RF MEMS

Theory, Design, and Technology

GABRIEL M. REBEIZ

A JOHN WILEY & SONS PUBLICATION

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RF MEMS

RF MEMS

Theory, Design, and Technology

GABRIEL M. REBEIZ

A JOHN WILEY & SONS PUBLICATION

Copyright ( 2003 by John Wiley & Sons, Inc. All rights reserved.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey.

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This book is dedicated to

My Father

My Uncle

My Brother

David B. Rutledge

Fawwaz T. Ulaby

and

Edward D. Surovell

Chapter Co-Writers*

N. Scott BarkerThe University of Virginia

Laurent DussoptCEA-LETI, France

Joseph HaydenIntel

Jeremy MuldavinMIT Lincoln Laboratory

Jad RizkIntel

Bernhard SchoenlinnerThe University of Michigan

Guan-Leng TanDSO National Laboratories, Singapore

*all graduate students or post-doctoral fellows of Gabriel Rebeiz

CONTENTS

Preface xvii

1 Introduction: RF MEMS for Microwave Applications 1

1.1 The Beginning of RF MEMS, 11.2 RF MEMS Configurations, 31.3 Comparison of MEMS Switches with GaAs PIN Diode and

Transistor Switches, 51.4 Application Areas of RF MEMS, 51.5 Case Studies in RF MEMS, 6

1.5.1 Case 1: RF MEMS in Switching Networks, 61.5.2 Case 2: RF MEMS in Low-Noise, Low-Power

Circuits, 91.5.3 Case 3: RF MEMS in Portable Wireless Systems, 91.5.4 Case 4: RF MEMS in Phased Arrays, 11

1.6 RF MEMS Development Around the World, 141.7 Integration of RF MEMS with Silicon and GaAs

Electronics, 151.8 Linearity and Intermodulation Products, 161.9 Hermetic or Nonhermetic Packaging, 191.10 Power Handling and Reliability, 19Bibliography, 20

2 Mechanical Modeling of MEMS Devices: Static Analysis 21

2.1 Spring Constant of Fixed–Fixed Beams, 21

vii

2.1.1 Spring Constant Component due to ResidualStress, 24

2.1.2 Nonlinear Stretching Component of the SpringConstant, 27

2.1.3 Critical Stress of Fixed–Fixed Beams, 282.1.4 Residual Stress and Young’s Modulus of Beams

Composed of Di¤erent Materials, 292.1.5 E¤ect of Holes in the Beam, 29

2.2 Spring Constant of Low-k Beams, 302.3 Spring Constant of Cantilever Beams, 312.4 Spring Constant of Circular Diaphragms, 342.5 Beam Curvature due to Stress Gradients, 342.6 Electrostatic Actuation, 362.7 Shape of the Deformed Beam Under Electrostatic

Actuation, 382.8 DC Hold-Down Voltage of MEMS Beams and

Cantilevers, 402.9 Forces on MEMS Beams, 432.10 Self-Actuation of MEMS Capacitive Switches, 432.11 RF Hold-Down Voltage of MEMS Capacitive

Switches, 462.12 Capacitance Ratio in Analog Mode, 47

2.12.1 Three-Plate Electrostatic Designs, 482.13 Stabilization of Electrostatic Actuated Beams, 49

2.13.1 Charge Stabilization Techniques, 522.14 Voltage Breakdown in MEMS Devices, 532.15 E¤ect of Temperature Variation, 532.16 E¤ect of Acceleration and Acoustic Forces, 542.17 Software for MEMS Analysis, 55Bibliography, 56

3 Mechanical Modeling of MEMS Devices: Dynamic Analysis 59

3.1 Linear (Small Displacement) Dynamic Analysis of MEMSBeams, 59

3.2 Gas Fundamentals, 603.3 Damping Coe‰cient/Quality Factor, 62

3.3.1 Damping Variation Versus Height, 633.4 Nonlinear (Large-Displacement) Dynamic Analysis of

MEMS Beams, 643.5 Switching and Release Time Calculations, 66

3.5.1 Switching Time, 663.5.2 Release Time, 69

3.6 Switching Mechanisms of MEMS Beams, 693.6.1 Steady-State Solution, 69

viii CONTENTS

3.6.2 Velocity, Acceleration, and Current, 703.6.3 E¤ect of the Fringing Capacitance, 713.6.4 E¤ect of the Damping Resistance, 723.6.5 Taylored Actuation Voltage, 73

3.7 Switching Energy, 733.8 Response to Applied Waveforms, 75

3.8.1 Response to Single Waveforms, 763.8.2 Response to Multiple Waveforms, 783.8.3 Response to Amplitude-Modulated (AM) Signals, 783.8.4 Response to Frequency-Modulated (FM) Signals, 79

3.9 Dynamic Self-Actuation and Release Analysis of MEMSBeams, 80

3.10 Generation of Intermodulation Products, 803.11 Brownian Noise Analysis, 83Bibliography, 85

4 Electromagnetic Modeling of MEMS Switches 87

4.1 Introduction, 874.2 Physical Description of MEMS Capacitive Shunt

Switches, 884.3 Circuit Model of the MEMS Capacitive Shunt Switch, 894.4 Electromagnetic Modeling of MEMS Shunt Switches, 90

4.4.1 Up-State Capacitance, 904.4.2 Down-State Capacitance and Capacitance Ratio, 914.4.3 Current Distribution, 934.4.4 Series Resistance, 954.4.5 Inductance, 964.4.6 Loss, 97

4.5 Fitting CLR Parameters to S-Parameter Shunt Capacitive-Swtich Measurements, 994.5.1 Up-State Capacitance, 994.5.2 Down-State Capacitance and Inductance, 1004.5.3 Series Resistance of the MEMS Bridge, 103

4.6 Inline MEMS Capacitive Shunt Switches, 1044.7 DC-Contact MEMS Shunt Switches, 1054.8 Physical Description of MEMS Series Switches, 1064.9 Electromagnetic Modeling of MEMS Series Switches, 108

4.9.1 Up-State Capacitance, 1084.9.2 Current Distribution, 1114.9.3 Down-State Resistance, 1114.9.4 Loss, 1124.9.5 Inductance, 113

4.10 Fitting CLR Parameters to DC-Contact Series SwitchMeasurements, 115

CONTENTS ix

4.10.1 Up-State Capacitance, 1154.10.2 Down-State Resistance and Inductance, 117

4.11 Example: The Rockwell Scientific MEMS Series Switch, 1184.12 Fitting CLR Parameters to Capacitive Series Switch

Measurements, 1204.13 Conclusion, 120Bibliography, 120

5 MEMS Switch Library 121

5.1 The Raytheon Capacitive MEMS Shunt Switch, 1215.2 The University of Michigan Capacitive MEMS Shunt

Switches, 1235.2.1 Low-Voltage (Low-Spring-Constant) Switches, 1235.2.2 Low-Height (High-Spring-Constant) Ti/Gold

Switches, 1245.3 The LG-Korea High-Capacitance-Ratio MEMS Shunt

Switch, 1255.4 The University of Illinois DC-Contact MEMS Shunt

Switch, 1265.5 The University of Michigan Inline DC-Contact MEMS

Shunt Switches, 1285.6 The National Taiwan University MEMS Capacitive and

DC-Contact Shunt Switch, 1305.7 Other MEMS Shunt Switches, 1315.8 The Rockwell Scientific DC-Contact MEMS Series

Switch, 1325.9 The Motorola DC-Contact MEMS Series Switch, 1335.10 The HRL DC-Contact MEMS Series Switch, 1345.11 The Northeastern University/Radant MEMS Inline DC-

Contact MEMS Series Switch, 1365.12 The Lincoln Laboratory Inline DC-Contact and Capacitive

MEMS Series Switch, 1375.13 The Omron DC-Contact MEMS Series Switch, 1395.14 The University of Michigan All-Metal MEMS Series

Switch, 1415.15 The Samsung Low-Voltage DC-Contact MEMS Series

Switch, 1425.16 The Berkeley MEMS Series and Shunt Switches, 1445.17 The Push–Pull DC-Contact MEMS Series Switch, 1455.18 Thermal-Electrostatic DC-Contact MEMS Switches: The

CEA/LETI ST-Microelectronics Switch, 1465.19 Magnetic Actuation: The Latching Microlab Series

Switch, 1475.20 Lateral DC-Contact MEMS Series Switches: The Cronos

Integrated Microsystems Switch, 148

x CONTENTS

5.21 Lateral DC-Contact University of California, Davis,Switch, 150

5.22 Piezoelectric Actuation, 1515.23 The HRL MEMS Rotary Switch, 1525.24 Other MEMS Series Switches, 153Bibliography, 153

6 MEMS Switch Fabrication and Packaging 157

6.1 Introduction, 1576.2 Fabrication of MEMS Capacitive Switches, 1586.3 Fabrication of MEMS DC-Contact Series Switches, 1616.4 Fabrication of Lateral DC-Contact Switches, 1646.5 MEMS Release Procedures, 1656.6 Substrate Transfer Process, 1676.7 Fabrication, Substrate Transfer, and Packaging of the

Omron DC-Contact Series Switch, 1696.8 Conventional Hermetic Packaging of MEMS Switches, 1716.9 On-Wafer Hermetic Packaging of MEMS Switches, 1736.10 RF Feed-Throughs for On-Wafer Hermetic Packages, 1806.11 Conclusion, 181Bibliography, 181

7 MEMS Switch Reliability and Power Handling 185

7.1 Failure Mechanisms of MEMS Capacitive Switches, 1857.2 Solutions to the Dielectric Charging Problem, 1897.3 Failure Mechanisms of DC-Contact Switches, 192

7.3.1 Contact Area, Hardness, and ContactResistance, 194

7.4 Contact Material Issues, 1987.5 Low- and Medium-Power Reliability Tests, 1997.6 MEMS Switches Under Medium- to High-Power

Conditions, 2027.6.1 Stand-O¤ Voltages of Series and Shunt Switches, 2027.6.2 SPST and SPDT Switch Circuits for High-Power

Applications, 2037.6.3 Hot and Cold Switching Conditions of DC-Contact

Switches, 2047.7 Capacitive Switches: High-Power Conditions, 205

7.7.1 Capacitive Shunt Switches, 2057.7.2 Capacitive Series Switches, 211

7.8 DC-Contact Switches: High-Power Conditions, 2117.8.1 DC-Contact Series Switches, 2117.8.2 DC-Contact Shunt Switches, 213

7.9 Increasing the Current Carrying Capabilities of DC-Contact Switches, 213

CONTENTS xi

7.10 High-Current Reliability Tests of DC-ContactSwitches, 215

7.11 Conclusion, 215Bibliography, 217

8 Design of MEMS Switch Circuits 221

8.1 Introduction, 2218.2 Biasing of MEMS Switches, 2228.3 Design of CPW MEMS Shunt Capacitive Switches, 223

8.3.1 C-Band to X-Band Designs, 2238.3.2 Millimeter-Wave Designs, 2258.3.3 W-Band Designs, 227

8.4 Inductive Matching of Shunt Capacitive Switches, 2278.4.1 The T Match, 2288.4.2 The p Match, 230

8.5 Microstrip Implementation of MEMS Shunt Switches, 2318.6 Design of CPW MEMS DC-Contact Shunt Switches, 2348.7 Design of MEMS DC-Contact Series Switches, 2348.8 Design of MEMS Capacitive Series Switches, 2368.9 Design of Series/Shunt MEMS Switches, 2398.10 Design of Single-Pole Multiple-Throw Switches, 240

8.10.1 Series Implementation, 2408.10.2 Shunt Implementation, 243

8.11 Design of Double-Pole Double-Throw (Transfer)Switches, 244

8.12 Design of Absorptive MEMS Switches, 2468.13 Inductively Resonant High-Isolation X-Band Capacitive

Shunt Switches, 2488.14 Measurements on High-Isolation Shunt and Series

Switches, 2508.14.1 A Ka-Band Tuned Switch, 2508.14.2 A Ka-Band Cross Switch, 2518.14.3 W-Band High-Isolation Switches, 2528.14.4 0.1- to 40-GHz Series/Shunt Switches, 2538.14.5 0.1- to 26-GHz MEMS Absorptive Switches, 255

8.15 Conclusion, 256Bibliography, 256

9 MEMS Phase Shifters 259

9.1 Introduction, 2599.2 Reflection-Type Phase Shifters, 262

9.2.1 N-Bit Shunt Switch Implementation, 2639.2.2 N-Bit Series Switch Implementation, 2659.2.3 One-Bit/N-Bit Reflection-Type Phase Shifters, 265

xii CONTENTS

9.3 Switched-Line Phase Shifters, 2679.4 Loaded-Line Phase Shifters, 2689.5 Varactor and Switched Capacitor-Bank Phase Shifters, 2739.6 Phase Shifters Based on Switched Networks, 2769.7 Phase Shifters Based on 1:N Switches, 2799.8 Phase Shifters Based on Antenna Feeds, 2809.9 Library of MEMS Phase Shifters, 280

9.9.1 Raytheon X-Band Reflect-Line Phase Shifters, 2819.9.2 HRL X-Band Reflect-Stub Phase Shifters, 2839.9.3 Rockwell Wideband 0.1- to 40-GHz Switched-Line

Phase Shifter, 2859.9.4 UoM/Rockwell DC-18-GHz 1:N Switched-Line

Phase Shifters, 2889.9.5 Raytheon Ka-Band Switched-Line Phase

Shifter, 2909.10 Other Phase Shifter Designs, 291Bibliography, 293

10 Distributed MEMS Phase Shifters and Switches 297

10.1 Introduction, 29710.2 Analysis of Distributed MEMS T Lines, 298

10.2.1 Inductance E¤ect on the Bragg Frequency, 29910.2.2 Loss, 300

10.3 Distributed MEMS T-Line Measurements, 30210.4 The DMTL Implementation, 30310.5 Phase Shift of the DMTL, 30610.6 Design of Capacitively Loaded Distributed T Lines, 306

10.6.1 Optimization, 30810.6.2 E¤ect of the Loading Capacitor, 30910.6.3 E¤ect of the Bragg Frequency, 31210.6.4 Scaling to Other Frequencies, 315

10.7 X-Band 2-Bit DMTL CPW Phase Shifters, 31510.7.1 Metal–Air–Metal Design, 316

10.8 X-Band 4-Bit DMTL Microstrip Phase Shifter, 31710.9 Analog and Digital Ka/V-Band and W-Band CPW

DMTL Phase Shifters, 32010.9.1 Analog Ka/V-Band and W-Band Designs, 32010.9.2 Digital 2-Bit Ka-Band Phase Shifters, 321

10.10 Wideband Distributed MEMS Switches, 32210.11 Conclusion, 323Bibliography, 324

11 MEMS Varactors and Tunable Oscillators 327

11.1 Introduction, 327

CONTENTS xiii

11.2 Review of Quality Factor Fundamentals, 32811.3 Tunable Electrostatic Parallel-Plate Capacitors, 33011.4 Tunable Thermal and Piezoelectric Parallel-Plate

Capacitors, 34011.5 Tunable Interdigital Capacitors, 34311.6 MEMS Switched Capacitors, 34811.7 MEMS Varactors with Discrete Position Control, 35111.8 MEMS-Based Voltage-Controlled Oscillators, 35411.9 Reliability of MEMS Varactors, 35411.10 Conclusion, 356Bibliography, 356

12 Micromachined Inductors 359

12.1 Introduction, 35912.2 Inductor Model and Q, 360

12.2.1 Frequency Response of Planar Inductors, 36112.2.2 Q of Planar Inductors, 36312.2.3 Measuring Q of Planar Inductors, 36512.2.4 E¤ect of the Metallization Thickness, 36612.2.5 E¤ect of the Parasitic Capacitance, 36712.2.6 Goals of Micromachined Inductor Design, 368

12.3 Micromachining Using Thick Metals Layers, 36812.4 Micromachining Using Substrate Etching, 37012.5 Micromachining Using Self-Assembly Techniques, 37312.6 Elevated and Solenoid-Type Copper Inductors, 37612.7 Conclusion, 380Bibliography, 380

13 Reconfigurable MEMS Networks, Filters, Antennas, and

Subsystems 383

13.1 Introduction, 38313.2 Reconfigurable Matching Networks, 38413.3 Currents on Reconfigurable Matching Networks, 39013.4 Reconfigurable Antennas, 39113.5 MEMS Physically Movable Antennas, 39713.6 Reconfigurable/Switchable Frequency-Selective Surfaces

and Quasi-Optical Components, 39913.7 Tunable Resonator Fundamentals, 40013.8 Distributed Capacitive Tuning, 40713.9 HF-UHF Tunable Filters, 40713.10 Millimeter-Wave Tunable Filters, 41613.11 Reconfigurable Circuits Using the Lincoln Laboratories

Approach, 422

xiv CONTENTS

13.12 Currents and Voltages on Tunable Filters, 42313.13 Conclusion, 425Bibliography, 426

14 Phase Noise Analysis of MEMS Circuits, Phase Shifters, and

Oscillators 429

14.1 Review of Brownian Noise, 42914.2 Brownian Noise E¤ects in MEMS Shunt Switches, 431

14.2.1 Phase Noise, 43214.2.2 Amplitude Noise, 433

14.3 Phase Noise Reduction Using N MEMS ShuntSwitches, 434

14.4 Phase Shifters Based on Shunt Switches, 43514.5 Phase Shifters Based on MEMS Varactors, 43614.6 Distributed Phase Shifters, 43814.7 Brownian Noise in MEMS Series Switches and Phase

Shifters, 44014.8 Brownian Noise in MEMS-Based Oscillators, 44014.9 E¤ect of Acceleration and Acoustic Noise, 44314.10 E¤ect of Constant Acceleration and Acoustic Waves on

MEMS-Based Oscillators, 44514.11 E¤ect of Bias Voltage Noise, 44514.12 Conclusion, 447Bibliography, 447

15 Future Work in RF MEMS 449

15.1 Summary of Accomplished Work, 44915.2 Future Work, 453

Appendix A Detailed Analysis and Measurements of Intermodulation

Distortion and Power Handling in RF MEMS Switches, Varactors,

and Tunable Filters 457

Appendix B Mechanical, Electrical, and Thermal Properties of RF

MEMS Materials 473

Index 479

CONTENTS xv

PREFACE

All that I wanted to do is to write a deep book. This is what I kept tellingmyself when I took walks and considered writing a book on RF MEMS. I justwanted to write a book unlike the myriad of ‘‘low-level technical manuscripts’’in print, a book that covered the theory, design, and technology of RF MEMSat a reasonably deep level. I started writing the book in October 1999, but hadto delete and rewrite many chapters because the understanding of the electro-magnetic and mechanical analysis of RF MEMS, and their associated reliabil-ity and packaging, actually matured in 2001. I also wanted to tell the readereverything I knew about this subject, and I only omitted a few things that arecovered under confidentiality and nondisclosure agreements.

I hope that you find this book honest in reporting the status of RF MEMStechnology. We have been under exclusive contracts from the U.S. Govern-ment and, as of September 2002, do not have private investment in RF MEMS.Sure, it is a great technology, but there are still power handling, reliability, andpackaging concerns; and most importantly, it is not yet clear if RF MEMS canbe produced at less than $1 per unit for large-volume commercial applications.All of these concerns are presented in the book, together with proposals on howto solve some of these problems.

In order to write such a book, I have had the pleasure to work with a won-derful team of scientists in RF MEMS: my graduate students. I have learned tocarefully listen to them and to accept the fact that they know more about theirresearch than I ever would. I have also learned to hire outstanding students,ask an inhumane amount of work from them, and then protect them from thecontract monitors—using any means possible—so as to let them explore deeplymany aspects of their work. We have had long discussions about virtually

xvii

everything on RF MEMS and micromachining, and they made sure that I wasnot committing any errors or omissions. Some of them have also helped withthe calculations and layout of the chapters. The students are: Chen-Yu Chi,Thomas Budka, Gildas Gauthier, Andrew Brown, N. Scott Barker, JeremyMuldavin, Joseph Hayden, Guan-Leng Tan, Laurent Dussopt, Jad Rizk, andBernhard Schoenlinner. I will miss working with them: By summer 2002, allof them (except Bernhard) will have graduated with a Ph.D. in ElectricalEngineering. Guan-Leng and Jeremy deserve particular thanks because theycontributed the most in terms of helping with the figures and in integrating thebook together. The students will receive 50% of the proceeds of the book.

No book of such detail can be written without help from industry and fromcolleagues in the academic sector. I am particularly grateful to the personaldiscussions with Professor Nick McGruer (Northeastern University), Rob Mi-hailovich (Rockwell Scientific), Captain Rob Reid (AFRL), Ezekiel Kruglickand Professor Kris Pister (University of California, Berkeley), Dan Hyman(Xcom Wireless), and Carl Bozler (MIT Lincoln Labs). I have learned quite abit from them.

Also, Je¤ DeNatale (Rockwell Scientific), Chuck Goldsmith, AndrewMalczewski, and Brandon Pillans (all at Raytheon), Professors Linda Katehi,Clark, Nguyen and Khalil Najafi (University of Michigan), Pierre Blondy(University of Limoges), Ronn Kliger (Analog Devices), Professors MiltonFeng and C. Liu (University of Illinois), Cli¤ Vaughan (Motorola), CraigKeast (MIT Lincoln Laboratories), Tomorono Seki (Omron, Japan), VeljkoMilanovic (University of California, Berkeley), Nils Hoivik and Professor Y.C. Lee (University of Colorado), Hongrui Jiang and Norman Tien (CornellUniversity), Professor Darrin Young (Case Western Reserve University), Vic-tor Lubecke (Lucent Technologies), Aleksander Dec and Professor KenSuyama (Columbia University), Professor Chuck Wheeler (University of Ari-zona), Professor Jose Lopez-Villegas (University of Barcelona, Spain), Profes-sor Joe Tauritz (University of Twente, Netherlands), Professor YongwooKwon (Seoul National University, Korea), Professor Euisik Yoon (KAIST,Korea), Cimoo Song (Samsung, Korea), Jae-Yeong Park (LG, Korea), Pro-fessor Gary Fedder (Carnegie Mellon University) and Professor ThomasWeller (University of South Florida) have all sent high-resolution files of theirwork or quickly answered questions by email. Thank you.

This book was completed under the generous support of the U.S. taxpayersin terms of contracts from DARPA, NASA, Air Force Research Labs, ArmyResearch O‰ce, and the National Science Foundation. In particular, the sup-port of Dr. John Smith, DARPA, was instrumental in the development of low-loss RF MEMS phase shifters and in the early-stage reliability work in RFMEMS switches. Also, the University of Michigan supported this book bygiving me time o¤ when I needed it and by providing all the necessary com-puter and printing facilities. Professor George Haddad, the best chairman onecan ever dream of, and Professor Fawwaz Ulaby, have been a source of con-stant support at UoM. I am fortunate to have been part of two outstanding

xviii PREFACE

academic institutions: The California Institute of Technology and the Univer-sity of Michigan, Ann Arbor. They are quite di¤erent in their outlook on aca-demic life and their role in society; but at the end of the day, they both strive tobe the best institutions for their role.

On the personal side, no one can live a happy life without an abundance oflove shared with family and friends. There were many people in this countryand in the world who have been very kind to me and who have made mytransition from Lebanon to Europe and the United States as easy as it can be.No one understands the meaning of being an immigrant unless they are immi-grants themselves, and I can tell you, sometimes it is very hard. Robert LouisStevenson said: ‘‘No man is useless while he has a friend.’’ I could not agreemore.

My anchors and family in Pasadena, California (1982–1988) were, and stillare, Dave Rutledge and Dale Yee and their kids; George, Andre, Arianneand Marc Helou; Rick and Kiyomi Savage (now in Washington State); BillDawkins and his family (now in Washington, D.C.); Tim Kay and his family;and my roommates, Jamil Taher-Kheli, David Schweizer, and Zoya Popovic(now in Colorado).

My anchors and family in Ann Arbor, Michigan are Fawwaz, Mary Ann,Neda, Laith, Ziza, and Jean Ulaby; Emilie and the entire VanDeventer family;Mariam and Hedger Breed and their four boys; Eric and Cindy Kaldjian andtheir three children; Josef and Emily Kellndorfer; Jim Bardwell and UrsulaJacob; Walid Ali-Ahmad (now in San Francisco); Angelos Alexanian (now inBoston); and Edward and Natalie Surovell.

When I travel in the United States, I visit and sleep in the homes of WalidAli-Ahmad, Tim and Stephanie Kay, Ayman and Rania Fawwaz, and Chen-Yu and Wen-chi Chi in the Bay area, California; the Dawkins family in Davis,California; the Mollenkopf family in San Diego; the Helou, Rutledge, Weinreband Nahman families in Los Angeles; Jamil Taher-Kheli and Kathy Gregorzekin Los Angeles; Henri and Karma Chaoul in Chicago; Bob and Gini Pringle,Rick and Diana Kay, Zoya Popovic and Dana, all in Colorado; the Sweetfamily in Utah; Sandra and Greg Shreve, Tom and Sandy Budka, and AngelosAlexanian in Boston; the Shediac family in Baltimore; the Rutledge familyin Fort-Worth, Texas; the Weikle, Kerr, Crowe, and Mattauch families inVirginia; the Kormanyos family in Seattle; the Savage family in Richland,Washington; the Helou family in Puerto Rico; the Frantz family in Louisiana;Carolyn Frantz, Neda Ulaby, and the Dawkins family in Washington, D.C.;and my cousins in Indianapolis, Columbus, Cleveland, Pittsburgh, and Boston.Thank you for opening your homes to me. It is infinitely better to have a dinnerwith you and sleep at your place than to stay in a 5-star hotel.

When I travel outside of the United States, I feel at home in France at theFaloughi and the Audi families in Paris, and I feel welcome in Switzerland atthe Perkins family in Geneva. In the Netherlands, it is Margriet Maria JacobaVerhoogt and the entire Verhoogt family in Leiden and Zoeterwoude whomake me feel cherished and loved, and Peter DeMaagt and Sylvia Touw have

PREFACE xix

been good friends. In Greece, the Alexanian family in Athens have treated meas their son; and in Germany, the Altho¤ family in Gluckburg, the Kellndorferfamily in Trostberg, the Schmidhammer family in Munich, and the Schullerfamily in Aachen have all being very loving. Chris and Lynne Mann haveopened their home to me in England, and I must admit that I was taken bytheir Luke the destroyer. In Sweden, Herbert and Hannele Zirath and ErikKollberg have been wonderful friends. In Japan, Koji Mizuno in Sendai hasbeen a mentor and a father figure to me; and in Singapore, there is alwaysChris Koh (my travel companion) and his mother and sisters waiting for me.And I promise one day to visit Philip and Trich Stimson in Adelaide, Australia.

And in Lebanon, the Abdallah, Geagea, Fattouh, Malouf, Baraka, Nahman,Azoury, Soukkar, Dabbous, Hanna, Chaoul, Thabet, and Ali-Ahmad familiesalways extend a very warm welcome to a crazy expatriate from the UnitedStates. The love and support of my own family, Michel, Badiaa, Uncle Jean,Tante Lina, Nagy, Maria, Tania, Karim, and Camille, cannot be described inwords.

Finally, one night, after drinking a couple of beers with my students, JoeHayden said: ‘‘We talk a lot about you behind your back. But there is onething that you need to know. None of us would have stayed in graduate schoolhad it not been for you.’’ I would like for my students to know that I would nothave remained a professor if it were not for them.

Gabriel Michel Rebeizrebeiz@umich.edu

Ann Arbor, MichiganSeptember 2002

P.S. We all make mistakes. Please forgive us, and send your corrections to theaddress above.

xx PREFACE

Gabriel M. Rebeiz graduated from the California Insti-tute of Technology and is currently a Professor of Elec-trical Engineering and Computer Science at the Univer-sity of Michigan, Ann Arbor. He leads a research groupin RF MEMS and high-speed RF-IC electronics, an-tennas, and systems and has graduated over 20 Ph.D.students. Professor Rebeiz has been a consultant toIntel, Agilent, DARPA, ESA (European Space Agency),Lockheed Martin, Rockwell, Boeing, Samsung, Hitachi,Takata, and so on. He is a Fellow of the IEEE and hasreceived the IEEE 2000 Microwave Prize for his work onRF MEMS phase shifters. Professor Rebeiz is the 1998Amoco Professor, given to the best undergraduateteacher at the University of Michigan, and was alsoelected by the students as the Eta-Kappa-Nu Professor ofthe Year (1998). He lives in Ann Arbor, Michigan.

1INTRODUCTION: RF MEMS FORMICROWAVE APPLICATIONS

Gabriel M. Rebeiz and Guan-Leng Tan

1.1 THE BEGINNING OF RF MEMS

Microelectromechanical Systems (MEMS) have been developed since the 1970sfor pressure and temperature sensors, accelerometers, gas chromatographs, andother sensor devices. MEMS switches for low-frequency applications have alsobeen demonstrated in the early 1980s but remained a laboratory curiosity for along time. They are essentially miniature devices that use a mechanical move-ment to achieve a short circuit or an open circuit in a transmission line. Butin 1990–1991, under the support of DARPA (Defense Advanced ResearchProjects Agency), Dr. Larry Larson at the Hughes Research Labs in Malibu,California, developed the first MEMS switch (and varactor) that was specifi-cally designed for microwave applications [1]. However, and as usual with anyleap in technology, it was far from mature and had poor yield and virtually noreliability. Still, it demonstrated excellent performance up to 50 GHz, far betterthan anything that could be achieved with GaAs devices.

The initial results of Larson were so outstanding that they stirred the interestof several groups in the U.S. government; and by 1995, Rockwell ScienceCenter and Texas Instruments both had developed an outstanding RF MEMSswitch. The Rockwell switch was a metal-to-metal contact type, suitable forDC-60 GHz applications, while the Texas Instruments switch was a capacitivecontact switch, suitable for 10–120 GHz applications. The rest is history;by 1998, the University of Michigan, The University of California, Berkeley,Northeastern University, MIT Lincoln Labs, Columbia University, AnalogDevices, Northrup Grumman, and several other companies were actively pur-suing RF MEMS devices. By 2001, there were more than 30 companies work-

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ing in this area, including the giants of consumer electronics, such as Motorola,Analog Devices, Samsung, Omron, NEC, and ST-Microelectronics.

RF MEMS has seen an amazing growth in the past 10 years due to its im-mense commercial and defense potential. The reason is that while there weretremendous advances in GaAs HEMT devices (high-electron mobility transis-tor) and in silicon CMOS (complementary metal-oxide-semiconductor) tran-sistors, there was barely an advance in semiconductor switching diodes from1985 to 2000. In 1980, the cuto¤ frequency of silicon CMOS transistors wasaround 500 MHz and is currently around 100 GHz. Also in 1980, the cuto¤frequency of GaAs HEMT devices was 10–20 GHz and is now above 800GHz. However, the cuto¤ frequency of GaAs or InP p-i-n diodes improvedfrom around 500 GHz in 1985 to only 2000 GHz in 2001. Clearly, a radicalnew technology was needed to push the cuto¤ frequency of switching devices to40,000 GHz for low-loss applications, and this was achieved with RF MEMSdevices.

A survey of RF MEMS research leads to four distinct areas (Fig. 1.1):

. RF MEMS switches, varactors, and inductors that have been demonstratedfrom DC-120 GHz and are now a relatively mature technology. Except forthe micromachined inductors, MEMS switches and varactors move severalmicrometers when actuated.

. Micromachined transmission lines, high-Q resonators, filters, and antennasthat are suitable for 12–200 GHz. They are generally integrated on thin-dielectric membranes or use bulk micromachining of silicon, but are staticand do not move [2].

. FBAR (thin film bulk acoustic resonators) and filters that use acousticvibrations in thin films and that have demonstrated excellent performanceup to 3 GHz with very high Q (>2000). Recently, FBAR technology re-sulted in miniature low-loss filters for wireless applications [3].

. RF micromechanical resonators and filters that use the mechanical vibra-tions of extremely small beams to achieve high-Q resonance at 0.01–200MHz in vacuum. In this case, the mechanical movements are of the orderof tens of angstroms. Very-high-Q resonators (>8000) have been fabri-cated using this technology up to 200 MHz, but two-pole filters have onlybeen demonstrated up to 10 MHz. This technology still needs a lot ofwork before it is ready for commercial applications in miniature 0.1–3 GHz filters. Still, it may be an excellent solution for reference clockcircuits [4].

This book concentrates solely on RF MEMS switches, varactors, and in-ductors and does not cover any of the remaining topics in RF MEMS. Thisallows us to cover deeply all the areas associated with these devices, starting bymechanical and electrical modeling, to fabrication, reliability, and packaging,and concluding by their applications in high-isolation switch circuits, low-lossphase shifters, and tunable antennas, filters, and networks.

2 1 INTRODUCTION: RF MEMS FOR MICROWAVE APPLICATIONS

1.2 RF MEMS CONFIGURATIONS

There are two distinct parts to an RF MEMS switch or varactor: the actuation(mechanical) section and the electrical section (see Table 1.1). The forces re-quired for the mechanical movement can be obtained using electrostatic, mag-netostatic, piezoelectric, or thermal designs. The switches can also move verti-cally or laterally, depending on their layout. To date, electrostatic-type thermalswitches and magnetostatic switches have been demonstrated at 0.1–100 GHzwith high reliability (100 million to 60 billion cycles) and wafer-scale manu-facturing techniques. As for the electrical part, a MEMS switch can be placedin either series or shunt configurations and can be a metal-to-metal contactor a capacitive contact switch. This means that one can build at least 32(2� 2� 2� 4) di¤erent type of MEMS switches using di¤erent actuationmechanisms, contact, and circuit implementations.

Electrostatic actuation is the most prevalent technique in use today due to itsvirtually zero power consumption, small electrode size, thin layers used, rela-

Figure 1.1. (a) Agilent FBAR [3], (b) University of Michigan micromachined membranefilter [2], (c) SEM of Radant MEMS switch [5], and (d) a two-pole 7-MHz filter basedon micromechanical resonators [4].

1.2 RF MEMS CONFIGURATIONS 3

tively short switching time, 50–200 mN of achievable contact forces, and thepossibility of biasing the switch using high-resistance bias lines. However, inmany cases, it requires an actuation voltage of 30–80 V, and this necessitatesthe use of CMOS upconverters to raise the input 3–5 V control voltage tothe actuation voltage. In many designs, a thermal actuation is coupled with anelectrostatic (voltage) hold, or a magnetostatic actuation (current in a coil) iscoupled with a permanent magnetic field. Both result in virtually zero powerconsumption once the switch is actuated. Still, they require a substantialamount of current for the switching cycle and, therefore, must be biased using

TABLE 1.1. Di¤erent Configurations of MEMS Devices

Actuation Mechanism

Voltage(V)

Current(mA)

Power(mW) Size

SwitchingTime (ms)

ContactForce(mN)

Electrostatic 20–80a 0 0 Small 1–200 50–1000Thermal 3–5 5–100 0–200b Largec 300–10,000 500–4000Magnetostatic 3–5 20–150 0–100b Medium 300–1,000 50–200Piezoelectric 3–20 0 0 Medium 50–500 50–200

Movement

Vertical Typically results in small size devicesLateral Typically results in large size devices

Contact Type (Switches only)

Metal-to-Metal DC-60 GHzCapacitived 6–120 GHz

Circuit Configuration

Series DC-50 GHz with metal-to-metal contact and low up-statecapacitance.

10–50 GHz with capacitive contactd and low up-state capacitance.

Shunt DC-60 GHz with metal-to-metal contact and low inductance toground.

10–200 GHz with capacitive contactd and low inductance toground.

aVoltage can be reduced to 5 V using low spring constant designs, but at the expense of stiction and

reliability.

bPower is virtually zero with an electrostatic or permanent magnetic field hold.

cSize can be made quite small with the use of a vertical design.

dCan be extended to 2 GHz using high-er dielectrics.

4 1 INTRODUCTION: RF MEMS FOR MICROWAVE APPLICATIONS

low-resistance (gold or Al) lines. The low-resistance lines couple to the micro-wave t-lines; therefore, careful design must be done for complicated switchingnetworks requiring a large number of switches and bias lines.

1.3 COMPARISON OF MEMS SWITCHES WITH GaAs PIN DIODEAND TRANSISTOR SWITCHES

Table 1.2 shows a comparison between electrostatic MEMS switches and GaAsPIN diode and transistor switches. It is hard to make an accurate comparisonover a wide range of RF power levels since the size of diode and transistorswitches can be easily increased for high power applications. This, in turn, hasa substantial e¤ect on the switch isolation, insertion loss, switching speed, andpower consumption. Still, it is evident that MEMS switches, with their ex-tremely low up-state capacitance (series switches) and their very high capaci-tance ratio (capacitance contact switches), o¤er a far superior performancecompared to solid-state switches for low to medium power applications (Fig.1.2).

1.4 APPLICATION AREAS OF RF MEMS

The question is: What do you do with a device that is relatively small, has vir-tually no mass and is not sensitive to acceleration, consumes no DC power, can

TABLE 1.2. Performance Comparison of FETs, PIN Diode, and RF MEMS

Electrostatic Switches

Parameter RF MEMS PIN FET

Voltage (V) 20–80 G3–5 3–5Current (mA) 0 3–20 0Power consumptiona (mW) 0.05–0.1 5–100 0.05–0.1Switching time 1–300 ms 1–100 ns 1–100 nsCup (series) (fF) 1–6 40–80 70–140Rs (series) (W) 0.5–2 2–4 4–6Capacitance ratiob 40–500b 10 n/aCuto¤ frequency (THz) 20–80 1–4 0.5–2Isolation (1–10 GHz) Very high High MediumIsolation (10–40 GHz) Very high Medium LowIsolation (60–100 GHz) High Medium NoneLoss (1–100 GHz) (dB) 0.05–0.2 0.3–1.2 0.4–2.5Power handling (W)

be manufactured on low-cost silicon or glass substrates, and has a cuto¤ fre-quency which is 30–50 times better than anything that can be attained withGaAs technology? The answer is: A lot. First, it results in outstanding isolationand insertion loss at microwave frequencies and can replace the GaAs switchesin cellular telephones resulting in much lower DC-power consumption andlonger battery life. It can also be used in phase shifters, which are essential formodern telecommunication, automotive, and defense applications, in low-losstunable circuits (matching networks, filters, etc.), and in high-performance in-strumentation systems. Table 1.3 summarizes the application areas of RFMEMS devices and the lifetime and number of cycles required. We have alsosummarized some of the subsystems and circuits that can benefit from thistechnology in Table 1.3.

1.5 CASE STUDIES IN RF MEMS

This section presents several case studies in RF MEMS devices for switchingnetworks, portable wireless systems, phased arrays, and low-noise oscillatorsand amplifiers. It is evident that RF MEMS can be readily used in defense orhigh-value commercial applications (satellite systems, base stations, etc.). How-ever, their use in low-cost commercial systems is still under investigation due totheir relatively high cost resulting from the hermetic packaging requirements ofRF MEMS switches and filters.

1.5.1 Case 1: RF MEMS in Switching Networks

Switching networks are used in virtually every communication system andinclude SPNT (single-pole N-throw) switches for filter or amplifier selection,

Figure 1.2. Simulated isolation of MEMS, PIN, and FET series switches.

6 1 INTRODUCTION: RF MEMS FOR MICROWAVE APPLICATIONS