DESIGN AND MODELLING OF PIEZOMEMS - Sintef

DESIGN AND MODELLING OF PIEZOMEMSDESIGN AND MODELLING OF PIEZOMEMS- METHODOLOGIES AND CASE STUDIES

Gerold Schropfer, [email protected]

International Workshop on Piezoelectric MEMS, May 18th-19th, 2010, Aachen

Outline

• Introduction• Modelling methodologies for PiezoMEMS• PiezoMEMS modelling case studies

ResonatorsEnergy HarvestersPZT MoveMEMS design kit

CantileversMirror

• Conclusions• Conclusions

About Coventor

Coventor:

• Coventor offers Design Tools and Platforms for MEMS and ICs

• 15 years experience

• Leader in MEMS design software

• US based

• Strong European R&D

Products:

CoventorWare™

Coventor Infrastructure

Process & Materials DataProcess & Materials Data

MEMulator-SEMulator3D

Fab Process Modeling





3D CAD Tools

SolidWorksPro-Engineer

I-DEASAutoCAD

3D CAD Tools

SolidWorksPro-Engineer

I-DEASAutoCAD

EDA Simulators

SimulinkSaber

CadenceMentor

EDA Simulators

SimulinkSaber

CadenceMentor

SEMulator3D™ MEMS+™ Platform

Introduced 2001

3D Field Solvers

Abaqus (Dassault)Fluent, Flow3D

ANSYS,Ansoft, etc.

3D Field Solvers

Abaqus (Dassault)Fluent, Flow3D

ANSYS,Ansoft, etc.

2D LayoutGDS2, CIF,

DXF (AutoCAD)

2D LayoutGDS2, CIF,

DXF (AutoCAD)

ARCHITECT3D(based on Saber)

Schematic-DrivenMEMS Design

DESIGNER2D & 3D Geometry(Physical Design)

DESIGNER2D & 3D Geometry(Physical Design)

ANALYZER3D Field Solvers

(Verification)

ANALYZER3D Field Solvers

(Verification)

INTEGRATORReduced-Order Model

Extraction

INTEGRATORReduced-Order Model

Extraction

Introduced 2005 I t d d 2009

MEMS design(previously MEMCAD, MIT spinn-off in 1995)

Introduced 2001

Virtual fabrication MEMS + IC development

Introduced 2005 Introduced 2009

MEMS Designer’s Challenges

3D Nature / Structures3D Multi-Physics

Reliability3D Multi Physics

(coupled)

Variety of MEMS Processes

Co-Design of Die and Package

Coupling of MEMS

P f D d ti

Variability in Process and Material

with Electronics

Performance Degradation (induced by fabrication or use)

Variability in PiezoMEMS Process and Materials

Design Design Design ToolToolTool

Input Data

Result Output

Material Properties Piezo-Coeff. Young's Modulus

Device Performance Membrane Deformation

Young s Modulus Stress etc.

Process Geometry Film Thickness

Resonance modes etc. System Performance

Feedback Control Noise etc

Sidewall angles etc. Layout Geometry

Length, width etc.

Noise etc.

Variability in input Uncertainty in output

Models of MEMS

Representations of MEMS are required in many contexts System/Control

),( txfkxxcxm MEMS high-level design Circuit-level MEMS+IC

MEMS detailed 3DLayout

Process Modelling

Process Modelling

http://www.synopsys.com/Tools/TCAD/CapsuleModule/sprocess_ds.pdf

Process EmulationLayout Tools: 2D Verification TCAD: Process SimulationProcess Emulation

Mapping process to model steps (very efficient)

Able to model complete process sequences

Layout Tools: 2D Verification

Feasible on an entire chip. Check design rules, verify

layout, etc. Does not capture 3D effects

TCAD: Process Simulation

Accurate but time consuming Simulates single steps

(implant, etch,…) Feasible for small areasprocess sequences

Able to model large area Fully 3-D

Does not capture 3D effects No direct link to the process.

Feasible for small areas Often 2D, rarely 3D.

Scope Fidelity

MEMS Behavioral Model Library

• Macro or behavior models (ideally analytical)Beams & Suspensions (Bernoulli Beam Theory)Plates (Rigid, Flexible MITC Plate Theory)

Sensing Electrodes and Comb Finger Drives (Conformal Mapping Theory)

• Solved in electrical circuit simulators (analogy electrical and mechanical)

[CoventorWare 2010 Architect3D reference documentation]

MEMS Behaviour Model Libraries

• Models built based on parameterized library components

IC schematic or 3D building blocks

Traditionally: Schematic entry based library Recently: 3D model library

Which aproach to use for piezoMEMS design ?

Behaviour Models:System level designEasier design automation and EDA

FEM/BEM :Geometric FlexibilityCaptures field details

integrationShort simulation time enables

Transient analysisRapid optimization

such as stress distributionAddresses physics not amenable to

behavioral modelingsuch as gas damping

Statistical analysis, such like yield or sensitivity analysis

Arbitrarily accurate via mesh refinement

MEMS-IC Co-Design(Integration of MEMS and EDA tools)

Ref. G. Schröpfer, G. Lorenz, S. Rouvillois, J.Chianetta, et al., A Novel EDA-Compatible Methodology for Design and Simulation of MEMS with IC, 7. GI/GMM/ITG-Workshop on Multi-Nature Systems, Ulm, Germany, 3 February 2009

Outline

• Introduction• Modelling methodologies for PiezoMEMS• PiezoMEMS modelling case studies

ResonatorsEnergy HarvestersPZT MoveMEMS design kit

CantileversMirror

• Conclusions• Conclusions

Film Bulk Acoustic Resonator (FBAR)

3D model of a “generic” FBARg

• RF signal across device produces longitudinal vibrations piezo layerR h fil thi k i i t l lti l f h lf th i l l th • Resonance when film thickness is integral multiple of half the signal wavelength

• At resonance sharp change in electrical impedance (frequency selective filter)• Designed for strong resonance with narrow bandwidth (wireless communication)

FBAR FEM Modelling

Animation of resonance mode

PiezoElectric strain coefficients for ZnO

Real and Imaginary charge on top and bottom electrode as a function of frequency electrode as a function of frequency

Impedance as a function of frequency

Modal Harmonic Analysis for PiezoMEMS

Modal Harmonic Analysis…• A set of vibration modes for the model are first calculated. These modes are used

to approximate the harmonic responseto approximate the harmonic response• Modal harmonic is almost always computationally less expensive than direct

harmonic

• Includes coupling between electric field strength and mechanical stress/strain

Modal Harmonic PZEFrequency Response

0,7Modal Harmonic & Direct Harmonic Comparison

Modal Harmonic

0,5

0,6Modal Harmonic

Direct Harmonic

Direct Harmonic ‐ Detailed

0,3

0,4

MaxX_

Mag

0,7d l

0,1

0,2

0,4

0,5

0,6

Mag

Modal Harmonic

Direct Harmonic

Direct Harmonic ‐Detailed

0

735000000 740000000 745000000 750000000 755000000 760000000 765000000 770000000Frequency (Hz)

0 1

0,2

0,3

0,4

MaxX_

M

0

0,1

749000000 751000000Frequency (Hz)Coventor Inc. Confidential Slide 16

Q-Factor and Damping

Resonator analysis requires Q-factor calculation, which depends on different damping mechanism:

11111

Gas DampingThermo-Elastic Damping

OTHERANCHORTEDGASTOTAL QQQQQ11111

Anchor Loss Others: Complex Harmonic Loading, structural or surface effects

Quality CADQuality Factor Explanation CAD

Solution(s)

QGAS Gas damping, can be reduced by reducing ambient pressure FEM (specific module)

Thermoelastic Damping -- As a vibrating body is strained, the M h i l FEM QTED

Thermoelastic Damping As a vibrating body is strained, the temperature changes in proportion to the strain; when temperature gradients occur, heat conduction causes irreversible energy loss

Mechanical FEM or behavior model(TED option)

QAnchor Loss -- A fraction of elastic energy is transmitted via the anchors to the surrounding support structure where it is Mechanical FEM with

Coventor Inc. Confidential Slide 17

QANCHORanchors to the surrounding support structure where it is dissipated. Also referred to as support loss, clamping loss, or attachment loss

QuietBoundary Surface BC

QOTHEROther Loss Mechanisms which may include structural dissipation (crystallographic defects) and surface effects

Mech. FEM with Rayleigh Damping Coef.

Piezoelectric Energy Harvester

•Silicon-based fabrication using AlN as piezoelectric material•Three wafer process, bonded by SU-8

harvesting capacitor

adhesivebonds

capacitor

1281 7 mm31281.7 mm

mass beam

[HOLST IMEC]

Reference: D. Hohlfeld ea.“Experimental Validation of Aluminum Nitride Energy Harvester Model with Power Transfer Circuit”, Eurosensors 2009 and also to be published Sensors & Actuators, 2009

Finite Element Model for Piezoelectric Harvester

• predictsresonance frequencyresonance frequencyoutput voltage or charge under open and short circuit condition

• requires material damping• requires material damping

S. Matova, Proc. Eurosensors XXII

uit v

olta

ge /

Vop

en c

ircu

frequency / Hz


Euler-Bernoulli Beam with Piezoelectric Patch

• Non-linear Bernoulli beam with piezoelectric transducerIncludes lumped and distributed elementsActive part : potential differences → forcesSensing part : displacement → charge

• Implemented in Coventor Model Library (Architect3D)p y ( )

3.00E-06load matching

anchor

beam mass1.50E-06

2.00E-06

2.50E-06Po

wer

(W)

0.00E+00

5.00E-07

1.00E-06

RMS

P

1.0E+04 1.0E+05 1.0E+06 1.0E+07

Rload (Ohm)


Model Validation :Short Circuit

• Short circuit condition (Rload = 200 Ω)• Frequency deviation due to beam thickness variation q yand precise material parameter characterization

8.0

FEA l d i it

5 0

6.0

7.0

A)

FEA closed circuit

Measured Rload = 200 Ohm

Architect3D Rload = 200 Ohm

3.0

4.0

5.0

Cur

rent

(uA

0 0

1.0

2.0

0.5 g excitation0.0

1100 1110 1120 1130 1140 1150 1160

Frequency (Hz)Reference: D. Hohlfeld ea.“Experimental Validation of Aluminum Nitride Energy Harvester Model with Power Transfer Circuit”, Eurosensors 2009 and also to be published Sensors & Actuators, 2009

Model validation : open circuit

• Short circuit condition (Rload = 5.3 MΩ)• Good match in output magnitudep g

2.5

3.0

FEA open circuit

1 5

2.0

2.5

ge (v

)

Measured Rload = 5.3 MOhm

Architect3D Rload = 5.3 MOhm

1.0

1.5

Volta

g

0.0

0.5

1100 1110 1120 1130 1140 1150 1160

0.5 g excitation

Frequency (Hz)


Circuit Elements for FEM Piezo Direct Harmonics

• Piezo harmonic analysis of MEMS incorporated into an electrical circuitresistors, inductors and capacitors

• For such applications as:• For such applications as:Energy harvesters: vibration of a piezoelectric device provides electrical current to other components in the circuitActive damping: piezoelectric material is dd d t l h i l t t t added to a larger mechanical structure to

control its motion by converting vibration energy into electrical current that is directed through a resistor and dissipated as heat

PZT

Fix

PZT

Structural Layer

Ref: Erturk, A. & Inman, D. J. A Distributed Parameter Electromechanical Model for Cantilevered Piezoelectric Energy Harvesters, J of Vibration and Acoustics, 130, 4, August 2008.

PZT Energy HarvesterPower Response

1,0E‐03

Power Response Function1,0E‐03




Power Response Function

1,0E‐04

1E2Ω

1,0E‐04

1E2Ω 1E3Ω

1,0E‐04

1E2Ω 1E3Ω 1E4Ω

1,0E‐04

1E2Ω 1E3Ω

1E4Ω 1E5Ω1,0E‐04

1E2Ω 1E3Ω

1E4Ω 1E5Ω

1E6Ω

1,0E‐05er (W

)

1,0E‐05er (W

)

1,0E‐05er (W

)

1,0E‐05er (W

)

1,0E‐05er (W

)

1 0E 06

,

Powe

1 0E 06

,

Powe

1 0E 06

,

Powe

1 0E 06

,

Powe

1 0E 06

,

Powe

1,0E‐061,0E‐061,0E‐061,0E‐061,0E‐06

1,0E‐07

47 47,5 48 48,5 49 49,5 50 50,5 51

Frequency (Hz)

1,0E‐07

47 47,5 48 48,5 49 49,5 50 50,5 51

Frequency (Hz)

1,0E‐07

47 47,5 48 48,5 49 49,5 50 50,5 51

Frequency (Hz)

1,0E‐07

47 47,5 48 48,5 49 49,5 50 50,5 51

Frequency (Hz)

1,0E‐07

47 47,5 48 48,5 49 49,5 50 50,5 51

Frequency (Hz)

Design Kit Motivation

DesignDesignHandbookHandbook

FoundryFoundry

… use tools to build a bridgeDesigner

MoveMEMS PZT Design Kit Experiments vs. Simulation

• Deflection of test cantilever

ModelExperiments

Canitilever 6-3 up to 30 V

25 000

5 000

10 000

15 000

20 000

Hei

ght (

nm)

0V10V20V0 V 2nd20V25V

Monte Carlo Simulation with thickness of all layers as statistical parameter (nominal distribution assumed)

-5 000

00 0.2 0.4 0.6 0.8 1 1.2

Distance (mm)

30V

Piston Mirror

• Ref. Thor Bakke, Andreas Vogl, Oleg Żero, Frode Tyholdt, Ib-Rune Johansen, and Dag Wang, A novel ultra-planar, long-stroke, and low-voltage piezoelectric micromirror JMM 2010micromirror, JMM 2010

Mirror Model with MITC shell elements

PiezoMEMSProcess Design Kit (PDK)

• Library of foundry specific process emulation files • Specific material property databases Spec c a e a p ope y da abases• Layout template file with design rule check• Parametric model library elements • Compatible to design handbooks• Combined with fabrication run, e.g. Multi-Project-Wafer

Materials’Properties

Process Parameters

Fabrication System and MEMS IC Co-design

Layout3D Model

FEM/BEM Analysis

MoveMEMS PZT Process Data MEMS IC Co design 3D Model AnalysisProcess Data

[EC NMP Project piezoVolume]

Towards a PiezoMEMS Eco System

Parametric design format provides a new standard to facilitate the communication between the partners of the eco-system

Parametric Parametric PiezoMEMS Design

MEMSUserFAB Model

P tPDK

MEMSDeveloper/Layout

Parameters

Models

PDK

Developer/Designer

Layout

Conclusions

• PiezoMEMS design requires different methods for different applications and modelling levels

FEM and behaviour models (circuit design)FEM and behaviour models (circuit design)• Knowledge of process and material properties is key

“Robust” designs compensate for process variability• In workIn work

Advanced PiezoMEMS models MoveMEMS PZT design kit are

• Recommend holistic and integrated approach g ppMEMS, electronics, packagingValidated models… to avoid inconsistencies between eco-system partners

As wanted … As packaged … As fabricated … As modeled … As designed …

Acknowledgement

“The research leading to these results has received funding from the European Community's Seventh Framework Programme (FP7/2010‐2013) under grant agreement n° 229196”Seventh Framework Programme (FP7/2010 2013) under grant agreement n 229196

www.piezovolume.com

DESIGN AND MODELLING OF PIEZOMEMS - Sintef

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