the x axis of the mirror center. Within the system-modeling environment, symbols representing each of the extracted sub-compo-nents (mass, spring, damper, etc.) are connected with wires to represent the forces between connected items. The sys-tem simulator would then solve the following force-balance relationships:

where M and I are mass and moment of inertia, K and G are stiffness and torsion modulus, Dz and Dθ are damping coefficients, V is the applied voltage, and C is the capacitance. The two degrees of freedom are z (the translation in the Z-direction), and θ (the angle of rotation about the X-axis).

In reality, the degrees of freedom are always coupled, meaning that the motion of the body along one degree of free-dom affects the motion along another. This coupling occurs through different mechanisms: inertial coupling (includ-ing the Coriolis effect, centrifugal/centripetal force, etc.), elastic coupling, dissipative coupling, and electrostatic coupling. To reflect these couplings the above equations can be rewritten as follows:

These equations can be generalized for more degrees of freedom to model devices with more complex motion.

In the process of creating a macromodel, the user reduces the need for a solution of coupled partial differential equa-tions of an FE model with thousands of degrees of freedom to a solution of a handful of ordinary differential equa-tions for the macromodel. The macromodeling solvers provide an automated tool for the designer, which increases the efficiency of the design process considerably.

After individual components of the model have been characterized, the next step is to describe them in a formalized protocol or procedure, so that they can be connected to each other in a systematic way. A library of standard MEMS elements can be developed, which further facilitates the design process. This formalized protocol has been developed for electrical circuitry and is called netlisting or template creation. Model creation can be done in one of several known hardware description languages (HDL), such as SPICE, MAST, SIMULINK, Verilog-A, etc.

With CoventorWare the user can create models in Saber MAST or Verilog-A language. The software is integrated with the Saber design and simulation tool, which allows the user to begin the MEMS design from the mask or 3-D level and finish it at the system level.

Mz·· Kz– Dzz·V 2

2-------dC

dz-------+–=

Iθ·· Gθ– Dθθ· V 2

2-------dC

dθ-------+–=

Mz·· K z θ,( )z– Dz z θ,( )z· V 2

2-------∂C z θ,( )

∂z--------------------- Inertial Forces+ +–=

Iθ·· G z θ,( )θ– Dθ z θ,( )θ· V 2

2-------∂C z θ,( )

∂θ--------------------- Inertial Moments+ +–=



Demonstrated TechniquesThis tutorial presents a complete mirror system design exercise: the first part of the tutorial outlines how to use the macromodeling modules to generate the components of the design, and the second part of the tutorial outlines how to simulate the design in Architect. The documentation assumes familiarity with the various point solver modules in the tool suite. The Beam Design Tutorial, starting on page T2-1, provides numerous examples for learning the software basics. The mirror model used for this tutorial is identical to the device used in the first mirror tutorial (page T3-2).

The tutorial covers these techniques:how to generate an electrostatic spring macromodel using SpringMM (page T3-41)how to set trajectories in SpringMM (page T3-44)how to visualize SpringMM results (page T3-45)how to plot SpringMM results (page T3-47)how to generate a non-linear, single-ended mechanical spring using SpringMM (page T3-48)how to generate a macromodel representing the mass and tensor of inertia of the movable parts (page T3-54)how to assemble a schematic using the generated macromodels and Saber generic components (page T3-65)how to set up pull-in analysis in Analyzer (for comparison with Architect results) (page T3-75)how to simulate pull-in with Architect (page T3-80)how to apply damping coefficients in Architect (page T3-82)how to run a transient analysis in Architect (page T3-82)

Please note that the system model of the considered mirror design could be built and simulated with the parametric Architect components from the EM Library (page A5-1). The following tutorial should not be seen as an alternate approach, but rather as a simple example to guide you through the various steps of model extraction. The true value of model extraction lies in complementing existing parametric Architect libraries.

Tutorial FilesMacromodel extraction requires an understanding of the physical analysis combined with user experience. Several assumptions are made at this step, and the accuracy of the analysis depends upon the validity of these assumptions:

The movable mass (reflecting surfaces) of the mirror behaves as a rigid body; only the tethers are deformable.The tethers are massless; all the mass is assumed to be lumped in the body of the mirror.All capacitance is between the bottom surface of the mirror and the top surfaces of the electrodes. Some of the fringing field effects are therefore ignored.

Based on these assumptions, the following model files were created for this tutorial. All can be found in the Mirror_Design project directory, which the user imports in the beginning of the tutorial. When the user clicks on the drop-down list in the Model/Mesh field, the following models appear:

tether: As the name implies, this file contains the FE model of a single tether. Because both tethers are iden-tical, only one is analyzed to obtain the macromodel of the mechanical spring.cap: This file contains the electrodes and the mirror without the tethers. MemElectro will extract a surface mesh for these entities.mass: This file contains the FE model of the mirror body and tethers. By including the FE models of both tethers in the model file, the proper patch locations can be specified.

Unlike components from the EM Library, macromodeling components cannot be viewed in Scene3D.



mm_mirror: this file contains the FE model of the entire mirror design. It is included so that the user can run the FEM analysis for comparison with the system model results.

In addition to the model files required by the macromodeling modules, prebuilt macromodel and schematic files can be found under the Mirror_Design\Schematics directory.

3.3.2: Macromodel GenerationThis part of tutorial outlines how to build the macromodels of a mirror. Its individual components are analyzed with two degrees of freedom to create polynomial equations that become the basis for template descriptions of the model behavior. Individual model files of the components are provided, which are used to produce a set of macromodels files that may be placed in a schematic for system simulation.

InitializationBegin the tutorial by starting the software and importing the necessary tutorial directories.

Electrical SpringThis sequence uses the SpringMM solver to calculate the electrostatic force along the specified degrees of freedom and to generate a surface function for the electrostatic force. When the user selects the electrical spring option in the solver Settings dialog, SpringMM uses MemElectro as the point solver, so the MemElectro Settings dialog must be properly configured before proceeding with the SpringMM solver.

Figure T3-23 shows the electrical spring model used. The model does not have to be meshed with a surface mesh; MemElectro can extract a surface mesh from a volume mesh.

Figure T3-23 Electrical Spring Model


1. Start CoventorWare.2. Import the Mirror_Design project

directory and create a settings file.

a. Start CoventorWare.b. In the Project Browser, click on the Import Tutorials icon.c. In the Import Tutorial dialog that opens, select Mirror_Design.

If you ran the first mirror tutorial, you already have this directory in your workspace. You do not need to import it again.

d. Click on OK.e. Use the Settings field to create a settings file named

Macromodel_Mirror.mpsf. Click on Open.

electrode2

electrode1

mirror



MemElectroBefore setting the SpringMM solver to generate an electrical spring model, be sure the MemElectro Settings dialog is set properly.


1. Set MemElectro to run with the cap model and the default solver settings.

a. In the Function Manager, click on the Analyzer tab.b. Select the MEMS Domain option.c. From the Solver (effects) pull-down menu, select MemElectro.d. Click on the drop-down arrow to the right of the Model/Mesh field, and

select the cap model.e. Click on the Solver Setup icon.f. Check that the MemElectro Settings dialog that opens matches the

default settings shown below.g. Click on OK.




2. Configure the SpringMM solver to run with the cap model.

a. From the Analyzer tab, select SpringMM as the Solver.b. Set the Model/Mesh to cap.c. Click on Solver Setup.

3. Set SpringMM to extract an electrical spring with full-factored DOFs.

a. Set the Spring Physics to Electrical.b. Set the DOF to FullFactored.

Your solution will fully couple the degrees of freedom selected for the problem. Additional details on these DOF settings can be found on page N2-2 and page N6-1.

c. Set Restart from previous result to No.

Use the Restart option if you are rerunning an aborted job.d. Click on Next.


4. Designate the mirror as the moving part. a. In the ElectSpring BCs window, click on part.b. Click on List.c. Select mirror as the moving part; click on OK.

The mirror moves, and the electrodes remain stationary.d. Click on OK.




5. Designate the mir_bot patch as the rotation center.

a. In the ElectSpring BCs window, click on patch.b. Set mir_bot as the rotation center.

Choose the patch that is as close as possible to the center of rotation.c. Click on OK.


6. Set Dz and Rx trajectories as shown below. a. Click on trajectories.b. Apply the Steps type to the Dz and Rx lines.c. For the Dz trajectory, set the steps as: –0.2 on the Start line; 0.2 on the

Stop line and 4 on the Steps line.

All displacements are in microns.d. For the Rx trajectory, set the steps as: –7 on the Start line; 7 on the Stop

line and 10 on the Steps line.

All rotations are in degrees.e. Click on OK in the trajectories dialog when finished.

5 steps are actually generated for the Dz trajectory, and 11 steps are generated for the Rx trajectory. Because the degrees of freedom are coupled, the solver computes a total of fifty-five simulation runs.

7. Start the SpringMM simulation. a. In the ElectSpring BCs window, click on Run.b. Save the analysis as elect_spring.c. Click on Yes to save the settings when prompted.

MemElectro is started from this ElectSpring window. It calculates the capacitance matrix for each trajectory step.



To see exactly how the capacitance measurements are performed, view the 3D results in the Visualizer. The results produce a combination of two movements, as shown in Figure T3-24.

The vertical motion of the mirror in five steps in the Z direction. This produces an increasing gap between the mirror and the electrodes, reducing the capacitance. You can see this trend in the capacitance results table.The rotational motion of the mirror in eleven steps around the X axis. This increases the capacitance between the mirror and one of the electrodes while decreasing the capacitance between the mirror and the other elec-trode. If you check carefully, you can see this trend in the capacitance results table. The next step will demon-strate how to plot these results.

Figure T3-24 Electrical Spring Model


8. Review the capacitance results. a. When the simulation is finished, from the Job Queue dialog, make sure the elect_spring job is selected, and click on the View Results icon.

b. Select Capacitance from the Tables drop-down menu, and click on the View Table icon to verify the results shown below.

The solver calculated the matrix of coefficients of capacitance at every point along the trajectory.

The table shows all six degrees of freedom and the capacitance.

Dz trajectory

Rx trajectory



When finished, the electrostatic characteristics of the model are fully specified for a polynomial curve fitting in the next step.

Create Electrical Spring Macromodel

In the previous run, the MemElectro solver computed the capacitance matrix for the model. Next, the polynomial fit routine is run to obtain the polynomial coefficients needed for analytical representation of the capacitance.


9. Configure the Create Macromodel dialog as shown below.

a. In the Analysis Results window, click on Create.b. Set the dialog as shown below.

The Split-Least-Square option specifies the curve-fitting algorithm to use when plotting the results. See page N2-19 for more explanation.

Select a Surface Plot Type with independent variables Rx and Dz and dependent variable Capacitance (of electrode2)

The Model Order setting creates a fourth-order polynomial for the model.

The values for the Rx and Dz degrees of freedom will be stored in the macromodel. They will also be plotted.

You are configuring the Create Macromodel to store the desired information in the MAST format.

You may use any string as a Component Label, but capital letters and spaces are not allowed anywhere in the string.



Figure T3-25 Surface Plot of Electrical Spring Polynomials


10. Plot the capacitance results. a. In the Create Macromodel dialog, click on Fit and Plot.

After you click on Fit and Plot, a plot window appears. The plotted curve in Figure T3-25 shows the same characteristics as the Capacitance table. You would see the same results in the Visualizer output of the Capacitance.

b. Select File > Exit in the plot window.


11. Create the electrical spring macromodel. a. In the Create Macromodel dialog, click on Save Macromodel.

The SpringMM module creates a macromodel template file based on the coefficients generated.

The model .sin file and an associated symbol and help file are generated.

Part entries are made in the .aimpart user file in the user’s home directory for use with the Part Gallery in Saber.

b. Click on OK in the Create Spring Macromodel dialog.c. Click on Close in the Analysis Results window.

Control returns to the Analyzer tab.



Mechanical SpringThis sequence uses the SpringMM solver to generate the hypersurfaces representing the elastic force and moments in the degrees of freedom space. Figure T3-26 shows the model and the relevant patch designations. The tether model is meshed with a 27-node parabolic brick.

Figure T3-26 Mechanical Spring Model

MemMech

While all solver control is through SpringMM, it uses the MemMech solver in the calculation. For correct results, you must configure the MemMech Setting dialog and clear the MemMech boundary conditions dialogs of any preset con-ditions. Because this tutorial starts with a new project file, all the boundary condition dialogs are inactive by default, and the Settings dialog has the default settings.


1. Set MemMech to run with the tether model and the default solver settings.

a. From the Analyzer tab, select MemMech from the Solvers pull-down menu.

b. Set the Model/Mesh file path to the tether model.c. Click on the Solver Setup icon.d. In the MemMech Settings dialog that opens, confirm the standard

settings as shown below.

The MemMech Settings dialog must be set properly in order to obtain correct results.

e. Click on OK.

fix_end1 (at the bottom of the anchor)

joint_end1




2. Set up SpringMM to run with the tether model.

a. From the Analyzer tab, select SpringMM as the solver.b. Set the Model/Mesh file path to the tether model. c. Select create a new analysis from the Analysis drop-down menu, and

click on the Solver Setup icon.

3. Set SpringMM to extract an mechanical, nonlinear, single-ended spring with full-factored DOFs.

a. In the Settings dialog, for Spring Physics, select Mechanical.b. For Mechanical Spring Type, select Nonlinear, single-ended.c. Set the DOF for a FullFactored simulation.d. Set Restart from previous result to No.e. Click on Next.


4. Fix the fix_end1 patch of the tether. a. In the SpringMM BCs window, click on fixed_patches.b. On the first line, apply the fixAll type to the fix_end1 patch.c. Click on OK.


5. Displace the joint_end1 patch of the tether. a. Click on displaced_patch.b. Apply the Displace FixType to the joint_end1 patch.c. Click on OK.



Figure T3-27 Mechanical Spring Moment Results


6. Verify the trajectory settings are set as they were for the electrical spring simulation (see page T3-44).

a. Click on trajectories.b. Make sure the Dz and Rx lines are set as they were for the electrical

spring simulation (see page T3-44).c. Click on OK.

7. Start the SpringMM simulation. a. In the MechSpringBCs window, click on Run.b. Save the analysis settings as mech_spring.

MemMech is started from this MechSpringBCs window.

The solver calculates reaction forces and moments and repeats the calculations for each trajectory step.


8. Verify the moments and reaction force results as shown in Figure T3-27 and Figure T3-28.

a. When the simulation is finished, click on the View Results icon.b. Select Moments table and verify the results shown in Figure T3-27.

The table displays reaction moments (torques) as the result of rotation of the joint_end1 patch.

c. Select Reaction Force, and verify the results shown in Figure T3-28.

The table displays reaction forces as the result of translational displacements of the joint_end1 patch.



Figure T3-28 Mechanical Spring Reaction Force Results

To visualize the reaction force, moment, and stresses in the tethers, set the Load Result to All results and open the Visualizer. The files produce a combination of two movements, as shown in Figure T3-29:

Figure T3-29 Mechanical Spring Model

The vertical motion of the joint_end1 of the tether (with the fix_end1 fixed) in five steps in the Z direction. This produces a +Z displacement at the joint_end1 and changes the reaction force associated with it. The rotational motion of the joint_end1 of the tether (with the fix_end1 fixed) in eleven steps around the X axis. This produces a twisting of the tether, changing the moment associated with it.

When finished, the mechanical characteristics of the spring model are fully specified for polynomial curve fitting in the next step.

Dz trajectory

Rx trajectory

fix_end1

joint_end1



Create Mechanical Spring Macromodel

You have completed a computation pass that included the MemMech solver run under SpringMM control. The solver computed the reaction forces and moments for the spring model to create a spring constant matrix. The next step is to obtain the polynomial coefficients needed for analytical representation of the elastic properties.


9. Configure the Create Macromodel dialog as shown below.

a. In the Analysis Results window under Macromodel, click on Create.b. Set the dialog as shown below.

The Split-Least-Square option specifies the curve-fitting algorithm to use when plotting the results. See page N2-19 for more explanation.

This is a simulated plot of moments in the X direction.

The plot coordinates are the Rx and Dz degrees of freedom.

The fourth order polynomial is selected.

You may use any string as a label, but capital letters and spaces are not allowed anywhere in the string.



After you click on the Fit and Plot button, the plot window appears, as shown in Figure T3-30. The plotted curve shows the same characteristics as the numerical results obtained with the SpringMM module.

Figure T3-30 Surface Plot of Mechanical Spring Polynomials

You may repeat the steps to plot reaction forces for other components of the matrix.

This concludes the mechanical spring solver sequence.


10. Plot the moment results for the Rx and Dz degrees of freedom.

a. Click on Fit and Plot.

The plot coordinates are the Rx and Dz degrees of freedom.b. After viewing the plot, close the Visualizer.


11. Create the mechanical spring macromodel. a. In the Create Macromodel dialog, click on Save Macromodel.

The SpringMM module creates a macromodel template file based on the coefficients generated.

The model .sin file and an associated symbol and help file are generated.

Part entries are made in the .aimpart user file in the user’s home directory for use with the Part Gallery in Saber.

b. Click on OK in the Create Spring Macromodel dialog.c. Click on Close in the Analysis Results window.

Control returns to the Analyzer tab.



InertiaMMThis sequence uses the InertiaMM solver to compute the mass and tensor of inertia of the movable parts of the mac-romodel. Figure T3-31 shows the model and the relevant patch designations. The mirror and tethers that support the mirror are meshed with a parabolic extruded mesh. To view this mesh, select the Analyzer tab, set the Model/Mesh file path to the mass model, and click on the Start Preprocessor icon.

Figure T3-31 InertiaMM Model


1. Set up InertiaMM to run with the mass model.

a. From the Analyzer tab, select InertiaMM as the solver.b. Set the Model/Mesh file path to the mass model.

The mass model has a mesh of the mirror and tethers.c. Click on the Solver Setup icon.

2. Configure the Settings dialog to run with the Original analysis type.

a. In the InertiaMM Settings dialog, select Original from the Analysis Type drop-down menu.

The mass model has not undergone any deformation, so the Original Analysis Type is selected.

b. Click on Next.

fix_end2

fix_end1top

mir_bot

mir_side2 / teth_joint2mir_side1 / joint_end1



Figure T3-32 InertiaMM Results


3. Select the mirror part to be included in the solver calculations.

a. In the Inertia BCs window that opens, click on part.b. In the part dialog that opens, set the Names List to mirror.

In this step you are selecting which parts to include in the calculations. c. Click on OK.

4. Start the simulation. a. Click on Run.b. Save the analysis results to mass.c. Save the settings when prompted.

The solver calculates the mass and centroid of the model.


5. Verify the InertiaMM numerical results. a. When the simulation is finished, select mass from the Analysis drop-down menu, and click on the View Results icon.

b. Select center_of_mass from the Tables drop-down menu, and click on the View Table icon.

c. Verify the table shown in Figure T3-32.

The table shows the mass and center of mass location for the model.d. Select moments_of_inertia and verify the results.

The table shows the moments of inertia for the model. The tensor of inertia is a symmetrical 3x3 matrix, which can be represented by the six terms shown below.

e. Select moi_at_center_of_mass and verify the results.

The table shows the moments of inertia at the center of mass of the model.



This completes the steps needed to characterize the electromechanical device in its degrees of freedom space and to generate all the data stored in various result files in the specified directories.

Several files are produced and stored in the default Mirror_Design\Schematics directory, including template (.sin), symbol (.ai_sym), and help (.hlp) files for Saber simulations.

This completes the model extraction procedure. The next tutorial section details how to construct a schematic with the macromodels generated in this tutorial.


6. Create the inertia macromodel using the settings shown below.

a. In the Analysis Results window, click on Create.b. Set the Create Macromodel dialog as shown below.

You are appending the inertia template with the mir label.

The macromodel will include the Dz (z) and Rx (rx) degrees of freedom.

c. Click on Save Macromodel.d. Click on OK.e. Click on Close in the Analysis Results window.



DampingMMIn this section, you will learn how to set up and run a DampingMM analysis for the mirror design. You will extract the macromodels that will be used to study mirror performance using Architect.

The two tethers are excluded from the solid model because their damping force is insignificant compared to the damping force caused by the rotation of the mirror. The simulation uses a symmetric model to reduce the required computations. Figure T3-33 shows the simulation model.

Figure T3-33 Mirror Meshed Model

SideSide

Side

Side

Side

Side

Bottom

Top



Rotational Squeezed Film Damper

Figure T3-34 DampingMM Settings


1. Set up DampingMM to run with the Damping model.

a. From the Analyzer tab, select DampingMM as the solver.b. Set the Model/Mesh file path to the Damping model.c. Click on the Solver Setup icon.

2. Set the DampingMM settings as shown in Figure T3-34.

a. Set the DampingMM Settings as follows:Rarefaction (Knudsen/Slip)?: NoSymmetry Factor: 2Starting Frequency: 1000Ending Frequency: 1.0E9Number of Frequencies: 30Reduced Model Order: 4

In the dialog, shown in Figure T3-34, we use a symmetry factor of 2 because the model includes only one half of the device.When the mass remains rigid, we use the Rigid Body setting and we do not perform a mode shape analysis. The frequency range for the simulation is 1 kHz -1000 MHz. The number of frequencies affects graphing only (not execution time).

See “Squeezed Film Damping” on page N4-3 for more information on setting up the DampingMM Settings dialog.

b. Click on Next.



Figure T3-35 Damping Surfaces for Rotational Squeezed Film Damper


1. Set the DampingSurfaces as shown in Figure T3-35.

a. In the DampingMM BCs dialog, click on DampingSurfaces.b. Set the Damping Surfaces as follows:

FixType: SqueezedFilmPatch1: bottomLoadValue: Squeeze_RotationEdit Squeeze_Rotation: see Figure T3-35.

The LoadValue for Squeeze_Rotation includes the gap thickness, which is 2 µm (from the mirror bottom to the electrode), the rotation axis (1, 0, 0), and the center of rotation (0, 0, 3.25).

See “Damping Surfaces Boundary Conditions Dialog” on page N4-24 for more information.

c. Click on OK.



Figure T3-36 EdgeBCs Dialog


2. Set the EdgeBCs as shown in Figure T3-36.

a. From the DampingMM BCs dialog, click on EdgeBCs.b. Set the EdgeBCs dialog as shown in Figure T3-36.

Edge corrections can only be applied to free edges, which model the corner turning of a fluid at an edge.

This setup defines the plane of symmetry at the face where the mirror was partitioned.

c. Click on OK.

See “Edge Boundary Conditions Dialog” on page N4-25 for more information.


3. Run the analysis and save it as rotation_squeeze_film.

a. From the DampingMM BCs window, click on Run.b. Save the analysis as rotation_squeeze_film.

For a more detailed explanation of the DampingMM module, see “DampingMM Macromodel Extraction” on page T4-103.


4. Verify that the Damping and Spring Torques graph is as shown in Figure T3-37.

a. When the simulation is finished, and click on the View Results icon.b. In the Analysis window, from the Graphs drop-down menu, select

Damping and Spring Torques.

c. Click on the View Graph icon.

d. From the menu bar at the top of the window, select Plot > Axis.e. From the Range tab, check the box Use Log Scale.f. Click on Close.g. Verify that the graph is as shown in Figure T3-37.



Figure T3-37 Damping and Spring Torques for Rotational Squeezed Film Damper

Figure T3-38 Damping Torque Coefficient for Rotational Squeezed Film Damper


5. Verify that the Damping Torque Coefficient graph is as shown in Figure T3-38.

a. View the Damping Torque Coefficient graph.b. From the Visualizer menu bar, select Plot > Axis.c. Under the Range tab, check the box Use Log Scale.d. Click on Close.e. Verify that the graph is as shown in Figure T3-38.

6. Close the Visualizer. a. In the Visualizer, select File > Exit.



Figure T3-39 Create Rotational Film Damping Macromodel

Translational Squeezed Film Damper


7. Create a macromodel using the rotation_squeeze_film analysis results. Set the fields as shown in Figure T3-39.

a. In the Analysis Results window, click on Create....b. Set the fields in the dialog as follows:

Format: MASTComponent Label: rotational_film_dampingAdd to user library? Yes

See Figure T3-39.c. Click on the Save Macromodel button.d. Click on OK in the DampingMM Message dialog and on the Create

Macromodel dialog.e. Close the Analysis Results window.


1. Create a new analysis for the Damping model.

a. In the Function Manager, in the Analyzer tab, make sure that the Model/Mesh selected is Damping.

b. For the Analysis field, select create new analysis.c. Click the Solver Setup icon.d. Verify that the DampingMM Settings are as shown in Figure T3-34, and

then click Next.

The DampingMM Settings should not change from the previous analysis.

2. Set the DampingSurfaces as shown in Figure T3-40.

a. From the DampingMM BCs window, click on DampingSurfaces.b. Change the LoadValue to Squeeze_Normal and set the value to 2.

Squeeze_Normal is used for translational motion.

See Figure T3-40.c. Click on OK.

The EdgeBCs remain the same.

3. Run the analysis. a. From the DampingMM BCs window, click on Run.b. Save the analysis as translational_squeeze_film.



Figure T3-40 Damping Surfaces for Translational Squeezed Film Damper

Figure T3-41 Damping and Spring Forces for Translational Squeezed Film Damper


4. Verify that the Damping and Spring Forces graph is as shown in Figure T3-41.

a. When the simulation is finished, click on the View Results icon.b. In the Analysis window, from the Graphs drop-down menu, select

Damping and Spring Forces.c. Click on the View Graph icon. d. From Visualizer menu bar, select Plot > Axis.e. From the Range tab, check the box Use Log Scale.f. Click on Close.g. Verify that the graph is as shown in Figure T3-41.

5. Verify that the Damping Force Coefficient graph is as shown in Figure T3-42.

a. Open the Damping Force Coefficient graph.b. Verify that the graph is as shown in Figure T3-42.

6. Close the Visualizer. a. In the Visualizer, select File > Exit.



Figure T3-42 Damping Coefficient for Translational Squeezed Film Damper

Figure T3-43 Create Translational Film Damping Macromodel


1. Create a macromodel called translational_film_damping using the dialog shown in Figure T3-43.

a. In the Analysis Results window, click on Create....b. Set the fields in the dialog as follows:

Format: MASTComponent Label: translational_film_dampingAdd to user library? Yes

See Figure T3-43.c. Click on the Save Macromodel button.d. Click on OK in the DampingMM Message dialog and in the Create

Macromodel dialog.



3.3.3: System Model of the Mirror: Schematic CreationIn this section, you will create a system model using the macromodels created in the first part of tutorial and other parts from the MAST Library. You will then perform a series of simulations. The tutorial compares system model results with those obtained using the FEM approach, and shows excellent correlation between the two solution meth-ods.

Schematic AssemblyThis tutorial sequence assumes that the user is familiar with the Saber framework and the general features introduced in the Saber tutorial starting on page A3-2. If not, go through that tutorial before attempting to continue with this one.


1. Select the mirror.proc process file. a. In the Function Manager, click on the Architect tab.b. Click on the arrow to the right of the Process file field and select the

mirror.proc file from the drop-down menu.

A process file is used to define the knot properties. The z component of the knot location is the center of the layer thickness, which is defined in the process file.

The process file provided with this tutorial is the original process file used for the creation of the 3-D models used for model extraction.

2. Start Saber. a. Make sure that the Schematic field is displaying create a new schematic.

b. Click on the Saber icon.

c. Maximize the Schematic window.

This starts the SaberSketch software. The new schematic already includes the reference frame (page A4-10) and COVENTOR symbol (page A4-9).



Figure T3-44 User CoventorWare Library in Parts Gallery


3. Place the electrical spring macromodel you created, in the schematic. a. Click on the Parts Library icon on the bottom of the Saber

Sketch window.b. In the Parts Gallery pane, make sure the Browse pane is active, and select

User CoventorWare Library. See Figure T3-44.c. Select the Electrostatic Spring category, and then select

espring_mir_rx1z1_o4.

The electrostatic spring symbol and model were created during the macromodeling sequence, and written to the User CoventorWare library (a personal catalog written in the .aimpart_user file in the home directory).

d. Click on Place Part (or double click on espring_mir_rx1z1_04 in the parts list.

The electrostatic spring symbol appears in the Schematic window (see Figure T3-45)

4. Place the DampingMM macromodels you created, in the schematic.

a. Under User CoventorWare Library, select the DampingMM category.b. Select and Place the following parts:

Film Damping (rotational_film_damping_rot) Film Damping (translational_film_damping_trans

Note that the original component labels given have been appended with _rot and _trans as appropriate. See Figure T3-44.

c. Right click on the rotational film damper and select Flip > Left-Right.

See Figure T3-45.



Figure T3-45 Extracted Mirror Models


5. Place the mechanical spring macromodel and the inertia macromodel, in the schematic.

a. In the Parts Gallery Categories list, double click on the Mechanical Spring folder.

b. Double click on the tether_mir_rx1z1_o4 part to place.c. From the Proof Mass folder, place the inertia_mir_rx1z1 part.

The five symbols you placed are shown in Figure T3-45.d. Do not close the Parts Gallery pane.




6. Place two universal ground symbols, a short, a pulse voltage source, a translational stop model, and a rotational stop model in the Schematic window.

a. From the Parts Gallery pane, click on the Search tab.

b. In the Search String field, type gnd, then click on the Search icon.

c. Double click on the Ground, (Saber Node 0) symbol to place. Place nine more instances of the ground symbol.

d. In the Search String field, type short, then click on the Search icon.e. Double click on Short to place.f. Search for source.g. Scroll down, to find the Voltage Source, Pulse and double click on it to

place.h. Search for stop.i. Double click on Stop, Translational, Elastic to place.j. Double click on the Stop, Rotational to place.k. Search for connector.l. Place the Mechanical bus connector.m. Close the Parts Gallery pane.

The translational and rotational stop components require the OPT_TEMPLATE_LIB license feature. If you do not have this license feature, you can still run the tutorial simulations. But when you are running the transient analysis to determine pull-in, you will have to stop the simulation when you see warnings of "Reference point is outside the extracted range." Manually stop the simulator by clicking the Interrupt icon. Then select Results > View Plotfiles in Scope, and click on OK to view the Last plotfile.




7. Place the needed components as shown in Figure T3-46.

a. Rearrange the placed symbols on the screen in the approximate positions shown in Figure T3-46:

Use the Zoom and Pan icons to see all the terminals for proper placement and connection.To copy a part, select it, then press Ctrl + C or select Edit > Copy.To paste a part, press Ctrl + V or select Edit > Paste.To paste a part you can also click on an existing symbol to identify it, then click with the middle mouse button to paste. To rotate or flip a part, select it, and then right click to select Rotate or Flip. Note that a part is rotated in the counterclockwise direction.

For more guidelines on arranging parts, see page A3-5.

8. Wire the components as shown in Figure T3-46. Name the central wires dz and rx.

a. Connect the terminals with wires, being careful to make the correct connections.

To connect the terminals, you can click on the terminal of one part, and then click on the corresponding terminal of the part you wish to connect to. To connect all the terminals of one part to all the terminals of another part, position the parts so their respective terminals overlap, and then move the parts away from each other.

To connect the v_pulse and the shorted ground to the E-Spring, create a small wire connected to the E1 terminal. Right click on the wire and select Rip Wire. Then connect the v_pulse to the 1 signal and the short to the 0 signal.

For help on wiring parts in a schematic, see page A3-6.b. When you finish, verify the complete schematic model of the system as

shown in Figure T3-46.

The schematic reflects the changes still to be made in subsequent steps and enlarges the text for better viewing.

c. Double-click on the central wire connecting the z terminals of the translational stop and the bus connector.

d. In the Wire Attributes dialog, change the Name to dz, then click on Apply. Leave the dialog open.

e. Click on the wire connecting the rx terminals of the rotational stop and the bus connector. Name it rx. Click on Apply, then on Close.

Debug wire connection problems by accessing the Schematic Editor menu bar: select Edit > Find > Select..., choose a Wire Search Type, and Select a Saber-named wire from the list. The connections will highlight in green on the screen. See the dialog below.



Figure T3-46 Complete Schematic Model

In the schematic shown above, the E-Spring, Tethers, and Inertia models are the main mirror components created dur-ing the macromodeling sequence. The generated macromodels are members of the Architect family, so they share the reference frame definition (see page A4-10) and a common mechanical interface (see page A2-1).

All Architect components and wires in the same schematic are subject to a common coordinate system called the ref-erence frame. All extracted macromodels have two standard parameters, Origin and Orientation, that are used to define the position and the orientation of the underlying substructure in the reference frame (see page N2-30 for usage in SpringMM macromodels, and page N3-6 for usage in InertiaMM macromodels). The default values of both param-eters only need to be changed if the reference frame does not match the coordinate system of the extracted 3-D model.

For the sake of simplicity and in order to avoid unnecessary confusion, it is a good practice to work with the defaults as much as possible. For our mirror schematic we will therefore define our reference frame as aligned with the coor-dinate system of the initial 3-D model in Figure T3-22. With the parameter defaults, the Inertia, the E-Spring and the Tether model on the right-hand side already “know” their correct position and orientation in the reference frame. Because both tethers were extracted from the same 3-D model (see Figure T3-29), the parameters of the tether on the left-hand side need to be modified. Note that just copying and flipping the tether symbol is not sufficient. The place-ment of the symbol in the schematic is irrelevant as long as the parameters of the symbol are adjusted to account for the difference in orientation and origin.



The Properties window also allows access to a Help screen (along the menu bar, click on Help > Help on Part). The Help menu for CoventorWare macromodels looks different from the help for the Saber symbols because these mes-sages are generated from the .hlp files built during macromodel creation. A sample Help screen is shown below.


9. Change the labels on each tether. Assign the properties of the left tether model as shown below.

a. Double click on the right tether symbol and change the label to Tether. Click on OK.

b. Double click on the left tether symbol and change the label to Tether.c. Click on the origin Value field. In the dialog that opens, make the X value

of the origin negative.

If you click on the origin parameter of the right tether, you will see that its default origin at X is 3.9u; this marks the center position of the spring patch in the mesh model coordinate system. For the left tether, this value is made negative, therefore connecting this tether to the left side of the plate.

d. Click on the orientation Value field. In the dialog that opens, define the rz value as 180.

Change the default orientation of the local mesh coordinate system in the reference frame with Orientation.The rz =180 value accounts for the tether being flipped; so the tether’s fixed end is pointing in the negative X direction.

e. Click on OK.

The knot1 value will be set in a later step.



The help window includes information about the origin of the macromodel and descriptions of the available model parameters.

All components that are connected by the same mechanical wires have to have identical knot parameters. Please refer to page A2-1 for more details on the mechanical interface and the concept of knots. For our mirror design we are most interested in the motion of the plate center. We will therefore place the knot in the plate’s center of mass by specifying the mirror layer.


10. Specify the mirror layer for the knot1 property of all four macromodels.

a. Select the inertia, mechanical spring, and electrical spring macromodels while holding down the Shift key.

The knot parameter of all selected models will be specified at the same time.

b. Release the Shift key.c. Move your mouse pointer over one of the selected macromodels and

click on the right mouse button.d. Select Properties.e. Double click on the knot Value field.f. Double click on the z_layer field, and specify the mirror layer, as shown

in the dialog below.

Because you are specifying a layer from the process description, the knot location is defined by the depth of that process layer.

g. Click on OK.



The translational and rotational stops in the mirror schematic (compare with Figure T3-46) are applied to the knot’s Dz and Rx degree of freedom, respectively. Both stop models will ensure that the plate motion is restricted to the extracted range of values (set in the SpringMM trajectories dialog).


11. Double click on the voltage model and assign the properties as shown below.

a. Double click on the v_pulse symbol.b. Set the dialog as shown below. Make sure to enter the correct units.c. Click on OK.


12. Double click on the rotational stop model, and assign the properties as shown below.

a. Double click on the stop_r symbol.b. Set the dialog as shown below.

The rotational stop will restrict the knot (plate) rotation within -0.1 and 0.1 rad (-7 to 7 degrees).



The schematic is now complete: all components have been placed, all wires have been connected, and all properties have been assigned. Save your work, and then create the netlist required to perform the simulation.


13. Double click on the translational stop model, and assign the properties as shown below.

a. Double click on the stop_t symbol.b. Set the dialog as shown below.

The translational stop will restrict the knot’s (plate center) vertical motion within -0.2µm and 0.2µm.


14. Save the schematic and netlist. a. From the Schematic Editor menu bar, select File > Save.b. In your Mirror_Design\Schematics directory, save the schematic as

macromodel_mirror (with no extension).c. From the Schematic Editor menu bar, select Design > Netlist.

If no errors were made while assembling the schematic, the netlisting will proceed quickly.

The netlist function transforms the captured schematic into a program-readable file that contains all instances of models and their connections in the circuit.

You can view the Netlist Transcript window by selecting View > Show Netlist Transcript.

A Saber schematic cannot have a name starting with a number.



3.3.4: FEM Performance AnalysisThis section briefly shows the results obtained using the CoventorWare FEM solvers. The results for modal and pull-in analysis of the mirror design can then be compared to the results from the system model, which you will perform in the next section. Note that the system model approach makes a number of simplifying assumptions, so the Saber results will be somewhat different.

Rather than proceed through all the steps of the FEM analysis, the results are presented here. The multi_mesh _prebuilt model, which was used to generate the results, is included in the tutorial model database if you would like to run the simulations. It is identical to the multi-volume model created in first Mirror Design tutorial (see page T3-14).

Below is the table of mode frequencies obtained through a MemMech modal analysis extracted for four modes (see page T3-22 for the setup). For the two degrees of freedom system model, only two modes of oscillations are present: a rotational mode around the X-axis (mode #1 in the table), and a translational mode along the Z-axis (mode #4 in the table).

Figure T3-47 Modes Shapes for Modes 1 and 4

Another set of results that is useful for comparison between the FEM and system model simulation is a simple DC sweep analysis, which reveals the pull-in phenomenon. Figure T3-48 shows the pull-in results obtained with CoSolve. For this problem, the boundary conditions were set as follows:

MemMech Surface BCs: fixAll boundary condition applied to torsion tether ends fix_end1 or fix_end2.A RigidLink between master and slave patches. (Note: rigid links are set to save time and simulation effort, but at the expense of accuracy.)CoSolve Settings: Voltage as the Independent variable, Detect Pullin Analysis Option, Relaxation Iteration Method.CoSolve Trajectory BCs: Delta trajectory steps from 0 to 25 in increments of 2.5 volts.CoSolve ConductorBCs: electrode2 has 1 volt and a Voltage1 variable applied.CoSolve VoltageBCs: tl trajectory applied to Voltage1.

Mode 1 rotational Mode 4 translational



Figure T3-48 Pull-In Results with CoSolve

Pull-in occurs at around 20.6 volts. In the next section, you will use Saber to generate system model results to com-pare to the FEM results presented here.



3.3.5: System Model Performance AnalysisThis section performs a system model analysis of the mirror using Saber. It demonstrates transient analysis and the simulation of the device in a fraction of the time of a full FEM analysis for similar accuracy. In the sequence, you can compare the results with those from the previous section using CoventorWare FEM solvers. DC operating point, small signal AC, DC transfer, and transient analyses will be performed.


1. Simulate the schematic. a. From the Schematic window, select Design > Simulate.

The Simulate function reads the netlist file into Saber and checks for any model errors. It also enables a second row of icons.

b. Click on the icon to view any errors in the Transcript window.6c. Verify that the simulator shows “Saber Ready” in the top right corner.

2. Run a DC operating point analysis and extract the results for dz and rx. a. Click on the DC Operating Point icon.

b. For Monitor Progress, enter 100.c. For Display After Analysis, click on Yes.d. Click on Open Display Form.e. Click on the Waveforms tab and enter /dz /rx for the Signal List.f. Click on Close, and then on OK.g. View the results in the Report Tool window.

The Analysis takes into account only initial values set in the source Property dialogs.

Note that the dz results are very small and represent numerical noise. So this result may vary from machine to machine.




3. Run a small signal AC analysis with the parameters described in the Detailed User Procedure column. Plot the results in CosmosScope.

a. In the Sketch window, click on the Small Signal AC icon.b. For Start Frequency, enter 1.c. For End Frequency, enter 3meg.d. Increase the Number of Points from 100 to 1000.e. For Monitor Progress, enter 100. f. For Plot After Analysis, click on the down arrow, and select Yes - Open

Only.g. Click on the Input Output tab.h. For Signal List, enter /dz /rx and click on OK.

The c_sin sources on the left hand side of the reference frame symbols serve as the stimuli of the AC sweep. Hence, the plate mass is indirectly exited by the vibration and oscillation of the reference frame (substrate)

This simulations yields mechanical results for comparison with FEM analysis.

i. When the simulation is finished, in the signal list window that opens, use the Ctrl key to select dz and rx; click on Plot.

j. Verify your results in CosmosScope as shown below.

The plot shown above has a white background. To set the plot to a white background, select Graph > Color Map > Mono or Map 2. The Mono option displays the plot on a white background with a black plot curve. The Map 2 option displays the plot on a white background with a color plot curve.



Next, the pull-in characteristics of the mirror will be explored by gradually increasing the voltage applied to the elec-trodes.


4. Adjust the display of the signals to show the maximum peak measurements for the dz and rx signals.

a. In the legend area to the right, left click on the Phase rx line, and then right click and select Delete.

b. Repeat for the Phase dz signal.c. For each trace, click on the plot, then click on the Measurement icon at

the bottom of the Scope window.d. Click on the Measurement button (labeled At X), and select General >

Local Max/Min.

The sequence performs an AC analysis of the system model with mechanical harmonic excitation. Results should resemble the picture below.

Observe the excellent rotational frequency match: 134.74 kHz (FEM modal analysis mode 1 results on page T3-75) vs.134.44 kHz for the rotational resonance around the X-axis.

Observe the excellent translational frequency match: 381.7 kHz (FEM modal analysis mode 4 results on page T3-75) vs. 405.81 kHz for the translational resonance along the Z-axis mode.




5. Change the schematic to apply a slowly increasing voltage to the electrode.

a. Save the schematic design as Macromodel_Mirror_PWL.ai_dsn.b. Replace the pulse voltage source with a Piecewise Linear Voltage source

(Voltage Source, PWL) from MAST Parts Library/Electronic/Electrical Sources/Voltage Sources.

c. Double-click on the source. In the Properties dialog, click on the pwl field.d. In the Graph Editor that opens, set the first point to time = 0, voltage = 0.

Press the tab key to enter the next point.e. Set the second point to time = 25, voltage = 25. Click on OK to close the

Graph Editor, and click on OK to close the Property editor.

To find the pull-in voltage, slowly increase the voltage over 25 seconds at a rate of 1 volt per second.

6. Run the simulation to compute the response to the varying voltage. a. Click on the Transient Analysis icon.

b. For End Time, enter 25.c. For Time step, enter 0.1.d. For Monitor progress, enter 10.e. Set Run DC Analysis First to Yes.f. For Plot After Analysis, select Yes - Replace Plots.g. Click on the Input Output tab. Enter /dz /rx for the Signal List.h. Click on OK.

In the Saber Transcript window you will see every 10th time point that the simulator solves the force balance equations. As the simulator approaches the pull-in voltage (around 20V), it will take gradually smaller time steps to resolve the pull-in voltage accurately.

When the simulator reaches the pull-in voltage, it must determine the new solution contacting the stops. This step of finding this pull-in state sometimes generates warning messages because the solver will often overshoot the valid range of the extracted models in an attempt to find a solution. Always check the simulation result after one or more warnings appear. Note that suppressing the range check by setting the common model parameter display_messages=none can speed up the simulation significantly.

In some cases, a simulation may fail with an error indicating too many iterations. The physical system and its mathematical model become unstable around the pull-in voltage, and there is no equilibrium state because the electrostatic forces of attraction dominate the elastic reaction forces. For example, if the stop models are removed, then after pull-in, there is no force-balance solution for the solver to find.

Experienced users of ARCHITECT will note that a slow transient analysis was used here instead of the typical DC Transfer analysis. A slow transient analysis can be more robust and is the only option available when using the Saber translational stop model.

If you do not have the translational and rotational stop components in your schematic, you will have to stop the simulation when you see warnings of "Reference point is outside the extracted range." Click on the Interrupt icon to stop the simulation. Then select Results > View Plotfiles in Scope, and click on OK to view the Last plotfile.



Figure T3-49 Transient Pull-in Results


7. Plot the dz and rx results in CosmosScope. a. When the simulation is finished, in the Graph window, right click and select Clear Graph.

b. In the signal list dialog, Ctrl select dz and rx; click on Plot.c. Click on the rx signal to select. Select the Measurement icon General/

Threshold (at Y) for plot annotation. Enter -0.1 in the Y value field. d. For the dz signal, select the Measurement icon’s General/Local Max/

Min.e. Verify the results as shown in Figure T3-49.

The correlation with pull-in curve obtained with the FEM approach is good. The FEM simulation results on page T3-76 shows a pull-in voltage of 20.6-20.9 volts, and Saber shows a voltage around 19.8 volts.

Note that the goal of this simulation was the determination of the pull-in voltage only. The behavior after and during pull-in is not physical for this simulation since we have not included any damping. Next we, will perform a transient simulation with appropriate damping and on a realistic time scale.

f. Exit the CosmosScope and SaberSketch windows.



Until this point, the motion of the rigid plate was not affected by any form of damping. The effects of gas damping have been added to our schematic by extracting rotational and translational squeezed film damping macromodels with CoventorWare’s DampingMM module. In this next simulation we will run another transient simulation that will demonstrate how damping affects the mirror movement. This transient simulation has a smaller end time and a faster rise time than the previous transient simulation, so the damping effect becomes more important.

Figure T3-50 Transient Analysis Setup


1. Open the original schematic (with the pulse source).

a. From the Function Manager Architect tab, select macromodel_mirror.ai_sch from the Schematic drop-down menu.

b. Open the schematic.

2. Netlist and simulate the design. a. Netlist and simulate the design.

3. Run a transient analysis with the parameters as shown in Figure T3-50.

a. Click on the Transient Analysis icon. b. For End Time, enter 7m.c. For Time Step, enter 0.1u. d. For Monitor Progress, enter 100. e. For Run DC Analysis First, select Yes.f. For Plot After Analysis, select Yes - Open Only.g. Click on the Input Output tab.h. For Signal List, enter /dz /rx.i. Click on OK.

The transient analysis of the system model takes only a few minutes and is therefore orders of magnitude faster than the calculation of the transient response using the FEM approach.



Figure T3-51 Damping Results


4. Plot the dz and rx results in CosmosScope. a. In the signal list window, Ctrl select dz and rx; click on Plot.b. Verify your results in CosmosScope.

The good match of FEM results and system model simulation results observed in previous steps assures that the results of this transient analysis are realistic and reliable.

c. Click and drag on the x axis to zoom in on the signals between 500u and 1.2m.

From the plots it is clear that damping plays a major role in the performance of the device when operating at faster speeds.

Zoomed in

Initial



3.3.6: SummaryThis tutorial demonstrates the techniques required to perform a system-level simulation using a simple system model example. The results are compared with CoventorWare FEM solver simulation results and show good correlation. While the FEM approach is more accurate, the system model approach significantly speeds the computation process.

Because the system model approach makes approximations and compromises in setting up and running the simula-tion, the user should examine the numbers and graphs carefully to be sure the results are acceptable. If not, the prob-lem may not be with Saber but with the assumptions and setup conditions used in creating the macromodel components. Accuracy of the system model simulation depends on the accuracy of the polynomial fit obtained while characterizing the individual macromodels in the macromodeling solvers. Accuracy can be improved if the range of macromodel characterization coincides with the operating range of the system model. In addition, more accurate models are created in the macromodeling solvers when fewer simplifying assumptions are made. For example, the m_cap parallel plate capacitor model can be replaced with a model that includes volume-meshed electrodes, a vol-ume-meshed mirror, and a ground plane to more accurately model capacitance effects. Furthermore, to take cross couplings between the two electrodes into account, the complete mechanical structure plus electrodes can be extracted as a single electromechanical spring. The complete system model of the mirror could be built with only two extracted models: one inertia and one electromechanical spring.

3.3.7: References1 N.R.Swart, S.F.Bart, M.H.Zaman et. al. AutoMM: Automatic generation of Dynamic Macromodels for MEMS

Devices. Proceedings of the IEEE, 11th Annual International Workshop on MEMS, Jan. 25-29, 1998, pp.178-183.

2 S. D. Senturia, CAD Challenges for Microsensors, Microactuators and Microsystems. Proceedings of the IEEE, Special Issue on MEMS, August, 1998.


Section 4: Gyroscope Design Introduction Version 2008M


4.1: IntroductionCoventorWare provides a comprehensive, integrated suite of tools for MEMS that enables rapid exploration of pro-cess and design options. The Architect suite allows system-level designers to simulate and rapidly evaluate multiple design configurations using a top-down, system-level approach. When the overall model has been sufficiently designed and analyzed, the schematic can be exported and viewed in Designer’s 2-D Layout Editor or used to create a 3-D model, then meshed and resimulated using Analyzer’s FEM and BEM solvers. The Integrator suite allows users to create custom macromodels from FEM/BEM meshes that can then be incorporated in an Architect system model. This section shows how the entire CoventorWare suite can be used to build, simulate, and optimize a design using the example of a Z-plane gyroscope.

The tutorials in this section demonstrate Architect, Designer, Analyzer, and Integrator capabilities, includingSchematic Creation: This tutorial demonstrates how to build an accurate system-level model of the Z-plane gyroscope model using Parametric Electro-Mechanical Library components. This section starts on page T4-5.Schematic Layout Verification: This tutorial shows how to open a schematic in Scene3D to view a 3-D model that corresponds the current schematic configuration. This step helps you verify that your individual components have the right dimensions and that they are wired together correctly. This section starts on page T4-31.Architect Analysis: This tutorial shows how to use ARCHITECT Saber to analyze, validate, and optimize the model through the use of parametric analyses that vary both structural parameters of the gyroscope and environmental conditions. This allows refinement of the model for verification at the system level. This sec-tion begins on page T4-32.FEM and Architect Comparison: This tutorial demonstrates how to use the extracted 3-D model to verify some of the system-modeling results with finite element and pull-in analysis using the two Analyzer modules MemMech and CoSolve. This section starts on page T4-73.Mesh Convergence Study: This section shows how to validate a device mesh by varying the mesh element size and mesh element type. It presents mesh convergence study results for the gyroscope and gives recom-mendations for optimizing a mesh. This section begins on page T4-87.Design Modification Using Integrator: This tutorial demonstrates how certain aspects of the parametric schematic can be enhanced using the macromodel extraction. It shows how to use Integrator’s SpringMM module to generate a macromodel from a U-shaped beam and then use the macromodel in the original gyro-scope system-model. This section begins on page T4-141.Package Design with Analyzer: This tutorial demonstrates the effects of the ambient temperature of a pack-age on the performance of a packaged sensor. The package is a modified version of Kyocera’s SMD_KD_V99902_A model, while the sensor is the tutorial gyro modified with anchors on the beams and combs. This section starts on page T4-151.

4.1.1: Tutorial RequirementsAn Architect PEM license is required to run these tutorials. The license includes a standard Saber installation and the Parametric Electromechanical Library.

The following files are also required to run the tutorials:

...\Gyroscope\Devices\Gyro.proc.This process file has the deposit, etch, and material descriptions to be used in the schematic and in the FEM validation.


Section 4: Gyroscope Design Introduction Version 2008

...Gyroscope\Schematics\gyro_prebuilt.ai_sch - Final gyroscope schematic.The schematic file gyro_prebuilt.ai_sch is not needed for users who intend to go through the tutorial from begin-ning to end, though it may be used to validate the design. It is provided for users who wish to bypass schematic work and begin with simulation, netlisting, and design analysis. The prebuilt schematic and associated files are copied to the Schematics directory when importing the tutorial files at the beginning of the tutorial sequence.

4.1.2: Gyroscope OperationMicromachined (gyroscope) sensors measure angular velocity by utilizing the Coriolis effect, a direct consequence of a body’s motion in a rotating frame of reference. In a fixed frame of reference, assume that a mass oscillates with velocity vy (in the Y direction). If the frame of reference begins to rotate at a rate Ωx about the X-axis, this mass is then subject to a Coriolis force and a corresponding acceleration equal to 2Ωx x vy. The Coriolis acceleration, az, is perpendicular to the plane containing the velocity (oscillation) and the rotation vector. The Coriolis effect may thus be thought of as an energy transfer process from a primary mode (Y) of oscillation into a secondary mode (z) that can be measured. It is this excitation of the secondary resonance mode that forms the basis of detection using the Coriolis effect. Highly symmetrical elements such as rings, cylinders, or disks use the resonant frequency, which is degener-ate. There are two distinct modes of resonance sharing the same oscillation frequency. The resonant frequency degen-eracy causes the primary mode (excitation signal) to be in phase-quadrature with the secondary mode (sense signal), thus maximizing coupling between the two modes and improving accuracy and sensitivity.

The Z-plane gyroscope in this tutorial uses a perforated rectangular plate mass suspended by four two-segment flex-ures, two comb drives, and three electrodes. The gyroscope is designed to resonate in its fundamental mode parallel to the substrate plane (Y direction) and is excited via two comb drives as shown in Figure T4-1. If the gyroscope is subjected to an external angular velocity about the X-axis, the velocity of the mass in the Y direction results in a Cori-olis force acting on the mass in the vertical Z direction of the substrate. Because the perforated mass and the rectangu-lar electrodes include a parallel plate capacitor, the resulting oscillatory motion is electrically sensed in this direction, which enables determination of the inertially induced Z-displacement, and hence rotation of the gyroscope about the X-axis.

Figure T4-1 Gyroscope Model

Comb (drive) capacitorElectrode

Parallel plate (Coriolis sense)

Electrode

Electrode underplate not seen

capacitor


Section 4: Gyroscope Design Introduction Version 2008M

4.1.3: Gyroscope Design Parameters The gyroscope schematic, dimensions, and other geometrical properties, along with mechanical and electrical proper-ties are shown in Figure T4-2. The properties are listed in Table T4-1.

Figure T4-2 Gyroscope Dimensions


Section 4: Gyroscope Design Introduction Version 2008

Table T4-1 Gyroscope Properties

Properties Variable Name Value

Electrical Characteristics

DC value of comb voltage source dc_comb 13.4

DC value of electrode voltage source dc_electrode 0.1

resonance frequency in the direction of excitation f_yr 7177.4

Dimensions

length of vertical beam suspensions length_beam1 600u

length of horizontal beam suspensions length_beam2 150u

width of vertical beam suspensions width_beam1 7u

width of horizontal beam suspensions width_beam2 5u

distance between perforation holes plate_line_width 20u

plate size in X direction plate_size_x 400u

plate size in Y direction plate_size_y 400u

number of plate holes in X direction plate_num_holes_x 10

number of plate holes in Y direction plate_num_holes_y 10

electrode protrusion in X direction electrode_protrude_x -plate_line_width/2

electrode protrusion in Y direction electrode_protrude_y -(plate_size_yplate_num_holes_y + plate_line_width/2)

length of comb fingers finger_length 80u

width of comb fingers finger_width 6u

distance of finger center lines finger_pitch 20u

overlap of comb fingers finger_overlap 40u

number of fingers finger_num 20

lateral offset of fingers finger_lateral_offset 0

finger anchor width finger_anchor_width 24u

plate curvature coefficient c 0

Damping Coefficients

X-translation damping coefficient plate_damping_cx 100n

Y-translation damping coefficient plate_damping_cy 100n

Z-translation damping coefficient plate_damping_cz 400n

X-rotation damping coefficient plate_damping_crx 1m

Y-rotation damping coefficient plate_damping_cry 1m

Z-rotation damping coefficient plate_damping_crz 4m


Section 4: Gyroscope Design Schematic Creation Version 2008M

Layer thickness information is extracted from the process file. Young’s modulus, Poisson’s ratio, and density infor-mation is extracted from the Material Properties Database file.

4.2: Schematic CreationIn this section you will assemble a system model of the gyroscope using the Architect module, components of the Parametric Electromechanical Library, and other provided generic components (for example, voltage sources).

The tutorial demonstrates several techniques:how to input process information to a schematichow to assign global design variables for use in any schematic componenthow to use the EM parametric library to create a Z-plane gyroscopehow to create the wires that connect the componentshow to assign values and properties to componentshow to use design symmetry to make schematic creation and property assignment easier

4.2.1: Schematic Creation GuidelinesRefer to the reference section beginning on page A5-1 for descriptions of library components used in this section and in the rest of the tutorial. The procedures assume familiarity with the Saber environment. For an introduction to Saber, see page A3-1.

ComponentsThe gyroscope consists of beams, a perforated rectangular plate mass, three rectangular electrodes, and two comb drives. Beams are considered as purely mechanical components and are described in this system model using the parametric EM library component beam. The inertial behavior of the central plate of the gyroscope is captured in the parametric EM library component rigid_plate. A capacitor is formed by the perforated plate and the electrode. This capacitor is electrostatically represented by the electrode library component. Combs (whose mass is incorporated in the rigid_plate) are described in this system model using the straight_comb to represent the electrostatics.

ConnectivityThe gyroscope schematic contains both electrical and mechanical components. Each component has one or more ter-minals. These terminals belong to one physical domain. Two quantities are associated with each terminal: across quantity and through quantity. These quantities vary depending on the terminal’s domain:

For the mechanical domain, two types of degrees of freedom are present: Translational DOF, for which across quantity is position (x, y, z) and through quantity is force (Fx, Fy, Fz), and Rotational DOF, for which across quantity is orientation (rx, ry, rz) and through quantity is torque (Mx, My, Mz).

For the electrical domain, across quantity is potential and through quantity is current.

The mechanical domain interface is contained in a bus port. Bus ports are single connections that contain six wires representing the six mechanical degrees of freedom (x, y, z, rx, ry, rz). Having a single bus wire instead of six wires makes schematic wiring easier. The resulting schematics are smaller and clearer than they would be if each compo-nent had six wires. The mechports_bus_connector component can be added to the schematic to extract the individual wires for plotting in CosmosScope. It can also be used to connect bus models with the six-wire models.


Section 4: Gyroscope Design Schematic Creation Version 2008

A connection between two or more terminals creates a node. Like terminals, nodes can only belong to one physical domain. The node’s domain is inherited from the terminals connected to this node. This leads to the following rules:

Mechanical domain terminals can only be connected to other mechanical domain terminals. Electrical domain terminals can only be connected to other electrical domain terminals.

KnotsThe user must define a knot (a point in space with a defined position) each time a node is created in the mechanical domain (see “Mechanical Interface and Knot” on page A2-1). All parts with a standard mechanical interface have a knot property. Guidelines for setting knots include the following:

For a node associated with one or more parametric mechanical parts, the knot coordinates specified by the user refer to its initial position in the reference coordinate system. Because a parametric mass is rigid, only one knot is needed. This knot does not have to be the center of mass. A parametric beam has a knot associated with each end. The knot positions of connected parts must be identical. For example, two connected beams share the same knot at the node where the ends meet.

All parts that are connected with the same mechanical wires must refer to the same mechanical knot (have the same coordinate value for the knot property) to ensure the system model will simulate correctly. The initial knot position does not affect the accuracy of the simulation. However the initial position of the knot is important for the interpreta-tion of the simulation results. Because the connected mechanical wires provide the values of the relative motion and rotation of the knot, it is important to know the original position of the knot in the reference coordinate system.

When only two parts are connected together, the knot should reflect the connection point in space. When more than two parts are connected together, the knot should reflect a point such as either the center of mass or a common inter-section point.

4.2.2: InitializationDuring this initialization process, you will specify a Material Properties Database, select a process file, and create a name for the working schematic.


1. Start CoventorWare and import the Gyroscope tutorial.

a. Start CoventorWare.b. In the Projects dialog that opens, click on the Import Tutorials icon.c. In the Import Tutorials navigation dialog, select the Gyroscope

project from the list. Click on OK.d. In the Projects dialog, a default Settings file appears on the Settings

file line. Click on Open.e. Select the Architect tab.



Figure T4-3 Gyroscope Process


2. Set the Material Properties and Process files. Open the Process Editor and review the process.

a. Using the folder icons to the right of the Materials and Process fields, select mpd1.mpd as the Materials file and gyro.proc as the Process file.

b. Click on the Process Editor icon.

c. Review the process. Note the normal distributions set for the two etch steps. These settings will be used for Architect Monte Carlo analysis (see page T4-53).

d. Close the Process Editor.


3. Start a new schematic and save the project with the name gyro.

a. Click on the Schematic icon drop-down menu. Select New from Process.

The Schematic field default is create a new schematic.

Architect uses ...\Design_Files\Gyroscope\Schematics as the default directory for schematic designs and simulation results.

b. Maximize the Architect Sketch window and the schematic window.

The schematic starts with a reference frame and COVENTOR symbol.

c. Select File > Save from the menu bar and name the schematic gyro.



Reference Frame

Inertial boundary conditions are expressed as motions and rotations of the reference frame in the inertial coordinate system. Unlike the reference frame, the inertial frame has a fixed position in space and serves as the general reference for all inertial properties. Linear accelerations and angular velocities of the reference frame relative to its axis are applied by using the general component ref_frame. The ref_frame component is essential for the simulation of struc-tures with inertial properties. Conversely, system models with no inertial properties (such as purely optical models) have no need for a reference frame.

Figure T4-4 Using the Parts Gallery Search Function

Especially for smaller schematics, it may be more convenient to have a smaller reference frame. In Figure T4-7 you can see how large the default size reference frame is in the schematic for this tutorial. To reduce the size of the reference frame, right click on it and select Symbol View. Selecting the small option will shrink the reference frame. Note that you may then need to rearrange and reconnect the inputs and outputs so their wires do not overlap. You may also have to rename the wires.


4. Replace the control sine source at terminal wx with a control pulse source.

a. Select the sine source that is connected to wx in the Reference Frame by clicking on it.

b. With the object selected, right click in the open canvas (not on the selected part) and select Get Part > Parts Gallery.

The Parts Gallery pane is dockable, meaning that it can be detached from the Saber Sketch window, moved, and resized. To move it, click and hold on the triple bar beside the Parts Gallery label, and then drag it to the desired location.

c. Click on the Search tab.d. In the Search field, enter c_pulse, then click on the Search String

icon.

e. Click on Control Source, Pulse and then click on Replace Active

Part in Schematic. Leave the Parts Gallery open.



Figure T4-5 Values for Control Pulse Source


5. Set the source values to those shown in Figure T4-5.

a. Double-click on the new part to open the Properties dialog for the new source, and enter the values shown in Figure T4-5.

This gyroscope is designed to detect and measure a rotational rate along the X-axis. The rotational rate and its timing characteristics, required for transient analysis, are specified in this step.

The rotational rate has a “hat” profile with a delay of 5ms. The rise and fall times are 6ms, while the width is 15ms. The amplitude is 1 rad/s.

Note the green and half-green indicators on the right. These make values and attributes visible in the schematic. The color of the visibility indicator has the following meaning: black corresponds to no display, half green displays the value only, and full green displays both name and value. Click on them to turn them off.



4.2.3: Set Design Variables

Figure T4-6 Coventor Symbol Properties Dialog


1. Edit the COVENTOR symbol attributes with the values shown in Figure T4-6.

a. Double click on the COVENTOR symbol to edit its attributes. b. Scroll down to the bottom of the dialog.c. Click in the New Property Name field, and enter length_beam1. For the

value, enter 600u.d. Press the Tab key to create new rows.e. Add the other design variables shown in Figure T4-6. These variables

will be used to define the mass plate, beams, combs, and electrodes.

Table T4-1 on page T4-4 also list these variables and includes an explanation of the properties that these variables represent.

The objective is to optimize the design of the gyroscope. The design variables initialized in the COVENTOR symbol are referenced in the part parameters and will be used for optimization.

f. Save the schematic.

Note that the some of the values shown in Figure T4-6 include curly braces. Architect requires that variables within expressions that define other variables be surrounded by these braces. Curly braces are not interchangeable with parentheses.



4.2.4: Place and Connect Parametric Component SymbolsIn this sequence, you will place the parametric components used to build the gyroscope. Before beginning, consider how the symmetry of the design can be used to make placing components and assigning their variables easier. Each component may require many parameter settings that include complex equations, negative signs, underscores, etc. These parameter definitions must be entered correctly to obtain correct results. By placing a component, entering its parameters, and then copying and pasting any additional components needed, you will usually only have to make changes in component orientation and will not have to re-enter all the parameters. Figure T4-7 shows the schematic that will be created by the tutorial sequence. The tutorial sequence that follows shows how to place one comb and two beams, define their parameters, and then copy and paste the additional components. You will then have to change only the signs of the parameters that vary according to component orientation.

Figure T4-7 Schematic to be Created



Figure T4-8 Parts Gallery - Parametric Libraries


1. Place and orient an L-Beam in the schematic. Refer to Figure T4-9 to determine locations and orientations for these parts.

a. In the Parts Gallery select the Browse tab.b. Click on the + sign beside the Coventor Parts Library folder.c. Navigate to the Parametric Libraries\Electro-Mechanics\Beam

and Suspension components.

By clicking once on any item in the Available Parts list, the component symbol appears in the viewing pane. Double-clicking or clicking on the Place Part icon after selection will place one instance of the part in the schematic.

d. Click on the L-Beam part and place it in the schematic. Drag it to the correct location in the upper left portion of the canvas (see Figure T4-9). Use the Rotate and Flip options as necessary.

Single-clicking on any component selects that component. Right-clicking then opens a menu from which the Rotate and Flip options are available (or select Schematic > Rotate or Schematic > Flip from the menu bar). Rotation is counter-clockwise.

Use the Zoom to Fit icon to resize the working area as necessary.

2. Place an Anchor component in the schematic. a. Use the Search function to locate the Anchor component. Place the anchor at beam_ end2 of the L-Beam.



Table T4-2 Coventor Parametric Components Needed for Gyroscope Assembly


3. Place a rigid plate, an electrode, and a straight comb in the schematic.

a. Place an instance of the Rigid Plate component below the horizontal suspension of the L-Beam on the left side of the schematic.

Table T4-2 shows the Parts Gallery location of all the parametric components.

b. Place a Rigid Plate Fixed Electrode opposite the Rigid Plate, on the right side of the schematic. Orient by rotating it 270 degrees.

The gyroscope system model (schematic) uses components from the library that are interconnected by wires. The wires represent "across" and "through" quantities at the junction of the parts. Both physical orientation and relative position should be taken into account when placing parts on the canvas. This will give a better representation of the final microstructure shape.

c. Place an instance of the Straight Comb with Stator in the schematic.

Symbol name Symbol Categories path Part Quantity

rigid_plate /Coventor Parts Library/Parametric Libraries/Electro-Mechanics/Rigid Plate

Rigid Plate 1

rigid_plate_ fixed_ electrode

/Coventor Parts Library/Parametric Libraries/Electro-Mechanics/Rigid Plate

Rigid Plate Fixed Electrode/Contact

1

straight_comb_stator

/Coventor Parts Library/Parametric Libraries/Electro-Mechanics/Comb Structures

Straight Comb with Stator

1



Figure T4-9 Position of Components

As you copy and place more components in the schematic, you should note and verify the following points of sym-metry:

Beam ends numbered 1 are always toward the center of the design.The anchor component is connected to the beam end numbered 2. The location of the COVENTOR logo in each component provides another helpful visual clue for ensuring that parts have been flipped or rotated properly.



The schematic should look like Figure T4-10:

Figure T4-10 Initial Wired Schematic


4. Refer to Figure T4-10 to connect the L-Beam, Rigid Plate, Comb, and Electrode terminals with wires.

a. Create the central schematic wire: on the comb component click on the yellow square underneath the number 1 in a circle (this is the bus wire terminal), and then drag the mouse down past the plate and electrode components. Drag the mouse down far enough to allow for an addition comb component and two sets of beam components. Double click to end the wire.

b. Click on the wire terminal at end 1 of the L-Beam and drag until it is connected to the central wire you just created. Click to create the connection.

c. Click on the anchor component, and move it toward end 2 of the L-Beam until it overlaps with its terminal. Then move the anchor back to see the wire that is created.

d. Click on the terminal of the Rigid Plate, then drag to and click on the central wire.

e. Click on the terminal of the Electrode (make sure to select the terminal labeled x1<05>, and not the M terminal), and drag and click on the central wire.

Note that if the wires are connected correctly, when passing the mouse over the wire, the central wire should turn red and should have the same bus name.



4.2.5: Assign Properties to Placed SymbolsOnce the components are placed, they need to be customized by setting properties.

Set Beam Component Properties

Figure T4-11 L-Beam Attributes (Upper Left)


1. Double-click on the beam and assign property values as shown in Figure T4-11.

a. Double click on the L-Beam. Set the properties as shown in Figure T4-11.

The name of the beam is selected to refer to its location.

The physical properties are inherent in the layer material, and are imported from the Material Properties database.

b. When the parameter field requires multiple entries, click on the parameter field, and enter the values in the sub-dialog that opens.



Each parameter dialog requires many settings, and the settings include numerous negative signs, equal signs, and underscores. These must be entered correctly to obtain correct results.

Symbols can be copied from the prebuilt gyro_prebuilt.ai_sch file included with the tutorial. You can delete an existing L-Beam symbol from your schematic and replace it with the symbol from the prebuilt schematic with a copy and paste procedure. Right click and select Re-Reference after this substitution to relink the symbols and maintain the connectivity.


2. Set the properties for the Anchor, as shown below.

a. Double click on the Anchor.b. Set the label, knot1, origin, and fixed_to layer values as shown below.

The knot1 X and Y coordinates default to the X and Y coordinates of the origin. The Z coordinate is defined by the z_layer value, which should be the same layer as the beam to which the anchor is attached.

The origin defines the reference point on the substrate. The X and Y coordinates of the origin should be at the same location as the X and Y coordinates of end2 of the beam to which the anchor is attached. The Z coordinate is defined by the fixed_to_layer value.



Table T4-3 L-Beam Attributes (Upper Right)


3. Copy and place three sets of the L-Beam with its anchor. Use Figure T4-7 on page T4-11 as a guide.

a. Click and drag a box around the L-Beam and the anchor. Both components should appear highlighted.

b. Right click and select Copy.

When selecting Copy, make sure the mouse cursor is not over the selected symbols, otherwise the copy function will not work.

c. Click to the right of the central wire opposite the beams you just copied then right click and select Paste.

d. Right click on the copied components and select Flip > Right-Left.e. Connect the beam_end1 terminal of the newly created L-Beam to the

central wire.f. Paste two more copies of the L-Beam/anchor set in the lower left and

lower right quadrants of the schematic. Use the Flip > Right-Left or Up-Down options to orient the components correctly. Use Figure T4-7 on page T4-11 as a guide.

g. Connect the beam_end1 terminals of the L-Beams to the central wire.

4. Set the parameters for the L-Beams you just created, using Table T4-3, Table T4-4, and Table T4-5 as guides.

a. Double click on each of the beams you just created and change the required parameters, using Table T4-3, Table T4-4, and Table T4-5 as guides. All other parameters remain the same.

Because you copied and pasted the first beam, you only have to change the labels and the beam position values. The X value of the position is positive for the beams on the right and negative for the beams on the left. The Y value is positive for the upper beams and negative for the lower beams. The joint angle is positive for the upper right and lower left beams, but negative for the upper left and lower right beams.

Name L-BeamUR

label L-BeamUR

position by_origin\ origin: x=plate_size_x/2+plate_line_width/2 y=plate_size_y/2 position=end_point1 angle=0, length1=length_beam1length2=length_beam2joint angle=90



Table T4-4 L-Beam Attributes (Lower Left)

Table T4-5 L-Beam Attributes (Lower Right)

Table T4-6 Anchor Attributes

Name L-BeamLL

label L-BeamLL

position by_origin\ origin: x=-plate_size_x/2-plate_line_width/2 y=-plate_size_y/2, position=end_point1 angle=180length1=length_beam1length2=length_beam2joint angle=90

Name L-BeamLR

label L-BeamLR

position by_origin\origin: x=plate_size_x/2+plate_line_width/2 y=-plate_size_y/2 position=end_point1angle=0length1=length_beam1length2=length_beam2joint angle=-90


5. Set the parameters for the anchors you just created, using Table T4-6 as a guide.

a. Double click on each of the anchors you just created and change the required parameters, using Table T4-6 as a guide.

Remember that the origin coordinates of each anchor should be the same as the beam_end2 coordinates of the beam to which the anchor is attached.

Name Upper Right Anchor Lower Left Anchor Lower Right Anchor

label AnchorUR AnchorLL AnchorLR

origin x=210u+length_beam1y=200u+length_beam2

x=-(210u+length_beam1)y=-(200u+length_beam2)

x=210u+length_beam1y=-(200u+length_beam2)

If you change the ref name in the Property Editor dialog, do not use spaces. Layout extraction (see page T4-31) will fail if any of the components have spaces in their ref names.



Set Rigid Plate Component PropertiesThe Rigid Plate (Figure T4-12) consists of three components: a rectangular plate and two straight combs.

Figure T4-12 Rigid Plate Components


6. Set the properties for the Rigid Plate. The values are shown in Figure T4-13.

a. Double click on the Rigid Plate.b. Click on the value field for the parameters listed below, and fill in the

sub-dialogs that open, using Figure T4-13 and Figure T4-14 as a guide:knotdampingcurvaturerectangular_platesstraight_combs

The physical properties are the density and damping coefficients.

The plate mass is geometrically described by its height and its constituting sub-geometric components: one rectangular plate and two straight combs.

Some attributes have been assigned variable names or equations including variables names. This feature will allow the user to analyze performance by varying selected parameters. Recall that these parameters or variables should be defined and initialized in the COVENTOR properties dialog.

straight_comb1

rect_plate1

straight_comb2



Figure T4-13 Rigid Plate Attribute Properties Dialog with Subdialogs

Dialogs continued on next page.



Figure T4-14 Straight Comb Properties for Rigid Plate



Set Electrode Component Properties

Figure T4-15 Electrode Attributes


7. Set the Rigid Plate Fixed Electrode attributes as shown in Figure T4-15.

a. Double click on the Rigid Plate Fixed Electrode symbol, and select Properties.

b. Set the electrode attributes as shown in Figure T4-15.

The electrode is a rectangular plate.



Set Straight Comb Component Properties

Figure T4-16 Straight Comb Attributes


8. Set the attributes of the straight combs, using the values shown in Figure T4-16.

a. Double click on the straight comb symbol (straight_comb_stator) to open the Properties dialog. Set the attributes as shown in the left dialog in Figure T4-16.

The numerical settings were reduced to speed up the simulation time for transient analysis. For more information on this settings, see page A5-83.

9. Copy the straight comb, and then paste another comb instance. Connect it to the end of the central wire and assign the appropriate parameters.

a. Click on the comb to select it. b. Right click and select Copy.c. Move the mouse to the end of the central wire, below the lower set

of beams, and then right click and select Paste.d. Connect the newly created comb to the end of the central wire.e. Assign the properties shown below.

Note that except for the negative values for the origin and the angle, the combs have the same numerical properties.

10. From each of the Cap<0:4> bus terminals, create a short, vertical wire.

a. Click on the Cap<0:4> bus terminal of each comb and drag out a short distance to create a short, vertical wire. Double click to end the wire.

Upper Straight Comb Lower Straight Comb



4.2.6: Add Additional Components

Mechanical Stimuli Components Mechanical stimuli are accelerations and rotational rates in the inertial coordinate system applied to the gyroscope. Mechanical stimuli defined in the inertial coordinate system are applied to the gyroscope through the Reference Frame included in the schematic. See Section 5 for more information.

Figure T4-17 Common Properties Dialog


1. Verify that the ac_mag is set to 1 for all six sources connected to the reference frame.

a. Use Ctrl to multi-select the sources connected to the ax, ay, az, wx, wy, and wz terminals of the reference frame. Double click on any of the selected sources to open a Common Properties dialog (Figure T4-17).

b. Verify that the ac_mag field is set by default to 1.

For small signal analysis in the frequency domain, the connected sources (sine and pulse) already have the required properties, ac_mag and ac_phase, properly set by default.



Electrical Stimuli ComponentsThe various parts needed to set up the electrical stimuli components are listed in Table T4-7.

Table T4-7 Parts Needed to Set Up Electrical Stimuli

Symbol name Symbol Categories Path Quantity

gnd Ground, (Saber Node 0) /MAST Parts Library 7

v_sin Voltage Source, Sine /MAST Parts Library/Sources, Power, Ground/Electrical Sources/Voltage Sources

1

v_dc Voltage Source, Constant Ideal DC Supply

/MAST Parts Library/Sources, Power, Ground/Electrical Sources/Voltage Sources

2

vcvs Voltage Source, VCVS /MAST Parts Library/Sources, Power, Ground/Electrical Sources/Voltage Sources/Controlled Voltage Sources

1



Figure T4-18 DC Electrode Attributes


2. Place a grounded DC source in the schematic, as shown in Figure T4-21. Open an attributes dialog for the source, and enter the specifications shown in Figure T4-18.

a. Place the electrode stimuli components v_dc and gnd in the schematic.

b. Connect the electrode terminal E to the DC source and the DC source to ground (see Figure T4-21).

A DC voltage source is used to bias the electrode E of the parametric electrode.

c. Specify the DC source attributes as shown in Figure T4-18.

A DC voltage is applied between electrodes E (parametric_electrode electrical terminal) and F (parametric_straight_comb electrical terminal). It will allow electrostatic tuning of the resonant frequency sensing mode.

The design value dc_electrode was defined in the COVENTOR symbol, as shown on page T4-10. The DC value of the source will be the same as the defined dc_electrode value in the COVENTOR symbol.

d. Connect the electrode terminal M to a ground.

3. Connect a wire to the electrode’s Cap terminal, and name it cap.

a. Click on the Cap terminal and drag out a short distance to create a short, horizontal wire. Double click to end the wire.

b. Double click on the wire you just created.c. In the Wire Attributes dialog that opens, in the Name field, enter

cap.d. Click on Apply, then on Close.



Figure T4-19 Schematic of Electrical Stimuli Circuit

Table T4-8 Attributes for Electrical Stimuli Circuit


4. Place the v_dc, v_sin, vcvs, and gnd in the schematic and set the properties. Refer to the finished schematic, Figure T4-19 and Table T4-8 for specifications.

a. Place the comb electrodes stimuli components v_dc, v_sin, vcvs, and gnd in the schematic.

b. Connect the F terminals of the upper and lower combs to the components you just placed, as shown in Figure T4-21.

c. Set the properties of the different parts according to the schematic in Figure T4-19 or the entries in Table T4-8.

The global variables, set in the COVENTOR symbol, aref_yr: frequency of the voltage sine source.dc_comb: dc value of the dc voltage source.

d. Connect the M terminals of the two straight combs to ground.

The driving mode is actuating the gyroscope mass between comb terminals F and M.

The M terminals for the combs and electrode are short-circuited because they are at the same potential.

e. Attach a gnd component to the combs’ Eb and Et terminals.

Symbol Property Value

v_sin ref v_sin_comb

amplitude 2

frequency f_yr

ac_mag 0

vcvs k -1

v_dc ref v_dc_comb

dc_value dc_comb



Mechports_Bus_Connector

Figure T4-20 Dialog for Changing Wire Attributes


1. Place a bus_connector component below the rigid plate.

a. Place a bus_connector directly under the right upper beam and above the electrode (see Figure T4-21). The connector is located in Coventor Parts Library/Shared Parts/Interface Components

The bus_connector component can be added to the schematic to extract the individual wires for plotting in CosmosScope.

b. Connect the connector terminal to the central bus wire.

2. Rename the wires of the connector to correspond with the connector terminal names.

a. Click on the x terminal of the bus_connector, drag the wire a short distance away from the connector, then double click to end the wire.

b. Repeat with each of the bus_connector terminals.c. Double click on the terminal x wire. d. In the Wire Attributes dialog, change the Name to x, and click on

Apply. Leave the dialog open.e. Repeat the process and rename the wires connected to terminals y,

z, rx, ry, rz accordingly.f. Close the dialog when finished.

For future simulation and result post-processing tasks, it will be easier to refer to the net x position value rather than the wire names that were assigned by default.



4.2.7: Final SchematicThe final schematic should look like Figure T4-21:

Figure T4-21 Final Schematic


Section 4: Gyroscope Design Schematic Layout Verification Version 2008M

4.3: Schematic Layout Verification During schematic creation, many parameters have been entered in the Properties dialog for each component. These parameters must be carefully selected and entered in order to maintain consistency. For example, this gyroscope uses beams that are in the Y or X direction. End point coordinates beam_end1 and beam_end2 of beams must have the same X value (Y direction) or the same Y value (X direction). Inconsistencies in the design are usually difficult to find. To solve this problem, the following section provides a first level of verification and demonstrates the following techniques:

how to netlist the schematic and correct any errorshow to view the 3-D model in Scene3D to validate the system design


1. Netlist the schematic and open the model in Scene3D.

a. In the menu select Design > Netlist.

Netlisting can often highlight hookup errors. Such errors may appear in a dialog during the netlist procedure.

b. Click on the Show/Hide Guide icon.

c. Click on icon on the right of the simulation icon bar to open

the SaberGuide Transcript window. d. Select Design > Simulate.

Additional errors may be detected by simulating the design after netlisting. After selecting Simulate, look for errors in the Saber Transcript window.

Note that a new icon bar and some new menus also appear.e. Select Architect > Open in Scene3D.

If any component is not configured correctly, it will have a warning or error icon beside its entry in the Component Tree. Right click on the component or knot, and select Show Errors/Warnings/Info.

f. Leave the Scene3D window open.

If you do not have a license for Scene3D, you can extract a 2-D layout to verify your schematic: From the Architect Sketch window, select Architect > Export for Designer. From the Function Manager’s Designer tab, select New from Architect from the Layout Editor icon’s drop-down menu.


Section 4: Gyroscope Design Architect Analysis Version 2008

4.4: Architect AnalysisArchitect can simulate the behavior of the gyroscope. The simulation results can then be used to optimize the perfor-mance of the device. This tutorial sequence demonstrates the following techniques:

how to conduct a DC Operating Point Analysis that provides the initial solution for all other analyses how to determine voltage ranges of operation, including pull-in, using the DC Transfer function how to manipulate plot results in CosmosScopehow to determine resonant frequencies using the Small Signal AC functionhow to optimize design performance by varying structural parameters such as mass value or plate size, beam lengths and widths, or number of comb fingershow to conduct sensitivity and Monte Carlo analyseshow to conduct transient and Small Signal AC analyses to determine detection amplitude and response timeshow to use the Vary function to investigate the impact of plate curvature on the design

For detailed descriptions, debugging techniques and calibration of the Architect analyses used in this section, see the saber_user.pdf, located in \CoventorWare2008\architect\SaberDesignerInstall\webworks_docs\saber.


Section 4: Gyroscope Design Architect Analysis Version 2008M

4.4.1: DC Operating Point AnalysisDC analysis is a two-step verification for the completeness of the schematic. First, before performing the DC Operat-ing Point Analysis, Saber generates a netlist. If some required attributes are missing or if some design variables have no numerical value, Saber will fail to read this netlist. If this happens, refer to the SaberGuide Transcript window. An error message should explain which component is incorrect. Second, DC analysis results give a fast overview of attribute correctness: X, Y, and Z coordinate values.

Figure T4-22 Operating Point Report

If you skipped the schematic construction steps, start by loading the tutorial schematic gyro_prebuilt.


1. Open the Operating Point Analysis dialog, and click on OK. Then, generate an Operating Point report and compare the report with Figure T4-22.

a. Click on the DC Operating Point icon. b. In the Operating Point Analysis dialog that appears, click on OK. c. From the Saber Transcript window menu, select Results >

Operating Point Report. d. Click on the Waveforms tab, and in the signal list, clear any signals

that may appear and type /x /y /z. Click on OK.e. Verify the results that appear in the report window (Figure T4-22).

The x and y values may vary, but the z value is the only significant result.

The elevation z is positive nonzero mainly due to the vertical asymmetry in the electric field lines at the comb fingers, which produces a net (upward) force in the positive Z direction.



4.4.2: DC Transfer (Sweep) Analysis

Pull-in Voltage


1. Perform a DC Transfer analysis on the z wire. Increase the voltage from 0 to 5 volts in steps of 0.25.

a. Click on the DC Transfer icon.

b. In the DC Transfer Analysis dialog, set the input in the Basic tab as shown below.

c. Click on OK.

In this analysis, the voltage of the electrode is increased from 0 to 5V. As seen in the Pull-in voltage in Figure T4-23, the mass pulls in at around 3.25 volts.

Also shown on the pull-in plot in Figure T4-23 is the DC operating point, which corresponds to dc_electrode = 0.1.

Previous Users of ArchitectBecause we want to visualize the 3-D results, we will not specify any signals on the Input/Output tab. If you specify any particular signal, Architect will solve only for that signal and will not have enough information to visualize the device.

Unless the display_messages is set to none, the comb component will print out warning messages whenever the movable fingers leave their valid range of motion. Note that these warnings might only appear during solver iteration, but not for the actual result of the iteration. Warnings are printed during the simulation despite that the final simulation results appear to be within valid limits.The user should always check the simulation results after one or more warnings appear. Note that suppressing the range check with display_messages=none can speed up the simulation significantly.

Set or verify each value




2. Plot the results of the analysis in CosmosScope. Position the legend to the right of the plot, and set the range display for the graph from 0 to 3.6.

a. When the simulation finishes (about 30 seconds), scroll down to the bottom of the small signal list dialog that opens. Double click on the z signal to plot it.

Two windows opened: the Signal Manager window, and a window with a list of signals.

b. Maximize the Scope window and Graph0 window.c. Click on the z signal legend and then select the Measurement

Tool icon from the bottom row of icons.d. In the Measurement dialog that opens, click on Apply and

Close. In the graph, move the probe (looks like a circle with crosshairs) to the point where the plot begins a sharp descent.

The probe tool can be used to give a precise measurement of the pull-in voltage.

e. Right click on the bottom axis and select Attributes. In the dialog, set the Range from 0 to 3.6. Click on Apply and Close.

Changing the Axis Attributes changes the range displayed. The range selected is the area of interest.

f. Click on the measurement value and slide to view other values.g. When finished, File > Exit the Plot window.

To obtain a more accurate pull-in, rerun the DC Transfer Analysis with a zoomed in Sweep Range. Example: 3.2 to 3.4 by 0.01.

Measurement dialog Axis Attributes dialog



Figure T4-23 Pull-in Analysis Results

The plot shown in Figure T4-23 has a white background. To set the plot to a white background, select Graph > Color Map > Mono or Map 2. The Mono option displays the plot on a white background with a black plot curve. The Map 2 option displays the plot on a white background with a color plot curve.


3. Visualize the displacement results in Scene3D. a. In the Scene3D window, click on the Show/Hide Simulation Results icon.

b. Click on the Open Plotfile icon , and in the dialog that opens, select the gyro.dt.ai_pl file, then click on Open.

c. Set the Scale to Z and enter 10 as the scale factor. The resulting geometry is shown in Figure T4-24.

d. Set the Exaggeration in the Z direction to 3.e. Click on the Play icon to view gyro movement in response

to the increase in voltage.f. Use the Pause and Forward One Frame icons to isolate

the step where pull-in occurs.

Figure T4-25 shows that the pull-in occurs between 3.25 and 3.3 volts.



Figure T4-24 Scene3D Displacement Results

Figure T4-25 Zoomed View of Pull-inVoltage of 3.25 shows pull-in beginning Voltage of 3.3 shows pull-in complete



Impact of Driving Bias Voltage on Levitation


4. Run a DC transfer on the v_dc.v_dc_comb with an increasing bias voltage from -25 to 25 volts. Display results for the z signal.

a. Click on the DC Transfer icon.b. In the DC Transfer Analysis dialog, set the input in the Basic tab as

shown below.

In this analysis, the bias voltage is increased from −25 to +25 volts using the v_dc.v_dc_comb.

c. In the Input Output tab, set Plot file to levitation.

By specifying a name for the plot, you ensure that the plot file for the previous DC transfer analysis is not overwritten.

d. When the simulation finishes, select the z signal in the Plot window. See Figure T4-26.

Notice the symmetry in the plot. Levitation force is caused by vertical asymmetry due to the presence of the ground plate. On the bottom side field lines leave the stator fingers and go into the ground. On the top side the field lines leaving the stator fingers are forced to end at the movable finger top side, resulting in a net force upwards.

e. Exit the Plot window when finished.

Set bias voltage range here

Change voltage source



Figure T4-26 Elevation Due to Bias Voltage

Figure T4-26 shows a plot with the grid displayed. To display a grid, right click on the plot and select Toggle Grid Axis or select the Toggle Grid icon.


5. Visualize the displacement results in Scene3D. a. In the Scene3D window, click on the Open Plotfile icon , and select the levitation.dt.ai_pl file.

b. Set the Scale to Z and enter 10 as the scale factor. c. Set the Exaggeration in the Z direction to 10.d. Click on the Play icon to view levitation of the gyro.

Figure T4-25 shows that the gyro position at the voltages -25, 0, and 25. Note that the movement of the gyro follows the plot you viewed in CosmosScope.



Figure T4-27 Gyroscope Levitation

4.4.3: Small Signal AC Analysis

Resonance Frequencies


1. Perform an analysis of the device as all small signal sources are varied from 1 kHz to 50 kHz. a. Click on the Small Signal AC icon.

b. Set the parameters as shown in Figure T4-28.

AC analysis will be performed, varying all small signal sources from 1kHz (Start Frequency) to 50kHz (End Frequency).

The Plot After Analysis option is Yes - Open Only. c. Click on OK.

CosmosScope opens at the end of the simulation (which should take about 4 seconds).

-25 volts 0 volts

25 volts



Figure T4-28 Dialog Settings for Small Signal AC Analysis


2. Plot the results for x, y, and z in CosmosScope.

a. In CosmosScope, select x, y, and z in the signal selection window and click on Plot.

Plot the x, y, and z resonance frequencies on the same graph.b. Maximize the Architect window and the Graph0 window. See Figure T4-29.

Notice that the y and z resonant frequencies are close to each other while the x resonant frequency is far from them. Because the gyroscope has crab leg attachments, the x resonant frequency is still far away from the driving mode (y) resonant frequency and sensing mode (z) resonant frequency.

c. Ctrl select the legends of the x, y, and z Phase(deg) plots. Right click and select Delete Signal from the menu.

d. Click on the y dB(m) legend, and then drag it to the x dB(m) legend. This plots the y signal in the same graph as the x signal.

e. Select the z dB(m) plot, and drag it to the x, y signal plot.f. From the Saber Scope menu, select Graph > Legend > Float. g. Click on the Measurement Tool icon. From the Measurement field drop-down

arrow select the General > Local Max/Min measurement option to annotate the peak signal points. Click on Apply. Then select the other two signals in turn from the Signal field drop-down menu. Apply the Measurement settings to each one. Click on Close. See Figure T4-30.

The peak in each plot represents the modal frequency in that direction.h. Exit the Plot window.



Figure T4-29 Plot Selection

Figure T4-30 Small Signal AC Analysis: Resonance Frequencies



Figure T4-31 Harmonic Response of Modal Frequencies

Because this class of gyroscope is designed to sense rotation only while the perforated mass is oscillating in steadily in the Y direction, it is very important to have accurate results for y resonant frequency. Rerunning the small-signal AC analysis in a refined frequency range of 7.0 to 7.2k gives more accurate results for the Y resonant frequency, as shown in Figure T4-32. This result was used to set the f_yr variable in the COVENTOR symbol and will be important when running the transient analysis simulation (see page T4-60).


3. Visualize the resonant frequency results in Scene3D. a. In the Scene3D window, click on the Open Plotfile icon , and select the gyro.ac.ai_pl file.

b. Set the Scale to Z and enter 5 as the scale factor. c. Set the Exaggeration in the X/Y and Z directions to 50.d. In the Frequency field, enter 30871.2 (the modal frequency for

X), and click on the Harmonic Play icon e. View harmonic response in the X mode. When finished, click

on the Pause icon.f. View the harmonic response at the frequency of 7180.2 (the

modal frequency for Y).g. View the harmonic response at the frequency of 7474.5 (the

modal frequency for Z).

Figure T4-31 shows the harmonic response at the X, Y, and Z modal frequencies.

Z mode

X mode Y mode



Figure T4-32 Resonant Frequency for Y



Resonance Frequencies: Impact of Length_Beam1 ParameterIn this step vary the parameter length_beam1 and investigate the impact on resonant frequencies.


1. Perform a vary analysis using looping commands to vary the length of beam 1 in the outer loop while performing a small signal AC analysis in the inner loop. For the small signal analysis, use a frequency range from 1k to 50 k for 1000 points. Vary the beam length from 300u to 700u in increments of 5 (see Figure T4-33).

a. Click on the Vary icon. b. In the Looping commands dialog, click on vary.c. From the Parameter Sweep (Loop #1) dialog Parameter Name field,

select Browse Design. Double click on Parameters to expand, then scroll down and select length_beam1.

d. Set the rest of the Parameter Sweep variables according to Figure T4-33, then click on Accept.

e. In the Looping commands dialog, select Add Analysis > Within Loop(s) > Small Signal AC.

f. Click on acanalysis in the Looping commands dialog.g. In the Small-Signal Frequency Analysis dialog, set

Start Frequency to 1k and End Frequency to 50kNumber of Points to 1000Run DC Analysis First to Yes. From the Input/Output tab, set the Plot File field to vary_beam1.

For each value of length_beam1, the DC operating point is different, so you must run a DC analysis before the small signal AC analysis.

h. From the Looping Commands dialog, select Add Analysis > Within Loops > Command Line.

i. In the field that appears, enterlist parameters / /.../*.* (ofile "gyro.vary_beam1_arch3d"

This step is only necessary when using Scene3D to view the different results for each vary step. This line creates a file of properties that is used to create the geometries in Scene3D for each vary step. This file, together with the plot file specified in the Small Signal AC dialog, can then be used to view the deformed geometry. Because the property file and the plot file are used as a pair, in the above step, the plot file specified has the same name as the suffix in this line. Note that this line can be copy/pasted from the Saber Transcript window with the filename being the only change. For more information on how to set up a vary analysis for viewing in Scene3D, see page A11-6 of the Architect Reference.

2. Start the analysis. a. Click on Accept.b. In the Looping commands dialog, click on OK.



Figure T4-33 AC Analysis in length_beam1 Parameter Sweep


3. Visualize the varying beam lengths in Scene3D. a. When the simulation is complete (about 1 minute), in the Scene3D window, select File > Open, and select the gyro.vary_beam1_arch3d file.

b. Use the down arrow to view each variation on the beam length. Each step is shown in Figure T4-34.

c. Leave the gyro.vary_beam1_arch3d file open.



Figure T4-34 Gyroscope Model with Varying Beam Lengths

length_beam1 = 300 µm length_beam1 = 400 µm

length_beam1 = 600 µmlength_beam1 = 500 µm

length_beam1 = 700 µm



Figure T4-35 Resonance Frequencies for Varying Beam Lengths

As noted earlier, for this class of gyroscope, it is very important to have accurate results for y resonant frequency. So in the next steps, we will visualize the harmonic response in the y mode for each beam length variation. According to the plot above the resonant frequencies in the y mode can be estimated as follows:

For beam_length1 of 300 µm, the resonant frequency is about 18000.For beam_length1 of 400 µm, the resonant frequency is about 12500.For beam_length1 of 500 µm, the resonant frequency is about 9000.


4. View the analysis results in CosmosScope. a. In the Transcript window select Results > View Plotfiles in Scope. In the View Plotfiles window that opens, click on OK.

b. Set up the plot as in the previous section. See page T4-41 for the procedure.

c. Close the two signal windows.d. Select the y signal legend. Right click and select Member Attributes. In

the window that opens, click on Show All Labels. Click on Close.e. Pass the mouse over the label group until a Place Labels vertical line

appears. Drag the line left to increase the distance between the labels. You can also drag each label individually. See Figure T4-35.

When the lengths of horizontal beams increase, y and z mode resonance frequencies decrease, while the x mode frequency remains almost the same.

The relative position of the y and z mode resonant frequencies change and the resonance matching occurs around length_beam1 = 400µm.

For good cross talk performance, the x mode resonant frequency should be as far as possible from the y and z mode resonant frequencies, but these last two frequencies should not be too low.



For beam_length1 of 600 µm, the resonant frequency is about 7000.For beam_length1 of 700 µm, the resonant frequency is about 5500.

We will use Scene3D to verify and visualize these values.


5. Visualize the harmonic response in the y mode for each beam length variation.

a. In Scene3D, click on the Show/Hide Simulation Results icon and then on the Open Plotfile icon. Select the gyro.vary _beam1.ai_pl file.

b. Set the Scale to Z and enter 5 as the scale factor. c. Set the Exaggeration in the X/Y to 1000 and in the Z direction

to 100.d. Change the Frames value to 1000.e. For beam_length1 = 300u, enter 17500 in the Frequency field,

and use the Next Frame animation icon to advance through the frequency results until you see the maximum displacement in the Y direction; this will be the resonance frequency in the Y mode.

The Y and Z modes are very close, so when you cycle through the results, you will also see displacement in the Z direction.

f. When you have isolated the Y resonance frequency, click on the Harmonic Play icon to view the harmonic response.

g. Use the down arrow to advance to beam_length = 400u.h. Enter a value of 12000 in the Frequency field and use the Next

Frame icon to isolate the resonance frequency for Y. When you have isolated it, view the harmonic response.

i. Find and view the harmonic response in the Y mode for the other beam_length1 values.



Figure T4-36 Resonant Frequencies for Varying Beam Lengths

length = 300 µmfrequency = 18294

length = 400µmfrequency = 12490

frequency = 9196length = 500µm





Resonance Frequencies: Impact of Length_Beam2 ParameterIn this step we will vary the parameter length_beam2 and investigate its impact on resonant frequencies in the Y and Z directions. The goal of this step is to find the value for length_beam2 where both resonance frequencies match.

Figure T4-37 AC Analysis in length_beam2 Parameter Sweep


1. Use the Looping commands dialog to vary the parameter length_beam2 in the outer loop and perform a small signal AC analysis in the inner loop. Refer to Figure T4-37 for parameters.

a. Click on the Vary icon.b. In the Looping commands dialog, set the variables as shown in

Figure T4-37.

Note the change to the Small Signal AC settings.

To remove the Saber line, click on the arrow beside it and select Delete.

c. Four additional steps after the AC loop will record and plot the resonance frequencies for y and z, respectively. To add them select Add Analysis > After Loop(s) > Batch Measure and View Plotfiles in Scope.

d. In the Batch Measurement dialog, for the Input Plot File, Curve Name, and Output Plot File, enter the text; do not use the down arrow to browse.

e. In the Looping commands dialog, click on OK.



Figure T4-38 Resonance Frequencies Versus length_beam2

The x resonant frequency fx does not really matter for normal operation of the devices. However, it is important for the robustness and the insensitivity of the device resulting from acceleration along X. To keep cross sensitivity low, the resonance frequency should be as large as possible.


2. Display the analysis results in CosmosScope as shown in Figure T4-38.

a. When the simulation is complete, plot the two graphs X_Max(MAG(y)) and X_Max(MAG(z)) in the same graph.

The progress of the simulation can be monitored in the SaberGuide Transcript window.

The two graphs hold results of the AC peak measurements in the vary loops.

b. Close the three signal windows.

c. Select one of the graphs and click on the At X Measurement icon.

d. Drag the measurement indicator to the point where the two plots intersect. This measurement indicates the value of length_beam2 for which both frequencies match, as shown in Figure T4-38.

The frequencies shown match for a length_beam2 = 280.54u

A match between the Y and Z resonant frequencies guarantees the best sensitivity of the gyroscope. Thus, the driving voltage excites the detection mode when the driving and detection frequencies are matched. However, the signal to noise ratio increases as the Y and Z resonant frequencies get closer to each other. The noise in the signal is mainly caused by the levitation force. Transient analysis will help shed light on the impact of frequencies matching or mismatching on the detection signal for a certain sensing rotational signal.



4.4.4: Sensitivity and Monte Carlo AnalysisSensitivity analysis is an alternate and very effective method for studying the impact of design parameters on a given performance measure such as resonance frequency, DC point displacement, transient amplitude, etc. With sensitivity analysis, the sensitivity to a parameter is calculated by a measurement-based perturbation method. A specified param-eter p is perturbed from its nominal value, and the effect on a specified performance measure F for the design is deter-mined as shown below:

To provide meaningful comparisons, the results are usually normalized:

wherep the nominal value of the perturbed parameter

the amount by which the parameter is perturbedF the nominal value of the performance measure

the amount by which the performance measure changes in response to the parameter perturbation

Saber uses the following process to execute the sensitivity analysis:

1. Increase the parameter value by the value defined in the Perturbation field.

2. Run the specified analyses.

3. Calculate the specified measurements.

4. Repeat steps 1-3 for each parameter in the Parameter List field.

5. Repeat steps 2 and 3 using the nominal parameter values.

6. Calculate the sensitivity based on the difference between the nominal and perturbed parameter values accord-ing to the equation for sensitivity given above.

In this tutorial section, we will investigate the sensitivity of the resonance frequency of the gyroscope’s driving mode (y) to the following design parameters: width_beam1, width_beam2, length_beam1, and length_beam2, as well as the Young’s Modulus and the height of the poly layer.

sensitivity δFδp------=

sensitivity F F⁄∆( ) p p⁄∆( )⁄ F∆ sensitivity F p p⁄∆( )⋅ ⋅=⇒=

∆p

∆F



Figure T4-39 Settings for Sensitivity Analysis


1. Run a sensitivity analysis on the resonance frequency in the Y direction. Refer to Figure T4-39 for parameters.

a. Click on the Sensitivity icon.

b. Click on the down arrow next to the Parameter List and choose Browse Design.

c. In the Set Parameter List dialog double-click on Parameters, and use the -> button to move the following parameters to the Selected column: length_beam1, length_beam2, poly_layer->material->elastic->isotropic->e, poly_layer->thickness, width_beam1, and width_beam2.

The process-dependent variables are automatically assigned and updated by the CoventorWare GUI. The global process variable names start by layername_layer-> followed by the name of the particular sub-parameter.

d. Complete the Sensitivity Analysis dialog as shown in Figure T4-39, then click on OK.



Figure T4-40 Sensitivity Report

The resonance frequency of the driving mode is most sensitive to the design parameter length_beam1. A sensitivity of -1.4 means that a 1% perturbation of the horizontal beam length results in a 1.4*1%= 1.4% decrease in the investi-gated resonance frequency. In absolute terms, increasing the horizontal beam length from 600µm to 606µm results in a decrease of the resonance frequency of 1.4%*Nominal Value*6µm/600µm=100.6Hz.It is important to keep in perspective the absolute changes in parameters. A 1% change in the horizontal beam length length_beam1 is 6µm, whereas a 1% change in horizontal beam width is 0.07µm. Due to inaccuracies in fabrication process, the designer would most likely expect changes in the beam width larger than 0.07µm and changes in the hor-izontal beam length of much less than 6µm. For this reason, it is worthwhile to scale the sensitivities shown above to a common absolute perturbation. We could then identify those dimensions whose changes push one or more of the key performance measures outside the desirable performance regime.

Let's assume that fabrication-induced deviations of the in-plane dimensions are up to 0.2um. Let's further assume that the acceptable driving frequency range is to within 150Hz from the nominal value (7.1869kHz). Then, for instance, the absolute change in the driving frequency for a 0.2um change in length_beam1 would be 0.2um/6um*100.6Hz = 3.35Hz, which is well within the acceptable range. Table T4-9 shows changes in the driving frequency due to 0.2um (absolute) perturbations of the all the in-plane design variables for this sensitivity analysis.


2. A Sensitivity report will appear. Compare the report with Figure T4-40.

a. Verify the results that appear in the report window (Figure T4-40).



Table T4-9 Driving Frequency Change Due To Parameter Variations

It is obvious that the width of the horizontal beams causes a problem. A change of 0.2 µm in width_beam1 results in a change of 215.61Hz in the driving frequency, which is outside the acceptable design regime (defined as +/-150Hz of the nominal value). Thus, the sensitivity analysis has immediately given us an indication that the current design suf-fers from sensitivity to changes in the width of the horizontal beams which will most likely lead to yield problems during mass production of the current design.

In the next step we will use the statistical Monte Carlo analysis function to investigate the yield impact of the assumed parameter changes in more detail. Monte Carlo analysis uses component tolerances and statistical distribu-tions to randomly vary system parameters during successive simulations. Trends in the data reveal the influence of particular parameters on performance; you can then identify where to change tolerances to improve yield and reduce cost.

Parameter variations of SABER design and model parameters are assigned distributions in the process file. In our particular example, the four in-plane design variables from Table T4-9 length_beam1, length_beam2, width_beam1 and width_beam2 have normal distributions around their nominal values. These distributions are defined in the pro-cess file using a offset with a normal distribution for the two etch actions (see page T4-7).

Variable name Nominal Value in µm

Expected change in µm

Perturbation (%) Sensitivity F in Hz

length_beam1 600 0.2 0.0333 -1.4 -3.35

width_beam1 7 0.2 2.8571 1.05 215.61

width_beam2 5 0.2 4.0000 0.351 100.9

length_beam2 150 0.2 0.1333 -0.351 -1.34


3. Run a Monte Carlo analysis on the resonance frequency in the Y direction with 500 sample points. Refer to Figure T4-41 for parameters.

a. Click on the Monte Carlo icon.

b. Click on the mc loop button and specify 500 runs.c. Add and specify a Small Signal AC analysis inside the loop.d. Add a Batch Measure, a Histogram, and two View Plotfiles in Scope

blocks after the loop. Refer to Figure T4-41 for parameters.

The measure block will automatically record the resonance frequencies of all 500 Monte Carlo runs in the output plot file measure_out. Then measure_out serves as the input to the pfhistogram block, which converts the statistical data into a histogram plot file called histogram_out.

In the plot block, select Plotfile Names from the Plot File pull-down menu. Type the file name.

e. In the Looping commands dialog, click on OK.

The analysis will take several minutes.

∆



Figure T4-41 Settings for Monte Carlo Analysis



Figure T4-42 Measurement Settings


4. Display the analysis results in CosmosScope as shown in Figure T4-43.

a. Plot the two graphs X_Max(MAG(y)) and rel_count into CosmosScope.

b. Select graph X_Max(MAG(y)) and click on the Measurement

Tool icon. at the bottom of the SABER scope window.

Select Statistics > Yield from the Measurement field. See Figure T4-42 for parameters.

The settings will perform a yield measurement in the acceptable driving frequency range of +/- 150 Hz of the nominal value of 7187Hz.



Figure T4-43 Results of the Monte Carlo Analysis

The histogram on the top of Figure T4-43 shows the relative distribution of the resonance frequency of the gyro-scope’s driving mode. The graph highlights the statistical probability of certain frequencies. The graph on the bottom shows the measured frequency points for each of the 500 sample points of the Monte Carlo run. The results of the yield analysis indicate that 71.2% of the device samples will have a driving frequency within the required limit of the nominal value +/-150Hz.

The reliability of a statistical analysis depends largely on the in-depth knowledge of the fabrication technology being used. The realistic yield analysis usually requires a much larger number of variable parameters and sample points than shown in the previous example. Depending on the access to certain fabrication tolerances, the Monte Carlo anal-ysis function can be a powerful tool to help optimize the manufacturability of a MEMS design by giving valuable insight into the sources of manufacturing performance variation. Results of Monte Carlo analysis can also serve as valuable inputs for the optimization of MEMS fabrication processes.

The appearance of the graphs in Figure T4-43 will vary from run to run due to the statistical nature of the Monte Carlo analysis. Needless to say, the accuracy of statistical analysis depends strongly on the number of sample points taken. The bigger the number of runs included in the Monte Carlo analysis, the more accurate and reproducible the results.



4.4.5: Transient Analysis Transient analysis simulates the response of a device to any time-varying input and is most often used to simulate responses similar to what one might measure on a fabricated device. In this section, transient analysis will be used to analyze the response time as well as the detection amplitude of the gyroscope. While transient analysis is the most powerful analysis technique for understanding device performance, it is also the most computationally time consum-ing. In this section and Section 4.4.6 we will also explore how to combine other analysis techniques with transient analysis to determine the same device characteristics in far less simulation time.

Setting Up the Time-Varying SourcesThe gyroscope schematic has two sources of time-varying input: the sinusoidal voltage applied to the combs to keep the mass oscillating in the Y-direction, and the pulse source representing the changing angular velocity of the sensor and its substrate about the x-axis. For this tutorial, the sinusoidal driving signal will have an amplitude of 2 volts as specified earlier and a frequency equal to its natural frequency. The angular velocity input will be a hat profile (spec-ified earlier in the settings) of the pulse source connected to the wx terminal of the reference frame. This angular velocity turns on at 5 ms, takes 6 ms to rise to 1 rad/s, remains on for 15 ms, and then takes 6 ms to return to 0.

The DC voltage offset (dc_comb) of 13.4 volts is the voltage at which the desired stroke of the comb drive (+/-10µm) is achieved for a sinusoidal voltage of amplitude 2 volts applied at its resonance frequency. This optimal voltage was determined by running a vary loop of Small Signal AC analyses varying the global variable dc_comb to determine the value that gives a resonant peak of amplitude 10µm. The interested reader is encouraged to confirm these results. Note that by default, CosmosScope plots the AC analyses in dB. This can be changed to amplitude by double-clicking on the desired signal in its legend and modifying the appropriate attribute.

Transient Analysis for the Mismatched Frequency DesignThis class of gyroscope is designed to sense rotation only while the perforated mass is oscillating steadily in the Y-direction. When a fabricated gyroscope is first powered-up there is a short delay due to inertial and damping effects until the mass is steadily oscillating at its full stroke. Similarly for this simulated gyroscope, the steady state must be achieved before attempting to sense. The simplest approach to achieve this steady state would be to run the transient analysis for an initial quiet period that is long enough to reach steady state. But this initial start-up time can be on the order of hundreds of milliseconds, while one only needs to simulate the sensing response for tens of milliseconds. Run the following quick simulation to illustrate this.


1. Netlist the design with f_yr set to 7177.4 and dc_comb set to 13.4.

a. Double click on the COVENTOR symbol. b. Verify that the global variable f_yr is to 7177.4.

The f_yr variable is the y mode resonant frequency; it is set to the value determined in the small signal AC simulation (see page T4-42).

c. Verify that the dc_comb is set to 13.4.d. If you made any changes, netlist the schematic.



Figure T4-44 Transient Analysis Form


1. Run a transient simulation for 1 millisecond starting from the result of a DC analysis. The settings are shown in Figure T4-44.

2. Plot y.

a. Click on the Transient icon.b. Set the following:

End Time = 1mTime Step = 1uMonitor Progress = 10 Run DC Analysis First = Yes Plot After Analysis = Yes - Open Only

c. Click on OK to launch the simulation.d. Click the >cmd icon at the top-right of the SaberSketch window to

open the Saber Transcript window to watch the simulation progress.

e. When the simulation completes, the plot file will open in CosmosScope showing all the top-level signals.

f. Scroll down to the bottom of the signal list and double-click on the signal y.

The settings above request a simulation from t = 0 to t = 1 ms with an initial time step of 1 microsecond. The simulator will adjust the time step after that as needed.

Monitor Progress = 10 requests that the status of the simulation be printed to the Transcript window every 10 time steps.

Because no signal list was specified in the Input Output tab of the Transient Analysis form, all top-level signals were saved in the plot file.



The result of the simulation should be similar to the plot shown in Figure T4-45. The oscillation in Y after 1 ms is only 125 nm, which is far from its expected steady state value of 10 µm. Because the angular velocity that will be sensed lasts only 15 ms, most of the simulation time would be spent achieving the steady state oscillation.

Figure T4-45 Transient Simulation from a Quiet State

To avoid the initial start-up transient, we wish to start the simulation from the steady state rather than from the quiet DC state. The steady state can be computed directly by solving the governing system of equations in the frequency domain via a small signal AC analysis. The values of all the voltages and positions that result from the AC analysis can then be used as the starting point for a subsequent transient analysis. Because the results of the AC analysis will be used for a transient simulation, the AC magnitude and phase must match the amplitude and phase of all sources in the schematic, and the frequency of all sinusoidal sources must match the frequency specified for the Small Signal AC simulation. The next procedure illustrates how to input the Small Signal AC results to a transient analysis.


3. Turn off the AC source of all sources that are not sinusoidal, and set the sinusoidal source to have an AC value that matches its amplitude.

4. Run an AC Signal Analysis with the Start and End Frequency set to 7177.4 Hz and steady_state as the End Point File set to steady_state as shown in Figure T4-46.

a. Select all six sources connected to the Reference Frame. Double click and set ac_mag to 0.

b. Double click on the sinusoidal voltage source component named v_sin.v_sin_comb. Set ac_mag to 2 to match the amplitude.

c. From the menu bar select Design > Netlist and Design > Simulate.d. Click on the Small Signal AC icon.e. Set the Basic tab as shown below.f. From the Input/Output tab, set the End Point File to steady_state.

AC analysis is used for driving source/frequency/amplitude, and all information is saved into an end point file that serves as a starting point for the transient analysis.

g. Run the simulation.



Figure T4-46 Small Signal Analysis Settings for Steady State

Next, we will use this Initial Point File as the starting point for a transient simulation to observe the sensor perfor-mance in response to an angular velocity.


5. Change the numerical settings of the combs to one.

a. Select the combs and open the Properties Editor.b. Scroll down to select the numerical_settings parameter.c. Change the integration_points and the comb_cell values to one.

For this particular design, changing these settings will speed up the transient simulation without affecting the accuracy of the results. For more information on the numerical_settings parameter, see page A5-83.

d. Select Design > Netlist.



6. Run a transient analysis simulation for 40 ms using the Initial Point file from the previous procedure and the settings as described in the Detailed User Procedure.

a. Click on the Transient icon.b. In the Basic tab of the Time-Domain Transient Analysis dialog, set:

End Time to 40mTime Step to 1uMonitor Progress to 10Run DC Analysis First to NoPlot After Analysis to Yes - Open Only

Run DC Analysis is No because we will use the Initial Point File instead.

c. In the Input Output tab, set Initial Point File to steady_state.d. In the Calibration tab, set

Truncation Error to 0.001Truncation Error Norm to 1

e. In the Integration Control tab, set Method to Trap.f. Click on OK.g. Wait until run is completed (may take up to 30 minutes).

With an angular rotation wx specified as a hat profile through the pulse source, and with the driving mode signal excited at the resonance frequency, run a transient analysis from 0 to 0.04s that starts from the steady-state profile obtained by running the menu command in the previous step.

Settings must be entered accurately. Verify that the Initial Point File is set to steady_state and Integration Control Method is set to Trap.




Figure T4-47 Transient Analysis (length_beam2=150u)


7. Plot the detection, driving and sensing signals. Compare them with the results shown in Figure T4-47.

a. In the Plot window, plot the detection (z), driving (y), sensing signals (wxr), and electrode capacitance (cap).

b. Verify the results shown in Figure T4-47.

Notice that the detection signal starts to rise at about 0.005s, synchronous with the sensing signal. Further notice that the detection signal starts decreasing to a minimum at the same time the sensing signal does.

The general behavior of the detection signal is similar to the sensing signal in terms of delay, rise time, width, and fall time.

The amplitude of the electrode capacitance is about 3.6fF. Note that the electrode capacitance amplitude follows the angular rate signal.

The amplitude of the driving motion (y) is slowly declining over time. This may be surprising because the in-plane mode was excited at its resonance frequency. The reason for this behavior is called numerical damping, which is an intrinsic property of numerical transient solvers. The amount of numerical damping imposed on the system depends on the transient solver settings Truncation Error, Truncation Error Norm, and Integration Method. Of the two Saber transient solvers, the Trap solver imposes less numerical damping and is therefore recommended for resonant sensor structures such as resonators and gyroscopes. The Truncation Error, specified in the Calibration tab, defines the maximum allowable error at each time step of the transient simulation. The smaller the truncation error, the more accurate the simulation. However, the smaller the truncation error, the smaller the time step, and thus the longer the simulation time. The cost of a highly accurate simulation with little numerical damping is a dramatic increase of the simulation time.

The transient simulation time can be dramatically reduced by grounding degrees of freedom in the schematic. Grounding the central wires (x, rx, ry and rz) of the gyro will reduce the simulation time by almost 50% without having any effect on the results shown in Figure T4-47.




8. Visualize the transient results in Scene3D. a. In the Scene3D window, click on the Open Plotfile icon, and select the gyro_transient.tr.ai_pl file.

b. Set the Scale to Z and enter 5 as the scale factor. c. Set the Exaggeration in the X/Y directions to 3.d. Use the Play button to view the transient response of the

gyroscope.

Figure T4-31 shows the harmonic response at the X, Y, and Z modal frequencies.

0 sec 0.01 sec

0.04 sec

0.02 sec 0.03 sec



Matching Resonance Frequencies for Driving and Detection ModeA second transient run shall reveal the design trade-off of matching resonance frequencies for the driving and the detection mode.


1. Netlist and simulate the design with the length of beam2 set to 280.5u and f_yr value set to 6552.6.

a. Double click on the COVENTOR symbol. b. Set length_beam2 to 280.5u and f_yr to 6552.6.

The frequency is derived from the run plotted in Figure T4-38.c. From the menu bar select Design > Netlist and Design > Simulate.

2. Run the AC Steady State command with a frequency of 6552.6.

a. Under the Architect menu in SaberSketch, select AC Steady State Transient.

b. In the Steady State Analysis dialog set the Frequency to 6552.6 and verify that the Initial Point File Prefix is steady_state

c. Click on Apply and Close.

An AC analysis is used to generate an initial point file steady_state6552_6 that enables a transient simulation starting from a steady state driving mode.

3. Run the transient simulation again using the steady_state6552_6 file.

a. Click on the Transient icon.b. Set the tab settings as described on page T4-64.c. From the Input Output tab, set the Plot File field to tr6552_6.d. Modify the Initial Point File to steady_state6552_6.e. Click on OK.

With an angular rotation wx specified as a hat profile through the pulse source, and with the driving mode signal excited at the resonance frequency, run a transient analysis from 0 to 0.04s that starts from the steady state profile obtained by running the macro in the previous step.

f. Wait until run is completed (may take up to 20 minutes).

4. Plot the results of the simulation in CosmosScope.

a. In the Plot window, plot the electrode capacitance (cap), the sensing (wxr), driving (y), and detection (z) signals.

b. Verify the results shown in Figure T4-48.

Observe that the detection signal starts to rise at about 0.0075s, which is delayed by 0.0025s from the sensing signal.

Note that the detection signal persists long after the sensing signal has decreased to zero.

The maximum amplitude of the electrode capacitance is about 50f F, which is more than 15 times than in the previous simulation run with length_beam2 = 150u.



Figure T4-48 Transient Analysis (length_beam2 = 280.5u)

Unless otherwise specified, in the rest of the tutorial length_beam2=150u and f_yr=7.1774k.

A design with a match between the Y and Z resonant frequencies guarantees a maximum output signal. However, the dynamic behavior is comparably slow compared to designs with mismatching frequencies. The right distance between the detection and driving frequency is a trade-off between output signal amplitude and response dynamic and therefore, one of the most important design criteria of gyroscopes. The objective is to have a detection signal that mimics the general behavior of the sensing signal with a significant capacitance output for a electronic readout circuit.



4.4.6: AC Analysis: Determining the Detection Amplitude This section shows the user that transient analysis is not always necessary. One way to get the amplitude of the detec-tion signal for a certain value of the sensing (rotation) signal is by running an AC analysis as follows.


1. Run a small signal AC analysis with the parameters given. Display the results in CosmosScope.

a. Use the previous file settings with length_beam2=150u and f_yr=7177.4.

b. Select the wx c_pulse source on the left edge of the reference frame. Set initial to 1.

This setting applies a constant sensing (rotation) signal whose value is equal to the maximum of the pulse used for the transient simulations.

The driving signal is the same as that used for the transient simulation.

c. Double click on the sine source connected to the F terminals of the combs. Make sure the ac_mag is set to 2.

d. Run a Small Signal AC analysis with these settings:Start Frequency 7.0kEnd Frequency 7.6kNumber of Points to 1000Increment Type to LinRun DC Analysis First to YesPlot After Analysis to Yes - Open Only From the Input Output tab, set the Plot File field to detect_amp.Set the End Point File field to ac.

e. In the Plot window, display y and cap. f. Ctrl select the phase graphs and delete them. g. Select each remaining plot and click on the right mouse button.

Select Attributes from the menu and change the View to Mag(y).h. Verify the results shown in Figure T4-49.

The electrode capacitance (cap) has two peaks: the resonance frequency of the detection mode at 7467.3Hz and the driving mode frequency of 7177.2 Hz. The signal amplitude at the driving mode frequency is about 1.7fF (half the peak to peak value), which is matching the capacitance amplitude in Figure T4-47.

This analysis reveals that for a constant sensing (rotation) mode signal, the detection mode oscillates at the driving mode frequency with an amplitude equal to that obtained by a time-consuming transient analysis.



Figure T4-49 Detection Amplitude

4.4.7: Impact of Plate CurvatureMEMS structures are typically deformed by surface stress caused by the manufacturing process. The common Archi-tect parameter curvature can be used to study the impact of rigid plate curvature on the device performance. The cur-vature parameter is available in the rigid plate, beam, electrode and the comb components. Please refer to the individual component description chapters on pages A5-10, A5-18, A5-49 and A5-56 for more details.

With the six sub-parameters of the component parameter curvature (x0, y0, c1, c2, c3, c4, c5), the user can specify a parabolic curvature surface of a rigid plate in the reference coordinate system (see page A5-137):

The constants of curvature profile are usually derived from interferometric measurements of the released structure or by measuring the vertical position of designated points such as plate corners or the plate center. Alternatively, if the material stress gradients of the fabrication process are well known, plate bending can be analyzed in a FEM verifica-tion step using MemMech.

For the following simulation we assume a symmetric bending of the perforated plate with its local minimum in the center of the plate. We therefore only need to specify the polynomial constants c1 and c2 of the equation above.

z f x y( , ) c1 x x0–( )2 c2 y y0–( )2 c3 x x0–( ) y y0–( ) c4 x x0–( ) c5 y y0–( )+ + + += =



We will start by specifying a fixed curvature by setting the design variable to c=1. The simulated parabolic curvature surface of a rigid plate will consequently be set to (compare with A5-10):

The corners of the plate will consequently experience a vertical displacement of 88.2 nm (the upper right corner of the perforated plate has the coordinates x=210µm, y=210µm).

Figure T4-50 Operating Point Report


1. Verify that the components that are connected to the central wire have the curvature parameter set to (c1=c, c2=c).

a. Select the rigid_plate, electrode, combs, and beams that are linked by the central bus wire using the Ctrl button of the keyboard.

b. Release the Ctrl button, click on the right mouse button, and select Properties.

The property dialog will only show the common parameters of the selected components.

c. Verify that the common parameter curvature is c1=c, c2=c.

We have defined the two polynomial constants c1 and c2 by the design variable c, which is defined in the COVENTOR symbol.

d. Close the Property dialog when finished.

Selecting multiple schematic components by holding down the Ctrl button is a convenient method to set and verify common component parameters like knot1, curvature, display_messages, layer, etc.


2. Set the design variable c=1. a. Double click on the COVENTOR symbol to edit its attributes.b. Change the value of the design variable c from 0 to 1.

3. Run a DC Operating Point analysis. a. Click on the DC Operating Point icon. b. In the Operating Point Analysis dialog that appears, click on OK.

4. Generate an Operating Point report. Compare the report with Figure T4-50.

a. From the Saber Transcript window menu, select Results > Operating Point Report.

b. Click on the Waveforms tab. In the signal list, clear any signals that may appear and type /z /cap. Click on OK.

c. Verify the results that appear in the report window, as shown in Figure T4-50.

z f x y( , ) x2 y2+= =



The applied curvature causes a central knot (center of the plate) to move 244 nm in the negative Z direction, which is about 282 nm below the initial equilibrium without curvature; compare with Figure T4-22.The new equilibrium is mainly the result of the curvature-caused offset of the beam ends that are connected to the plate (see Figure A5-10). The second pin, cap, shows the curvature-caused capacitance between the detection electrode and the curved plate. The apparently tiny curvature is causing a capacitance reduction of about 16%, which will have a important effect on the sensitivity of the device.

Fabrication defects like plate curvature and beam side wall angles are often the cause of mismatches between mea-sured and simulated data. Furthermore, unsymmetrical plate curvature (a mismatch between the plate center and the local minimum x0, y0 of the assumed parabolic shape) are often the source of unexpected device behavior like stag-gering motions and an increased cross sensitivity.

The Saber vary analysis is a convenient way to investigate the reasons for a mismatch between measured data and ideal device behavior.

Figure T4-51 DC Vary Analysis Settings


5. Vary the c parameter from 0.5 to 2 by 0.5. In the inner loop, run a DC analysis, and display the output for z and cap, as shown in Figure T4-51.

a. Click on the Vary icon.

b. In the Looping commands dialog, vary /c from 0.5 to 2 by 0.5.c. For the inner loop run an DC analysis:

From the Input/Output Tab, set the Signal List to /z /cap For End Point Plot File, select Specified from the drop-down arrow, and enter curvature_dc in the value field.

d. After the loop select the View Plotfiles in Scope option; compare with Figure T4-51. Click on OK.

e. In the Plot window, verify the DC values for z and cap. See Figure T4-52.

f. File > Exit the Architect program.

The curvature vary analysis must not include the value c=0 referring to a plate without curvature. The vary analysis will fail and show the error message:*** ERROR "CLASS_STAMP_CHANGE" *** Alter would cause “typology change”. The reason for this error message is a performance optimization in the beam component that gets triggered by the curvature parameter. Beams with curvature->c1=0, c2=0 have a slightly faster simulation performance.


Section 4: Gyroscope Design FEM and Architect Comparison Version 2008M

Figure T4-52 Results of the Vary Analysis

In similar fashion, the vary analysis can be used to investigate the impact of plate curvature on the resonance frequen-cies or even on the transient performance. For our gyro example, the curvature effect on the first resonance frequen-cies is very small.

4.5: FEM and Architect ComparisonThis section demonstrates the following techniques:

how to mesh the 3-D model created from the layout extracted from the Architect schematichow to conduct a modal analysis of the FEM mesh using Analyzer’s MemMechhow to conduct a pull-in analysis using Analyzer’s CoSolve

The tutorial then presents a comparison of the system model results with FEM analysis results for resonance frequen-cies and pull-in behaviors.


Section 4: Gyroscope Design FEM and Architect Comparison Version 2008

4.5.1: Mesh Creation

If you do not have a license for Scene3D, you can still build a solid model from your schematic: Open the schematic you want to extract, and from the Architect Sketch window, select Architect > Export for Designer. From the Function Manager’s Designer tab, select New from Architect from the Preprocessor icon’s drop-down menu.


1. Use the Preprocessor icon’s New from Architect option to create a 3-D model of the gyroscope.

a. Save the settings file as fem_gyro.mps.b. From the Architect tab, make sure the gyro.ai_sch is selected.

The gyro schematic must have been opened in Scene3D for the following procedure to work. If you did not open the schematic in Scene3D, use the Architect > Export for Designer option inside Architect before continuing.

c. Navigate to the Designer tab of the Function Manager.d. Make sure the Apply Offset Values option is unchecked.e. From the Preprocessor icon’s drop-down menu, select New from

Architect.f. Save the model as gyro.

2. Place the electrode and plate layers into the mesh folder.

a. Hide the Substrate layer.b. Right-click on the elec layer and add it to the mesh model. Repeat

this procedure for the poly layer. These layers now appear in the Mesh Model section of the Geometry Browser.

3. Name parts of the gyro as shown in Figure T4-53.

a. Choose Part Selection Mode from the toolbar.

b. Click on one of the beams. The plate and all beams are selected.c. Right-click on the part, or on the highlighted item in the Geometry

tree, and select Set Name. Enter the name gyro.d. Using the same method, name the two combs Ucomb and Lcomb,

and the electrode parts elect_lower, elect_center, and elect_upper, as shown in Figure T4-53. If necessary, hide the gyroscope to see the underlying electrodes.



Figure T4-53 Gyro Part Assignments


4. Name all the end faces for the stators and tethers fix.

a. Select the Face Selection Mode.

b. Using orientation and zoom features, right-click on an end face and set the name to fix. Set this same name for each tether end face, and also for both comb stator end faces. See Figure T4-54.

Ucomb

Gyro

Lcomb

elect_center

elect_upper

elect_lower



Figure T4-54 Naming Tether and Comb Stator End Faces as fix


5. Use the Properties dialog to suppress the electrode from any mechanical simulation.

a. In the Part Selection Mode right-click on the electrode parts and select Properties.

b. In the Properties dialog, check the Suppress, except for MemElectro.

6. Assign the following conductor names:elect_lowerelect_centerelect_uppercomb_lowercomb_upperplate

a. Click on the Conductor Selection Mode icon. Assign the following conductor names:

elect_lowerelect_centerelect_uppercomb_lowercomb_upperplate

tether end face

comb stator end face

comb stator end face

tether end face

tether end face



Meshing

Figure T4-55 Mesher Settings Dialogs


1. Choose a Extruded/Split and Merge mesh for both mesh regions and prescribe a parabolic element order. For the electrodes, assign an element size of 10. For the gyro, assign an element size of 14.

a. Right-click on region that contains the electrodes and select Mesher Settings.

b. In the dialog that opens, select the following settings:Extruded bricks Mesh TypeSplit and Merge AlgorithmParabolic Element order.Extrude Direction ZElement size 10 in the Planar and Extrude directions.

c. Right-click on the region that contains the gyroscope, and select the same settings as used for electrodes, except enter an Element size of 14.

The gyro has so many features that MemElectro creates a very refined mesh along its edges. But the large, unfeatured rectangles that make up the electrodes do not get refined much at all. So the element size for the electrodes is reduced in comparison to the gyro.

2. Generate the mesh. a. Click on the Generate Mesh icon to generate the mesh for both regions.

The resulting mesh is shown in Figure T4-56.

The mesh dimensions for this tutorial were selected to optimize accuracy and simulation time. When meshing your own designs, you should conduct a mesh convergence study to find the mesh that gives acceptable results, while minimizing simulation time. The section that begins on page T4-87 shows how to conduct a mesh study.

Electrode Settings Gyro Settings



Figure T4-56 Generated Mesh



4.5.2: FEM Simulation

Modal AnalysisIn this next procedure, modal analysis is performed on the gyro. MemMech solves an eigenvalue problem to find the natural frequencies and mode shapes of the structure. We will view the modal results and compare them to those of the system model.

Figure T4-57 MemMech Preliminary Settings


1. Configure the MemMech Settings dialog to run a modal analysis with 6 modes.

a. Choose the MemMech solver.b. Select the model for the Model/Mesh field.c. In the Analysis field, select create a new analysis.d. Click on the Solver Setup icon.e. Set the dialog as shown in Figure T4-57. Note that this mechanical

simulation has six modes.f. Click on Next.



Figure T4-58 Modal Domain Results

The results for X, Y, and Z translational modes are shown in Table T4-10 for both system and FEM analyses. Also shown are the system model results for the case when massive beams were used instead of massless beams.

Table T4-10 Analysis Result Comparison

The two different Architect results show slight differences, depending on the beam components used. The simulation results in the first line were done using linear_massless_beam_1_2seg and the second using linear_beam_1_2seg beam components (see the beam reference chapter on page A5-9 to learn more about the different beam components).

The two in-plane modes fx and fy show good match between Architect (massive beams) and the FEM. Only the out-of-plane results (fz) show a slight different of about 4%. The difference between the FEM and Architect model might be explained by flexibility of the perforated plate. The Architect model approximates the perforated plate to be rigid and leads therefore to a slightly stiffer response for the out-of-plane mode fz. Also, the FEM mesh density used for the simulation is not sufficient to match the rotational out-of-plane modes correctly. Mechanical FEM simulations that involve beam torsion require a mesh density of at least four bricks in the beam’s cross sections for accurate results. For tutorial purposes, a simpler mesh was created, but mesh convergence studies are always strongly recom-mended in order to gauge the accuracy of the results. For an example of a mesh convergence study, see page T4-87.


2. In the SurfaceBCs dialog, fix the ends of the tether and combs.

a. Click on SurfaceBCs.b. For Set1, set FixType to fixAll for Patch1 fix.c. Click on OK.

3. Start the simulation. a. Click on Run in the MemMech BCs window.b. Name the analysis MechGyro and save your settings.

4. View Mode Domain results. a. The results for the six modes (see Figure T4-58) are viewed by choosing the Mode Domain table from the results window.

Analysis fx fy fz

Architect (massless beams) 30871 7180.2 7474.5

Architect (massive beams) 29105 7033.0 7278.3

FEM 29402 7042.6 7004.4

Mode number 5 2 1



Pull-in AnalysisA pull-in analysis is an electromechanical analysis that is conducted in CoSolve. A voltage trajectory is specified, and the displacement is calculated for each voltage up to the pull-in voltage, which is the greatest voltage for which an equilibrium position can be found. At each point of this trajectory the mechanical solver MemMech and the electro-static solver MemElectro are employed. In this section, you will configure MemElectro, MemMech, and CoSolve.

MemElectro Turbo

This tutorial simulation shows the benefit of the Turbo feature, which is accessed from the MemElectro Set-tings\Advanced dialog and is turned on by default. The Turbo feature creates a more efficient mesh because it refines the surface mesh at the model edges, instead of throughout the entire model. For a model with parabolic bricks, Turbo can cut simulation time to as much as one-eighth the time of a non-Turbo simulation.

If you ran this simulation without the Turbo feature, your simulation time would be significantly longer. On a com-puter with dual 3 GHz processors and 2 GB of RAM, this simulation without Turbo takes 12 hours. With Turbo, the simulation on the same machine takes 4 hours. Note that the pull-in results will be different. The non-Turbo mesh will give slightly more accurate results because it has a more refined mesh. The trade-off is simulation time.

To further speed up the Turbo simulation, you can partition the device, and then run with the symmetry feature. This technique is described on page T4-88. For more information on the Turbo feature, see page R3-31.

For more information on optimizing meshes, see the mesh convergence study beginning on page T4-87.


1. In the MemElectro solver:Accept the default solver settings.Designate elec_center as a variable.Apply a voltage of 13.4 to the combs.

a. Select the Analyzer tab of the Function Manager.b. Choose the MemElectro solver.c. Select the gyro model in the Model/Mesh field.d. Click on the Solver Setup icon, then click on Next.e. Choose Conductor BCs and set a Variable value of Voltage1 for the

Conductor elect_center. f. For comb_upper and comb_lower, apply a voltage of 13.4.

By applying a voltage to the combs, you are creating the same setup that was used in the Architect pull-in simulation. In Architect, the voltage was applied to the combs using the global variable dc_comb.

g. Click on OK.h. Click on Close to return to the Function Manager.




2. Configure MemMech to run without modal analysis.

a. Return to the Function Manager and choose the MemMech solver. b. Click on the drop-down arrow beside Analysis field and select create a

new analysis, then click on the Solver Setup icon.c. Set Additional Analysis to none.d. Click on Advanced.e. Set the Solver Memory field to 75% of the amount of RAM that is in

the computer you are using. For example, if you have 1 GB of RAM, set this field to 750 MB.

CoSolve simulations are memory-intensive. Increase MemMech’s memory allotment so the simulation will go faster.

f. Click on OK.

3. Set up a CoSolve simulation with the gyro model.

a. Change the solver to CoSolveEM.b. Select the model.c. Set analysis to create a new analysis, then click on Solver Setup.

4. Set up a trajectory run using the Relaxation Iteration method.

a. In the CoSolveEM Settings dialog, select Voltage as the Independent Variable.

b. For Analysis Options, select Detect Pull-in.c. Set the Iteration Method to Relaxation. d. Click on Next.

5. Set a trajectory that varies the voltage from 0.5 to 5 in 0.5 steps.

a. Click on trajectory.b. Set the trajectory dialog as shown below.

6. In the Voltages dialog, set a t1 absolute trajectory, with a pullin value of 0.15.

a. Click on Voltages.b. In the Voltages dialog set Voltage1:

Trajectory to t1Type to AbsolutePullIn to 0.15.

c. Click on OK.

7. Start the simulation. a. In the CoSolveEM BCs window, click on Run. b. Name the analysis CoSolveGyro when prompted, and save settings.



This simulation may take several hours. The simulation shown in this tutorial took about 4 hours to complete on a computer with dual 3 GHz processors and 2 GB of RAM. Your simulation time will vary according to your computer resources.

When running CoSolve, it is not uncommon to see the MemElectro warning: "Raw Cap. matrix (see log) should have + diagonal and - off-diagonal terms." When electrostatic results have high accuracy, the capacitance matrix should have the form that the diagonal, or self-capacitance terms are positive, while the off-diagonal or cross-capacitance terms are negative. The magnitudes of these terms will be such that the column and row sums are zero. Therefore, an examination of the raw capacitance matrix can suggest the accuracy of the computation.Finding terms that do not conform to this sign pattern is an indication that the computation may not be as accurate as desired. However, the absolute value of the terms must be considered. If there are off-diagonal terms with positive sign, but their magnitude is several orders down from the largest terms in the matrix, this should not be a concern, and the solution is likely to be good to engineering accuracy. As always in FEM or BEM numerical analysis, a convergence study is required for a complete understanding of the accuracy of the computations.


8. View simulation results. a. When the simulation is complete, from the Job Queue dialog, make sure that the CoSolveGyro simulation is selected, then click on the View Results icon.

b. In Analysis Results window select the Displacement Table results, as shown in Figure T4-59.

Observe the effect on mass displacement as the electrode voltage increased. At 3.125 volts, the mass is 0.32 µm below its initial position. Note that this table only includes steps that converged.

c. Select the Displacement Graph. Verify the MinZ values corresponding to different values of t1, as shown in Figure T4-59.

To view only the MinZ plot, in the plot window, double click on any of the plots. In the dialog that opens, click on the MinZ map name to highlight, then click and hold on Map Show. Select Show Selected Only.

The published graph format was created using a Visualizer macro. See page R9-34 in the CoventorWare ANALYZER Reference for details.

d. Review the Summary table, which shows how many iterations each step needed to converge and which steps did not converge.



Figure T4-59 Displacement Results

Figure T4-60 Pull In Results Window


9. Verify the pullin results. a. Select the Pullin table results.

The pull-in result is actually a range of voltages. In this case, pull-in occurs between 3.25 and 3.375 volts, which is the largest tolerance allowed by the 0.15 volt pull-in error setting.



Non-Turbo Results

If you ran the simulation without the Turbo feature, your pull-in results should be similar to the ones shown below. The Turbo and non-Turbo results are different despite that they were created using the same nominal mesh size in the Preprocessor and using the same simulation setup.

Figure T4-61 Pull-in Results without Turbo

Why the different results? Because the Turbo mesh creates a different number of surface panels. The volume and sur-face element counts are reported in the Preprocessor’s Mesh Quality window. MemElectro refines the surface mesh to create panels; this number is reported in the log window. MemElectro non-Turbo refines the surface mesh by dividing them into eight panels. MemElectro Turbo only refines those surface elements near the feature edges.

Table T4-11 Element Count Comparision

To judge the accuracy of any mesh, whether you are using Turbo or not, you must conduct a mesh convergence study. The section that begins on page T4-87 presents a detail mesh convergence study of the gyroscope mesh.

Elements Turbo Non-Turbo

Volume 8431 8431

Surface 20148 20148

Refined Panels 40416 80592

With design projects that have complex designs, large meshes, or numerous simulations, the project database can get very large; and the database file may get fragmented because it starts as a small file and grows incrementally as more data is added. If this happens, run Disk Defragmenter (accessed from Start > Programs >Accessories > System Tools). You can also copy the CPDB and GBAK files, delete the originals, and work with the copies to ensure that these files are also defragmented.



4.5.3: FEM and Architect ResultsAs a comparison, Figure T4-62 shows Architect pull-in results generated with a DC transfer analysis (page T4-34).

Figure T4-62 System Model Pull-In Analysis

Architect shows a pull-in at 3.25 V. Compare this result to the FEM analysis results shown in Figure T4-60 and Fig-ure T4-61. The system model offers an accurate tool for solving this type of problem at a fraction of the time needed for the FEM analysis. The Architect pull-in analysis took less than a minute seconds on a 3 GHz dual processor, 2 GB machine. The FEM\Turbo analysis with Turbo took about 4 hours.

A mesh convergence study is required for a definitive comparison of FEM/BEM analysis with Architect analysis. See the section beginning on page T4-87 for details.


Section 4: Gyroscope Design Mesh Convergence Study Version 2008M

4.6: Mesh Convergence StudyThe Gyroscope Tutorial starting on page T4-1 shows users how to conduct an Architect analysis of a simple gyro-scope. It also shows how to run FEM analysis on a model created from the layout extracted from the Architect system model. In order for a comparison of Architect results with those of FEM/BEM to be meaningful, we must know the accuracy of the FEM/BEM results. For any device, to judge the accuracy of FEM/BEM results, you must conduct a mesh convergence study. The study could include modal frequencies and generalized masses, capacitance matrix entries, forces, and displacement of the proof mass as a function of applied voltage. Of particular interest is the pull-in comparison because coupled electromechanical analysis is at the heart of the MEMS design cycle, and when accu-rate, Architect is significantly less expensive computationally than Analyzer.

In the FEM analysis tutorial, you were given mesh dimensions that were a trade-off between simulation results and computational resources. This section will explore alternate mesh dimensions and mesh types and their impact on the simulation accuracy.

4.6.1: General Mesh Convergence StrategyTo conduct a mesh convergence study, the general strategy is to create multiple models that have different element sizes. You may want to vary the mesh in only one direction of interest. For example, if your device will experience a lot of stress in the Z direction, you may want to vary the mesh only in that direction. The basic procedure for conduct-ing a mesh study is outlined below:

1. Create multiple models that have different meshing characteristics. Vary the mesh as follows:first model with element size = Xsecond model with element size = X / square root of 2third model with element size = X / 2Element size may also require local changes to map smaller features with refined mesh. Other variables may include linear or parabolic element order and various mesher algorithms.

2. Give all the models the identical face names, part names, conductor/dielectric names. Using the same names with each model allows the same project settings to be applied.

3. Compare relevant results to determine if convergence is obtained.4. Plot results vs. mesh, refine mesh further if convergence is not reached.

Convergence in one type of simulation does not imply convergence in all types of simulation. When conducting a mesh study, consider which type of physical phenomenon is important, then choose your module accordingly.

In this mesh convergence study, we will first vary the size of the mesh elements using one mesh type, and compare results. Then we will try different meshing types using the same mesh sizes. and compare results.

Gyroscope Mesh SeriesBy performing analyses with a series of systematically refined meshes, we can expect to be able to make a judgment as to the accuracy of the solutions. An important criterion for this to be true, however, is that the meshes be systemat-ically refined, which means that all elements are reduced in size by the same factor. As mesh density increases, the requirement for systematic refinement relaxes, but because efficiency demands that we use the coarsest meshes possi-ble that will still allow a judgment of accuracy, we may not be working at mesh densities where careful refinement can be ignored.

In concept there are two meshes to consider: one is the volume mesh for the FEM analysis, and the other is the sur-face mesh for BEM analysis. The surface mesh consists of the faces of the volume elements, plus a refinement of these at model edges, which MemElectro creates automatically.

In the case of the volume mesh, we expect that the deflections to be computed by MemMech are small enough that no more than one element in the vertical dimension will be needed, so convergence will depend on the density in the hor-izontal directions. Note that nearly all of the deflection will take place in the tethers.


Section 4: Gyroscope Design Mesh Convergence Study Version 2008

In the case of the surface mesh, again the vertical surfaces are less important than the horizontal surfaces, so conver-gence will largely depend on refinement in the horizontal directions. However, getting the charge distribution correct on both the horizontal and the vertical surfaces depends on refinement of these surfaces as the model edges are approached. Again, MemElectro will do that automatically, and we need not worry about it.

So we would like to build meshes that have a single volume element in the vertical direction and are systematically refined in the horizontal directions. However, the hole pattern requires that the largest usable element is 20 microns in the horizontal directions, and the next largest is 10 microns. This suggests that the best systematic refinement would be successive quadrupling of the number of elements, but successive doubling is more practical from a computational cost perspective.

The mesh sequence used for this study is as close to successive doubling as we can get, considering the constraint above:

The coarse mesh is created with a 20 micron element size.The medium mesh is created with a 14 micron element size, thus reducing all elements in size by √2, except those between the holes.The fine mesh is created with a 10 micron element size, reducing all elements in size from the coarse mesh in size by 2.The ultra-fine mesh is created with a 7 micron element size, reducing all the elements in size from the medium mesh by 2.

The mesh study also varies the meshing type. It includes simulation results for Manhattan meshes, extruded meshes, and tetrahedral meshes with the same mesh sizes.

Symmetry FeaturesBecause we will be reducing the element size, we will be increasing simulation time. To reduce simulation time as much as possible, we use MemElectro symmetry boundary conditions.

You can also reduce simulation time by partitioning the model so that you can simulate half of the device. Most of the simulations in this section were performed on the entire device on a computer with a 3.2 GHz processor and 2 GB of RAM, but if you would like to run the simulations yourself, you may want to save simulation time and resources by partitioning the model.

Figure T4-63 shows one possible way the gyro may be partitioned. A partition plane was created using the coordi-nates (-210, 0, 12.05), (210, 0, 12.05), (0, 0, 2.05). For more information on partitioning, see page D4-6.

Figure T4-63 Partitioned Gyro and Electrode

The mesh study results shown in this section were generated in CoventorWare 2004. Results generated with CoventorWare 2008 would be slightly different because of improvements to the meshers. The mesh study strategy presented here is not limited to a particular design or to particular version of CoventorWare.



If you partition the model, you must apply additional boundary conditions:Give the faces on the gyroscope and the electrodes that were created along the partition plane the same name; for example: symmetry.In MemElectro, apply the SymmetryBCs boundary condition to the symmetry patch. In MemMech, apply the SymmetryPlane surface boundary condition to the symmetry patch.

4.6.2: Manhattan MeshFor most rectilinear device geometries such as the gyro, Manhattan meshing produces the best meshes. So we will start the mesh convergence study with this mesh type. However, the proof mass of this gyro consists of a square plate perforated with many release holes, and it has comb fingers along two sides. This combination causes difficulties because the comb finger placement relative to the hole placement causes high aspect ratio elements for any but an extremely fine (large number of small elements) mesh, as shown in Figure T4-64.

Figure T4-64 Manhattan Mesh Applied Gyro

A better approach is to partition the proof mass. The placement of the partitions has to be such that the comb finger areas are separated from the area with holes. This is what has been done to produce the mesh shown in Figure T4-65. Note that the smaller elements needed for the fingers are isolated by the partition from the area of larger elements around the holes. A close-up view of the mesh is shown in Figure T4-66, where the partition plane location is also indicated. Compare this with the mesh shown in Figure T4-64.

Note the thinelements created through the plate



Figure T4-65 Manhattan Mesh after Partitioning

Figure T4-66 Closeup of Partitioned Mesh

Figure T4-67 shows the fine mesh used in the study. This mesh has 5296 hexahedral volume elements for FEM mechanical analysis and 34926 quadrilateral elements for BEM electrostatic analysis. As will be shown, this mesh is the best choice for reasonable accuracy with acceptable computational cost. The elapsed time for a coupled electro-mechanical analysis (CoSolve) with such a mesh is approximately 2 hours (Intel Pentium 4 @ 3.2GHz), and the memory allocation is less than 400 megabytes if one plane of symmetry is exploited (not shown in figures).

Partition Plane



Figure T4-67 Fine Mesh

Table T4-12 shows the element count for the meshes. "Volume Elements" are those used for FEM analysis in Mem-Mech. "Surface Elements" are the base mesh for MemElectro. Volume element and surface element counts are reported in the Preprocessor’s Mesh Quality window (accessed from the Mesh menu). "Refined Elements" are the elements automatically constructed by MemElectro from the surface elements.This element count is reported in the CoventorWare Log window. Figure T4-71 on page T4-96 shows an example of a MemElectro mesh.

Table T4-12 Manhattan Mesh Element Counts

ConvergenceWhile our analysis goal is the coupled physics computation of the deflection of the proof mass as a function of the voltage bias applied between the proof mass and the electrodes, judgment of convergence should begin with quanti-ties that are less costly to compute. The obvious choice is uncoupled analyses.

Using MemMech, we can compute the modal response of the tethered proof mass, which allows us to judge whether there are sufficient elements to capture the stiffness accurately. There is no geometric inaccuracy in any mesh for this model, so we are always guaranteed to calculate the mass accurately. Therefore the calculated modal frequency is an indicator of the convergence of the mechanical response of the model.

Using MemElectro, we can compute the capacitance between the proof mass and the electrodes as a guide to conver-gence. However, for the deflection simulation we intend to do, capacitance may not be a good indicator of conver-gence. In the deflection calculation the electrostatic force will be applied to the mechanical structure, so the convergence of the force is more pertinent. Note that the force is the derivative of the capacitance with respect to dis-placement, so the convergence of the force should be expected to be slower than that for the capacitance. Therefore it is the convergence of the force between the electrodes and the proof mass that should be examined.

Mesh Volume Elements Surface Elements Refined Elements

coarse 2015 6238 19828

medium 2625 7722 22232

fine 5296 14412 34926

ultra-fine 9442 32862 58788



In Table T4-13, the quantities under discussion are presented as a function of the mesh density. The table shows the convergence of elementary quantities for mechanical and electrostatic analysis. "Modal Frequency" is the frequency for the vertical bending mode of the proof mass on its fixed-ended tethers. "Capacitance" is the absolute value of the capacitance matrix entry for the six-conductor gyro that gives the relationship between the center electrode and the proof mass. "Force" is the vertical component of the electrostatic force between the proof mass and the electrodes under a 1-volt bias.

Table T4-13 Mesh Study Results

Plotting the results for the frequency and force against the reciprocal of the number of elements allows an estimate of the accuracy of the computations. These plots are shown in Figure T4-68:

Figure T4-68 Plots of Frequency and Force Results

The left end of the abscissa is zero, indicating the infinite limit of the number of elements. Therefore the intersection of the data curve with the ordinate is the answer to the continuous problem. (This is a graphical approximation to the procedure known as Richardson extrapolation.) Because the log of the data is plotted, if we have a systematic mesh refinement and sufficient mesh density to reveal the asymptotic convergence rate of the algorithm, the data should be well represented with a straight line. In many cases, the present one included, this will be difficult to achieve because error introduced by the BEM acceleration algorithm (precorrected-FFT) will distort this asymptotic trend and the intersection may be difficult to judge.

The data collected from the four meshes appear typical in that the asymptotic convergence rate is more apparent as the mesh get finer. Recognizing that, we can judge the intersection reasonably accurately using the results from the three finest meshes. From Figure T4-68 we can estimate:

The correct modal frequency is approximately 7030, so the error for the fine mesh is 10, or 0.14%.The correct force is approximately 0.2, so the error for the finest mesh is 0.025, or 13%.

Mesh Modal Frequency Capacitance Force

coarse 7.05441e+03 5.18038e-01 1.21406e-01

medium 7.05259e+03 5.91076e-01 1.51045e-01

fine 7.04010e+03 6.23706e-01 1.74091e-01

ultra-fine 7.03647e+03 6.24080e-01 1.75386e-01



Clearly the error in the analysis of displacement as a function of applied bias voltage will be driven by the error in the computation of the electrostatic force.

Interpretation of ConvergenceGiven the convergence data for the elementary quantities, we can make a judgment about which mesh to use for cou-pled electromechanical analysis. Of course we would like to use no finer a mesh than needed for the accuracy we desire.

When coupled electromechanical analysis is undertaken, in essence we solve the equation

for x, the mechanical displacement, subject to the force, F, from electrostatic analysis, and the stiffness, k. If the errors in F and k are known, then the error in x can be deduced. From the convergence study we have estimates for the errors in force and in frequency, ω for any given mesh. The error in the stiffness must be estimated. The stiffness and the frequency are related by

Letting a tilde denote computed quantities and a subscript e denote error quantities, the correct frequency is

Therefore,

If k is replaced with its computed and error representations,

This reduces to

which indicates that the relative stiffness error is twice the relative frequency error, and like the computed frequency, the computed stiffness converges from above. As expected, the model structure becomes less stiff, and its modal fre-quency decreases as the number of elements is increased.

Now we can estimate the displacement error we should expect using any of the meshes for which we know the error in the elementary quantities. Taking a similar approach, the displacement computation is a generalization of the expression

So for computed and error quantities we have

Converting to relative errors and using the binomial theorem gives

A priori, we have no reason to consider the stiffness error to be higher order, as we imply above, but the data in Table T4-13 shows that indeed the stiffness computation error in MemMech is small compared to the force computation error in MemElectro.

kFx /=

2ωmk =

eωωω += ~

2)~( emk ωω +=

)~2~(~ 22eee mkk ωωωω ++=+

)~/(~2~22 ωω

ωω

eee O

kk

+=

kFx /=

)~/()~(~eee kkFFxx ++=+

)~/(~~ kkOFF

xx

eee +=



In conclusion, the convergence study for the elementary quantities indicates that the relative error we can expect in the CoSolve computation of displacement as a function of applied voltage bias should be approximately the same as the relative error in the MemElectro force computation.

These meshes have been used to compute the displacement of the proof mass in response to an applied voltage bias between the proof mass and the electrodes. The complete results are shown in Figure T4-69, and additional results are shown in Table T4-14 and Figure T4-70.

In Figure T4-69 we can see the increase in displacement for a given voltage as the mesh is refined. This agrees with the fact noted above that the electrostatic force is converging from below. It can also be seen that the result from Architect indicates that the Architect model is either mechanically stiffer or generates less electrostatic force, or both, than a reasonably accurate FEM/BEM model.

Figure T4-69 Comparison of Displacement for Manhattan Meshes

In Table T4-14 the pull-in voltage from the results in Figure T4-69 are listed. The pull-in voltage is the last applied voltage for which equilibrium can be computed. Any voltage greater than the pull-in voltage causes the proof mass to displace until restrained by contact with the electrode. An additional error is introduced by the pull-in voltage con-cept: the reported pull-in voltage is equal to or less than the actual pull-in voltage for the given mesh up to the value of the pre-set voltage tolerance (set in the CoSolve Voltages window). For these data, the voltage tolerance was 0.125 volts.

Table T4-14 Pull-In Voltages

In Figure T4-70, the data of Table T4-14 are plotted so that Richardson extrapolation can be used to determine the correct pull-in voltage. From this plot we can estimate that the correct value is approximately 2.9 volts. Apparently the error in the result from the finest mesh is approximately 8%. This is almost 40% less than what was predicted by

Mesh Pull-in Voltage

coarse 4.25

medium 3.5

fine 3.13

ultra-fine 3.13



the analysis of the force alone. This is probably not simply a fortunate turn of events. The computation of the force in MemElectro for any given mesh is likely to be more accurate as the gap between the proof mass and the electrode is reduced because the resolution of the edge effects is less and less important. Therefore convergence estimates based on the force analysis probably are conservative.

Figure T4-70 Pull-in Convergence

Comparison with ArchitectCoventorWare Architect results are included in the displacement versus voltage plot of Figure T4-69. For Architect the pull-in voltage is approximately 3.2 volts. Compared with the extrapolated, correct value from the CoSolve con-vergence study of 2.9 volts, Architect has an error of 10%.

In the gyroscope tutorial, the modal frequency results for Architect are listed in Table T4-10 on page page T4-80. For the vertical mode, the Architect result is 7.28e+3. This value has a 4% error compared to the extrapolated, correct value from the MemMech modal simulation. Table T4-10 of the tutorial also records the modal frequencies for other modes, and these data suggest that the Architect results for the two horizontal modes are considerably more accurate. In the Architect model of the gyro all parts are rigid except the tethers. For the horizontal modes, this is an accurate model, but for the vertical mode, error is introduced by this approximation because the perforated plate section of the proof mass is, in fact, somewhat flexible. This flexibility is included in the MemMech model of the proof mass.

Therefore, we can hypothesize that unlike CoSolve, the error in an Architect simulation of electromechanical dis-placement arises from both the error in the representation of the stiffness and the electrostatic force. We should be able to confirm this by setting up a situation in Architect that is analogous to the force computations done for the ele-mentary-quantity convergence study. To obtain a force value in Architect to compare with the “Force” column of Table T4-13,

1. Attach position sources to the translation and rotation ports of the proof mass and pin the positions at zero.2. Apply 1 volt to the proof mass electrode.3. Examine the force required by the vertical position source to hold its position.

The force required was found to be 1.7718e-1. According to the convergence study, this value is slightly closer to the extrapolated, correct value of 0.2 than any of the MemElectro results in Table T4-13, having an error of 12%.

In conclusion, we note that Architect and Analyzer agree well for the pull-in results shown in Figure T4-69. The two finest meshes used in Analyzer are slightly more accurate than Architect. The study of the underlying electrostatic



and mechanical results indicates that for the fine mesh, Analyzer electrostatic computations are similar in accuracy to Architect computations, while the accuracy of the Analyzer mechanical computations is superior to Architect and accounts for most of the difference in the complete pull-in response.

MemElectro MeshMemElectro refines the input mesh at model edges. This helps to capture the charge buildup there. An example of the mesh created by MemElectro is shown in Figure T4-71:

Figure T4-71 MemElectro-Created Mesh

4.6.3: Extruded MeshingIt is easier to create extruded meshes than Manhattan meshes dependent on partitioning. The extruded meshes are never as nice looking, but are they effective? To determine this, we present a brief convergence study with three meshes made by the extruded mesher. The extruded mesher was used with the split and merge option to create meshes of parabolic hexes. Meshes roughly equivalent to the partitioned Manhattan meshes were created so that a comparison can be made for the simulation results. The element counts for the extruded meshes are shown in Table T4-15.

Table T4-15 Extruded Mesh Element Counts

Note that for the same nominal element sizes set in the “mesher settings” dialog, the extruded mesher always pro-duces slightly finer meshes than the Manhattan mesher, at least on this geometry. The extruded fine mesh is shown in Figure T4-72.


coarse 3619 9668 26670

medium 6449 16384 37604

fine 9660 23727 48588



Figure T4-72 Extruded Fine Mesh

The results from the extruded meshes are shown in Table T4-16:

Table T4-16 Convergence for Extruded Meshes

Figure T4-73 compares frequency for the vertical model and electrostatic force results for the Manhattan and extruded meshes:

Figure T4-73 Manhattan and Extruded Mesh Comparison

Mesh Modal Frequency Force

coarse 7.01637e+03 1.52585e-01

medium 7.00426e+03 1.64784e-01

fine 6.99972e+03 1.72552e-01



Following the procedure demonstrated above for determining the correct value, the data from the computations with the extruded meshes lead to the following conclusions:

The correct modal frequency is approximately 6990, which differs from the result with the Manhattan mesh. Although for a given number of surface elements, the results calculated for an extruded mesh are slightly less accurate than those from a Manhattan mesh, the extruded mesh series, like the Manhattan mesh series pre-dicts that the correct force is approximately 0.2.

The difference in the modal frequency results for the two meshing algorithms probably arises from the slight stiffen-ing effect of using tied links across the partition that enable the Manhattan meshing. This produces a converged value for the Manhattan mesh series that is 0.6% larger than the converged result for the extruded mesh series. This small difference cannot be expected to have a significant impact on the pull-in results for the extruded meshes.

Indeed it does not. Figure T4-74 shows the pull-in results for the extruded fine mesh, the Manhattan fine mesh, and for Architect. These results show that for the extruded mesh, the net effect of the reduced stiffness and the reduced electrostatic force is that for any given the voltage bias, the displacement is less than that for the Manhattan mesh.

Figure T4-74 Pull-in Comparison

Extruded AlgorithmsThe Extruded meshing algorithm has three meshing algorithms: Pave, Partition, and Split and Merge. The default Pave algorithm does not work well with Manhattan geometries. If you mesh the gyro with this algorithm and run the pull-in simulation, you will not see any pull-in for the trajectory used in the tutorial and the mesh study.

The Partition and Split and Merge options generate acceptable meshes, and the pull-in results for both algorithms are the same. The Split and Merge option was used for the tutorial and mesh study because the simulation time was less than for the Partition option.



4.6.4: Tetrahedral MeshingTetrahedral (or “tet”) meshes are the most general; that is, they can be created on any geometry. Like extruded meshes, tet meshes are never as nice looking as Manhattan meshes, and like extruded meshes the question arises whether they are effective. To determine this, we present a brief convergence study with three tet meshes. The tet meshes were created with the default settings values and the same mesh sizes as the Manhattan and extruded meshes. The intent was to construct tet meshes with densities that are roughly equivalent to the extruded and partitioned Man-hattan meshes so that a one-for-one comparison could be made for the simulation results. However, that goal could not be achieved because meshes built with tetrahedral elements will always have a smaller value for the ratio of sur-face to volume elements than meshes built with hexahedral elements. The element counts for the tet meshes are shown in Table T4-17. Note that for the same nominal element sizes set in the Mesher Settings dialog, the tetrahedral mesher produces finer meshes, particularly in the volume, than either the extruded or Manhattan meshers, at least on this geometry (compare with the element counts shown on page T4-91 and page T4-96).

Table T4-17 Tet Element Counts

The tet medium mesh is shown below:

Figure T4-75 Tet Medium Mesh

The results from the tet meshes are shown in Table T4-18. The data are plotted in Figure T4-76.


coarse 16292 15338 30988

medium 29724 25030 48493

fine 66617 40700 74931



Table T4-18 Convergence for Tet Meshes

Figure T4-76 Pull-in Comparision of Manhattan and Tet Meshes

Following the procedure demonstrated above for determining the correct value, the data from the computations with the tet meshes lead to the following conclusions:

The correct modal frequency is approximately 6970, which is different from both the result with the Manhat-tan mesh series and the result with the extruded mesh series. The tet mesh modal frequency is less than the other results, but only 0.3% less than that of the extruded mesh. But as will be shown below, the efficiency of the tet meshes for other MemMech computations is apparently quite poor.For the electrostatic force computation, the tet mesh results are roughly consistent with the extruded and Manhattan mesh results. However, the extrapolation process predicts that the correct electrostatic force is less than the value of 0.2 predicted by the other mesh series. The efficiency of the tet meshes for electrostatic computations is similar to that of the other mesh types.

Figure T4-77 shows the pull-in results for the tet coarse mesh, the Manhattan fine mesh, and for Architect. The tet coarse mesh was chosen because the computational effort for the pull-in analysis for the coarsest tet mesh is greater than that of finer meshes using the other meshing approaches; this is the result of the large number of volume ele-ments in the tetrahedral meshes. The lack of computational efficiency for the tet meshes is quite apparent in the fig-ure: despite the computational effort expended, the result for the tet coarse mesh has a much larger error than either the Manhattan fine mesh or Architect.

Mesh Modal Frequency Force

coarse 7.0935e+03 1.60670e-01

medium 7.0042e+03 1.67202e-01

fine 6.9940e+03 1.70051e-01



Figure T4-77 Displacement Comparison for Tets

4.6.5: Conclusions and RecommendationsThis study supports the following conclusions and recommendations:

Architect models can be quite accurate, and their inaccuracy can be explained in terms of the assumptions made in the models.For Analyzer, the convergence of elementary quantities computed by MemElectro and MemMech is a con-servative guide to the convergence of a coupled (CoSolve) simulation.Extruded meshes may not be as pretty as Manhattan meshes, but they are about as efficient for CoSolve sim-ulations. So where partitioning is required to optimize Manhattan meshing, extruded meshing may be pre-ferred.Tetrahedral meshes are also not as pretty as Manhattan meshes, but they lead to close to the same converged values for fundamental MemMech and MemElectro quantities. The problem with tet meshes is that they have a high number of volume elements for a given number of surface elements, as compared to the other mesh types, but at the same time, do not appear to be efficient for MemMech computations. So for pull-in analyses, tet meshes lead to higher computational effort and lower accuracy as compared to extruded or Manhattan meshes with a similar number of surface elements.



Notes


Section 4: Gyroscope Design DampingMM Macromodel Extraction Version 2008M

4.7: DampingMM Macromodel Extraction

4.7.1: IntroductionThis tutorial demonstrates how to extract reduced order squeezed-, slide-, and Stokes film flow macromodels from Analyzer for the z-plane gyroscope. It begins with a meshed model of the gyroscope adapted for squeezed- and slide- film flow assumptions and covers the steps necessary to produce squeezed and slide flow dampers for the driving and sensing modes of operation. It then continues with the extraction of Stokes flow models for the comb fingers in the driving mode of operation and finishes by examining the effects of slide film damping on gyroscope driving mode performance.

The driving mode is dominated by the lateral motion of the gyroscope plate as the alternating voltage on the comb fingers draws the plate back and forth. In this case, the damping tends to follow slide film physics, varying with plate oscillation frequency. The damping is proportional to the shear force acting on the plate and is a function of the plate surface area in contact with the gap between the plate and stationary electrode layer.

In the sensing mode, when the mass is subject to rotation about its axis, the Coriolis force accelerates the plate into the gap. This combined motion into the gap produces both a rotational and translational squeezed-film damping com-ponent. For squeezed-film physics, DampingMM bases macromodel extraction on a 2-D finite element solution of the linearized Reynold’s equation (page N4-3).

The damping effects due to the comb fingers in translation and rotation, neither slide nor squeezed-film physics, will be analyzed separately using the Stokes film flow solver in DampingMM.

The documentation was written for a user already familiar with the various point solver modules. It includes descrip-tions of the steps necessary to produce translational and rotational squeezed- (page T4-108) and slide- (page T4-120) film and Stokes flow (page T4-129) macromodels. A comparison of the extracted gyroscope plate dampers (squeezed- and slide-film cases) to parametric dampers from the Architect Library is also included (page T4-124). This tutorial also demonstrates how to place and use extracted macromodels in the gyroscope schematic, replacing the frequency independent damping properties of the rigid plate (page T4-135).

Figure T4-78 Gyroscope Solid Model


Section 4: Gyroscope Design DampingMM Macromodel Extraction Version 2008

4.7.2: Squeezed- and Slide-Film Macromodel ExtractionThe model used for this damper macromodel extraction has both tethers and comb fingers removed. The tethers are not included because their damping force is insignificant compared to the plate in both squeezed- and slide-film flows. The damping due to comb finger motion is not accurately captured by squeezed- and slide-film models and will instead be considered separately in the Stokes flow macromodel extraction section of this tutorial.

The meshed solid model shown in Figure T4-79 is used in all DampingMM simulations; it is half of the original plate. A symmetry plane has been introduced in the x-z plane at y = 0. This symmetric model is employed to reduce the computations required in the simulation. A quarter symmetry model could also have been used. The finite element mesh is composed of linear Manhattan type elements. These elements work fine for the damping calculations but would not be ideal for a mechanical simulation of plate motion where parabolic elements are more appropriate. Since the squeezed- and slide-film solvers are sensitive only to the plate in motion and the gap between it and the stationary surface, the electrode beneath the plate is not part of the finite element model. The gap between the electrode and the gyroscope plate is 1.6µm.

Figure T4-79 Symmetric Plate Damper Finite Element Model from the Gyroscope

InitializationThe tutorial uses prebuilt models. The sequence does not require any model creation steps.


1. Start CoventorWare. 2. Import the Damping project tutorial.3. Save the settings file as

film_damping.mps.

a. Start CoventorWare. b. In the Project Browser, click on the Import Tutorials icon.c. In the Import Tutorials dialog, select the Damping project from the list.

A .gbak file will be imported and converted to the format appropriate for your platform.

d. In the Projects dialog, Open the default file on the Settings file line. e. Set the Function Manager to the Analyzer tab.f. Set the Model/Mesh field to gyro_damping_PLATE-clip. g. From the Function Manager File menu, save your settings file as

film_damping.mps.



Examine ModelBefore starting the solver, examine the model face assignments that will be used in the simulation.

Figure T4-80 Model with Parts and Faces Annotation


1. View the names and part properties for the gyro_damping_PLATE-clip model.

a. Click on the Start Preprocessor icon to the right of the Model/Mesh field.b. In the Preprocessor, expand the Geometry Browser Mesh Model tree.c. Click on the Face selection mode icon.d. Click on the various surfaces of the model and note the face name

assignments.

Figure T4-80 shows an annotated view of the faces used to set boundary conditions.

e. After viewing the model, close the Preprocessor.

The MPD and process information for this model is the same as for the complete gyroscope. See page T4-7 for more details.

free_edge

hole (name of each face of every perforation;

symmetry_side

200 faces have this name)

comb_edge

bottom

top

free_edge



Naming Faces

For the squeezed- and slide-film solvers, certain edge and lateral surfaces must be named so that the appropriate boundary conditions can be assigned. Naming faces for devices with several perforations, like the gyroscope in this tutorial, can be very time consuming. There are fifty holes in this model, and each hole has four faces; every one of those faces must be named. Here are some techniques for making the task of naming faces easier:

Take advantage of any symmetry in the design; this will reduce the number of faces in the model. For exam-ple, the tutorial model uses half of the original design. So instead of 100 holes and 400 hole faces, the model has 50 holes and 200 hole faces.Use the Ctrl key to multi-select faces that should have the same name, then name them all at once.Use the Shift key to select all the faces in a part, and assign them all the same name. Then rename only the faces that are different.

DampingMM Setup and SolutionIn this section, we use the DampingMM module to extract dampers for each of the relevant degrees of freedom of the meshed model. For translation in the z-direction, a squeezed-film translational damper will be extracted; for the rota-tion about the x and y axes, translational squeeze dampers will be extracted; and for translation in x and y and rotation about z, slide-film dampers will be extracted.


1. Set up the Analyzer tab to point to the DampingMM solver for the gyro_damping_PLATE-clip model.

a. In the Function Manager Analyzer tab, set the Domain to MEMS and the Solver to DampingMM.

b. Set the Model/Mesh field to gyro_damping_PLATE-clip. c. Set the Analysis field to create a new analysis.

2. Set the DampingMM Settings dialog for the following analysis:

Squeezed or Slide Film Flow Physics with default ambient pressure and temperature and No adjustment for rarefaction.Symmetry Factor of 2 for the gyroscope section used,Rigid Body motion with a frequency range of 103 to 108 in 30 steps, andReduced Model Order of 4 for Architect simulation.

a. Click on the Solver Setup icon. b. In the Settings dialog, set the fields as shown in Figure T4-81, and

then click Next.

Read more about effective viscosity on page N4-3 in the Theory section.

A symmetry factor of 2 is used because the model includes only one half of the device.

The Rigid Body setting is used when the mass remains rigid and no mode shape analysis is performed. The frequency range for the simulation is 1 kHz -100 MHz. The number of steps affects graphing only (not execution time).

Reduced Model Order effectively sets the accuracy of extracted macromodel when used in Saber Architect; higher model orders are more accurate but can lengthen Architect simulation times.



Figure T4-81 Damping Settings Dialog

Setting Normalized template creation only? to No produces calculated results of the damping and spring forces/torques, coefficients, and phase shift. Setting this parameter to Yes is useful when extracting a macromodel only.



Squeezed-Film Translational Damping

Figure T4-82 DampingSurfaces Boundary Condition Setup


3. Set the DampingSurfaces dialog for the squeezed-film surface, bottom, in squeeze normal motion over the 1.6 µm gap.

a. Set the DampingSurfaces dialog as shown in Figure T4-82.

The LoadValue setting is the gap thickness, which is 1.6 µm (from the plate bottom to the electrode). You can measure these two gaps in the Preprocessor by selecting Tools > Dimension from the menu bar and selecting two vertices for each measurement.

The DampingMM BCs window includes an EdgeBCs button only if Squeezed or Slide Film Flow physics is selected in the DampingMM Settings dialog. This button does not appear for the Stokes Flow Physics choice.

It is also possible to simulate the slide effect of free_edge patches if they happened to be sliding against a stationary surface as they move in the squeezed direction. Consult page N4-11 in the DampingMM reference for more information on the valid configurations for co-simulation.



Figure T4-83 EdgeBCs Boundary Condition Setup


4. Set the EdgeBCs dialog:Assign an Edge to the edge line of the boundary between the plate bottom and comb surfaces.Assign an Edge_Correction to the sides of the plate that are not connected to the combs.Assign a Symmetry FixType to the side of the plate that is in the plane of symmetry.Assign a Perforation_Correction to the center hole edge lines, using a 10 µm radius.

a. Set the EdgeBCs dialog as shown in Figure T4-83.b. Assign an Edge FixTypes for bottom and comb_edge.

Edges are specified as the intersection of two patches, requiring the and keyword in the BC line.

c. Set an Edge_Correction as the FixType between the free_edge and bottom patches.

Edge corrections can only be applied to free edges, which model the corner turning of a fluid at an edge. For example, no edge correction can be applied to bottom and comb_edge, because that intersection is not a free edge.

d. Set Symmetry as the FixType for the intersection of the symmetry_side with the plate bottom.

This setup defines the plane of symmetry at the face where the gyroscope plate was partitioned.

e. Set Perforation_Correction as the FixType for all of the bottom and hole intersections. Set the LoadValue to half the hole length, which is 10 µm.

The Perforation_Correction FixType allows the solver to use flow resistance model equations at a perforation (or hole).

This setup defines the edge lines of the plate and gap boundaries for the holes.


5. Start the simulation using a sqz_film_flow directory.

a. Click on Run.b. Save the analysis as sqz_film_flow.



Figure T4-84 Damping and Spring Force Results for Squeezed-Film Damping


6. Verify the numerical and graph results for the Damping Force and Spring Force as a function of frequency, as shown in Figure T4-84.


b. In the Analysis window, select the Damping and Spring Forces table, click on the View Table icon, and verify the results shown in Figure T4-84.

c. Select the Damping and Spring Forces graph.d. Change the X-axis from linear to log: Select Plot > Axis and check Use

Log Scale under the Range tab. Verify the results shown below.

The results show that the damping force peaks at about 3 MHz.

The spring force rises rapidly. The air captured in the cavity is squeezed (akin to gas compressed by a piston in a cylinder). Because there is no real closed cavity in this case, at low frequencies air can escape with little resistance and the force is small. At high frequencies the air is held captive by its own inertia. Essentially, there is not enough time for the air to move out of the way as the structure oscillates. The air compresses, resulting in a spring force. Remember that the damping force itself is caused by viscous stresses. If the gas compresses and does not move much, then the damping force will be lower. This explains why the damping gets smaller as the frequency increases above about 3 MHz. This behavior is only valid for gases; liquids behave differently because they are nearly incompressible.



Figure T4-85 Damping Coefficient Table and Graph Results for Squeezed-Film Damping


7. Verify the numerical and graph results for the Damping Force Coefficient as a function of frequency, as shown in Figure T4-85.

a. Verify the Damping Force Coefficient table results shown in Figure T4-85.b. Select the Damping Coefficient graph; verify the results in Figure T4-85.c. Change the X-axis from linear to log using Plot > Axis and check Use Log

Scale under the Range tab.

The table shows the logarithmically-spaced computation point results.

The damping coefficient is constant until it starts to fall off at about1 MHz.



Figure T4-86 Phase Shift Table and Graph Results for Squeezed-Film Damping


8. Verify the numerical and graph results for the Phase Shift as a function of frequency, as shown in Figure T4-86.

a. Verify the Phase Shift table results shown in Figure T4-86.b. Select the Phase Shift graph, and verify the results shown in Figure T4-86.

Change the X-axis from linear to log using Plot > Axis and check Use Log Scale under the Range tab.

The Phase Shift graph is similar in shape to the Spring Force graph.



Figure T4-87 Symbol Data Results

Figure T4-88 Template Data Results


9. Verify the symbol data as shown in Figure T4-87.

a. Verify the Symbol Data table results as shown in Figure T4-87.

These values are used in the macromodel template.

The Squeeze Degree of Freedom listed in the table suggests the degree of freedom the damper should be attached to in an Architect schematic on the appropriate component.


10. Verify the Squeezed Film Patch Data as shown in Figure T4-88.

a. Verify the Squeezed Film Patch Data table results as shown in Figure T4-88.

The values are used in the macromodel template.

The data file contains the necessary DampingMM data for creating the template. It is stored in the scratch directory and can be deleted. However, once deleted, templates for a particular simulation run cannot be created without re-simulation.



Figure T4-89 Create Macromodel Dialog

Figure T4-90 Gyroscope Squeezed-Film Macromodel Symbol and Properties


11. Create a macromodel for the gyroscope, as shown in Figure T4-89.

a. In the Analysis window, click on Create.b. In the Create Macromodel dialog, set the fields as shown in Figure T4-89.

These settings create a new symbol and template file in your local Schematics directory.

c. Click on Save Macromodel.

You will get a confirmation message that the Symbol and Template files were generated.

The created symbol and properties dialog are shown in Figure T4-90.

When normalized template only is not indicated in the DampingMM solver, gas properties are automatically filled into the properties dialog.



Squeezed-Film Rotational Damping



1. Make sure the Analyzer tab still points to the gyro_damping_PLATE-clip model in DampingMM, but select create a new analysis in the Analysis field.



2. Leave the Physics settings dialog as is and continue to the DampingSurfaces BC dialog.

a. Click on the Solver Setup icon. b. Make sure the Settings dialog is as shown in Figure T4-81 on page

T4-107.

3. Set the DampingSurfaces dialog for the squeezed-film surface, bottom, in Squeeze_Rotation motion above a 1.6 µm gap.


The LoadValue for Squeeze_Rotation includes the gap thickness, which is 1.6 µm (from the plate bottom to the electrode), the rotation axis (1, 0, 0) and the center of rotation (0, 0, 7.05).

It is not necessary to change the edgeBCs for the squeezed-film rotational damping simulation.

4. Start the simulation. a. Click on Run.b. Save the analysis as rot_sqz_film_flow.



Figure T4-92 Damping and Spring Torque Results for Rotational Squeezed-Film Damping


5. Verify the numerical and graph results for the Damping Force and Spring Torques, as shown in Figure T4-92.


b. In the Analysis window, select the Damping and Spring Torques table, click on the View Table icon, and verify the results shown in Figure T4-92.

c. Select the Damping and Spring Torques graph and verify the results shown in Figure T4-92.




Figure T4-93 Damping Coefficient Results for Rotational Squeezed-Film Damping


6. Verify the numerical and graph results for the Damping Torque Coefficient as a function of frequency, as shown in Figure T4-93.

a. Select the Damping Torque Coefficient table, click on the View Table icon, and verify the results shown in Figure T4-93.

b. Select the Damping Coefficient graph; verify results shown in Figure T4-93.

Change the X-axis from linear to log using Plot Axis and check Use Log Scale under the Range tab.



Figure T4-94 Symbol and Patch Data Results for Rotational Squeezed-Film Damper


7. Verify that the numerical and graph results for the Phase Shift data agree with the translational squeezed-film damper results; they should be the same. See Figure T4-86.

a. Select the Phase Shift table, click on the View Table icon, and verify the results agree with those shown in Figure T4-86.

Results for the Phase Shift table may vary slightly, but the graphs should look almost identical.

b. Select the Phase Shift graph, and verify the results agree with those shown in Figure T4-86.


8. Verify the symbol and template data as shown in Figure T4-94.

a. Select the Symbol Data table, click on the View Table icon, and verify the results shown in Figure T4-94.

b. Select the Squeezed Film Patch Data table, click on the View Table icon, and verify the results shown in Figure T4-94.

table split for easier viewing



Figure T4-95 Macromodel Creation

Figure T4-96 Gyroscope Rotating Squeezed-Film Macromodel Symbol and Properties


9. Create a macromodel for use in the gyroscope, and save the template as film_damping_gyro_damping_plateclip_sqz_rot.

a. In the Analysis window, click on Create.b. In the Create Macromodel dialog, set the fields as shown in Figure T4-95. c. Click on Save Macromodel.

You will get a confirmation message that the Symbol and Template files were created.


When normalized template only is not indicated in the DampingMM solver, gas properties are automatically filled into the properties dialog.

10. When finished, close the Results window.

a. Close the Analysis results window.



Slide-Film Damping



1. Make sure the Analyzer tab still points to the gyro_damping_PLATE-clip model in DampingMM but select create a new analysis in the Analysis field.



2. Leave the Physics settings dialog as is and continue to the DampingSurfaces BC dialog.

a. Click on the Solver Setup icon. b. Make sure the Settings dialog is as shown in Figure T4-81 on page

T4-107.

3. Set the DampingSurfaces dialog for the SlideFilm surface, bottom, in Slide_Translation motion above a 1.6 µm gap.


The LoadValue setting is the gap thickness, which is 1.6 µm (from the plate bottom to the electrode).

It is not necessary to set edgeBCs for slide-film damping simulations.

4. Start the simulation. a. Click on Run.b. Save the analysis as slide_film_flow.



Figure T4-98 Damping, Spring, and Inertia Force Results for Slide-Film Damping


5. Verify the numerical and graph results for the Damping Force and Spring Force as a function of frequency, as shown in Figure T4-98.

a. When the simulation is finished, click on the View Results icon.b. In the Analysis window, select the Damping, Spring, and Inertia Forces

table, click on the View Table icon, and verify the results shown in Figure T4-98.

c. Select the Damping, Spring, and Inertia Forces graph and verify the results shown in Figure T4-98.

Change the axis from linear to log using Plot > Axis and check Use Log Scale under the Range tab.

The results show that the damping force does not become significant until approximately 10MHz.

In slide-film simulations the inertia force, instead of the spring force, is calculated by the model.



Figure T4-99 Damping Coefficient Table and Graph Results for Slide-Film Damping


6. Verify the numerical and graph results for the Damping Force Coefficient as a function of frequency, as shown in Figure T4-99.

a. Select the Damping Force Coefficient table, click on the View Table icon, and verify the results shown in Figure T4-99.

b. Select the Damping Force Coefficient graph; verify the results shown in Figure T4-99.

Change the axis from linear to log using Plot > Axis and check Use Log Scale under the Range tab.

The table shows the logarithmically-spaced computation point results.



Figure T4-100 Symbol and Template Data Results for Slide-Film Damper


7. Verify the symbol and template data as shown in Figure T4-100.


b. Select the Slide Film Patch Data table, click on the View Table icon, and verify the results shown in Figure T4-100.


8. Create a macromodel for use in the gyroscope, and save the template as film_damping_gyro_damping_plateclip_slide.

a. In the Analysis window, click on Create.b. In the Create Macromodel dialog, set the fields as follows:

Format: MASTComponent Label: film_damping_gyro_damping_plateclip_slideAdd to user library? Yes

c. Click on Save Macromodel.


While DampingMM computes and extracts a damping model for slide-film cases, it is also possible to manually calculate the plate area and input the result into a parametric slide-film damper (page A7-4).

9. When finished, close the Result window.




Figure T4-101 Gyroscope Macromodel Symbol and Properties for Slide-Film Flow

4.7.3: Comparison of Extracted and Parametric Plate DampersIt is possible to compare the frequency response of the extracted DampingMM dampers with the parametric plate dampers. The parametric plate dampers, having no perforations, are expected to exhibit considerably more damping, especially at high frequencies as the influence of the holes in the extracted dampers increases the critical frequency at which the compressive spring effect begins to dominate.

This section of the tutorial begins in and assumes some proficiency with Architect. The user will place the extracted components in the schematic alongside similar parametric plate dampers from the CoventorWare Architect Damper Library. A simple AC analysis will be run to determine differences between the dampers over a wide frequency range.


1. Open Saber. a. From the Function Manager, navigate to the Architect tab.b. Open a New Blank schematic using the drop down menu by the Schematic

icon.

2. Place the extracted dampers in the schematic.

a. In the Architect schematic window right-click, and select Get Part > By Symbol Name.

b. Click the Browse button in the dialog that opens.c. Navigate to your Shared/Saber_Models directory, and sequentially select,

Open, and Place each of the following dampers into the schematic: film_damping_gyro_damping_plateclip_trans, film_damping_gyro_damping_plateclip_sqz_rot, film_damping_gyro_damping_plateclip_slide_trans

3. Using the parts gallery, place a Translational Damper (Squeezed, Generic), a Rotational Damper (Squeezed, Generic), and a Translational Damper (Slide, Generic) into the schematic.

a. Open the Parts Gallery.b. Navigate to the damper library under Coventor Parts Library/Parametric

Libraries/Dampersc. Select and Place the Translational Damper (Squeezed, Generic).d. Select and Place the Rotational Damper (Squeezed, Generic).e. Select and Place the Translational Damper (Slide, Generic).



Figure T4-102 Architect Schematic for Comparing Extracted and Parametric Dampers

4. With the parts gallery still open, place 4 position sources (sine), 2 angle sources (sine), 9 Saber nodes (ground), and a COVENTOR symbol.

a. Use the search tool in the parts gallery to find and place each of the following components: Position Source, Sine 4Angle Source, Sine1 2Ground (Saber Node 0) 9 COVENTOR symbol 1

The COVENTOR symbol contains the architect_temperature and architect_pressure global variables necessary for both the extracted and parametric dampers.

5. Connect the schematic as shown in Figure T4-102.

a. Connect the positive end of a position source to the gap and pos pins of the translational dampers (both extracted and generic).

See Figure T4-102 for help with assembly.b. Connect an angle source to the ang pins of the rotational type dampers. c. Ground the negative terminal of each source.d. Ground the gap pins of the extracted and generic rotational squeezed-film

dampers and the generic translational slide-film damper

These gap pins are grounded because the gap is not changing in the AC simulation.





6. Set source amplitudes and frequencies to 1.

a. Select all the sources in the schematic using Shift + click or Ctrl + click.b. Double click on one of the sources.c. In the Common Properties dialog that opens, enter 1 for both the amplitude

and frequency parameters.d. Click on OK to accept the changes.

7. Give each source a unique name based on whether it is attached to an extracted or parametric damper and whether the motion type of the damper is squeezed translation, squeezed rotation, or slide translation.

a. Give each source a unique name in the ref field as follows:Double click on the position source connected to the extracted translational squeezed-film damper (the macromodel with only a gap pin). Name this source ex_sqz_trans.Double click on the position source connected to the parametric translational squeezed-film damper. Name this source p_sqz_trans.

b. Continue this process for each of the four remaining sources using the convention ex for extracted, p for parametric; sqz for squeezed-film, sli for slide-film; and trans for translational, rot for rotational.

8. Give the parametric dampers a gap of 1.6um.

a. Select all three parametric dampers.b. Double click on one of the dampers to open the Common Properties dialog.c. Enter 1.6u for the initial_gap property.

9. Set the gas parameter of the parametric dampers to air.

a. With the common properties still open, verify that the gas property is set to air.

b. Click on OK to accept the Common Property changes.

10. For each parametric squeezed-film damper, set the shape to a 400u by 400u rectangle.

a. Select both parametric squeezed-film dampers.b. Double click on one of the dampers to open the Common Properties dialog.c. Click in the shape field, then in the rectangular value field to open the x and

y dialogue.d. Enter 400u for x and y.

11. For the parametric translational slide-film damper, set the area to 0.16u.

a. Double click on the parametric translational slide-film damper.b. Set the area field to 0.16u.c. Click on OK.

12. In the Coventor symbol, set the architect_temperature and architect_pressure variables to 300 K and 101300 Pa.

a. Double click on the Coventor symbol.b. Scroll down in the property dialogue to architect_temperature.c. Change the default to 300.d. Find architect_pressure and change its value to 101300.e. Click on OK.

13. Save the schematic as damper_comparisons.

a. Save the schematic using File > Save from the menu bar.b. Save the file as damper_comparisons.

14. Netlist and simulate the schematic. a. From the menu bar, choose Design > Netlistb. From the menu bar, choose Design > Simulate.

15. Run a DC operating point analysis. a. Click on the DC Operating Point icon.

b. Click on OK to accept the default settings.



Figure T4-103 Comparison of Extracted and Parametric Translational Squeezed-Film Dampers

16. Run an AC analysis over a 1k to 100meg frequency range for 30 points. Set Plot After Analysis to Yes - Open Only. Plot only the data from the sources.

a. Click on the Small Signal AC Analysis icon. b. In the dialog that opens, enter 1k for the Start Frequency.c. Enter 100meg for the End Frequency.d. Set the Number of Points to 30.e. Select Yes - Open Only from the Plot After Analysis drop-down menu.f. Click on the Input Output tab and from the drop-down menu of the Signal

List, choose Browse Design.g. Select all the sources in the Design Instance/Node List and move them to the

Selected Items category by clicking on the -> button. Also add generic_sli_trans_plate_damper_order5.generic_sli_trans_plate_damper_order5_1. Click on OK to close this dialog.

h. Click on OK in the Analysis window to run the analysis.i. CosmosScope will open once the analysis is complete.

17. Verify the graph results for the translational squeezed-film damping and spring forces for both the parametric plate and the extracted plate with holes, as shown in Figure T4-103.

a. When CosmosScope opens, expand the pos_sin.ex_sqz_trans analog signal and double click on force_mks.

b. Open the signal attributes for the dB plot by right-clicking on the legend and selecting Attributes. Change the view to real(y). This is the spring force for the extracted plate damper with holes.

c. Open the signal attributes for the Phase plot and change the view to imag(y). This is the damping force for the extracted plate dampers with holes.

You may also verify that the extracted damper results agree with the DampingMM FEA results.

d. Now expand the pos_sin.p_sqz_trans analog signal and double click on force_mks.

e. Drag the parametric dB plot onto the real(y) extracted spring force plot and the parametric Phase plot onto the imag(y) extracted damping force plot.

f. Open the signal attributes for the dB plot and change the view to real(y). This is the spring force for the parametric plate damper with no holes.

g. Open the signal attributes for the Phase plot and change the view to imag(y). This is the damping force for the parametric plate dampers with no holes.




Figure T4-104 Extracted and Parametric Rotational Squeezed-Film Dampers

Figure T4-105 Extracted and Parametric Translational Slide-Film Dampers


18. Verify the graph results for the rotational squeezed-film damping and spring torques for both the parametric plate and the extracted plate with holes, as shown in Figure T4-104.

a. Select Graph > Clear Graph. b. Expand the ang_sin.ex_sqz_rot analog signal and double click on torq_mksc. Expand the ang_sin.p_sqz_rot analog signal and double click on torq_mks.d. Change the dB plots to real(y) spring torque plots and the Phase plots to

imag(y) damping torque plots.e. Combine the plots as before.


19. Verify the graph results for the translational slide-film damping and inertia forces for both the parametric plate and the extracted plate with holes, as shown in Figure T4-105.

a. Clear the graph.b. Expand the pos_sin.ex_sli_trans analog signal and plot force_mks.c. Expand the pos_sin.p_sli_trans analog signal and plot force_mks.d. Change the dB plots to real(y) inertia force plots and the Phase plots to

imag(y) damping force plots.e. Combine the plots as before.



4.7.4: Stokes Flow Damping This tutorial performs a Stokes Flow analysis on the gas damping characteristics for the gyroscope comb fingers as they move in the Y direction, using a simple point solver run and a parametric study. The parametric study is required to acquire sufficient damping constant data to create a usable macromodel. The design is shown in Figure T4-106.

Examine ModelReview the gyro-combs-clip model for this tutorial.

Figure T4-106 Gyro Combs Design

CoventorWare 2008 includes a new solver for the Stokes equation. We have tuned this solver to meet our customers' need for solving problems with many degrees of freedom. Therefore, users will find that for any given mesh, the new solver is slightly more accurate than the old solver, requires only 15% of the memory as the old solver, but simulation times may be more than twice as long.


1. Save the settings file as stokes.mps.2. View the names and part properties for the

gyro-combs-clip model.

a. From the Function Manager, click on the Analyzer tab.b. From the File menu, save your settings file as stokes.mps.c. Set the Model/Mesh field to gyro-combs-clip.d. Click on the Start Preprocessor icon to the right of the Model/Mesh

field.e. In the Preprocessor, expand the regions and layers of the Mesh tree.f. Verify the Geometry Browser in Figure T4-106.

The design uses a Manhattan mesh type with a linear element order and a mesh size of 2 for each direction.

stator

rotor

electrode



Stokes Setup and SolutionThe remainder of the setup uses the DampingMM module.

Figure T4-107 Damping Settings Dialog


1. Set up the Analyzer tab to point to the DampingMM solver and the gyro-combs-clip model.


b. Set the Model/Mesh field to gyro-combs-clip.c. Set the Analysis field to create a new analysis.

2. Set the DampingMM Settings dialog for Stokes Flow as shown below.

a. Click on the Solver Setup icon. b. In the DampingMM Settings dialog, set the fields as shown in

Figure T4-107.c. Click on Next.



Figure T4-108 Damping Parts Boundary Condition Setup

Figure T4-109 Force Results


3. Set the Damping Parts BC dialog:Set a Velocity for the rotor part Set a Part Translation about the Y axis

through the middle of the rotor.

a. Set the Damping Parts dialog as shown in Figure T4-108.

The Velocity boundary condition sets up a translating motion through the Y axis with a velocity of 1.

To specify translation through the Y axis, set the Velocity_Y field to 1 and set the other velocity fields to 0.

To determine the center of the top plate, you must examine the layout and process file (see page T4-7), or make measurements in the Preprocessor. The parts are designed with the origin at the center of the gyro layer. The electrodes are 0.45 µm thick with a gap of 1.6 µm. Set the Center_X and Center_Y fields to 0, and the Center_Z field to 0.45 + 1.6 + 10/2 = 7.05 µm.

4. Start the simulation. a. Click on Run.b. Select Yes in the warning dialog.c. Save the analysis as Stokes.

5. Verify the numerical results for the Forces on Parts, as shown in Figure T4-109.

a. When the simulation is finished, in the Job Queue dialog, click on the View Results icon.

b. In the Analysis window, select the Forces & Moments table, click on the View Table icon, and verify the results shown in Figure T4-109.

The table shows the force and moment results for the simulation.

6. When finished, close the Result window. a. Close the Analysis Stokes results window.

In an actual model, the user should run a mesh convergence study to determining the validity of the results.

Next, you will run a parametric study to compute enough data for macromodel creation.



Figure T4-110 Parametric Study Trajectory and Variable Setup


7. Set up a parametric study to vary the offset of the stator in the Y direction from -16 to 16 in increments of 4, with an Offset variable set in the Dimensions dialog.

8. Start the simulation.

a. In the Function Manager Analyzer tab, click on the drop-down arrow beside the View Results icon and select Solver Setup.

b. Skip the Settings dialog. In the DampingMM BCs window, click on Parametric Study.

c. Click on Trajectories.d. For t1 set a Delta trajectory type with a Start of -16, a Delta of 4, and a Stop of

16. Set the Label to offset.e. Click on Dimensions.f. Assign the Transform1 line to trajectory t1. Use the Offset Transform type

applied to the rotor in the dY direction.g. In the Parametric Study window, click on Run.h. Save the analysis as Stokes_ParaStudy.



Figure T4-111 Parametric Study Table Results

Figure T4-112 Symbol and Template Data Results for Stokes Damping


9. Verify the numerical results for the Damping Coefficient, as shown in Figure T4-111.

a. When the simulation is finished, click on the View Results icon.b. In the Analysis Stokes_ParaStudy window, select the Damping Coefficient

table, click on the View Table icon, and verify the results shown in Figure T4-111.


10. Verify the Symbol Data as shown in Figure T4-112.




Figure T4-113 Comb Finger Macromodel Symbol and Properties for Slide-Film Flow

When considering implementing the model in the gyroscope tutorial, recall that the model accounts for only two complete fingers. Because the option for symmetry is not available in Stokes, the user may have to replicate the sym-bol a given number of times to account for all fingers, or the user could run Stokes on a complete comb model.


11. Create a macromodel for use in the gyroscope, as shown in Figure T4-113; save the template as stokes_damping_comb_trans_y.

a. In the Analysis window, click on Create.b. In the Create Macromodel dialog, set the fields to save a MAST template

named stokes_damping_comb_trans_y. c. For Add to user Library? select Yes.d. Click on Save Macromodel.

You will get a confirmation message that the Symbol file was created.


12. When finished, close the Result window.


It is also possible to run Stokes for translation of the comb fingers in the z-direction.



4.7.5: Slide-Film Damping Effects on Gyroscope Driving ModeIn the gyroscope tutorial, accounting for damping is accomplished with the 6 DOF damping parameters of the rigid plate (cx, cy, cz, crx, cry, crz). Recall the values used in the tutorial: (100n, 100n, 400n, 1m, 1m, 4m). In this portion of the DampingMM tutorial, the values of cy, cz, and crx will be blanked to 0 and the film dampers extracted from page T4-120 will be used. The slide-film damping value near the driving mode frequency (7177.2kHz) is approxi-mately 1.59e-6 Ns/m, as shown in Figure T4-99. This is more than ten times the damping assumed in the rigid plate. The change in driving mode performance due to this increased damping will be demonstrated using the AC analysis technique described in the gyroscope tutorial (page T4-69). This type of degradation of the driving mode in ambient conditions is often overcome by operating the gyroscope in an evacuated (low pressure, vacuum encapsulated) pack-age. Architect can quickly scan the design space for the appropriate pressure conditions by sweeping the global vari-able architect_pressure.

Figure T4-114 Gyroscope Schematic


1. Begin by opening the Architect schematic gyro_prebuilt.ai_sch.

a. Import the Gyroscope tutorial if necessary.b. Select the Architect tab.c. Select the Browse icon next to the schematic field to import a schematic.d. Navigate to the Gyroscope/Schematics directory and click on the file

gyro_prebuilt.ai_sch.e. Click the Open Specified Schematic button to open the schematic in Architect

(see Figure T4-114).

It is important to make sure that the schematic is unmodified. The steps in this tutorial assume that the schematic is as loaded from the Gyroscope tutorial.



Figure T4-115 Gyroscope Schematic with Slide Damper


2. Set the wx source/initial value to 1 and the sinusoidal source/ac_mag to 2.

a. Select the wx c_pulse source on the left hand side of the reference frame. Set initial to 1.

b. Select the sinusoidal source attached to both F terminals of the combs. Set ac_mag to 2.

3. Place the extracted slide-film damper into the schematic and connect it to the y-pin of the bus connector symbol.

a. Right click in the schematic window, select Get Part > By Symbol Name.b. In the dialog that opens, click on the Browse button.c. Find and select the extracted file with the label:

film_damping_gyro_damping_plateclip_slide_trans

The model is located in the /Shared/Saber_Models directory of your work directory.

d. Click Place, then close the dialog.e. Connect the damper to the y-pin of the bus connector symbol. The schematic

should appear as in Figure T4-115.



Figure T4-116 Properties for gas_override


4. Edit the symbol properties of the slide-film damper to set the gas_override values to undef.

a. Right click on the extracted slide-film damper symbol and select Symbol Editor.

b. Double click on the Film Damper label to open the symbol properties.c. Click on the gas_override property and modify the settings to match those


The symbol properties are set to the ambient conditions of the DampingMM simulation because the normalized template switch was turned off. Recall that when the gas_override is not set to undef, the override properties have precedence over the gas properties. This feature would render a vary analysis on architect_pressure useless.

d. Click on OK and then save the symbol file.e. Close the symbol file.

5. Repeat Steps 3 and 4 for the extracted squeezed translational and rotational dampers.

a. Right click in the schematic window and select Get Part > By Symbol Name.b. In the Get and Place dialog that opens, click on Browse.c. Find and select the extracted files with the labels:

film_damping_gyro_damping_plateclip_trans and film_damping_gyro_damping_plateclip_sqz_rot

d. Click on Place for each damper, then close the dialog.e. Connect the dampers as shown in Figure T4-117.f. Ground the other wires of the bus connector.g. For each damper, right click on the symbol and select Symbol Editor.h. Double click on the Film Damper label to open the symbol properties.i. Click on the gas_override property and modify the settings to match those


6. Edit the Coventor plate_damping symbol properties by setting them to zero.

a. Double click on the COVENTOR symbol to edit the global variables.b. Find the plate_damping_cy variable and change 100n to 0.c. Find the plate_damping_cz variable and change 400n to 0.d. Find the plate_damping_crx variable and change 1m to 0.

The rigid plate damping effects are now turned off for motion of the plate in the y, z, and rx directions and replaced by the damping effects of the extracted film dampers.



Figure T4-117 Schematic Zoom of Squeezed- and Slide-Film Damper Attachments


7. Run an AC analysis over the 7.0kHz to 7.6kHz range and view the results in CosmosScope.

a. Click on the Small Signal AC icon, and set the following parameters:Start Frequency: 7.0kEnd Frequency: 7.6kNumber of Points to 1000Increment Type to LinRun DC Transfer Analysis FirstPlot After Analysis to Yes - Open OnlyInput/Output tab Signal List to /y /capClick on OK.

b. In the Plot window, display the y and cap magnitudes; i.e. double click the plotfile entries then select Attributes from the menu and change the View from dB(y) to mag(y).

c. Verify the results shown in Figure T4-118.

Compare these results with those in Figure T4-49. Notice the degradation in the driving mode response in the y magnitude plot.



Figure T4-118 Detection Mode Response at 101325Pa

Figure T4-119 Vary Analysis Settings for Sweep on architect_pressure


8. Run an AC vary analysis on architect_pressure and plot the results in CosmosScope.

a. Select the Vary icon and set the dialogs as shown in Figure T4-119.b. Click on OK to run the vary analysis.c. In the Plot window, display the y magnitude; i.e. double click the plotfile

entry, select Attributes from the menu, and change the View from dB(y) to mag(y).

d. Verify the results shown in Figure T4-120.

The phase plots are deleted and the frequency axis of the y magnitude plot is zoomed to display the results more clearly.

Notice that at architect_pressure = 470Pa, the 10um driving mode amplitude is regained.



Figure T4-120 Driving Mode Displacement in Vary Analysis on architect_pressure

Figure T4-121 Driving Displacement and Detection Mode Signals at 470Pa


9. Investigate the detection mode response at 470Pa.

a. Double click on the COVENTOR symbol.b. Change the architect_pressure variable from 101325 to 470.c. Save the schematic and netlist.d. Open the AC analysis form and rerun the analysis with the previous settings.e. In the Plot window, display the y and cap magnitudes.f. Verify the results shown in Figure T4-121.

Again, the phase plots are deleted and the axes of the cap magnitude plot are altered to display the signal response at the driving mode frequency more clearly.

The driving mode displacement is roughly 12µm and the signal capacitance is roughly 0.164fF when it is baseline subtracted from the resonance peak of the detection mode. Further sweeps on pressure could more closely match these results with the Gyroscope tutorial results.


Section 4: Gyroscope Design Design Modification Using Integrator Version 2008M

4.8: Design Modification Using IntegratorWhen designing with Architect you may encounter geometries that cannot be described using existing components from the Architect libraries. Many cases can be resolved with CoventorWare's Integrator. Integrator is a tool that cre-ates Architect models automatically from FEM/BEM models.

In this chapter you will learnhow to simulate and extract a double-ended linear spring macromodel using Integrator's SpringMM modulehow to substitute the macromodel in place of the gyroscope schematic’s beam modelshow to run a DC operating point analysis on the revised designhow to run a DC transfer analysis on the revised design

The tutorial model is a U-shaped beam. The meshed model is provided for you and is shown in Figure T4-122. The beam was constructed to have roughly the same length and span as the beams used in the gyroscope schematic (see page T4-3). It was meshed with the same mesh type and element size used to mesh the extracted gyroscope model (see page T4-77). The Partition algorithm was used to create a better mesh through the curved portion of the beam. For this particular example, a J-shaped beam Architect library component could have been used, but this tutorial shows the user how to incorporate macromodels with parametric models with a simple U-shaped beam.

Figure T4-122 U-Shaped Beam


Section 4: Gyroscope Design Design Modification Using Integrator Version 2008

4.8.1: Macromodel Creation To analyze the behavior of the U-shaped beam using Saber, we first need to create a macromodel of the double-end spring that can be used in a schematic. For this exercise a model has already been created, and it resides in the project’s database. This section details how to extract the macromodel from this model.

Figure T4-123 Patch Assignment


1. Start CoventorWare, and open the gyroscope project. a. Start the software, and in the Project Browser that opens, select the Gyroscope project.

b. Create a new settings file named ubeam.c. Click on Open.

2. Set up a macromodeling spring simulation with the ubeam model.

a. In the Function Manager, click on the Analyzer tab.b. Select SpringMM from the Solver drop-down menu.c. Click on the arrow to the right of the Model/Mesh field and

select the ubeam model.d. Click on the Solver Setup icon.

3. Set up a double-ended spring analysis. a. In the Settings dialog, select Mechanical for the Spring Physics.

b. For the Mechanical Spring Type, select Linear double-ended.c. Click on Next.

4. In the double ended spring dialog, assign patch gyro_end as PatchName1 and patch anchor_end as PatchName2. Then start the simulation.

a. In the DoubleEndSpring BCs window that opens, click on double ended spring.

b. Set the dialog as shown in Figure T4-123.

The patch assigned to PatchName1 will correspond to the end of the model labeled 1 in the generated model; the patch assigned to PatchName2 will correspond to the end of the model labeled 2 in the generated model.

c. In the DoubleEndSpring BCs window click on Run.d. Save the analysis as d_spring.



Figure T4-124 Step, Reaction Force, and Moment Results


5. Verify the simulation results shown in Figure T4-124.

a. When the simulation is finished, in the Job Queue dialog make sure the d_spring simulation is selected, and click on the View Results icon.

b. In the Analysis Results window, view the Reaction Force and Moments tables. Verify the results shown in Figure T4-124.

The Rz, Ry, Rx, Dz, Dy, and Dx columns that appear at the beginning of both the Reaction Force and the Moments tables have been removed from the Moments table for easier viewing.

table has been split for easier viewing

table edited for easier viewing




6. Create the macromodel of the double-ended spring. a. In the Analysis Results window, click on Create.b. Set the Create Macromodel dialog as shown below.c. Click on Save Macromodel.d. When the template has been created, click on OK.



4.8.2: Schematic ConstructionThis section outlines how to incorporate a macromodel into a schematic that uses parametric models. You will replace the parametric beams with four instances of the extracted spring.


1. Select a gyro.proc file and the gyro schematic, then start Saber.

a. From the Architect tab click on the arrow beside the Process file field and select the gyro.proc file.

b. From the Architect tab, click on the drop-down menu beside the Schematic field, and select gyro.

c. Click on the Saber icon to the far right of the Schematic field.

2. Save the file as gyro_ubeam. a. In the SaberSketch window, select File > Save As.b. Save the file as gyro_ubeam.

3. Delete all the beam and anchor models from the schematic.

a. Use the Ctrl key to select the four beam models, the four anchor models, and the wires that connect them to each other.

b. Right click and select Delete.

4. Place four instances of the double end spring model in the Sketch window.

a. In the Sketch window, right click and select Get Part > Parts Gallery.

b. In the Parts Gallery pane:Double click on User CoventorWare Library.Double click on Double End Spring.Double click the massless_2end_spring_ubeam symbol to place it.

c. Place three more instances of the double ended spring.

5. Connect a double ended spring model where each of the beams used to be.

a. Wire each double ended spring model into the schematic.

Use the right click > Flip option to orient the models correctly. Make sure that end 1 of the model is connected to the bus wire as in Figure T4-125.

6. Connect end 2 of each double ended spring model to a fixed knot.

a. In the Saber Parts Gallery, navigate to Coventor Parts Library/ Shared Parts/Knot Boundary Conditions.

b. Place four instances of the Fixed Knot.c. Connect one to the free end (end 2) of each double ended

spring model.



Figure T4-125 Schematic with Double Ended Springs

Table T4-19 U Beam Attributes (Upper)


7. Double click on each of the macromodels and change the properties shown below:

a. Double click on each macromodel and change the properties that are listed in Table T4-19 and Table T4-20.

The origin for each macromodel is changed to be the same location as beam_end1 of the original beams (see page T4-16).

The orientation of all but the upper left macromodel must be changed. The orientation property changes the default orientation of the local mesh coordinate system in the reference frame. The rz = 180 and/or rx = 180 accounts for the tether being flipped.

8. Save, netlist, and simulate the schematic. a. Select File > Save.b. Select Design > Netlist.c. Select Design > Simulate.

These steps will check the schematic for any errors.

Name Left Right

label BeamUL BeamUR

knot1 (x = 0, y = 0, z_layer = poly) (x = 0, y = 0, z_layer = poly)

origin (x = -210u, y = 200u, z = 7.05u) (x = 210u, y = 200u, z = 7.05u)

orientation — (rx = 0, ry = 0, rz = 180)



Table T4-20 U Beam Attributes (Lower)

4.8.3: System AnalysisNow that you have substituted the U-shaped macromodel for the L-shaped beam configuration, you can run any of the simulations that you ran on the original gyroscope. This section shows the DC Operating Point and DC Transfer analysis results for the gyroscope with the U-shaped beams and compares them with the original results.

DC Operating Point

Figure T4-126 DC Operating Point Results

Name Left Right

label BeamLL BeamLR

knot1 (x = 0, y = 0, z_layer = poly) (x = 0, y = 0, z_layer = poly)

origin (x = -210u, y = -200u, z = 7.05u) (x = 210u, y = -200u, z = 7.05u)

orientation (rx = 180, ry = 0, rz = 0) (rx = 180, ry = 0, rz = 180)


1. Run a DC operating point analysis.a. Click on the DC Operating Point icon. b. In the Operating Point Analysis dialog that appears, click on OK.

2. Generate an Operating Point report. Compare the report with Figure T4-126.

a. From the Saber Transcript window menu, select Results > Operating Point Report.

b. On the Waveforms tab, in the signal list, clear any signals that may appear and type /x /y /z. Click on OK.

c. Verify the results in the report window (right side of Figure T4-126).

original results results with U-beams



DC Transfer (Sweep) Analysis


1. Perform a DC Transfer analysis on the z wire. Increase the voltage from 0 to 5 volts in steps of 0.25.

a. Click on the DC Transfer icon.

b. In the DC Transfer Analysis dialog, set the fields in the Basic tab as shown below.

c. In the Input Output tab, set the signal list to /z.d. Click on OK.

In this analysis, the voltage of the electrode is increased from 0 to 5V in increments of 0.25.



Figure T4-127 Pull-in Results with U Beams

Figure T4-128 Original Pull-in Analysis Results


2. In CosmosScope plot the value at X = 0.1. a. When the simulation finishes (in about 30 seconds), select the z signal from the small signal list window that opens. Click on Plot.

b. Click on the z legend signal and then select Measure icon from the bottom row of icons.

c. In the Measurement dialog that opens, click on Apply and Close. In the graph, move the probe (looks like a circle with crosshairs) to the point where the plot begins a sharp descent.

The probe tool can be used to give a precise measurement of the pull-in voltage.

As seen in Figure T4-127, the pull-in voltage is around 4.25 volts. Compare it with the pull-in results for the original gyro, as shown in Figure T4-128.

d. When finished, File > Exit the Plot window.



Notes


Section 4: Gyroscope Design Package Design Tutorial Version 2008M

4.9: Package Design Tutorial

4.9.1: IntroductionCoventorWare can be used to examine the interaction of device and package behavior. A very important part of the MEMS design cycle is incorporating the device into an appropriate package, which is never simple and may require several design iterations. The conditions of stress, temperature, and other effects experienced by the package during operation can severely influence the performance of the device. Also, in most cases there is an order of magnitude difference in the model dimensions between the device and the package, and this makes efficient modeling difficult. CoventorWare enables the user to simulate the mechanical behavior of the device when subject to the deformations of the package using a hybrid modeling approach. This approach combines the FE solver analysis with system-level modeling in a circuit simulation environment. The hybrid approach exploits the complementary strengths of each of these modeling methods, namely the ability of field solvers to analyze arbitrarily complex geometric shapes and the optimized computational performance of behavior models.

The package used in this tutorial is based on a design from the Kyocera Standard Package Library, which was devel-oped for CoventorWare with joint collaboration with Kyocera. This library facilitates the selection process by provid-ing ready-made package models, which can in turn be used to analyze the effects of the packages on MEMS devices. The Standard Package Library also provides the layout and process files for the models so that users can modify a design to best fit their device. The package used in this tutorial is a Surface Mount Device (SMD) that is a modified version of Kyocera’s SMD_KD_V99902_A model. Its die attach was resized to accommodate the size of the sensor.

The device is the gyroscope design presented in the tutorial starting on page T4-1.

The tutorial shows how to model package/device interaction in two sequences: First, the FE solver analyzes the pack-age, and then the results from this analysis are input to an Architect schematic that represents the device. The first tutorial sequence uses the FE solver MemMech to model the deformation of the package. In the first simulation, a thermal boundary condition representing power dissipated from the device is used to analyze the package deforma-tion. The second simulation analyzes the effect of a range of ambient temperatures on the package by applying a tra-jectory set of boundary conditions during the analysis.

The second tutorial sequence demonstrates how to input the package FE solver results to the Architect schematic that represents the device, and then use Architect to simulate the package/device interaction. In the Architect simulation, the user will vary the position of the device in the package to determine its optimal placement.

This tutorial is intended for advanced CoventorWare users. For learning Analyzer basics, see the first Beam Design tutorial starting on page T2-1. For learning Architect basics, see the Gyroscope tutorial starting on page T4-1.

Demonstrated TechniquesIn addition to exploring the package modeling, the tutorial exercises reinforce concepts presented for the base point solvers. The exercises demonstrate the following techniques:

how to perform a thermomechanical analysis on a package component using MemMech (page T4-152)how to set a HeatFlux boundary condition (page T4-157)how to view the mesh in the Visualizer (page T4-159)how to use the Visualizer Probe tool (page T4-159)how to use the Query function to extract curvature results (page T4-162)how to use the parametric study function to apply a range of temperatures to the package (page T4-163)

For more information about Kyocera packages or to place an order, please contact Kyocera at [email protected].


mailto:[email protected]

Section 4: Gyroscope Design Package Design Tutorial Version 2008

how to apply Analyzer package results to an Architect schematic representing the device (page T4-172)

4.9.2: Package Thermomechanical Analysis This tutorial performs a thermomechanical analysis on a package component, based on a heat flux imposed from the device mounted in the package. The results are used to analyze the resultant stresses on the device, illustrating how power dissipated from the device can cause package curvature, which is transferred back to the device as stresses. The package model is shown in Figure T4-129.

Figure T4-129 Package Model with Part Names Shown

The simulations in this chapter require a large temporary file space to store the intermediate files created during the computations. These temporary files may require up to 650 MB of additional space.

body

die_attach

Seal ring (Fe_Ni_Co alloy)

View of pins on bottom of model

castellation(tungsten material)

(alumina material)

(acrylic material)

(tungsten material)



InitializationThe tutorial uses a prebuilt 3-D model. The sequence does not require any model creation or patch assignment steps, but you will generate a preset mesh.

Examine ModelBefore starting the solver, examine the properties of the model that will be used in the simulation.


1. Start CoventorWare. 2. Open the Gyroscope tutorial.3. Save the settings file as package.mps.

a. Start CoventorWare. b. In the Project Browser, open the Gyroscope tutorial.

The exercise assumes that you have already imported the Gyroscope tutorial. If not, use the Import Tutorial icon, and select this project from the list.

This tutorial directory has the gyroscope schematic used in the tutorial. The package will be imported from the Database Browser.

c. From the Function Manager File menu, save the settings file as package.mps.


1. Set the Materials field to the Kyocera_Ceramic_Package.mpd.

a. Set the Materials file field to Kyocera_Ceramic_Package.mpd.

2. Import the Tutorial_Example package. a. In the Function Manager click on the Analyzer tab.

If the Analyzer tab is active, the Materials file field cannot be edited.b. Click on the Browse icon beside the Model/Mesh field.

c. In the Database Browser, click on the Import Package icon.

d. Select the Tutorial_Example package.

This model is similar to SMD_KD_V99902_A package. Its die attach has been resized to accommodate the sensor used in the tutorial. The Kyocera packages come with prebuilt cat and proc files so that the user can tailor a package for a particular design. This package has already been modified so that the user does not have to go through the steps of modifying the layout, rebuilding the model, and renaming faces.

e. Select the package_for_gyro model and click on OK.

3. View the face assignments for the model. a. Click on the Start Preprocessor icon to the right of the Model/Mesh field.b. In the Preprocessor, expand the Geometry Browser Mesh Model tree.c. Click on the face names in the Geometry Browser to view the

corresponding faces in the model. You will need to rotate the model to see the pin faces. The faces are identified in Figure T4-130.

Only the top face of the die_attach part and the bottom faces of the pins are named because they will be used to assign boundary conditions.



Figure T4-130 Package Mesh with Patch Assignments

Table T4-21 Material Properties for Package

The layout file for each package library has the two cells: topcell, which has a reference unit of mm, and um_scale, which has a reference unit of microns.The library has already has a 3-D model that was built with the um_scale cell. If you decide to rebuild the 3-D model, make sure to select the um_scale cell from the Top Cell drop-down menu, which accessed from the Designer tab.


4. View the material properties for the package model.

a. In the Geometry Tree, click on a layer with the alumina name assigned, then right click and select Properties.

b. In the Properties dialog, click on the MPD Editor icon, and verify the ALUMINA_A440 properties shown in Table T4-21.

c. Click on the die_attach part and verify the properties.d. Click on one of the metal layers or the castellation layer and verify its

properties.

The seal ring will not be involved in the simulation, so its material properties are not relevant.

Propertyalumina parts die_attach pins, castellations,

metal parts Units

Alumina_A440 Acrylic Tungsten_Kyocera

Elastic constants - E 3.1e+05 3.00e+03 3.45e+05 MPa

Elastic constants - nu 2.4e-01 3.9e-01 3.0e-01

Density 3.6e-15 1.0e-15 1.65e-15 kg/µm3

TCE 7.1e-06 1.1e-05 4.6e-06 1/K

Thermal Conductivity 1.4e+07 1.4e+05 1.67e+08 pW/µm · K

Specific Heat 7.7e+14 1.34e+14 pJ/kgK

Electrical Conductivity 1.84e+13 pS/µm

Dielectric 9.8e00 3.5e00

dietop

fix

fix



Mesh Creation


5. View the mesher settings for Region 1, and then generate the mesh.

a. Right click on Region 1, and select Mesher Settings.b. Check that the mesher settings are as shown below.

The Linear Element Order was selected to speed up the simulation. For this simulation the material properties are not defined as temperature dependent, so the device will not undergo dramatic stress or displacement. Under these circumstances, the Linear option will give acceptable results.

Note that the die_attach part has a finer mesh. The planar element size is 300.

c. Right click on the lid layer, and select Mesher Settings.d. Uncheck the Generate Mesh option in the bottom of the dialog, then click on

OK.

The lid is not included in the simulation that follows, so unchecking the mesh option for the lid layer removes it from the resulting mesh and the subsequent simulation.

e. In the main Preprocessor window, click on the Generate Mesh icon.

The resulting mesh is shown below.



MemMech Setup and ComputationAll solver control is through MemMech for this segment. The results generated in this section will be used as input for the sensor model in the next section.

Figure T4-131 MemMech Settings for Package Analysis


1. Set the MemMech solver for the package_for_gyro model.

a. In the Function Manager Analyzer tab, set the Solver to MemMech.b. Select the package_for_gyro model.c. In the Analysis field select create a new analysis.

2. Set the MemMech Settings dialog for Thermomechanical physics.

a. Click on the Solver Setup icon.b. In the MemMech Settings dialog, choose Thermomechanical

physics.

The rest of the dialog settings remain the same.c. Click on Next.



Figure T4-132 Package Boundary Conditions


3. Set the SurfaceBCs dialog to fixAll each of the pins (the bottom fix patch) in the package.

4. Set the Surface BCs dialog to apply a heat flux of 300 pW/µm2 to the place where the sensor device will be mounted (the dietop patch).

a. Set the SurfaceBCs dialog as shown in Figure T4-132.

The bottom fix patch of each of the pins in the package is held stationary.

A heat flux of 300 pW/µm2 is applied to the dietop patch where the device is mounted. This simulates the thermal effects on the package resulting from the power dissipation from the device.

5. Set the VolumeBCs dialog to apply a fixed 300 K temperature to each of the package pins.

a. Set the VolumeBCs dialog as shown in Figure T4-132.

The pins are held at 300K while the heat flux source is applied, creating a thermal stress through the package volumes.

6. Start the simulation. a. Click on Run.b. Save the analysis as package.

The simulation may take as long as 30 minutes.



Figure T4-133 Package Analysis Table Results


7. Verify the mechDomain and rxnForces tables shown in Figure T4-133.

a. When the simulation is finished, click on the View Results icon.b. In the Analysis window, select the mechDomain table, click on the View

Table icon, and verify the results shown in Figure T4-133.

The mechDomain windows shows the maximum displacement and its vector components.

c. Select the rxnForces table and verify the results shown in Figure T4-133.

The reaction forces are at the bottom of the pins.


8. View the 3-D stress results in the Visualizer, as shown in Figure T4-134.

a. In the Analysis window, click on the View 3D Results icon. b. In the Visualizer, from the menu bar, select Plot > Contour/Multi-coloring.

Choose Mises Stress from the drop-down menu.

c. In the tool bar to the left of the display, click on the rotate about Y icon.

d. If necessary, select View DataFit.e. Observe the stress results, as shown in Figure T4-134.

The stress color map shows stress in the pins area. However, the area of concern is on and around the surface where the device is mounted. With some changes, the Visualizer will show curvature in the package that results in a stress on the device.



Figure T4-134 Package Stress Results


9. View the Displacement Mag. results, as shown in Figure T4-135.

10. Probe the displayed model to verify the numerical results in the large displacement areas, as shown in Figure T4-135.

a. Select View > Rotate, and in the dialog that opens, click on Default.b. From the menu bar, select Plot > Contour/Multi-coloring, and select

Displacement Mag. from the drop-down menu.c. Select Coventor >Part Visibility, and hide the lid part.d. Verify the results shown in Figure T4-135.

The color map shows displacement variation throughout the volume, including a relatively small change in the dietop area.

e. In the left sidebar, check Mesh.

f. From the Visualizer Sidebar Tools, select the Probe Tool icon.

g. Click with the cursor in the areas of large displacement to view the numerical values, as shown in Figure T4-135.

Press Ctrl while clicking to display mesh vertex points.



Figure T4-135 Displacement Magnitude and Probe Results



Figure T4-136 Exaggerated Displacement Results

The effect is now noticeable. These results will be used later to analyze the effect the curvature change has on the device. Before finishing this tutorial segment, extract the curvature numbers for further examination.


11. Verify the exaggerated displacement results, as shown in Figure T4-136.

a. From the menu bar, select Coventor > Geometry Scaling.b. In the Geometry Scaling dialog, check Deform Using Displacements, set

the Exaggeration field to 1000, and click on Apply. c. Verify the results shown in Figure T4-136.

The curvature is small, so it must be magnified to see the effect. Even a very small curvature change in this large package can have a significant effect on the comparatively small device mounted in it.

12. Exit the Visualizer. a. File > Exit the Visualizer.



Figure T4-137 Custom Query Setup

Figure T4-138 Curvature Table Results


13. Set up a Custom Query to extract Curvature results from the dietop patch.

a. In the Analysis results window, click on Custom Query.b. In the hierarchical menu that opens, click on On a Patch.c. For Query1, select the dietop patch and Curvature.d. Enter Curvature in the Query Label field.e. Execute the Query.

The result window now includes a new Curvature field for Table and Graphs.


14. Verify the Curvature table results shown in Figure T4-138.

a. In the Analysis results window, select the Curvature table, click on the View Table icon, and verify Figure T4-138.

The curvature and tilt data provide more information about the dietop results.

See the CoventorWare ANALYZER Reference, page R8-13, for more information about Curvature Query extraction.

15. When finished, exit the Analysis window. a. Close the Analysis results window.b. Save the project settings file.



4.9.3: Package Analysis with Variable TemperatureThis tutorial sequence builds on the previous sequence by solving for a range of boundary conditions for the package. To simulate the effect of ambient temperature change, the package is subjected to a trajectory set of temperature val-ues, ranging from 223 K to 423 K. The methodology for running this half of the tutorial is nearly equivalent to that performed in the previous sequence, with the addition of a parametric study. The models, part names, patches, result files, and material properties are the same as set up in the previous runs. The results will provide a distribution of val-ues for analysis and determination of the sensitivity of the device to package stresses.

MemMech Setup and Computation

Figure T4-139 Modified Surface and Volume BCs Dialogs

The simulation may take up to 1 hour to run.


1. Open the package settings file and rename it package_para.

2. Set the MemMech solver to run on the package_for_gyro model.

a. From the Function Manager, select File > Open, and reopen the package.mps file.

b. Save it as package_para.mps.c. In the Function Manager Analyzer tab, set the Solver to MemMech.d. Set the Model/Mesh field to package_for_gyro.e. Set the Analysis field to create new analysis.

3. Check that the MemMech Settings dialog is set the same as for the first package simulation (see page T4-156).

a. Click on the Solver Setup icon.b. In the MemMech Settings dialog, verify that Thermomechanical

physics is still selected.

4. Remove the HeatFlux BCType from the SurfaceBCs dialog.

a. In the SurfaceBCs dialog, remove the HeatFlux BCType from Set2.

In the initial simulation this BC was applied to simulate the thermal effects on the package resulting from the power dissipation from the device. For this setup, you are simulating the effects of ambient temperature on the package, so this setting is not needed.

5. Change the VolumeBCs dialog so the initial temperature is 223 K and set to be a variable.

a. Modify the VolumeBCs dialog as shown in Figure T4-139.

A variable temperature is used, with a starting point of 223 K.



Figure T4-140 Parametric Study Trajectory and Variable Setup


6. Set up a parametric study to vary temperature from 223 K to 423 K in 4 steps. Assign the PackageBC1 variable to the trajectory you set up.

a. In the MemMech BCs window, click on Parametric Study.b. Set a trajectory for t1 using an Enumerate trajectory type.c. In the Edit dialog, set the range as shown in Figure T4-140.

Set the values so the parametric study varies the temperature from 223 to 423K.

d. Label the trajectory as Temperature.e. Click on mechBCs and assign the mechBC1 variable to trajectory

t1 with an Absolute Type. See Figure T4-140.f. In the Parametric Study window, click on Run.g. Save the analysis as package_para.



Figure T4-141 Parametric Study Table and Graph Results


7. Verify the numerical results for mechanical and reaction force results, as shown in Figure T4-141.

8. Verify the graph results for minimum and maximum Z displacement results.

a. When the simulation is finished, click on the View Results icon.b. In the Analysis results window, select the mechDomain table, click on the View

Table icon, and verify the results shown in Figure T4-141.c. Select the mechDomain graph results, and click on the View Graph icon. d. In the graph area, double click on any of the plot curve lines. In the Mapping

Style dialog that opens, Ctrl select the NodeZDisplacement Maximum and Minimum plot curves (Map No. 7 and 8), click and hold on Map Show, and select Show Selected Only to view only these two plot curves.

Clicking on Mapping Style in the left sidebar opens the same dialog.

The published graph format was created using a Visualizer macro. See page R9-34 for details.

e. Verify the results shown in Figure T4-141.

The plot shows that the minimum absolute displacement values for the package occur at 293 K. The maximum displacement occurs at the maximum temperature. At temperatures significantly above or below room temperature (300 K) the package displacements (and resultant stresses) are relatively significant.

f. Select the rxnForces table and verify the results shown in Figure T4-141.

table split for easier viewing



Figure T4-142 Package Results Showing Curvature


9. Verify the exaggerated displacement results, as shown in Figure T4-142.

a. In the Analysis results window, click on the View 3D Results icon to view All results of the parametric study run.

b. From the menu bar, select Plot > Contour/Multi-Coloring. Select Displacement Mag.

c. Select Coventor > Part Visibility, and hide the lid part.d. Select Coventor > Geometry Scaling. In the Geometry Scaling dialog,

check Deform Using Displacements, set the Exaggeration field to 200, and click on Apply, then close the dialog.

e. From the menu bar, select Coventor > Result Selection. Click on Next to observe the results for each simulation steps.

Figure T4-142 shows the displacement results at 223K (Step1) and 423K (Step 4). At 223 K, the package contracts; at 423, it expands.

10. When finished, exit the Visualizer. a. File > Exit the Visualizer.

Step 1: 223K

Step 4: 423K



Figure T4-143 Curvature Table and Graph Results

These results show the temperature effects on the package and the points of maximum and minimum curvature.


11. Set up a Custom Query to extract Curvature results from the dietop patch.

a. In the Analysis results window, click on Custom Query.b. In the hierarchical menu that opens, click on On a Patch.c. For Query1, verify that the dietop patch and Curvature are selected.d. Verify that Curvature is the Query Label field.e. Execute the Query.

12. Verify the Curvature table and graph results shown in Figure T4-143.

a. In the Analysis results window, select the Curvature table, click on the View Table icon, and verify Figure T4-143.

b. Select the Curvature Graph and click on the View Graph icon.c. Configure the graph to view the dietop_Curvature_1 and

dietop_Curvature_2 plot curves. d. Verify the graph in Figure T4-143.

13. When finished, exit the Analysis window. a. Close the Analysis results window.



4.9.4: Package Analysis with LidThe package used in the previous tutorial included a lid, which was excluded from the mesh, and therefore, the design analysis. This section shows the package results for the device that includes the lid.

To include the lid in the package simulation:1. Open the package_for_gyro model in the Preprocessor.2. Right click on the lid layer, and select Mesher Settings.3. Select the Generate Mesh option in the bottom of the window.4. Regenerate the mesh. The results are shown below:

5. Rerun the parametric study simulation described on page T4-163 using the model that includes the lid. The results are detailed in the sections that follow.

Numerical ResultsThe mechDomain and rxnForce results are shown below. Compare them with results shown on page T4-165.



Graphical ResultsThe figure below shows the displacement Z and Y graphical results with and without the lid. Note that the displace-ment in Y direction with the lid is somewhat smaller than the one without lid because of the additional constraint. However, the package needs to expand somewhere, and the only way to is in Z direction. That is why we see the big changes in Z direction.

With Lid Without Lid



The flatness of the die attach surface has the most influence on the device. Curvature query results on the dietop for the package with and without the lid are shown below. The results show a significant change on the curvature with the lid. For tutorial purposes, the package was run without the lid, but in a real design, the effect of the lid on the package and the device cannot be ignored.

With Lid

Without Lid



Visualizer ResultsFigure T4-144 shows the package displacement at 423K. The Geometry Scaling option is set to Deform Using Dis-placements with the Exaggeration set to 200. The displacement without the lid is included for comparison.

Figure T4-144 Visualizer Results with and without the Lid223K

423K



4.9.5: Package Deformations in ArchitectIn this section we will demonstrate how to use a hybrid modeling approach to model the effect packaging has on a MEMS device. This approach combines the FE solver analysis with system-level modeling in a circuit simulation environment. The hybrid approach exploits the complementary strengths of each of these modeling methods, namely the ability of field solvers to analyze arbitrarily complex geometric shapes and the optimized computational perfor-mance of behavior models.

The gyroscope used in the package simulations can be accurately modeled in Architect, as demonstrated in the tuto-rial that begins on page T4-1. The package deformation results generated with MemMech can be input to the Archi-tect gyroscope schematic because the behavioral models can import package deformation data directly from the FE results stored in the project database. The anchor models used in the gyroscope schematic, for example, can read in displacement and rotation offsets from the FE analysis of the package based on their position in the local device coor-dinate system. The ambient temperature defined by a global variable in Architect’s COVENTOR symbol, can be altered in a vary loop to analyze the effects on design performance. The comb components also account for substrate deformation that results from packaging effects by giving vertical and horizontal displacements to the stator fingers based on their locations on the substrate. Similarly, the electrode component computes the electrostatic forces on the perforated proof mass by numerically integrating over the gap between the mass and the underlying electrode. The substrate deformation at the Gaussian integration points is extracted from the corresponding points in the FE package model during initialization of the circuit simulation. Figure T4-145 illustrates to gyroscope placement in the package before and after the package undergoes deformation:

Figure T4-145 Gyroscope Attached to Package

Initialization


1. Point the Process file field to gyro.proc. a. Make sure the Architect tab is active in the Function Manager.b. Using the folder icon to the right of the Process field, select

gyro.proc as the Process file.

c. Click on the Process Editor icon.

d. Review the process. e. Close the Process Editor.

package substrate

knot

anchor beam

gyro plate

gyro deformed by package deformation

undeformed gyro



2. Open the gyro_prebuilt schematic. a. From the Schematic field drop-down menu, select the gyro_prebuilt.sch.

You should use the prebuilt schematic provided with the tutorial because if you constructed your own schematic and ran the Architect simulations, you had to change several default settings. This tutorial exercise assumes that the gyro schematic has the initial tutorial settings.

b. From the Saber icon drop-down menu, select Open.c. Maximize the Architect Sketch window and the schematic window.


3. In the COVENTOR symbol, for the substrate_analysis property, point to the package_para analysis result and specify the origin at 0,0,-311u.

a. Double click on the COVENTOR symbol to open the properties dialog.

b. Click on the substrate_analysis property Value field.c. In the dialog that opens, click on the name Value field, and select

package_para.

The package_para result contains the simulation results for package deformation over a range of temperatures (see page T4-163 to see how the MemMech FEM solver was configured). These results will be input to the gyro schematic and used to simulate the effect package deformation has on the gyro simulations.

d. For the origin, specify x = 0, y = 0, and z = -311u.

When specifying an analysis result, you have to define the mesh coordinate frame in terms of the reference coordinate frame. The reference coordinate frame is defined by the Reference symbol, and its origin is (0, 0, 0). For the package used in the analysis results, the top surface of the device is at (0,0, 311u), so the origin of the mesh frame in terms of the reference frame is (0, 0, -311u). See Figure T4-146 for an illustration.




Figure T4-146 Specifying the Mesh Frame with Respect to Reference Frame


4. For the L-beams, set the primitive property to nonlinear_l_beam_2seg.

a. Use the Ctrl key to select the four L-Beams.b. Double click to open the Common Properties dialog.c. Click on the primitive property field. In the dialog that opens,

select nonlinear_l_beam_2seg, then click on OK.

In previous gyroscope simulations, we used the linear beam models to minimize simulation time. But in this simulation, the beam displacements caused by the package deformation are best modeled with the nonlinear beam models, which have no angular restrictions and can accurately model any given beam position in space. For more information on the various beam models, see page A5-9.

5. Netlist and simulate the schematic. a. In the menu select Design > Netlist.b. Click on the icon on the right of the simulation icon bar to open the

SaberGuide Transcript window. c. Select Design > Simulate.



Impact of Temperature on Resonant Frequencies

Figure T4-147 Varying Temperature


1. Perform a vary analysis using looping commands to vary the temperature from 220 to 450 in 4 linear steps in the outer loop while performing a small signal AC analysis in the inner loop. For the small signal analysis, use a frequency range from 6.5k to 7.5k k for 1000 points. (see Figure T4-147).

a. Click on the Vary icon. b. In the Looping commands dialog, click on vary.c. From the Parameter Sweep (Loop #1) dialog Parameter Name

field, select Browse Design. Double click on Parameters to expand, then select architect_temperature.

d. Set the rest of the Parameter Sweep variables according to Figure T4-147, then click on Accept.

e. In the Looping commands dialog, select Add Analysis > Within Loop(s) > Small Signal AC.

f. Click on acanalysis in the Looping commands dialog.g. In the Small-Signal Frequency Analysis dialog, set

Start Frequency to 6.5k and End Frequency to 7.5kNumber of Points to 1000Increment Type: LinRun DC Analysis First to Yes.

For each temperature, the DC operating point is different, which requires running a DC analysis before the small signal AC analysis.

h. Select Add Analysis > After Loop(s) > View Plotfiles in Scope.





3. View the y analysis results in CosmosScope. a. Plot the y signal.b. Right click on signal legend, and select Member Attributes. In the

dialog that opens, click on Show All Labels. Click on Close.c. Pass the mouse over the label group until a Place Labels vertical line

appears. Drag the line left to increase the distance between the labels. You can also drag each label individually.

We are most interested in the y plot because in subsequent simulations, we will be varying the position of the gyro along the y axis.



Impact of Device Position on Performance


1. Add an outer vary loop to vary the position of the gyro from -900u to 900u in 5 lin steps.

a. Click on the Vary icon. b. In the Looping commands dialog, select AddLoop > Vary. c. For the Parameter Name, select substrate_analysis > origin >

y. d. Set the Sweep Type to Linear Steps from -900u to 900u in 5 lin

steps.

These settings move the gyro from the bottom to the top of the die in the substrate and varies the temperature at each position. An AC analysis is simulated for each position and temperature.





3. View the y analysis results in CosmosScope. a. Plot the y signal.b. Click on the signal legend, then select the Measurement Tool icon

c. Click on Measurement At X, and select Levels > X at Maximum option. Click on Apply.

d. Click on the X_Max signal legend to select, then right click and select Member Attributes.

e. In the dialog that opens, click on Show All Labels. Click on Close. Pass the mouse over the label group until a Place Labels vertical line appears. Drag the line left to increase the distance between the labels. You can also drag each label individually.

f. Click on the X_Max signal to make sure it is active. Select the Measurement Tool icon, then select Levels > Peak to Peak.

g. Right click on the signal legend of the newly created PK2PK plot, and select Attributes. From the Symbol drop-down arrow, select the circle icon.

The Peak to Peak plot shows how much the frequency changes for a given device position. The smallest change can be found for offset = 900u. So the device is more insensitive to temperature changes when it is located at the very top of the die (offset=900u).

The asymmetrical results are most likely caused by the asymmetrical design of the package. As seen from the bottom (see Figure T4-130 on page T4-154), the package design is not symmetrical.


Section 5: RF Switch Design Version 2008M


5.1: IntroductionMEMS-actuated RF switches offer distinct advantages over their solid-state counterparts due to, for instance, their low power, low insertion loss, and high isolation. To rapidly design an RF switch to meet time-to-market constraints requires a design tool that can both quickly explore different design concepts, as well as quickly explore the design parameter space for a given design concept.

This tutorial demonstrates using the CoventorWare’s Architect and Analyzer for this purpose. In this tutorial we will explore both the electromechanical and RF characteristics of a cantilever beam resistive switch, illustrated in Figure T5-1. The beam has lower and upper contacts that act as a “make-or-break” section of an RF signal carrying line. As the cantilever is actuated by electrostatic forces from an electrode beneath it, the contacts eventually snap down, com-pleting the signal path circuit.

Figure T5-1 Cantilever Beam Resistive Switch

This tutorial will also demonstrate how CoventorWare’s tools can be used to run a virtual shock test of the RF switch that has been packaged in a HyCap package.

5.1.1: Demonstrated TechniquesThe first part of tutorial demonstrates the following techniques:

setting up a schematic to represent the switch (page T5-3)varying the voltage on the actuation electrode to analyze the electromechanical closing of the switch (page T5-6)varying the anchor length to analyze its effect on contact force (page T5-13)using small signal AC analysis to determine resonant frequency (page T5-17)varying the anchor width to analyze its effect on resonant frequency (page T5-19)using transient analysis to determine switching time (page T5-22)using a schematic that includes the electromechanical and RF components to investigate the effect anchor length has on S-parameters (page T5-25)

The second part of the tutorial documents how the final RF schematic was derived; it demonstrates the following techniques:

creating a contact resistance model using the mechanical contact force and contact area (page T5-29)investigating insertion loss and isolation for various voltages before, during, and after the closing of the switch (page T5-33)


Section 5: RF Switch Design Version 2008

adding transmission line (microstrip line) models to the design (page T5-37)creating your own microstrip discontinuity models using the MAST language (page T5-44)plotting on a Smith Chart (page T5-48)exporting the S-parameter results to Touchstone format (page T5-51)

The third part of the tutorial demonstrates how to use ANALYZER to conduct a pull-in analysis and then compares the ANALYZER and ARCHITECT results.

The fourth part of the tutorial demonstrates how to simulate a drop test of the switch in a Hycap package. It includes the following techniques:

calculating the mass of the packaged RF switch using Integrator’s InertiaMM module (page T5-74)applying a transform operation on a solid model (page T5-77)calculating the stiffness of this package hitting the floor using Analyzer’s MemMech module (page T5-78).entering the stiffness and the mass into the drop test schematic for the RF switch and observing the drop test performance of the switch (page T5-82).calculating the stress suffered by the mechanical beam using the maximum displacement (calculated in a previous step) as an initial boundary condition (page T5-87)

5.2: RF Switch Design in ArchitectThe RF design will be demonstrated in Architect using only a handful of parametrically defined library components. These library components are capable of accurately capturing the 3-D electromechanical behavior of the switch, as well as some of the RF electrical characteristics.

The first half of this tutorial explores the electromechanical behavior by examining pull-in behavior, contact force, mechanical resonant frequencies, switching times, and other transient effects. One of the greatest strengths of Archi-tect is the parametric description of the components. To highlight this strength we will see that with very little effort and computation time, we can examine aspects of electromechanical behavior as a function of the length of part of the cantilever structure.

The second half of the tutorial crosses physical domains by connecting the electromechanical switch to electrical components. It shows how users can combine the contact force, variable capacitance, and transmission line models from the Architect library with a user’s models of contact resistance and microstrip discontinuities. The end result is an estimate of RF characteristics such as insertion loss and isolation by using S-parameter extraction on the electrical circuit.

Architect also provides a rich set of tools for yield analysis by analyzing the effects of statistical process variation of the parameters of the design. For an example of such an analysis, see the Gyroscope tutorial starting on page T4-1.



5.2.1: RF Switch Schematic The RF Switch schematic, RF_Switch_Mech_Only.ai_sch, contains the standard Reference Frame and Coventor symbols required by all Architect PEM schematics and described in the Shared Parts Reference, beginning on page A4-10. The switch itself is built with members of the beam family of Architect electromechanical components. The components used in the schematic are all either mechanical beams, mechanical beams with electrostatic actuation, or contact surfaces. Each instance of these components has been given a label indicating its correspondence to the 3-D structure. The correspondence of the 3-D geometry to schematic components is illustrated in Figure T5-2.

Figure T5-2 Correspondence of Schematic Components to Solid Model

A: Anchor Beam models mechanics of narrow section connected to substrate anchor

B: Actuation Pad Beam with Electrode models mechanics, as well as electrostatic force of actuation electrode C: Separation Beam models mechanics of section separating the actuation electrode from the signal lines

D: Upper X Line Beam Electrode models electrostatics between beam tip section and RF-in signal line, as well

E: Beam models the mechanical tip elasticity

F: Lower X Line Beam Electrode models electrostatics between beam tip section and RF-out signal line, as well

as contact mechanics when the beam tip contacts the RF-in signal line

as contact mechanics when the beam tip contacts the RF-out signal line



The components labeled Anchor, Actuation Pad, Separation Beam, and Beam capture mechanical bending properties via Bernoulli beam theory. The components Actuation Pad, Upper X Line, and Lower X Line also can be electrostat-ically actuated and used to measure capacitance, and capture contact forces when any part of the beam touches the RF signal lines.

In this MEMS schematic, as well as standard electrical schematics, the locations of the components on the screen are chosen for convenience and do not represent their physical locations. Physical location is specified in the properties of the models, which can be viewed by double-clicking on any of the components. The material properties and phys-ical location data from the fabrication process is automatically imported from the CoventorWare MPD and the pro-cess file associated with the schematic.

The schematic editor enables not only the specification of components and their properties, but also their connectiv-ity, which is represented by the lines (wires) connecting the components. In the Architect design environment, por-tions of mechanical components that are connected together in the schematic will be required to move together in simulation. A wire or network of wires connecting components is analogous to the finite element concept of a node that connects finite elements. In this schematic, each network of wires represents six degrees of freedom (DOF) of mechanical motion, analogous to a six DOF FEA node.

From this we can see that the network of wires labeled tip<0:5>, which connects the right side of five components, represents a single six DOF wire representing the translation and rotation of the entire tip of the switch.

Finally, the component connected to the left of the Anchor beam keeps that end from moving, thus representing an ideal anchor to the substrate. More sophisticated models exist for modeling this anchor but are not used in this tuto-rial. For more information on package substrate deformation, see page A2-10 of the Architect Reference. For informa-tion on modeling flexible anchor posts, see page A5-43.

After assigning the components’ physical properties, it is helpful to view the physical structure before schematic-level simulation. In the next section, you will automatically create a 2-D layout from this schematic, and then proceed to a 3-D model.


1. Start CoventorWare, and import the RFSwitch project tutorial.

a. Start CoventorWare. b. Click on the Import Tutorials icon.c. In the Import Tutorials dialog, select the RFSwitch project from the list.d. In the Project Browser, Open the default file on the Settings file line.

2. Select the Switch.proc process file. a. In the Function Manager Process field, select Switch.proc.

3. Open the RF_Switch_Mech_Only schematic. a. Set the Schematic field to RF_Switch_Mech_Only.ai_sch.

This schematic contains only the electromechanical components of the switch.

b. Click on the Saber icon to open the schematic.

The reference frame size has been changed to small. To change it back to its normal size, right click on the reference frame and select Symbol View > Default.



5.2.2: Solid ModelIn this section, you will examine the 3-D solid model to verify the correct physical description of the components in the schematic.

Figure T5-3 RF Switch Model Viewed in Scene3D

If you do not have a license for Scene3D, you can extract a 2-D layout to verify your schematic: From the Architect Sketch window, select Architect > Export for Designer. From the Function Manager’s Designer tab, select New from Architect from the Layout Editor icon’s drop-down menu.


1. Verify the schematic by viewing the 3-D model in Scene3D.

a. Select Architect > Open in Scene3D.b. Set the Scale value to Z with a value of 5.c. Use the Rotate and Pan icons to get a better view of all of the

components of the model. d. Expand the Components tree to view the constituent parts of the

switch, as shown in Figure T5-3.e. Leave the Scene3D window open, and return to the Sketch window.



5.2.3: RF Switch Electromechanical AnalysisThis section of the tutorial explores the electromechanical behavior by examining pull-in behavior (showing three techniques to capture it), contact force, mechanical resonant frequencies, switching times, and other transient effects. One of the greatest strengths of Architect is the parametric description of the components. As an example of this strength, we will see that with very little effort and computation time, we can automatically vary the length of beam connected to the substrate anchor and compute the electromechanical behavior.

Closing the SwitchIn this section, you will sweep the actuation voltage from three different ways to close the switch and observe the contact force of the closed contacts.

Sweeping the Voltage by Running a DC Transfer

This tutorial exercise shows the quickest way to set up a pull-in analysis.

Figure T5-4 Contact Voltage of RF Switch


1. Simulate the design and run a DC Operating Point analysis.

2. Run a DC transfer analysis on the voltage source connected to the actuation pad from 0 to 20 volts in steps of 0.1 to determine the contact voltage.

3. Display results for tip[2] and measure the voltage for contact.

a. Select Design > Simulate.

b. Click on the DC Transfer icon.

c. Click on the arrow next to the Independent Source field to select Browse in Design. Select the v_pulse.acutation_source.

d. Sweep the voltage from 0 to 20 volts in increments of 0.1 volts.e. Set Run DC Analysis First to Yes and Plot After Analysis to Yes - Open Only.f. When the plot opens in CosmosScope, double click on @"tip[2]".

tip2 represents the Z node displacement. For more information on the ports in a bus wire, see page A2-1.

g. Click on the Measurement Tool icon and click on Apply. Find the voltage for contact; it should be about 13.7 volts. See Figure T5-4.

The plot shows the tip of the switch being pulled down at about 13.7 volts.

4. Save the displacement results to a text file.

a. Click on the tip2 signal to select it.b. Select File > Save Waveforms, and save the file as displacement.txt.

You are saving the displacement graph in ASCII text for comparing with Analyzer results in a later step.



Figure T5-5 Switch Pull-in


5. View the pull-in results in Scene3D. a. In the Scene3D window, click on the Show/Hide Simulation Results icon.

b. Click on the Browse icon and select the RF_Switch_Mech_only.dt.ai_pl.

c. Set the Scale to Z with a value of 10.d. Click the Play icon or use the slider to progress through the voltage steps and

view the pull-in of the two parts of the switch; see Figure T5-5.

The animation of the results show the tip of the switch pulling down between 14.2 and 14.4 volts. The animation matches the plot shown in Figure T5-4.

0 volts 10 volts

13.8 volts13.2 volts



Sweeping the Voltage by Running a Slow Transient

DC transfer simulations run quickly into convergence issues at the moment of pull-in and pull-out. The pull-in and pull-out events are huge discontinuities in the system solution that are inherently difficult to bridge for the solver. The success of a simulation often depends on a careful setting of the voltage stepping, sample-point densities, as well as the number of integrations points used in the electrode models. Transient simulations provide a robust alternative to DC transfer simulation if convergence in a DC transfer simulation is hard or even impossible to achieve. There are two different techniques available that both provide similar performance: running a slow transient simulation and using the arc length continuation voltage source. A slow transient simulation is the safest way to run a pull-in analy-sis, as the simulator will adapt its time steps to the nonlinearities encountered. Transient simulation is used here to drive the actuation voltage source, slowly enough to be in a pseudo-static case for each step. We use this tool to get to full contact and further. The pulse source of the actuation voltage is set up as a ramp from 0V to 40V in 10s.

Figure T5-6 Contact Voltage for All Nodes


1. Run a transient analysis up to 10s with a time step of 0.01s.

2. Plot results for the z position of k1, k2, k3 and tip nodes.

a. Click on the Transient icon.

b. Set the End Time to 10 and the Time Step to 0.01.c. Set Monitor Progress to 10.d. Set Plot After Analysis to Yes - Open Only. Click on OK.e. On the Algorithm Selection tab, set Target Iterations to 10.f. When the plot opens in CosmosScope, double click on the

@"k1[2]", @"k2[2]", @"k3[2]",and @"tip[2]" waveforms. Drag and drop all of them in the same stack region. See Figure T5-6.

g. Close CosmosScope.h. Leave the RF_Switch_Mech_Only schematic open.

The end of the tip is touching the contact The actuation beam is stillgoing down, which causesthe end of the tip to lift upAs the actuation voltage increases,

the tip of the beam flattens onto theactuation pad



Each beam component in Architect models the deformed shape by a third-order polynomial. As the beam model imposes a continuity of the derivatives between each components, the whole beam shape can be fitted with a polyno-mial, and the tip is lifting up when k3 lies on the pad with k2 and k1 still pulled down by the voltage source.


3. View the simulation results in Scene3D a. In Scene3D, load the RF_Switch_Mech_only.tr.ai_pl file.b. Use the Play icon to view the results.

The initial results are similar, but this technique shows pull-in over time. Because we can ramp up to 40 volts, we are able to see the pull down of the back of the beam, as well as the tip. The DC Transfer Analysis simulation could not have been completed for a range of 0 to 40 volts because of convergence problems.

3 sec 3. 5 sec

7.1 sec 7.4 sec



Using the Arc Length Continuation Voltage Source

In this next tutorial simulation you will use the arc length continuation voltage source to run pull-in\pull-out analysis. The advantages of this source over the DC transfer and slow transient simulations is that the arc length continuation method is more robust as the system is at equilibrium for each iteration step. This usually leads to less convergence issues and faster simulation time. For more information on the arc length continuation source, see page A4-11 of the Architect Reference.

Figure T5-7 Arc Length Continuation Source Schematic

On this schematic all components have been placed to run a pullin-pullout analysis using the arc length continuation voltage source. Note several probes along the switch, all connected to the source via a summation element. It is important when choosing the knots to be connected to the arc length continuation source to have enough connections for getting the evolution of the geometry for the whole pullin-pullout mechanism.


1. From the Architect tab, select the RF_Switch_Mech_Only_ArcLengthSource schematic, and load it into Saber.

a. From the Architect tab, select RF_Switch_Mech_Only_ArcLengthContinuation_Source.ai_sch, then click on the Saber icon.

b. From within SaberSketch, select Design > Use > RF_Switch_Mech_Only_ArcLengthContinuation_Source. The schematic is shown below.

c. Select Design > Netlist, then Design > Simulate.



Figure T5-8 Contact Voltage


2. Run a transient analysis up to 450s with a time step of 1s.

3. Plot results for the z position of k2 node vs. actuation voltage.


b. Set End Time to 450 and Time Step to 1.c. Set Monitor Progress to 10.d. Set Run DC Analysis First to Yes.e. Set Plot After Analysis to Yes - Open Only. Click on OK.f. On the Algorithm Selection tab, set Target Iterations to 10.g. When the plot opens in CosmosScope, double click on the

@"k2[2]" and v_actuation waveforms.h. Open the waveform calculator.i. Select @"k2[2]" signal. Copy and paste it (or click with the middle

mouse button) in the entry field. Copy and paste v_actuation signal in the entry field too.

j. Select wave > f(x). Click Graph X button. See Figure T5-8.

tip touches the pad

Back part of switchpulls down



Contact Force

The mechanical characteristics of the switch’s metal-to-metal contact greatly influence the resistance at the contact and are thus an important factor in determining insertion loss. In addition to handling electrostatics, the beam elec-trode is modeling contact between two layers. Some characteristics of the contact can be displayed in CosmosScope like the contact force or the contact conductance, as illustrated below. The contact_settings property in the properties dialog of the beam_electrode offers some parameters to be customized. You can switch off the built-in contact here, modify the contact energy or the contact conductance. A contact model is also available and provides some more flexibility. For this simulation, you will return to the RF_Switch_Mech_Only schematic.

Figure T5-9 Contact Area and Force


1. Reload the RF_Mech_Only schematic.2. Run another DC Transfer analysis from 12 to 28

volts in 0.5 volt steps, recording all signals.3. Plot results for the lower contact force value.

a. Select Design > Use > RF_Switch_Mech_Only.b. Click on the DC Transfer icon.c. Change the voltage sweep to cover 12 to 27 volts in 0.1 volt steps.d. On the Input Output tab, in the drop-down menu of signal list,

choose All signals.e. When the plot opens in CosmosScope, look for

beam_electrode_1seg.lower_x_line and expand it. In the properties that appear, expand beam_electrode.1. In this set of properties double click on contactforce. See Figure T5-9.

The contact force is in the micro-newton range; these values are similar to those found in [5].



Effect of Anchor Length on Contact Force

In this next tutorial exercise, you will vary the anchor_length and investigate the impact on contact force.


1. Perform a vary analysis using looping commands to vary the anchor_length from 40u to 80u in increments of 10u. Insert an inner loop that runs a DC transfer analysis from 10V to 20V by 0.05V. Set the sample point density to 100 and leave maximum Newton iterations to 200. Display contactforce signal of lower_x_line.

a. Click on the vary icon. b. In the Looping commands dialog, click on vary. c. In the Parameter Sweep (Loop#1) dialog, click on the down arrow

beside the Parameter Name field, and select Browse Design. Double click on Parameters to expand, then select anchor_length.

d. Set the rest of the Parameter Sweep dialog as shown below, then click on Accept.

e. In the Looping commands dialog, select Add Analysis > Within Loop(s) > DC Transfer

f. Click on dtanalysis and set the simulation parameters as shown below. Note that from the Input Output tab, for the Signal List you must select All Signals, and set the Plot File field to vary_anchor_length.

For each value of anchor_length, the DC operating point is different, which requires running a DC analysis before the DC Transfer analysis.

g. From the Looping Commands dialog, select Add Analysis > Within Loops > Command Line.

h. In the field that appears, enterlist parameters / /.../*.* (ofile "RF_Switch_Mech_Only .vary_anchor_length_arch3d"

This step is only necessary when using Scene3D to view the different results for each vary step. This line creates a file of properties that is used to create the geometries in Scene3D for each vary step. This file, together with the plot file specified in the Small Signal AC dialog, can then be used to view the deformed geometry. Because the property file and the plot file are used as a pair, in the above step, the plot file specified has the same name as the suffix in this line. Note that this line can be copy/pasted from the Saber Transcript window with the filename being the only change. For more information on how to set up a vary analysis for viewing in Scene3D, see page A11-6 of the Architect Reference.

i. Click on Accept.j. In the Looping commands dialog, click on OK.




2. View the analysis results in CosmosScope. a. When the simulation is complete, select Results > View Plotfiles in Scope. In the View Plotfiles dialog that opens, click on OK.

b. Plot contact_force.c. Select the contact_force signal legend. Right click and select Member

Attributes. In the dialog that opens, click on Show All Labels. Click on Close.

d. Pass the mouse over the label group until a Place Labels vertical line appears. Drag the line left to increase the distance between the labels. You can also drag each label individually. See Figure T5-10.

The plot shows that as the length increases, the contact force gets larger.

From the Input/Output tab, set the Plot File field to vary_anchor_length



Figure T5-10 Contact Force for Varying Anchor Lengths


3. Visualize the varying anchor lengths and the effect on contact in Scene3D.

a. When the simulation is complete), in the Scene3D window, select File > Open, and select the RF_Switch_Mech_Only.vary_anchor_length_arch3d file.

b. Set the Z scale to 10.

c. Use the down arrow to view each variation on the anchor length.

d. Click on the Show/Hide Simulation Results icon and then on the Open Plotfile icon. Select the RF_Switch_Mech_Only.vary _anchor_length.ai_pl file.

e. With anchor_length: 4e-05 selected, use the Next Frame animation icon to advance through the voltages until you see the switch make contact.

f. Select each anchor length, and advance through the voltage steps. The results are shown in Figure T5-11.

The Scene3D results verify the plot results shown in Figure T5-10: As the anchor length increases, the pull-in voltage decreases.



Figure T5-11 Effect of Anchor Length on Pull in

length = 80 µmpull in = 10 V

length = 70 µmpull in = 11.2 V






Frequency Response


1. Perform an analysis of the device as all small signal sources are varied from 1 kHz to 40 kHz. Plot the signal for @"tip[2]".

a. Click on the Small Signal AC icon. b. Set the parameters as shown below.

AC analysis will be performed, varying all small signal sources from 1kHz (Start Frequency) to 40kHz (End Frequency).

The Plot After Analysis option is Yes - Open Only. c. Click on OK.

CosmosScope opens at the end of the simulation.



Figure T5-12 Small Signal AC Analysis: Resonant Frequency


2. Plot the @"tip[2]" results in CosmosScope.

a. In CosmosScope, plot the @"tip[2]" waveform.b. Select the legend of the @"tip[2]" Phase(deg) plot. Right click and select

Delete Signal from the menu.c. Select the @"tip[2]" dB(m) plot.d. Click on the Measurement Tool icon. Click on the Measurement button

(labeled At X), and select the General > Local Max/Min measurement option to annotate the peak signal point. Click on Apply. See Figure T5-12.

The resonance frequency plot does not have a sharp peak because the frequency response is softened by the damping value defined with modal_damping parameter in the Coventor symbol.

e. Exit the Plot window.


3. Visualize the resonant frequency results in Scene3D. a. In the Scene3D window, make sure the RF_Switch_Mech_Only.arch3D file is active.

b. If needed, click on the Show/Hide Simulation Results icon, and then click on the Browse icon to select the RF_Switch_Mech_Only.ac.ai_pl file.

c. Set the Scale to Z and enter 10 as the scale factor. d. Set the Exaggeration in the X/Y and Z directions to 100.e. In the Frequency field, enter 12922 (the modal frequency), and

click on the Harmonic Play icon f. View harmonic response. You will see the switch oscillating up

and down. When finished, click on the Pause icon.



Effect of Anchor Width on Frequency Response

In this step you will vary the parameter anchor_width and investigate the impact on resonant frequencies.

Figure T5-13 Vary Parameters for Anchor Width


1. Perform a vary analysis using looping commands to vary the anchor_width from 10u to 70u in increments of 10u. Insert an inner loop that runs a small signal AC analysis with a frequency range of 1k to 100k for 1000 points (see Figure T5-13).

a. Click on the Vary icon. b. In the Looping commands dialog, click on vary.c. From the Parameter Sweep (Loop #1) dialog Parameter Name

field, select anchor_width.d. Set the rest of the Parameter Sweep variables according to

Figure T5-13, then click on Accept.e. Click on the down arrow beside the dtanalysis button, and

select Delete.f. In the Looping commands dialog, select Add Analysis > Within

Loop(s) > Small Signal AC. g. Click on acanalysis in the Looping commands dialog.h. In the Small-Signal Frequency Analysis dialog, set

Start Frequency to 1k and End Frequency to 50kIncrement Type to LinNumber of Points to 1000Run DC Analysis First to YesFrom the Input Output tab, set the Plot File field to vary_anchor_width

i. From the Looping Commands dialog, select Add Analysis > Within Loops > Command Line.

j. In the field that appears, enterlist parameters / /.../*.* (ofile "RF_Switch_Mech_Only_ .vary_anchor_width_arch3d"k. Click on Accept.l. In the Looping commands dialog, click on OK.

From the Input/Output tab, set the Plot File field to vary_anchor_width



Figure T5-14 Resonance Frequencies for Varying Anchor Widths


2. Plot the @"tip[2]" results in CosmosScope.

a. In the Saber Transcript window, select Results > View Plotfiles in Scope. Click on OK.

b. In CosmosScope, plot the @"tip[2]" in the signal.c. Select the legend of the @"tip[2]" Phase(deg) plots. Right click and select

Delete Signal from the menu.d. Select the @"tip[2]" dB(m) plot. Right click and select Member Attributes. In

the dialog that opens, click on Show All Labels. Click on Close.e. Pass the mouse over the label group until a Place Labels vertical line appears.

Drag the line left to increase the distance between the labels. You can also drag each label individually. See Figure T5-14.

f. Note the approximate resonant frequency for each anchor width.g. Exit the Plot window.


3. Visualize the varying anchor widths in Scene3D. a. In the Scene3D window, select File > Open, and select the RF_Switch_Mech_Only.vary_anchor_width_arch3d file.

b. Change the Z Scale to 10.

c. Use the down arrow to view each variation on the beam length. Each step is shown in Figure T5-15.



Figure T5-15 Varying Anchor Widths10µm 20µm

30µm 40µm

50µm 60µm

70µm



Modeling Switching TimeIn this tutorial sequence, you will use transient analysis to model switching time.


4. Visualize the harmonic response in the for each anchor width variation.

a. In Scene3D, click on the Show/Hide Simulation Results icon and then on the Open Plotfile icon. Select the RF_Switch _Mech_Only.vary _anchor_width.ai_pl file.

b. Set the Exaggeration in the X/Y to 100 and in the Z direction to 100.c. Change the Frames value to 1000.d. For anchor_width = 10u, enter 8000 in the Frequency field (estimated

from plot in Figure T5-14,) and use the Next Frame animation icon to advance through the frequency results until you see the maximum displacement in the Z direction; this will be the resonance frequency in the Z mode.

e. When you have isolated the resonance frequency, click on the Harmonic Play icon to view the harmonic response.

f. Use the down arrow to advance to anchor_width = 20u.g. Enter a value of 11000 in the Frequency field and use the Next Frame

icon to isolate the resonance frequency. When you have isolated it, view the harmonic response.

You may have to adjust the Exaggeration values to get a better view of the harmonic response.

h. Find and view the harmonic response for the other anchor_width values.


1. Open the COVENTOR symbol, and change the Voltage_Pulse value to 20.

a. Double click on the COVENTOR symbol.b. Change the Voltage_Pulse value to 20.

2. Open the pulse voltage source properties. Set the parameters as shown below.

a. Double click on voltage pulse source. Set the properties as shown below.

The variables used in this dialog are defined in the Coventor symbol.b. Renetlist the schematic.




3. Set up a transient analysis to run 1ms in time steps of 1u, and set the Algorithm Selection /Target Iterations to 10.


b. In the Basic tab, set the following:End Time = 1mTime Step = 1uMonitor Progress = 10Run DC Analysis First = Yes

c. In the Algorithm Selection tab, set the Target Iterations to 10.d. Click on OK to start the simulation.


4. Plot the tip[2] and v_actuation signals. a. In CosmosScope’s signal list dialog, double click on tip[2] to plot it. b. Plot the v_actuation signal.c. Right click on the v_actuation legend, and select Move to Stack

Region > Analog 0. The results are shown in Figure T5-16.

Note the finite time before the switch was stably closed.



Figure T5-16 Switching Time


5. Visualize the transient results in Scene3D. a. In the Scene3D window, make sure the RF_Switch_Mech_Only.arch3d file is active.

b. If needed, click on the Show/Hide Simulation Results icon, and then click on the Browse icon to select the RF_Switch_Mech_Only.tr.ai_pl file.

c. Set the Scale to Z and enter 10 as the scale factor. d. Set the Exaggeration in the X/Y and Z directions to 1.e. Use the animation controls to view the switching time.

As you view the animation, you will see that after the initial pull down and pull up, the switch oscillation decreases as damping takes effect.

90 µsec 600 µsec



5.2.4: RF Electrical AnalysisIn the previous section, the electromechanical behavior such as pull-in was explored. However, determining the volt-age at which the switch closes gives no insight as to whether the switch design will achieve a desired RF specification for quantities such as insertion loss or isolation.

To estimate these characteristics within Architect, the mechanical solution can be used to estimate the electrical capacitance of the open switch and the electrical contact resistance of the closed switch. This capacitance and resis-tance can then be used in conjunction with transmission line models and microstrip discontinuity models to compute S-parameters. The simulation in this section uses an already-constructed schematic that has the proper electrical com-ponents connected to the electromechanical components. It shows how the S-parameters of the switch change as function of the anchor_length.

Section that follows is optional; it shows how to construct the electrical part of the schematic.

Figure T5-17 RF_Switch_Txlines_Gap Schematic


1. Open the RF_Switch_Txlines_Gap schematic.

a. From the Architect tab, select the RF_Switch_Txlines_Gap schematic, then click on the Saber icon.

This prebuilt schematic already includes the RF electrical components. To understand how this schematic was developed, see the section starting on page T5-29.

b. Select Design > Netlist and Design > Simulate.



Figure T5-18 Vary Parameters For Anchor Length and Frequency Analysis


2. Run a vary analysis on the anchor length from 50u to 80u in increments of 10u. Insert an inner loop that runs a two-port frequency analysis using the setup described in the Detailed User Procedure.

a. Click on the Vary icon.b. In the Looping commands dialog, click on vary.c. In the Parameter Sweep (Loop #1) dialog Parameter Name field, enter

anchor_length.d. Set the rest of the Parameter Sweep variables according to Figure T5-

18, then click on Accept.e. Delete any other analysis that may appear in the Looping commands

dialog.f. In the Looping commands dialog, select Add Analysis > Within Loop(s)

> Two Port. g. Click on tpanalysis in the Looping commands dialog.h. From the Basic tab, select the settings shown below.i. From the Input Output tab, set the Two-Port Parameter type to

Scattering. Verify that the port1 and port2 impedances are 50 ohms.j. Click on Accept.k. In the Looping commands dialog, click on OK.

Two-Port Parameter:Scattering




3. View the results in CosmosScope. a. In the Saber Transcript window, select Results > View Plotfiles in Scope, and click on OK to plot the Last plotfile.

b. Expand the plotfile. The waveforms for all four S-parameters should be available; plot s11 and s12.

c. Select the legends of the Phase graphs and delete them.d. Right click on the legends of the remaining two signals and select

Attributes. Change the first View field from dB(y) to mag(y)e. Compare your results with those in Figure T5-19.

4. Close the switch and repeat the two-port analysis.

a. Change the initial value of the pulse voltage source connected to the actuation pad to 20 volts. This closes the switch.

b. Save, netlist, and rerun the two-port analysis.c. Set up the plots as in the previous step.d. Right click on each legend, and select Member Attributes. In the

dialog that opens, click on Show All Labels.e. Compare your results with those in Figure T5-19, which shows the

results for the open and closed switch. f. Close the RF_Switch_Txlines_Gap schematic.



Figure T5-19 Effect of Anchor Length on S-Parameters

The results from the open switch show S11 near 1 and S12 near 0 shows good isolation as expected. That is, most of the energy is reflected and very little is transmitted. As the frequency rises, slightly more energy does pass through due to the capacitive coupling between Upper X Line and Lower X Line in the discontinuity model as well as from the coupling to the common cantilever above. There is no variation with anchor length because the geometry at the tip does not change with anchor length.

The results from the closed switch show S11 near 0 and S12 near 1 because now most of the energy is transmitted. We also see that S12 as a measure of insertion loss shows improvement with increasing anchor_length. This makes sense because a longer anchor means that for a given voltage, there is less restoring force pulling the beam back up. Thus the contact force is greater, leading to a smaller resistance and thus less insertion loss.

Note that in this schematic, the transmission lines are lossless. In the next section we will explore the above schematic in much more detail plus look at plotting results on a Smith Chart and using lossy transmission lines.



Schematic Construction for RF Electrical AnalysisThis next section shows how the RF_Switch_Txlines_Gap was developed. It starts with the RF_Switch_Mech_Only schematic and then adds the components step-by-step.

In this section the capacitance and conductance as a function of the mechanical position of the cantilever, reported by the beam-electrode models (Upper X Line and Lower X Line), will be used. The conductance model built-in electro-static models can be customized, and it will be shown how here. These components will then be added to the sche-matic and connected in an appropriate electrical circuit to compute the isolation and insertion loss. To enhance the accuracy of these estimated S-parameters, this section will also demonstrate adding short sections of lossy transmis-sion lines computed by a 2-D finite element transmission line tool, as well as adding custom gap discontinuity models using the MAST hardware description language. The section ends by demonstrating how to export the computed S-parameter data to Touchstone format.

Modeling Contact ResistanceTurning the mechanical contact force and area information into electrical resistance requires a model of the current flow as a function of these contact parameters. The built-in contact resistance model in Architect is based on [7]. This get_contact_conductance.sin model is open and can be found in /CoventorWare2008/architect/ templates/ pem.

Built-in Contact Resistance Model

To use the built-in contact resistance model, the contact must be on in contact_settings property of electrostatic com-ponents. The conductivity at the interface of the two layers in contact is to be specified in electrode > conductivity. For this tutorial we will assume the contact conductivity to be 30 GS/m.


1. Open the RF_Switch_Mech_only schematic.2. Set the Voltage_Pulse value to 40.3. Change the contact conductance of the two tip

electrodes to 30 GS/m.

a. If not still open, open the RF_Switch_Mech_Only schematic.b. From the COVENTOR symbol, set the Voltage_Pulse value back

to 40.c. Select the Upper and Lower X Line symbols, and open the property

dialog of the two selected components.d. Set electrode > conductivity to 30g.

The contact conductivity is available as an internal variable and is plotted next:

e. Save the modified schematic. f. Select Design > Netlist and Design > Simulate.


4. Run a DC transfer analysis to view the change in conductance (and therefore resistance) as the switch closes.

a. Click on the DC Transfer icon.b. Set the DC Transfer analysis dialogs as shown in Figure T5-20.

The voltages in a list of set values must be separated by spaces.c. Click on OK. d. In CosmosScope, plot beam_electrode_1seg.upper_x_line >

conductance or beam_electrode_1seg.lower_x_line > conductance. The results are identical. See Figure T5-21 for the results.



Figure T5-20 DC Transfer Analysis Settings

Figure T5-21 Contact Conductance

As expected, the conductance curve increases with voltage after pull-in because there is more intimate contact between conducting surfaces. For example, 15 V the tip of the switch has pulled in, an the contact resistance is about 9.18 ohms. At 30V, where the switch collapses, the contact resistance drops to 0.26 ohms.



Customizing the Contact Conductance Model

Figure T5-22 Text of get_contact_conductance Function

This file is divided in three parts: the declaration of the function and its arguments, the definition of arguments, and then the core of the function, which starts with an opening curly brace and ends with a closing curly brace. To main-tain compatibility with other Architect models, only the content between this braces should be changed. This core function is also divided in three parts: the definition of local variables, the computation of contact conductance, and rules for handling special cases like dividing by zero or an infinite number (represented by inf in MAST).

The # character indicates a comment in MAST. For more information on this language, refer to the MAST Language Reference, found in \Coventor\CoventorWare2008\architect\SaberDesignerInstall\doc\pdf_docs.

To demonstrate how to use this file, we will double the contact conductance.


1. Copy the get_contact_conductance.sin file from your CoventorWare 2008 installation directory, and paste it in your project’s Schematics directory.

a. Locate the get_contact_conductance.sin in your \Coventor\CoventorWare2008\architect\templates\pem directory.

b. Copy the file, then paste it in your Schematics directory.c. Open the file you just created in a text editor.

Modifying the original file of the Coventorware installation would affect all simulations in all projects. Having a local copy of the function allows to have a customized model for the current project only.



Figure T5-23 Original and Customized Conductances


2. Double the value computed for contact conductance.

a. Change contact_conductance from sqrt(contact_conductivity**2/math_pi*4*abs(contact_force)/contact_hardness) to 2*sqrt(contact_conductivity**2/math_pi*4*abs(contact_force)/contact_hardness).

b. Save the file and quit the text editor.

3. Rerun the previous simulation, choosing to append the plots.

4. Delete the local copy of get_contact_conductance.sin after simulation.

a. In the Design menu, click Netlist RF_Switch_Mech_Only.

The local change is taken into account for the simulation, after the schematic is renetlisted.

b. Click DC Transfer icon.c. Change Plot After Analysis to Yes - Append Plots.d. When the simulation is over, delete get_contact_conductance.sin

located in the Schematics folder of the project directory.



Two-Port S-ParametersIn this section, you will create an electrical circuit that uses the contact resistance and the capacitance output pins of the Upper X Line and Lower X Line beam electrode models. This capacitance represents the capacitance between the RF signal lines and the cantilever as a function of the position of the cantilever. This capacitance is used to compute the isolation when the switch is not in contact or nearing contact. The electrical circuit can then be used to compute the appropriate S-parameters, as will be shown below.

In order to achieve a certain level of accuracy for the S-parameter computation, various circuit models of arbitrary levels of complexity are possible. The goal of this tutorial is only to demonstrate one possible circuit model as a rea-sonable estimate for the eventual computation of the S-parameters. Each user is encouraged to experiment with better models more appropriate for individual designs by using the techniques described in the rest of this tutorial.

Circuit Model for the Switch

The width of the switch is much smaller than a wavelength at gigahertz frequencies, so a lumped element model will be sufficient. In addition, the contact resistance dominates over any inductive effects at these frequencies, so an RC model is adequate. When the switch is open, the RF input and output lines are coupled primarily through capacitance to the cantilever, plus a resistance across the cantilever as shown in Figure T5-24a. Direct capacitive coupling between the signal lines will be left as an enhancement for a later tutorial exercise. When the switch is closed, the capacitors are shorted, and the switch is a resistor consisting of both contact resistance and the resistance across the cantilever, as shown in Figure T5-24b.

Figure T5-24 Circuit Model for Different Switch States

The circuits above will be implemented as one circuit in the schematic using the circuit shown in Figure T5-25. The Rc resistors represent the contact resistance and are in parallel with the capacitors for the open state. When the switch is open, the contact resistors are infinite, and when the switch is closed, the contact resistance is so small compared to the capacitors that the effect of the capacitors is negligible.

Figure T5-25 Circuit Implemented in Schematic

The schematic is implemented in the file RF_Switch_CRC.ai_sch, shown in Figure T5-26. The voltage source is nec-essary to define the input port for S-parameter computation in the next section. The shunt resistances define a DC path to ground for simulator convergence and are large enough for a negligible effect on the results. The shunt resis-tance can be viewed as modeling the eventual leakage of any charge induced on the cantilever.

(a) Switch open (b) Switch closed



Figure T5-26 RF_Switch_CRC Schematic

Extracting S-Parameters


1. Open the RF_Switch_CRC design. a. In the Function Manager Architect tab, select the RF_Switch_CRC schematic.

b. Click on the Saber icon to open the design.

2. Run a two-port analysis as outlined in the Detailed User Procedure.

a. Show the Saber Guide.b. Netlist and simulate the design.c. Select Analyses > Frequency > Two-Port.d. Enter the Basic tab settings from Figure T5-27.

The voltage source connected to the M_lower wire is used as the input port for two-port analyses, while the source attached to the beam electrode is still used to control the open/close state of the switch.

e. On the Input Output tab, set the Two-Port Parameter type to Scattering. Verify that the port1 and port2 impedances are 50 ohms.

f. Click on OK.



Figure T5-27 Two-Port Analysis Settings


3. View the results in CosmosScope. a. Expand the plotfile. The waveforms for all four S-parameters should be available; open s11 and s12.

b. Select the legends of the Phase graphs and delete them.c. Right click on the legends of the remaining two signals and select

Attributes. Change the first View field from dB(y) to mag(y)d. Compare your results with those in Figure T5-28.

4. Close the switch and repeat the two-port analysis.

a. Change the initial value of the pulse voltage source connected to the actuation pad to 33 volts. This closes the switch.

b. Save, netlist, and rerun the two-port analysis.c. Set up the plots as in the previous step, which should match those

on the right of Figure T5-28. Compare your results with the open switch case.

When the switch is closed, the path through the two-port is completely resistive and the S-parameters are constant.



Figure T5-28 S-Parameters of RF Switch in Open and Closed States

The S-parameters above are as expected. When the switch is open and the frequency is low, almost all the energy is reflected instead of transmitted, so S11 is nearly 1 and S12 is nearly 0 (good isolation). For high frequencies, the admittance of the capacitors becomes significant and some energy is transmitted, so S12 rises above 0. When the switch is closed, the resistance is small enough that most of the energy is transmitted and S12 is nearly 1 (small inser-tion loss).

Open Switch

Closed Switch



Adding Transmission Lines to a DesignLossy, multi-conductor transmission line models can be added to a design to model the connection of the switch to other devices or to the physical ports of the packaged device. In this section you will use the Transmission Line Tool to create a custom cross-section, then use the 2-D finite element solver to extract a model for use in the schematic.

Creating a Custom Transmission Line Model


1. Open the Transmission Line Tool. a. In Architect, select Tools > Model Architect.

b. Click on the Transmission Line Tool icon.

The icons across the top allow placement of ground planes, dielectrics, and conductors of arbitrary shape as needed to create the geometry of the cross-section at a given position in the transmission line. The line is assumed straight and of length L.

For additional explanation of the Transmission Line Tool, consult Help > Tutorials > txLineTool for a step-by-step tutorial on building and extracting a transmission line (similar to what is outlined below).

2. Create a transmission line by adding a ground plane, a dielectric layer, and a conductor. See Figure T5-29.

a. Click on the New Ground Layer icon.

The ground is automatically 7.5um thick with a conductivity of 5.76e7 S/m.

b. Click on the New Dielectric Layer icon to add a dielectric spacer/

isolation layer.

c. Double click on the dielectric layer and set its thickness to 45u.d. Right click on the dielectric layer and select Material. Change the

permittivity to 9.6.

e. Click on the New Rectangle Conductor icon and draw a

rectangle on the canvas of arbitrary dimensions.f. Double click on the rectangle and set its properties as shown in

Figure T5-29.g. Right click on the rectangle and select Material. Change the

conductivity to 3.55e7 S/m.

The rectangle’s conductivity is that of aluminum.

3. Save the transmission line. a. Save the transmission line as txline_45_45.



Figure T5-29 Transmission Line


4. Check rules and generate a template.5. Use the DC inductance and capacitance per unit

line length to calculate the characteristic impedance

a. Select Options > Field Solver and note the accuracy and grid factor settings.

b. Select Yes for COMPUTERS to calculate the skin resistance, RS.c. Select Options > Instance Parameters and note the settings.

Click on the help icon for explanations of these settings.

d. Click on the Check Rules icon. The results of the check should appear at the bottom of the Model Architect window. Fix any errors.

e. Create a template of the transmission line by clicking the Generate

Template icon.

f. Read the results and the note about fatal errors during simulation in the Txline Tool Generate Template dialog.

The DC inductance and capacitance per unit line length can be used to calculate the characteristic impedance. It should be about 50 ohms.



Adding Transmission Lines to the Schematic

In this section you will add the transmission line models to both input and output RF signal lines. Each line will be one quarter of a wavelength at the frequency of interest, 2.9 GHz. The S-parameters will be recomputed from the ends of these lines, instead of right at the switch, and compared to the original S-parameters.

Figure T5-30 Schematic with Transmission Lines


1. Place two instances of the transmission line in the schematic.

2. Save as RF_Switch_TxLines_No_Gap.ai_sch.

a. In the transmission tool dialog, click the Place Part icon twice.b. Save the schematic as RF_Switch_TxLines_No_Gap.

3. Change the length of the lines to 31.25m, the length of a quarter wave line at 2.9 GHz.

4. Make the transmission lines lossless and integrate them into the schematic as shown in Figure T5-30 and Figure T5-31.

a. Double click on the COVENTOR symbol and verify that xline_length is set to 31.25e-3.

b. Select both transmission lines and double click to open the Common Properties dialog.

c. Change l to xline_length; change ro and rs to 0 to temporarily make the lines lossless.

d. Connect the symbols as shown below in Figure T5-30. See Figure T5-31 for a more detailed view of the upper and lower transmission line connections.

e. Name the wire attached to the upper transmission line output v_out.



Figure T5-31 Detailed Top and Bottom Transmission Line Schematics

top transmission line

bottom transmission line




5. Save, netlist, and simulate the design. a. Save the schematic.b. Select Design > Netlist and Design > Simulate.

6. Run a two-port analysis. a. Set the voltage of the source connected to the beam electrode to 0.b. From the menu bar, select Analyses > Frequency > Two-Port.c. Set the Start Frequency to 2.9g. Leave the End Frequency blank.d. Verify that the Input Source is still v_dc.v_dc1.e. Set the Output Ports to /v_out, and select Yes for Run DC Analysis

First.f. On the Input Output tab, set the Two Port Parameter to Scattering. g. Click on OK.

7. Repeat the analysis for a closed switch.8. Verify that the S-parameters behave

appropriately. See Figure T5-32 for the expected value of S11 in each state.

a. Plot all four parameters and change the attributes to display magnitude instead of dB. The magnitudes of S12 and S21 should be nearly zero. S11 and S22 should have a value of -1, which is a magnitude of 1 and a phase of nearly 180 degrees. See Figure T5-32.

The 180 phase shift is due to the round trip traveled by the wave as it leaves the source.

b. Now close the switch by applying 33 volts to the voltage source connected to the beam electrode. Rerun the analysis and plot the s-parameters. Here, S11 and S22 should be nearly zero, while S12 and S21 should be -1. See Figure T5-32.



Figure T5-32 S-Parameter s11 of the RF Switch in Each State

As noted above, the S-parameters have phase-shifted 180 degrees. This is expected because for the open case, the incident wave for S11 traversed both down and back the quarter wave length line at the input, thus adding a half-wave-length of phase shift from what was measured without the lines. Because losses were turned off, the magnitude did not change. Similarly for the closed case, the incident wave traveled through both quarter wave lines before being measured at the second port, thus shifting S12 by 180 degrees.

closed switch

open switch



Adjusting Actuation Voltage to Meet a SpecificationHigher actuation voltages after pull-in increase the contact force, which in turn lowers the contact resistance and reduces insertion loss. However, arbitrarily high voltages are not easily available on-chip. In this section you will investigate the trade-off between insertion loss and actuation voltage for this design. You will also use Architect’s parametric variation capability to automatically vary the actuation voltage and immediately see the impact on the S-parameters. Note that this is only one example of parametric variation for design. After completing this tutorial, each user is encouraged to vary geometric parameters, such as the length or width, or both, to optimize this design.

Figure T5-33 S-Parameters s11 and s12 as Switch Closes

Because the switch is open at 14 volts and below, we see S11 is nearly 1 and S12 is nearly 0, as before. For voltages 15 and above, the switch is closed and the magnitude of S12 is less than 1 at first and rises closer to 1 as the voltage increases. Given an insertion loss specification, you can zoom in on this region of S12 near 1 to decide if the specifica-tion is met. Or even better, use the CosmosScope calculator to recompute this S-parameter data as a proper insertion loss metric.


9. Run a vary analysis on the voltage source attached to the beam electrode to see the behavior of the s-parameters as the switch closes.

a. Click on the Vary icon, then on the vary button.b. To set the Parameter Name, browse to the beam electrode’s voltage

source (v_pulse.actuation_source). Select initial value of this source as Parameter Name.

c. Set the Sweep Type to Set Values. Enter the following space-separated list of values: 0 10 15 20 30 35 40.

d. Click on Accept.e. Select Add Analysis > Within Loop(s) > Two-Port. The settings

from earlier should be imported.f. Click on OK to run the analysis.

10. Plot the magnitude and phase results on a linear scale.

a. Select Results > View Plotfiles in Scope, and click on OK to view the Last plotfile.

b. Plot the magnitude and phase of S11 and S12. See Figure T5-33 for results.

The slope between off and on is the result of contact resistance.



Adding Custom Microstrip Discontinuity Models (optional)In some cases, the gap between the microstrip lines alters RF performance. This gap is illustrated in Figure T5-34.

Figure T5-34 Gap Model

The effect on RF circuits of this and other discontinuities is well documented in RF engineering textbooks [2]. A sim-ple model of the gap, example_gap, is provided to help study the effects of the discontinuity on the RF switch; it con-sists of two shunt capacitances, C1, and a cross capacitance, C12 (shown below in Figure T5-35). The implementation of this model illustrates how to use the MAST hardware description language to create any discontinuity model. The interested reader can use a text editor to open the file example_gap.sin in the Schematics directory of the tutorial’s project. The file contains a subcircuit of the three capacitors. These are variable capacitors whose value is controlled by the MAST model contained in the file example_gap_vals.sin. This MAST model takes the geometric parameters as input and outputs three capacitance values [2]. It also illustrates how to use error checking to make user-friendly models. The MAST model could be modified to include frequency-dependent capacitance values; however, the model from [2] used in this tutorial is not frequency-dependent.

Figure T5-35 Microstrip Gap Discontinuity Model

At DC, there is no electrical effect of the gap. In AC cases there is a finite capacitive effect due to the line termination and also from field penetration from one line to the other. The latter changes are pronounced at short gaps and high frequencies. The model adopted for the gap assumes a quasi-static relationship with frequency and calculates the rel-evant capacitances as a function of the gap, line width, conductor-to-ground height, and isolation layer permittivity.

gap model captures capacitancebetween the ends of the two lines



Figure T5-36 Schematic with example_gap


1. Save the schematic as RF_Switch_TxLines_Gap.ai_sch.

2. Add the example_gap model to the schematic and assign it a width, gap, and height.

3. Build the schematic shown in Figure T5-36, deleting and rearranging components as necessary.

a. Save the schematic as RF_Switch_TxLines_Gap.b. Double click on the COVENTOR symbol and define three new

variables:gap_width = 45ugap_size = 50ugap_height = 45u

c. Add the example_gap symbol by right clicking in the canvas, selecting Get Part > By Symbol Name and browsing for example_gap.ai_sym.

d. Right click and Rotate the gap by 90 degrees.e. Double click on the gap and edit the following parameters:

width = gap_widthgap = gap_sizeheight = gap_heightdisplay_capacitances = 1

f. Edit the schematic so that the right side looks like Figure T5-36. Delete wires, rearrange parts, or add new parts as necessary.



Figure T5-37 Two-Port Analysis Settings


4. Rerun the vary analysis and plot the results. a. Save and netlist the schematic.b. Rerun the vary analysis.c. Plot the magnitude and phase results on a linear scale, as before, to

see if the gap altered the RF performance.

The results should be the same as those in Figure T5-33. These capacitances (C12 of approximately 1fA and C1 of approximately 100aA) are too small to make significant changes in the S-parameter behavior. Changing the frequency or the gap dimensions would affect the capacitive coupling.


5. Run a two-port analysis, once with the switch open and once with the switch closed.

a. Open the switch by applying 0 as the initial value of the voltage source connected to the beam electrode.

b. Select Analyses > Frequency > Two-Port and set the Basic tab settings as shown in Figure T5-37.

c. On the Input Output tab, select Scattering and the Plot File to tp_open. Run the analysis.

d. Change the beam electrode voltage source initial value to 33 volts, netlist and repeat the analysis, this time with a Plot File of tp_closed.

The two plotfile names ensure that the results from the second simulation do not overwrite the results from the first one.



Figure T5-38 Two-Port Frequency Analysis Results for an Open and Closed Switch


6. In CosmosScope, examine the S11 and S12 signals from each plotfile.

a. Plot the S11 and S12 parameters for the open state.b. For each curve, display mag(y) instead of dB and phasedeg(y)

instead of Cphase(y). c. Repeat for S11 and S12 of the closed state. d. Combine the S11 and S12 magnitudes and S11 and S12 phases for

the open switch. Then combine them for the closed switch. To combine two graphs, drag the legend of one onto the plot of the other. See Figure T5-38.

You should observe that the S-parameter magnitudes S11 and S12 take on a value of 1 or 0, depending on the switch state. The phase varies with frequency through multiple 360 degrees loops. The phase of S12 is shifted between the open and closed state, which accounts for the difference in traveling across 1 (open state) and 2 (closed state) transmission lines, respectively.

Switch Open

Switch Closed



Plotting Results on a Smith ChartPlotting the S-parameters on a Smith Chart, as described in this section, provides more insight into the device.

Figure T5-39 Open and Closed s11 Results on a Smith Chart


1. Plot the results on a Smith Chart. a. Click on the New Smith Chart icon.

b. Double click on the s11 plot in the tp_open plotfile dialog. Then add s11 from the closed plotfile dialog.

c. Compare your results with Figure T5-39.

To zoom, click and drag a box around the area of interest.d. In another Smith Chart, plot s12 from the open switch plotfile. See

Figure T5-40.

zoom of closed state



In this case, S11 has a radius very nearly 1 (Γ = 1). Depending on the wavelength of the incident wave, the phase of the load varies from inductive to capacitive. Because the data also falls on the r = 0 circle, the load is completely reac-tive; i.e., there is no resistive loss for any frequency (consult [3] for more information on Smith chart construction). However, when the switch is closed, the S11 circle centers on r, x = (1, 0) with a Γ approaching 0. In terms of isolation (S12, switch open, shown in Figure T5-40), Γ is nearly 0 at low frequencies, suggesting that little signal bleeds through to the output. As the frequency increases, S12 takes on a spiral shape of increasing radius, suggesting degra-dation of isolation at higher frequencies. In the closed state, S12 is similar in shape to S11 when the switch is open, suggesting little to no insertion loss in this ideal case.

Figure T5-40 Smith Chart Plot of s12 from Open Switch Results


2. Add the resistive losses back into the transmission lines.

3. Repeat the previous procedure and view the Smith charts.

a. Save the schematic as RF_Switch_TxLines_R_Losses.b. Select both transmission lines, and double click to open the

Common Properties dialog.c. Change the ro and rs fields back to their default values of 625.9779

and 0.005120096, respectively. If you click in the field that holds the current value, the default value will be displayed in the lower right corner.

d. Verify that includersimag is yes.e. Save and netlist the design. f. Rerun the frequency analysis for a closed switch (V = 33 V), and

plot the results on a Smith chart. See Figure T5-41.



Figure T5-41 Smith Chart of S-Parameters in Closed State, with Resistive Losses

Based on the Smith charts above, it appears that the resistive losses in the transmission line cause some reflection of signal back to the source (S11 increased and capacitive), and there is some resistive dissipation upon signal insertion because the magnitude of S12 is decreased and continues to decrease with frequency. This decrease can be attributed to the resistive skin effect.

zoom of S11



Exporting RF Data in Touchstone Format To perform more sophisticated RF analysis, the S-parameters computed to this point can be exported to Touchstone format for use in other RF and microwave simulation environments. This section demonstrates exporting a set of Touchstone files corresponding to different parameters of a Parametric Vary run. It also demonstrates using a double vary loop to explore the change in S-parameters as a function of both actuation voltage and the gap between the microstrip lines.

Figure T5-42 Vary Settings


1. Run a vary analysis similar to the one on page T5-43, but with an extra vary loop, as shown below.

a. Click on the Vary icon and follow the instructions on page T5-43 for a Vary analysis with a nested Two-Port analysis.

b. Verify that the Two-Port analysis settings are those listed on page T5-41, except for the plot file name. Change the plot file name to tp_sample_output.

c. Select AddLoop > Vary and click on the empty vary button to open the Parameter Sweep (Loop #2) dialog.

d. Select Browse Design from the pull-down menu beside Parameter Name. Double click on example_gap.example_gap1, then again on Parameters. Select gap and click on OK.

e. Set the Sweep Type to Set Values and enter 20u 50u. Verify that the settings dialog matches that shown in Figure T5-42.

f. Run the analysis.



Figure T5-43 ExportSParams Prompt

The macro creates a separate Touchstone file for each parametric case run in the vary analysis. The files have exten-sion .sp2 and are designated by the design file name followed by the two-port plotfile name, then a specific designator for each parameter (e.g., P0 = "value of parameter 0"). Inside each touchstone file, a block of comments links the actual parameter name with each "P" from the filename. For this example, two Touchstone files should be generated (one for 20u and one for 50u).

Figure T5-44 S-Parameters in Touchstone Format


2. Run the ExportSParams macro. a. In CosmosScope, click on the Macro Recorder icon.b. Select ExportSParams from the list of available macros and click

the Play macro icon.c. In the dialog that appears, enter the name of the plot file

(RF_Switch_TxLines_R_Losses.tp_sample_output) and the impedance. See Figure T5-43.

d. Click on Apply.

A list of files written to the design schematic directory is output by the macro upon completion.


3. Open the 50u result Touchstone file.4. Plot the magnitudes of S11 and S12, and

compare the results with those in Figure T5-33.

a. In the Signal Manager, click Open Plotfiles.b. Change the Files of Type field to TouchStone.c. Browse for RF_Switch_TxLines_R_Losses_tp_sample_output_v

_out_P0=50u.s2p.d. Click on Open.e. Plot the magnitudes of S(1,1) and S(1,2) from the S-Par group and

compare your results to those in Figure T5-33.



5.2.5: FEM and Architect ComparisonThis section demonstrates the following techniques:

how to mesh the 3-D model created from the layout extracted from the Architect schematichow to conduct a modal analysis of the FEM mesh using Analyzer’s MemMechhow to conduct a pull-in analysis using Analyzer’s CoSolve

The tutorial then presents a comparison of the system model’s results with FEM analysis results for resonance fre-quencies and pull-in behaviors.

Mesh Creation

If you do not have a license for Scene3D, you can still build a solid model from your schematic: Open the schematic you want to extract, and from the Architect Sketch window, select Architect > Export for Designer. From the Function Manager’s Designer tab, select New from Architect from the Preprocessor icon’s drop-down menu.


1. Use the Preprocessor icon’s New from Architect option to create a 3-D model.

a. Save the settings file as fem_switch.mps.b. From the Architect tab, select the RF_Switch_Mech_Only.ai_sch.c. Navigate to the Designer tab of the Function Manager.d. From the Preprocessor icon’s drop-down menu, select New from

Architect.e. Save the model as RF_Switch.

2. Hide the Substrate layer, and place the other layers in the Mesh folder.

a. In the Preprocessor, right click on the Substrate layer, and select Hide.

b. Right click on the pads layer and add it to the mesh model. c. Repeat this procedure for the btmlyr, midlyr, and toplyr layers.

3. Name the three sections of the beam beam_top, middle, and beam_bottom.

4. Name the electrode parts actuator, upperXline, and lowerXline and suppress them from any mechanical simulations.

a. Set the Z-scale to 10 for easier part selection.

b. Choose Part Selection Mode from the toolbar.

c. Click on the top of the beam. d. Right-click on the part, or on the highlighted item in the Geometry

tree, and select Properties. Enter the name beam_top.e. Using the same method, name the other two sections of the beam

middle and beam_bottom.f. Name the electrode parts actuator, upperXline, and lowerXline. For

each electrode, select Suppress, except for MemElectro.



Figure T5-45 RF Switch Parts

Figure T5-46 RF Switch Conductors and Dielectrics


5. Name the conductors and dielectrics as shown below.

a. Right-click on beam_top and select Properties. Choose the Dielectric Analysis Option.

b. Using the same method, designate beam_bottom as a Dielectric.c. From the Conductors/Dielectrics tree, right click on each Dielectric

and name it appropriately (top or bottom).d. Select each Conductor and name it according to Figure T5-46.

UXline

LXline

beam_top

actuator

beam_middle

beam_bottom

Uxline

Lxline

Metal

Actuator

Txline

beam_top(dielectric)

beam_bottom(dielectric)



Figure T5-47 Face Name Assignments

Figure T5-48 Meshed Model


6. Name the top of the beam, the bottom of the beam, the bottom of the transmission line, the tops of each electrode, and the fixed faces.

a. Choose Face Selection Mode from the toolbar.b. Name the top of the beam beam_top. c. Rotate the model and name the bottom of the beam beam_btm and

the bottom of the transmission line txline_btm.d. Name the top of the Upper X Line electrode uxline, the top of the

Lower X Line electrode lxline, and the top of the actuator actuator_top.

e. Rotate the model and name the back faces of each of the three beam sections fix, as shown below.


7. Generate a Manhattan bricks mesh with X and Y elements of size 5.

a. Right click on Region 1 and select Mesher Settings.b. Select a Manhattan bricks Mesh Type.c. Set the X and Y element size to 5.0. Leave the Z element size

unset.d. Choose the same Mesher Settings for Region 2.

e. Click on the Generate Mesh icon.

fix

beam_top

actuator_top

lxline

uxline not shown

txline_btm

beam_btm



FEM Simulation

Modal Analysis

In this next procedure, modal analysis is performed on the switch. MemMech solves an eigenvalue problem to find the natural frequencies and mode shapes of the structure. We will view the modal results and compare them to those of the system model.

Figure T5-49 MemMech Preliminary Settings


1. Configure the MemMech Settings dialog to run a modal analysis with 6 modes.

a. Choose the MemMech solver.b. Select the RF_Switch model for the Model/Mesh field.c. In the Analysis field, select create a new analysis.d. Click on the Solver Setup icon.e. Set the dialog as shown in Figure T5-49. Note that this mechanical

simulation has six modes.f. Click on Next.



Figure T5-50 Modal Domain Results

The Architect simulation generated a result of 12371 for the Z translational mode (see page T5-18), which is within 2.7% of the Analyzer result.

Pull-In Analysis

In this tutorial sequence, you will use Analyzer’s CoSolve to run a pull-in analysis. You will apply a linearly increas-ing voltage ramp and observe the effect on the switch. These results can then be compared to the Architect results while the release voltage is observed by a linearly decreasing voltage ramp.


2. In the SurfaceBCs dialog, fix the end of the switch.

a. Click on SurfaceBCs.b. For Set1, set FixType to fixAll for Patch1 fix.c. Click on OK.

3. Start the simulation. a. Click on Run in the MemMech BCs window.b. Name the analysis ModalSwitch and save your settings.

4. View Mode Domain results. a. When the simulation is finished, in the Job Queue dialog, click on the View Results icon.

b. In the Analysis Results window, select and view the Mode Domain table results for the six modes (see Figure T5-50).


1. For the MemElectro solver, select the RF_Switch model.

a. Select the Analyzer tab of the Function Manager.b. Choose the MemElectro solver.c. Select the RF_Switch model in the Model/Mesh field.d. Click on Solver Setup.

2. Configure the solver to useFor the Analysis Options, select Force on Conductor PartsFor Additional Analysis, select Force on Dielectric Parts

a. In the MemElectro Settings dialog, for the Analysis Options, select Force on Conductor Parts.

b. For Additional Analysis, select Force on Dielectric Parts.c. Click on OK.




3. Configure MemMech to run without modal analysis.

a. Return to the Function Manager and choose the MemMech solver. b. Click on the drop-down arrow beside Analysis field and select create a

new analysis, then click on the Solver Setup icon.c. Set Additional Analysis to none.d. Click on Advanced.e. Set the Solver Memory field to 75% of the amount of RAM that is in

the computer you are using. For example, if you have 1 GB of RAM, set this field to 750 MB.

CoSolve simulations are memory-intensive. Increase MemMech’s memory allotment so the simulation will go faster.

f. Click on OK to close the MemMech Settings dialog.

The SurfaceBCs dialog was set in the previous run and does not need to be changed.


4. Set up a CoSolve simulation with the RF_Switch model.

a. Change the solver to CoSolveEM.b. Select the model and create a new analysis, then click on Solver Setup.

5. Set up a trajectory run with Detect Pullin, using the Relaxation Iteration method.

a. In the CoSolveEM Settings dialog, set the Independent Variable to Voltage.

b. For Analysis Options Steps, select the Detect Pullin.c. Set the Iteration Method to Relaxation. d. In the Advanced settings dialog, increase the maximum number of

steps to 24.e. Click on Next.

6. Set a trajectory that varies the voltage from 0 to 20 in steps of 2.

a. Click on trajectory.b. Set the trajectory dialog as shown below.

7. In the Voltages dialog, set a t1 trajectory. a. Click on Voltages.b. In the Voltages dialog set the Voltage1 trajectory to t1.c. Click on OK.

8. In the ConductorBCs dialog, apply a voltage of 1 to the actuator. Designate it as a variable.

a. Click on ConductorBCs.b. Set the actuator voltage to 1 volt, and assign the Voltage1 variable.c. Click on OK.

9. Start the simulation. a. In the CoSolveEM BCs window, click on Run. b. Name the analysis SwitchPullIn.



This simulation may take several hours. The simulation shown in this tutorial took 2.5 hours to complete on a computer with dual 3.2 GHz processors and 2 GB of RAM. Your simulation time will vary according to your computer resources.


10. View simulation results. a. When the simulation is finished, click on the View Results icon.b. In Analysis Results window, select the Summary Table results, as shown in

Figure T5-51.

The t1 column shows the voltage steps executed during the simulation. The Iterations column shows the number of iterations CoSolve requires for convergence (to the 0.001 tolerance in the Settings dialog) for each step. At step_8, CoSolve produces a divergent result. CoSolve then cuts the next attempted voltage step in half (to 13 V) and calculates the result. The convergent solution causes CoSolve to increase the voltage by half. CoSolve continues the calculations until the difference between the last convergent and divergent results is less than 0.5 volts (tolerance set in the Voltages dialog).

c. View the Displacement table results.

Observe the effect on mass displacement as the electrode voltage increased.d. Select the Pullin table results.

The Pullin results window shows the voltage required for pull-in. Because CoSolve seeks a solution within the 0.5 volt tolerance, the voltage is expressed as a range between the final two computation values.



Figure T5-51 Pull-In Results

Figure T5-52 Displacement Graph


11. Verify the graph results shown in Figure T5-52. a. In the Analysis result window, click on the View Graph icon.b. In the Visualizer left panel, click on Mapping Style.c. Select the MinZ map name, then hold down Map Show and select

Show Selected Only. The results are shown in Figure T5-52.




12. Scale the Analyzer displacement results so they are in meters, as opposed to microns, using the Data > Alter > Specify Equations option.

a. From the Visualizer menu bar, select Data > Alter > Specify Equations.

The Visualizer allows you to create new variables using the ones currently available. But to create these variables, you must know the assigned number of the variable(s) you want to use and the last number in the variable list. The variable to be created must have a number one greater than the last variable in the list.

b. In the Specify Equations dialog, click on Data Set Info. Scroll down in the Variable list and note the variable number for MinZ (should be 9). Note that MinZ is also the last variable number.

c. In the Equation(s) field, enter V10=V9*1e-06.

Analyzer reports displacement in microns, but Architect reports displacement in meters. To plot them in the same graph, we must scale the Analyzer results so that they are using the same units.

d. Click on Compute.


13. Export the points to combine with Architect results.

a. Select File > Write Data File.b. Select the settings shown in Figure T5-53.

ASCII format is more general and can be read by text editors.

Point zone format means the variables will be written in column.c. Select the variables voltages and V10 and click on OK.d. Save it in your directory as displacement_analyzer.dat.



Figure T5-53 Write Data Settings

Figure T5-54 Text to cpf Format for 2D Plots


14. Save the Architect results in cpf format. a. Open the displacement.txt file with a text editor.

This file was created from the Architect results, see page T5-6 for more details.

b. Save it as displacement_comparison.cpf in the RF_Switch directory.

This format is specific to CoventorWare and allows to import into Analyzer Visualizer.

Figure T5-54 shows the original text file.c. Add the lines given in Figure T5-54 to create the cpf format.

Follow exactly the syntax.

The type 1-ordered means a 2D plot.



Figure T5-55 Adding a Zone to the CPF File to Compare Analyzer and Architect Results

Figure T5-56 Mapping Style with Added Maps


15. Add the data from the Analyzer pullin analysis. a. Open the displacement_analyzer.dat file with a text editor.b. Copy the lines with data and paste them at the end of the cpf file.c. Before those lines, define another plotZone.

The result is shown in Figure T5-55.


16. Import Architect results into Visualizer. a. In the Visualizer Window, select File > Load Data File(s).b. Select the CPF loader and click on Yes to replace the current dataset.c. Browse to the project directory RF_Switch, select

displacemetn_comparison.cpf.

In the frame that opens you only see Architect results. The Analyzer results are stored in another zone that needs to be mapped.

d. Click on Mapping Style, and then on Create Map.e. Add the Analyzer results as shown in Figure T5-56.

To make the Analyzer results easier to see, its symbols were filled using the Symbols tab option.

f. The result is shown in Figure T5-57.

17. Save the plots as a layout. a. Select File > Save layout as.b. Browse to RF_Switch project directory and select Packaged Data (.lpk)

as the type.c. Enter the file name displacement_comparison and save.



Figure T5-57 Architect and Analyzer Results in the Visualizer



5.3: Drop Test of RF Switch in a HyCap Package

5.3.1: IntroductionPart of the MEMS development process is reliability testing. One family of tests run in laboratories evaluates the influence of shocks on the microstructure.

The aim of this tutorial is to demonstrate how CoventorWare tools can be used to run a virtual shock test of a MEMS device. The tutorial will to study the behavior of a RF switch (modified version of the one used in Section 5) hitting a concrete floor after a one-meter fall from a tabletop. The advantage of a virtual test is to provide MEMS designers with detailed insight of how the structure’s sensitivity to impact. With this virtual modeling, the weak structural points can be identified, and the engineer’s intuitions can be confirmed by 3-D maps of stress levels.

The main tool used for this analysis will be Architect, which will simulate the RF switch displacements resulting from the shock load created by the drop. To obtain some necessary parameters, we will use Integrator’s InertiaMM module and Analyzer’s MemMech module. Finally, maximum stresses in the multilayer beam will be calculated and observed in MemMech. Figure T1-1 is a flow chart of CoventorWare drop test methodology.

Figure T5-58 Drop Test Methodology

Packaged switch

modelPackaged switch hitting

the floor model

InertiaMM run MemMech run

mass stiffness

Run Architect with drop test

maximum displacementat switch tip

switch model

MemMech run

maximum stresses

Define InertiaMM settingsto calculate the packagedswitch mass

Models provided; usefuldata is available in package library

Add concrete floor material to the MPD

Apply suitable boundaryconditions on the structure

Calculated from the displacementat anchor point

Generate Visualizer results, which can be comparedto calculated yield strength value



Hycap PackagingIn this tutorial we will use a Hymite package available in the CoventorWare Library. The HycapU_RF_C1C_Q08_BN is dedicated to MEMS and can handle RF signals. It has four pads: two pads can be used for RF and two pads can be used for DC/control signals.

Figure T5-59 HycapU_RF_C1C_Q08_BN Model

The solder used to seal this cap to the RF switch chip will not be taken into account because it is very thin and does not influence mechanical behavior of the packaged device.

Tutorial RequirementsTo run this tutorial, you must have the following licenses:

An Architect PEM license that includes a standard Saber installation, the Parametric Electromechanical Library.An Architect OPT_TEMPLATE_LIB license feature.An Analyzer MemMech license featureAn Analyzer InertiaMM license feature

5.3.2: InitializationThe tutorial uses a prebuilt 3-D model. You do not have to build the solid model or assign face names, but you will generate a mesh.

For more information about Hymite packages, see page R10-11 of the Analyzer Reference, or visit the company’s Web site at www.hymite.com.

cavity designed for the mobile parts ofthe MEMS device

available pads

Bottom Top

ground linked to four pads

for RF signal line and DC


http://www.hymite.com


5.3.3: Packaged RF Switch DesignIn this first exercise, you will model the switch in the package and use the mesh created from the model to calculate its mass.

ProcessIn this section you will examine the process description related to the packaged switch device. It is important to note the differences between this process and the process used in the preceding RF Design tutorial.


1. Start CoventorWare, and import the Droptest project tutorial.

a. Start CoventorWare. b. Click on the Import Tutorials icon.c. Select the Droptest project from the list.d. In the Project Browser, a default settings file appears on the Settings

file field. Click on Open.


1. Select the droptest.mpd Material Properties Database.

a. In the Function Manager MPD field, click on the Browse icon.b. Navigate to your project directory and select droptest.mpd.

2. Open the packaged_switch process. a. From the Function Manager’s Process select packaged_switch.proc from the drop-down menu.

b. Click on the Process Editor icon. The process is shown in Figure T1-3.

This process contains the RF switch MEMS layers combined with the package technology steps.



Figure T5-60 RF Switch Packaged with HycapU_RF Process

This process is the result of the addition of switch technology steps to the Hycap_U.proc file (stored at C:\Coven-tor\CoventorWare2008\apps\packages\Hymite\HyCapU_RF_C1C_Q08_BN\Devices). The first rectangle highlights the package steps; they have not been modified. The second rectangle highlights the switch chip; these steps represent a modified version of the switch used in the first RF switch tutorial.


3. Review packaged switch process steps. a. Click on Step 13 and read the comments.b. Do the same for Steps 14 and 22.c. Note that Steps 16 and 19 are disabled and replaced with Steps 17 and

20, respectively.

The Stack Material operation has been replaced with a Planar Fill to enable the creation of an anchor beam to the substrate.

d. Close the process file.

The switch is built on top of the Hycap for convenience. The cap will be placed on top of the switch chip during 3-D modeling.

package

switch chip



LayoutThe layout of the packaged switch is a combination of the Hymite package and the RF switch. Additional objects are also added to connect the switch to the package.

Figure T5-61 RF Switch Packaged with HycapU_RF Layout


1. Open the packaged_switch layout, and explore its construction.

a. From the Designer tab, select the packaged_switch.cat in the layout field, and then select packaged_switch_onchip for the Top Cell.

b. Click on the Layout Editor icon. The top cell of the layout is shown in Figure T5-61.

This layout is combines the RF switch layers with the package ones.

c. Open the Cell Browser by clicking on the top left icon.

The package and the lines have their own cells, which are referenced in the top cell.

d. Click on the circled dot to the left of the top cell line. It will open the hierarchy of the top cell.

e. Do the same for the package cell in the hierarchy and for the two Ex06 cells. See Figure T5-62 as a reference.

f. Close the hierarchy by clicking on the circled point of Top Cell line again.

g. Double click on lines cell to open it. It is shown in Figure T5-63.h. Do the same for the package cell.i. Close the Layout Editor.



Figure T5-62 Cell Browser

Figure T5-63 Separate Layouts for Switch, Package, and Connection LinesRF switch layout

HycapU_RF package Gold lines added to connect the switch to the package



3-D ModelOnce the layout and the process are defined, the 3-D model can be built and displayed in the Preprocessor.

Figure T5-64 Initial Packaged Switch Model


1. Use the package_switch.proc and the package_switch.cat files to build the solid model.

a. From the Designer tab, make sure the package_switch.proc and the package_switch.cat (with the package_switch_onchip top cell) are selected.

b. In the Model/Mesh field, select create new model, and click on the

Preprocessor icon.

c. Save the model as packaged_switch.

The package is located on the bottom of chip. In the next step we will use the transform operation to put it on top.



Figure T5-65 Solid Model Transformation


2. Use the Transform tool to rotate the layers of the package so that they are on the top of the chip.

a. Use the Ctrl key to select the SMD_Pads, Si_SMD_side, Si-Device_Side, and Au-SN layers.

b. Select Tools > Transform.c. In the dialog that opens, select the Rotation type, the X axis, an origin

of 0,0,0 and an angle of 180. Click on Apply.d. In the same dialog, select the Translation type, and a Translation Vector

of 0,0, 461. Click on Apply, then on Close.

Figure T5-66 shows the result of the two transformations.

Package top layers have a transparent rendering so that you can see the switch inside the package.



Figure T5-66 Resulting Solid Model with Zoomed View of Switch


3. Mesh the model with tetrahedron parabolic elements with an element size of 60.

a. Select all layers: click on the first one, then hold down the Shift key and click on the last one.

b. Right click and select Add to mesh model.

There should be only one region because all layers are touching.c. Right click on Region 1 and select Mesher Settings.d. Set the dialog as shown in Figure T5-67.e. Click on the Generate Mesh icon.

The mesher may take a few minutes.The result is shown in Figure T5-67.

f. Save the model and close the Preprocessor.

RF switch

Z scale = 5



Figure T5-67 Mesher Settings and Resulting Mesh

Calculating the Mass of the Packaged Switch

Figure T5-68 Mass Obtained from InertiaMM


1. Run InertiaMM on all parts of the switch. a. From the Function Manager’s Analyzer tab, select the InertiaMM solver.

b. From the Model/Mesh menu select packaged_switch.c. Check the Analysis field is create a new analysis.d. Click on the Solver Setup icon.e. In the InertiaMM Settings dialog, the Analysis Type should be Original.

Click on Next.f. In InertiaMM BCs window, click on part and then on list. Select ALL.g. In InertiaMM BCs window click on Run.h. Save the analysis as packaged _switch_mass.

No specific boundaries is required to calculate the mass.

2. View the results. a. When the simulation is finished, click on the View Results icon.b. In the Analysis results window, select the center_of_mass table results.c. Check the mass is equal to those shown in Figure T5-68.



5.3.4: StiffnessThe model of the RF switch device is now ready to undergo a drop. Following the flow chart of Figure T5-58, the first step in modeling impact is to create a model that includes the floor.

Adding the Floor to the ModelIn the following steps you will define the floor material and add it to the model.

Figure T5-69 Concrete Mechanical Properties


1. Add concrete to the MPD with a Young modulus of 18 GPa, a Poisson coefficient of 0.1, and a density of 2400 kg/m3.

a. From the Function Manager’s Designer tab, open the MPD editor.b. Click on New Material and name it concrete.c. Fill the properties as shown in Figure T5-69.

Only mechanical properties are needed. Note the units.d. Close the MPD.

The changes are saved automatically.


2. Create the process for the packaged switch on the floor by adding a 400 microns high concrete layer.

a. Open the packaged_switch.proc in the Process Editor.b. Save it as packaged_switch_onfloor.c. Select line 13 (silicon of 400 microns thickness).d. In the process library, right click on Stack Material and choose Insert

Above Current Step.e. Enter the properties for new line 13 as shown in Figure T5-70.f. Save and close.



Figure T5-70 New Process with Floor Layer


3. Build a solid model using the packaged_switch.cat and packaged_switch_onfloor.proc.

a. From the Designer tab, make sure the packaged_switch_onfloor.proc packaged_switch.cat are selected, and build the solid model.

b. Save the model as package_switch_onfloor.

4. Rotate and translate the model as described in the previous model creation (page T5-72). Scale the floor layer 30% in the X and Y directions

a. Rotate and translate the package layers as described on page T5-72, but translate the layers 861 microns in the Z direction (accounting for the additional concrete layer

b. Select the floor layer.c. Select Tools > Transform.d. Select the Scaling type and enter a 30% increase in X and Y directions

around its center (Z is ignored). See Figure T1-13.e. Click on Apply and on Close.



Figure T5-71 Solid Model of the Packaged Switch on the Floor after Transform Operation


5. Mesh the structure using parabolic tetrahedrons and an element size of 60.

a. Add all layers to the Mesh Model folder.b. Right click on Region 1 and select Mesher Settings.c. Select the Tetrahedrons Mesh Type, Parabolic Element order, and an

Element size of 60.d. Generate the mesh.

It may take few minutes.

6. Define a fixed patch on the bottom surface of the floor.

a. Use the Rotate icon to access the bottom surface of the floor. See Figure T5-72.

b. Select the Face selection mode icon. c. Click on the bottom surface to select it, then right click and select Set

Name. Enter fixall.d. Save the model and close the Preprocessor.



Figure T5-72 Define the Fixed Surface

Run MemMech to Calculate DisplacementIn the next exercise you will configure MemMech to simulate the drop. The displacement results on the anchor will then be used to calculate the stiffness.

This MemMech simulation requires a minimum of 750 MB of solver memory (set from the Advanced Settings dialog). You must have enough RAM to successfully run this simulation. If you do not have enough RAM but would like to continue with the tutorial, you can view the simulation results, then continue to the next section.


7. Set up a MemMech run using the packaged_switch_onfloor mesh and the default solver settings.

a. From the Analyzer tab, select MemMech as the solver.b. Select packaged_switch_onfloor as the meshed model.c. From the Analysis field drop-down menu, select create a new analysis

and click on the Solver Setup icon.d. Check the settings are those shown in Figure T5-73.e. Click on Advanced. Set the amount of memory dedicated to this run to

75% of computer RAM. You should have enough RAM to be able to set this value to at least 750 MB.

f. Click on Next.



Figure T5-73 MemMech Settings

Figure T5-74 Volume BCs for MemMech Run


8. In the SurfaceBCs dialog fix the fixall face. a. In the SurfaceBCs dialog, set Fixtype to fixall for the Patch 1 fixall.

9. In the VolumeBCs dialog, apply the Acceleration BCType to all the parts except the floor. Apply a LoadValue of -10 in the Z direction.

a. Set the VolumeBCs as shown in Figure T5-74 and click on OK.

All parts have a vertical acceleration except for the floor, which represents the surface the other parts hit.

b. Click on Run, and save the simulation results as package_stiffness.

This simulation takes about 20 minutes on a 3GHz computer running Windows XP, with the Solver Memory set to 750 MB.



Figure T5-75 Contour Settings and Resulting Display


10. Observe the displacement results in the 3-D Visualizer.

a. When the simulation is finished, click on the View Results icon.b. In the results window click on the View 3D Results icon.c. In the Visualizer, select Plot > Contour/Multi-coloring. d. In the Contour Details dialog, select the Displacement Z from the Var

drop-down menu.e. In the Visualizer window, click on Zone Style.f. Select the Si-SMD_Side zone name, click on Zone show and select

Deactivate.

Hiding these zones reveals the switch, where the maximum displacement occurs.

g. In the Zone Style dialog, activate Si-SMD_Side, then close the dialog.h. In the Contour Details dialog, click on More >>.i. In the Contour Details dialog select Coloring.j. Change the Min value to -3e-13 (see Figure T5-75).k. Compare with the result shown in Figure T5-75.

The cap membrane becomes visible because it is more flexible than the rest of the cap.

l. Close the Visualizer.

cap membrane



Figure T5-76 Query Setup and Result

To obtain the stiffness from this analysis, we consider that the relation between the force F applied on the structure and its displacement z is linear and corresponds to the formula:

F = -kz

with k the stiffness.

The force applied here is due to an acceleration. Its value is then equal to maz, with m, the mass, calculated in the Sec-tion (see page T5-74).

Finally, the stiffness k is obtained with

k = -maz/z = 1.177264e-6 x -10 / -2.458428e-13 = 4.7887e7 N/m in this tutorial.


11. Run a query for displacement in Z in the pads using coordinates (0,0,843).

a. In the Analysis result window click on Custom Query.b. Click on In a Region.c. Set the Query in a Region dialog as shown in Figure T5-76.

The defined point is the middle of anchor surface of the switch.d. Click on Execute.e. In the result window select the regionQuery table. The result should be

the same as those shown in Figure T5-76.

Note that the stiffness depends on the mechanical properties of the floor and package materials and also on the angle between the package and the floor. In this example the angle is 0 because the Z direction stays the same. For a tilted shock, just run a simulation with a tilted package using a transform/rotation operation on the solid model, Then mesh the two regions separately and define a tied link boundary conditions between both in the linkageBCs section. The acceleration will then be applied with a rotation angle using a vector transform part connected to ax, ay and az ports of the reference frame.



5.3.5: Drop Test

Architect SchematicThe schematic used in this simulation is provided for you. It is the combination of the RF_Switch_Mech_only sche-matic of Section 5.2.1 and the components needed for the drop test, which are added to the z acceleration input of the Reference Frame.

Figure T5-77 Architect Schematic with the Drop Test Added to the RF Switch

Some Architect components used in this schematic require the OPT_TEMPLATE_LIB Saber license feature. Contact a CoventorWare support representative for more information.


1. Open the packaged_switch_droptest schematic.

a. In the Function Manager, click on the Architect tab.b. In the Process field select packaged_switch.

Do not use the package_switch_on_floor process. The stop component in the schematic will represent the floor.

c. From the Schematic menu select packaged_switch_droptest.ai_sch.d. Click on the Saber icon. The schematic is shown in Figure T5-77 with

some blocks identified.

Some parameters have been changed compared to the original RF_Switch_Mech_Only schematic: the period for the pulse is now 8 ms and the modal damping b (stiffness coefficient of Rayleigh damping) is 25u.

For more information on Architect parts, refer to the Architect Reference, available in the CoventorWare installation directory at \Coventor\CoventorWare2008\docs\Architect.pdf.

derivation blockstop element

weight

inertia

RF switch



Figure T5-78 DC Operating Point Settings


1. Add the calculated data to the stop element and the mass.

a. Double click on COVENTOR symbol.

This element stores all global variables of a schematic. For more information on this part, in its Properties dialog select Help > Help on Part.

b. Define the value for package mass as 1.177264e-6.

This value was calculated with the InertiaMM solver (see page T5-74). The units are kg.

c. Open the properties of the stop symbol by double clicking and change the stiffness value calculated on the previous page: k=4.7887e7 N/m.

This part models a contact between two objects.d. Save.

2. Launch the simulator. a. Click on Design > Netlist packaged_switch_droptest.b. Click on Design > Simulate packaged_switch_droptest.

3. Run a DC Operating Point using the settings shown in Figure T5-78.

a. Click on the DC Operating Point icon.

This analysis is the necessary starting point for all analyses.b. Set the fields as shown in Figure T5-78.

device_pos 1 defines an initial position of 1 meter. This is how the drop height is defined.

accel_z -9.81 sets the initial acceleration at 0 because 9.81 is added after derivation to obtain a zero acceleration during the fall. Otherwise initial acceleration will be 9.81ms-2.

c. Click on OK.



Figure T5-79 Transient Analysis Settings


1. Run a transient analysis for 0.5 second with an original time step of 50u and a truncation error of 0.00005.

a. Click on the Transient icon.b. Set the Transient Basic tab as shown in Figure T5-79.c. Form the Calibration tab, set the Truncation Error 0.00005.d. Click on OK.e. Click on the cmd button to see the analysis progress.

2. Observe the results. a. Click on the Waveform Probe tool to create a probe window.b. Select the arrow and drag it to touch the pos_z wire.c. Move the mouse cursor along the Probe window edge. When the

rectangle is red, click and drag the window to the desired location on the canvas.

d. Do the same on wires: z_load, voltage and tip_z.

During the simulation the z_load will have some tiny peaks before the shock. They are due to mathematical parasitics introduced into the schematic by the voltage pulse source. The peaks corresponds to this source period.

e. The final results are shown in Figure T1-24.



Figure T5-80 Schematic with Probes at the End of the Transient Analysis

Looking at pos_z the drop can be observed. At around 0.45 seconds the packaged_switch reaches the floor and it bounces. At this moment the acceleration in Z has a half sine peak (see Figure T5-81). The amplitude of this peak is defined by the stiffness of the stop element as it describes the contact behavior of the packaged switch hitting the floor. In this analysis the damping is chosen at 0 to obtain a perfect half sine shape.

The shape is not corresponding perfectly to a half sine because the period is so small that Saber precision limit is reached. This numerical parasitic is due to the small mass of the packaged switch; it does not appear for heavier devices (1 mg instead of 1µg).



Figure T5-81 Z Acceleration Load on Switch

Figure T5-82 New Scale for Plots


1. Open a CosmosScope graph for tip_z signal to measure maximum amplitude of the switch bending.

a. Double click on the z_load probe window.

CosmosScope opens and the signal is plotted on a graph.b. Back in Architect canvas, do the same for tip_z and voltage.

The three signals are in the same plot window.c. Double click on the time scale of the graph. In the dialog that opens, set

the range between 0.447 and 0.453, as shown Figure T5-82.d. Put your mouse above voltage legend (the signal should be red) then

click and drag signal into tip_z plot.e. Click on the measurement tool icon.f. On Measurement line select Levels > X at Maximum.g. Choose signal tip_z.h. Click on Apply.i. The result is shown in Figure T5-83.



Figure T5-83 Impact of Shock Load on Switch Behavior

The maximum deformation of the switch is 1.3208 µm in positive Z direction. Note that the shock also causes an unwanted closure if the switch is actuated, as is the case here.

Stress Detailed with MemMechThe last step of this analysis is to observe the maximum stresses at weak points on the 3-D switch model, which were created by the bending induced by the shock.


1. Open the RF switch meshed model and note its mesh and face assignments.

a. Select RF_Switch for the Model /Mesh and open the Preprocessor.b. Note the mesh created on the switch.

The mesh is the same one used in the original RF Switch tutorial, with the addition of the tip face.

c. Navigate in the mesh model and find the three surfaces defined as fix patch and the tip surface. See Figure T5-84.

d. Close the Preprocessor.

shock

z max value

Normal operation of switch



Figure T5-84 RF Switch Meshed Model

Figure T5-85 :SurfaceBCs for Defining Displaced Switch


2. Run MemMech with a displacement boundary condition on the tip, with a displacement of 0,0,1.7236.

a. From the Analyzer tab, select the MemMech solver.b. Select create a new analysis, and click on the Solver Setup icon.c. Use the default solver settings (see page T5-79).d. In the SurfaceBCs dialog, define a fixall Fixtype on fix patch.e. On the second line, set Fixtype to Displace on patch tip with a load

type Displacement of value (0,0,1.3208). See Figure T5-85.

The Z value was obtained from the transient simulation plot shown on page T5-87.

f. Remove the boundary conditions set in the VolumeBCs dialog. g. Run the analysis with name switch_stress.

tip

fix (three faces at end of beam)



Figure T5-86 3D Map of Mises Stress for Switch Beam

Figure T5-87 Maximum Von Mises Stress Value

The criterion to characterize yielding is to compare the von Mises stress to the tensile yield strength of the material. In this case the material concerned is Si3N4. Its tensile yield strength can be a value between 68 to 172 MPa (Reference: AMS Engineered Material Reference Book, 2nd edition. M. Bauccio, Ed. ASM International, Materials Park, OH, 1994). The value found here is 65.9 MPa, which means the switch will not break.


3. Visualize results. a. When the simulation is finished, click on the View Results icon.b. In the Analysis result window open the 3-D Visualizer.c. In the Contour dialog window select Mises Stress.d. Use the Spherical rotation icon to rotate the structure so that you can

see the bottom of the switch.e. Note where is the maximum stress. See Figure T5-86.


4. Run a volume query on the bottom layer to extract the maximum von Mises stress.

a. Click on Custom Query.b. Select In a Volume.c. Set beam_bottom in the Name column and MaxMises in Field.d. Click on OK and then on Execute.e. Verify the table nameQuery results, as shown in Figure T5-87.



This tutorial demonstrated how to perform a shock test on a full device with a MEMS included in a package. This type of analysis can be applied on any kind of packaged structure.

RF simulations on the packaged switch were run with HFSS ANSOFT™ (http://www.ansoft.com/products/hf/hfss). The package was put on coplanar lines, as shown in Figure T5-88:

Figure T5-88 Package on Coplanar Lines

The results for the insertion loss (S21 in the closed or on state of the switch) and the isolation (S21 in the open or off state) are shown in Figure T5-89:

A complete study including gold and Si3N4 should be conducted to capture the global switch behavior. The aim of this stress comparison is only to give an example of what can be done.

Note that the compressive yield strength of silicon nitride is much higher: around 520 MPa. Those values are depend the fabrication technology and are not generic.


http://www.ansoft.com/products/hf/hfss


Figure T5-89 Insertion Loss and Isolation for RF Switch

For a well designed RF switch, the aim is to obtain a high isolation, which means the parasitic coupling between input and output is small, and a low insertion loss, which means the switch is conducting the signal with low losses (resis-tive at low RF frequencies and skin effect for higher ones). Depending on the application, the insertion loss is consid-ered to be large if it is more than one dB, which is only the case for very high frequencies (>35GHz). The isolation is poor around 20-25dB.

This simulation shows the package, which was designed for RF applications, does not significantly degrade the RF switch performance.

5.4: References1 Bahr, D.F., et al., Indentation induced film fracture in hard film - soft substrate systems, International Journal of

Fracture, 119/120 2003,339.

2 Chang (ed.), Handbook of RF/Microwave Components and Engineering, John Wiley & Sons: New Jersey, 2003.

3 Cheng, D.K., Field and Wave Electromagnetics, Addison-Wesley: Reading, 1990.

4 De Los Santos, H.J., Introduction to Microelectromechanical Microwave Systems, Artech House: Norwood, 1999.

5 Morris, A.S., et al., High-performance integrated RF-MEMS: part 2-switches, www.wispry.com/nws_articles.htm.

6 Tilman, H.A.C., MEMS components for wireless communications, Proceedings of Eurosensors, XVI, 2002.

7 Timsit, R. S., Electrical contact resistance: properties of stationary interfaces, IEEE Transac. on Components and Packaging Technology, 22(1) 1999, 85.


www.wispry.com/nws_articles.htm

www.wispry.com/nws_articles.htm


Notes


MEMS Design and Analysis Index Version 2008

MEMS Design and Analysis Index

AABAQUS

using external version with CoventorWare T2-33

AC analysisin Saber T3-78

AC magnitude T4-25

actuation voltageRF switch

adjusting actuation voltage T5-43

adding a new material to database T2-8

ambient flow T2-125

ambient temperature T2-125

amplitudein Architect simulations T4-69

Analyzerbuckling T1-5electro-thermomechanical analysis T1-6PZR analysis T1-5resistance and inductance analysis T1-6thermal transient analysis T1-6

arc length continuation voltage source T5-10

Architectbuckling T1-5drop test T5-82electromechanical analysis T5-6gyroscope design T1-3input FE results T4-172, T5-65latching magnetic relay design T1-4mirror design T1-2modeling switching time T5-22Monte Carlo analysis T4-53optical scanner design T1-4pull-in analysis T5-6pull-in analysis using slow transient T5-8PZR analysis T1-5RF electrical analysis T5-25RF switch design T1-3sensitivity analysis T4-53temperature effect on resonant frequencies T4-175transient analysis T4-60virtual shock test T5-65

Bbeam

in gyroscope design T4-146, T4-147in RF design T5-1varying length T4-45

beam design analysis2-D layout T2-15comparison of coarse and fine mesh T2-84contact simulation T2-86– T2-90create coarser mesh T2-82electro-mechanical simulation T2-39electrostatic simulation T2-28electrostatic spring softening T2-68– T2-69harmonic simulation T2-70– T2-78hysteresis T2-94– T2-97mechanical simulation T2-33mesh for Tutorial 1 T2-26modal simulation T2-61– T2-79model description T2-2process T2-13pull-in simulation T2-90– T2-93solid model T2-18varying beam thickness T2-98– T2-102

boundary conditionshow to null a boundary condition line T1-8not saved in a parametric study T2-51

buckling T1-5

Ccantilever beam

simulation of T2-115transient analysis T2-105– T2-114

centrifugal force T3-39

centripetal force T3-39

conductorsdesignation T2-10

contact area T5-12

contact BCoffset field T2-86, T2-95

contact force T5-12

contact resistance T5-29

Coventor, Inc. March 10, 2008 IX-1


contact surfacerigid T2-86

Convection Coefficient T2-125

convection-radiationMemMech boundary condition T2-124variable tagging in a parametric study T2-126

convergence studiesresults T4-80

Corioliseffect T3-39force T4-2

CoSolveEMdescription T2-39Maximum number of steps setting T2-91PullIn setting T2-92, T3-32relaxation algorithm T2-40settings for electrostatic spring softening T2-69solver setup T3-25start solver T2-41status indicator T2-90tolerance setting T2-91trajectory setting T3-30viewing results with Visualizer T3-27voltage ramp variable tagging T2-92with MemMech T2-39

coupled electrostatic analysis T2-45

COVENTOR symbolin gyroscope design T4-10

CoventorWare T1-1first time use T3-41how to use T1-1initialization procedure T2-4list of tutorials T1-2setup T2-4

curvature (Query) T4-162, T4-167

Ddamping

at high frequencies T4-110

DampingMMdescription T3-37slide film tutorial T4-120– T4-124squeeze film tutorial T4-108– T4-119Stokes Flow tutorial T4-129– T4-134

DC operating point analysis T4-33mirror schematic T3-77

DC transfer analysis T4-34

degrees of freedomin macromodeling solvers T3-37

depositbeam tutorial sequence T2-11in Process Editor T2-11

description T2-28

design optimization T2-98

dielectricconstant T2-10material T2-10

differential equationsin macromodels T3-39

directoriesnaming restrictions T2-6

double end springBCs window T4-142tutorial T4-141– T4-149

drop testarchitect schematic T5-82

Eelectrode

in gyroscope design T4-23

electrostatic actuation T3-38

Electrostatic Springcapacitance results T3-45MemElectro T3-42polynomial fit routine T3-46– T3-47setting trajectory T3-44Visualizer results T3-45

electrostatic spring softening T2-68– T2-69

electro-thermomechanical analysis T1-6

emissivity T2-125

enumeratetrajectory function T2-99

etchbeam tutorial sequence T2-11in Process Editor T2-11

exportRF data to Touchstone format T5-51– T5-52

IX-2 March 10, 2008 Coventor, Inc.


Fface T2-83

FEM analysis T3-75

file namesrestrictions T2-6

file organization T2-4

files.cat file T2-14for tutorials T1-7setting default directories T2-4settings T2-6viewing saved files T1-8, T2-29, T2-59

film convectiondefinition T2-124MemMech boundary condition setting T2-124variable tagging for a parametric study T2-126

finite element analysis T3-38

FlowMMdescription T3-38

Function Manageraccess to MPD T2-7description T2-5

Ggap model T5-44– T5-46

Geometry Browserbehavior T2-22

geometry scalingin Preprocessor T2-21in Visualizer T2-32

global variablesin gyroscope design T4-10

graphabscissa label for Parametric Study T2-52abscissa label for parametric study T4-164, T4-165abscissa label for parametric study results T2-55Parametric Study results T2-55

Grid tool T2-16

groundin Saber T3-68

ground layerin CoventorWare T2-12

gyroscope2-D layout extraction T4-31Architect design parameters T4-3components needed T4-13design schematic T4-30modal analysis T4-79Monte Carlo analysis T4-53operation T4-2package simulation T4-151process T4-7pull-in analysis T4-81sensitivity analysis T4-53simulation in Architect T4-1– T4-86transient analysis T4-60

Hharmonic analysis

how to set up T2-71introduction T2-70queries for displacement extraction T2-77setting frequency range T2-71, T2-74setting harmonic load T2-71simulation in Saber T3-79

HDLin Saber T3-39

Hycap packaging T5-66layout T5-69process T5-68

Iinductance analysis T1-6

inertiaincorporation in macromodel T3-54

inertial coupling T3-39

InertiaMM T3-54– T3-56description T3-37moments of inertia T3-55use to calculate mass T5-74

initialization procedure T2-4

insertion loss T5-12, T5-36, T5-49

installing files T2-4

Integratorspring extraction T1-7



isolation T5-36, T5-49

Kknot

definition in gyroscope schematic T4-16, T4-21, T4-23,T4-146, T4-147

with macromodel components T3-72

Kyocera package T4-151material properties T4-154

Llabel

for parametric study trajectory T2-52, T4-164parametric study graph example T2-55, T4-165

latching magnetic relay design T1-4

Layer Browserdescription T2-16

layersground layer in CoventorWare T2-12

Layout Editor.cat files T2-14access to layout functions T2-14how to create 2-D layout T1-4Layer Browser T2-16measuring layout T2-16setting grid T2-16with older file versions T2-16

layout generationof gyroscope design T4-31

license settings T2-4

lift-offsimulated with voltage T2-94

linkdefinition T3-14

log window T2-31

Mmacromodel

creation T3-37naming conventions T3-46patch-port correspondence T4-142

macromodelinggenerated files T3-56solvers T3-37

masscompute in reduced-order model T3-54

MAST language T3-39

material properties T2-8for individual designs T2-7for individual parts T2-20tutorial settings T1-7varying T2-52

Material Properties Databaseaccess from Function Manager T2-7access from Preprocessor T2-20default material properties T2-7

measurement tool T5-6

mechanical knot T4-6

mechanical simulationremove a part from T2-20

Mechanical Spring T3-48– T3-53MemMech T3-48moments results T3-45, T3-50reaction force T3-50setting trajectories T3-50

mechDomain T2-36

MemElectro T2-28, T3-41, T3-42compute capacitance of mode shapes T2-65matrix results explained T2-32Parametric Study T2-65Turbo feature T4-81with Electrostatic Spring T3-42

MemMech T3-48calculate stiffness T5-75configuration for CoSolveEM T2-39configure for harmonic analysis T2-71configure for modal analysis T2-61configure for thermal analysis T2-117convection-radiation boundary condition T2-124coupled electrostatic analysis T2-45description T2-33film convection simulation T2-124– T2-129modal analysis for gyroscope T4-79surface boundary conditions T2-34thermal conduction simulation T2-116– T2-123vary stress T2-50with external ABAQUS T2-33

mesh convergence study T2-26, T4-87



meshingchoosing an adequate mesh T2-26convergence studies T4-80extruded mesh example T3-12Manhattan mesh example T2-25remeshing an existing model T2-82tradeoff for using coarser mesh T2-84

microstrip discontinuity model T5-44– T5-46

mirror design2-D layout T3-3CoSolveEM analysis T3-23face assignments T3-10material properties T3-9mesh T3-8physical description T3-3process steps T3-5schematic representation T3-70simulation in Saber T3-77– T3-84solid model T3-38

modal analysisdefinition T2-61FEM validation T4-79frequency table T2-62generalized mass table T2-62how to set up T2-62Parametric Study mode transform T2-65

modescale

in Parametric Study dimension window T2-65shapes T2-63

capacitance of T2-65

moment T2-53, T2-54

momentssimulating with Mechanical Spring T3-50

moments of inertiarepresentation in InertiaMM module T3-55

Monte Carlo analysis T4-56

MPDaccess to T2-7

Nnames

assigning in Preprocessor T2-19preserving in model T2-83restrictions T2-6

normal distributiondefined in process T4-7

Ooffset

defining in a process T4-7used in contact boundary conditions T2-86, T2-95

optical scanner design T1-4

Ppackage design T4-151

curvature T4-167effect of device position T4-177input result to Architect schematic T4-172maximum absolute displacement T4-165minimum absolute displacement T4-165parametric study analysis T4-163– T4-167temporary file space requirements T4-152thermomechanical analysis T4-152, T4-152– T4-162trajectory settings T4-164vary temperature T4-163virtual shock test T5-65with Hycap package T5-66with Kyocera package T4-151with lid T4-168with RF switch T5-65

parabolic elements T2-25

parametricmodels

connecting T4-5

Parametric Studyconvection variable tagging T2-126description T2-50graph label T2-52graph of results T2-55how to set up trajectories T2-52mode transform T2-65perturbation button T2-127scaling function T2-99sensitivity analysis T2-126varying dimension T2-99with MemElectro T2-65with thermal conductivity T2-126

parametric studygraph label T4-164in package design T4-163– T4-167

partitionin the Preprocessor. T2-105

patchwhen user names are required T2-22



plate curvatureimpact on design T4-70

Preprocessoraccess to MPD T2-20keyboard shortcuts T2-22naming entities T2-19partitioning a model T2-105remesh function T2-82scaling a model T2-21Suppress function T2-20

Probe tool T2-128, T4-159

processcross-section view T2-11file

when to use T3-65mirror process steps T3-5older file versions T2-18

Process Editor3-D model construction T2-11access from Function Manager T2-12creating a new process flow T2-14

Project Browserdescription T2-6

projectshow to save T2-7selection and creation T2-6

pull inCoSolve setting T2-92, T3-32definition T2-90voltage required T2-90

pull-incomparing FEM and Saber results T3-75determining T4-34FEM T5-57FEM analysis of gyroscope T4-81

pull-in analysisin Architect T5-6, T5-8with arc length continuation voltage source T5-10

PZR analysis T1-5

QQueries

Curvature T4-162, T4-167Harmonic Response T2-77temperature extraction T2-122, T2-129

Rreaction force

simulating T3-50

reduced-order modeltheory T3-38using differential equations T3-39

reference frame T3-70, T4-8size T5-4

resistancecontact parameter T5-29skin T5-38

resistance analysis T1-6

resonance frequency T4-45

resonant frequencieseffect of anchor length

RF switcheffect of anchor width on resonant frequencies T5-19

influence of temperature T4-175

resultsview from previous simulations T2-29

RF Switchswitching time T5-22

RF switch T1-3calculating mass T5-74calculating stiffness T5-75contact force T5-12design in Architect T5-2drop test T5-82electrical analysis T5-25electromechanical analysis T5-6FEM and Architect comparison T5-53package design T5-65pull-in analysis T5-6

rigid platein gyroscope design T4-20

rigid surface T2-86

rotational stopin Saber T3-73

Ruler tool T2-16

rxnForces T2-36



SSaber

DC operating point analysis T3-77file name restrictions T3-74generic components

in gyroscope design T4-26MAST language T3-39reference frame T3-70transient analysis T3-80, T3-82

save a project T2-7

scalingParametric Study transform type T2-99

sensitivityanalysis T2-126, T4-53report T4-55

settingshow to save T2-6

simulation analysisDC operating point T4-33DC transfer analysis T4-34detection amplitude T4-69Monte Carlo T4-56resonance frequencies T4-45sensitivity T4-53small signal AC analysis T4-40transient analysis T4-60vary loops T4-45, T4-52, T4-58, T4-175, T4-177

small signal AC analysis T4-40

Smith chart T5-48tutorial example T5-48– T5-50

Solid Model toolfunction T2-18using older process files T2-18view 3D model T2-18

S-parameters T5-42, T5-47exporting to Touchstone format T5-51– T5-52on a Smith Chart T5-48– T5-50

spring constantextraction T1-7

spring extraction T1-7

SpringMM T3-41, T3-41– T3-53description T3-37MemElectro T3-41

squeeze film tutorial T4-108– T4-119

statusviewed in CoSolve tables T2-90

stiffnessusing MemMech T5-75

Stokes Flowtutorial T4-129– T4-134

stopsin Saber T3-73

straight combin gyroscope design T4-24

stressvary using Parametric Study T2-50

Suppress function in Preprocessor T2-20

SurfaceBCsspecifying surfaces for stimulus T2-34

sweep analysis T4-34

switchpull-in T5-57

system modeltheory T3-38

system-level simulationFEM verification T4-79gyroscope model T4-73

TTCE T2-115

set in Material Properties Database T2-115

temperatureeffect on resonant frequencies T4-175

temperature analysisfilm convection T2-124– T2-129thermal conduction T2-116– T2-123

thermal actuator T1-6

tied linkdefinition T3-14

torsional mirror3-D model T3-38DC operating point analysis T3-77design assumptions T3-40

Touchstone format T5-51– T5-52

trajectorysetting for parametric study T2-52, T4-164setting multiple runs T3-31



transformmodel thickness T2-100

transient analysis T4-60on a cantilever beam T2-105– T2-112thermal T1-6

translational stopin Saber T3-74

transmission linecreating

RF switchadding transmission lines T5-37

transmission line tool T5-37– T5-39

Turbo feature T4-81

tutorialsconventions T1-7helpful hints T1-7installation files T1-7list of T1-2overview T1-1system requirements T1-1

two-port analysis T5-34– T5-35, T5-41, T5-46

two-port S parameters T5-33

Uuser

settings T2-4setup T1-7, T2-4

using CoventorWare T1-1

Vvary analysis

in gyroscope design T4-72in RF switch design T5-43, T5-51

View resultsfrom previous solver runs T1-8

ViewResult files T1-8, T2-29, T2-59

virtual shock test T5-65

Visualizeranimate mode shapes T2-64deform using displacements T2-37enable warping function T2-37hide parts T2-37

how to view mesh T4-159patch naming T3-10Probe tool T2-128, T4-159rotate model T2-90scaling a model T2-32select plots in 2-D graphs T2-55view mode shapes T2-63view stress results T4-158viewing charge results T3-27viewing results in T3-45with CoSolveEM results T3-27YZ view T2-90

voltagecorresponding charge in MemElectro T2-31CoSolve voltage window T2-42varying in CoSolve T2-92

Wwires

changing attributes T4-29naming in Saber T3-69

wiringconnecting parts in Saber T3-69debugging in Saber T3-69

work directory T2-4

ZZ-plane gyroscope

overview T4-2


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