Optimal Synthesis Methods for MEMS

THE KLUWER INTERNATIONAL SERIESIN MICROSYSTEMS

Consulting Editor: Stephen SenturiaMassachusetts Institute 01Technology

Volumes published InMICROSYSTEMS

Optimal Synthesis Methods for MEMSG.K. AnanthasureshISBN: 1-4020-7620-7

Mlcromachlned MirrorsRobert A. ConantISBN: 1-4020-7312-7

Heat Convection In Micro DuctsYitshak ZoharISBN: 1-4020-7256-2

Materials & Process Integration for MEMSFrancis E.H. TayISBN 1-4020-7175-2

Microfluldlcs and BloMEMS ApplicationsFrancis E.H. TayISBN: 1-4020-7237-6

Optical Microscanners and Mlcrospectrometers Using Thermal Bimorph ActuatorsGerhard Lammel, Sandra Schweizer, Philippe RenaudISBN 0-7923-7655-2,

Scanning Probe LithographyHyongsok T. Soh, Kathryn Wilder Guarini, Calvin F. QuateISBN 0-7923-7361-8

Microsystem DesignStephen SentunaISBN: 0-7923-7246-8

Mlcrofabrlcatlon In Tissue Engineering and Bloartlflclal OrgansSangeeta BhatiaISBN 0-7923-8566-7

Mlcroscale Heat Conduction In Integrated Circuits and Their Constituent FilmsY. Sungtaek Ju, Kenneth E. GoodsonISBN 0-7923-8591-8

Mlcromachlned Ultrasound-Based Proximity SensorsMark R. Hornung, Oliver BrandISBN 0-7923-850S-X

Bringing Scanning Probe Microscopy Up to SpeedStephen C. Minne, Scott R. Manalis, Calvin F. QuateISBN 0-7923-8466-

Microcantilevers for Atomic Force Microscope Data StorageBenjamin W. ChuiISBN 0-7923-835S-3

Optimal Synthesis Methods for MEMS

G.K. Ananthasuresh University of Pennsylvania

~·

'' SPRINGER SCIENCE+BUSINESS MEDIA, LLC

Library of Congress Cataloging-in-Publication CIP info or: Ti tie: Optimal Synthesis Methods for MEMs Author (s): G.K. Ananthasuresh ISBN 978-1-4613-5101-6 ISBN 978-1-4615-0487-0 (eBook) DOI 10.1007/978-1-4615-0487-0

Copyright© 2003 bySpringer Science+Business Media New York Originally published by Kluwer Academic Publishers in 2003 Softcover reprint of the hardcover 1st edition 2003

AU rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photo-copying, microfilming, recording, or otherwise, without the prior written permission of the publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Permissions for books published in the USA: permissions@wkap. corn Permissions for books published in Europe: permissions@wkap.nl Printed on acid-free paper.

About the Cover: The cover page shows four examples of synthesized designs (top row) and the corresponding microfabricated prototypes (bottom row).

The synthesis solutions were obtained, respectively, by A. Saxena and G. K. Ananthasuresh (University of Pennsylvania), E.C.N. Silva and N. Kikuchi (University of Michigan), W. Ye and S. Mukherjee (Cornell University), and O. Sigmund (Technical University of Denmark).

The prototypes in the bottom row were microfabricated, respectively, by A. Saxena and G. K. Ananthasuresh using MCNC MUMPs, E.C.N. Silva and G. Nader (University of Săo Paulo, Brazii), W. Ye and S. MukheJjee (SCREAM process), and J. Jonsmann and S. Bouwstra (MIC, Technical University of Denmark).

Optimal Synthesis Methods for MEMS

Table of Contents

ForewordContributorsPreface

Chapter 1 INTRODUCTION

ixxixiii

1

I.2.2.13.3.14.5.

Design ofMicroelectromechanical SystemsSynthesis vs. AnalysisAn example: mode shape synthesis of a barOptimization as a synthesis toolComponents of an optimal synthesis procedureContents of the chaptersClosure

13458911

Chapter 2 SYNTHESIS FOR MECHANICAL BEHAVIOR 13

I.2.3.3.13.1.13.1.23.1.33.23.2.13.2.23.2.34.4.14.24.2.15.

IntroductionSynthesis of beam-like structuresTopology SynthesisFlexibility-stiffness formulationAn accelerometer with a built-in displacement amplifierA micromechanical AND logic gateSynthesized solutions as design aidsFlexibility-strength formulationModeling stress constraintsSensitivity analysis for stress constraintsAn exampleSynthesis for dynamic attributesSynthesis for desired natural frequenciesSynthesis for desired normal mode shapesMode shape synthesis for beamsConclusions

13151618202125252627313131322137

Chapter 3 SYNTHESIS OF ELECTROSTATICALLY ACTUATED MEMS 43

1.2.3.3.13.23.34.4.14.1.14.1.24.1.34.24.2.1

IntroductionGoverning EquationsShape Synthesis of Electrostatically Driven ActuatorsSimulation of the driving forceSensitivity analysisOptimizationAn Example: Variable Comb-drive Actuators2-D DesignsDriving forceSensitivity analysisThe inverse problem3-D DesignDriving force

43484950525455555657596465

4.2.24.2.34.34.3.14.3.25.

Sensitivity analysisThe inverse problemFabrication of a shaped motor - a demonstrationSCREAM I processTest resultsClosure

666770727576

Chapter 4 SYNTHESIS METHODS FOR ELECTROTHERMAL ACTUATION79

1.2.2.12.22.32.42.53.3.13.23.34.4.14.24.35.6.6.16.26.36.46.57.8.8.18.28.39.

IntroductionGeneralization of the BasiC electro-thermal actuatorChanging dimensionsChanging material propertiesChanging thermal boundary conditionsChanging electrical boundary conditionsElectro-thermal-compliant designsModelingElectrical analysisThermal analysisElastic analysisSynthesisDesign parameterizationProblem statementSolution procedureNumerical examplesAlternative implementation using "line elements"Line elementsFinite element modeling with line elementsProblem formulationSensitivity analysis and solution procedureNumerical examples with line elementsAdvanced exampleMicroFabricationPennSOILExcimer laser micromachiningElectro-plating combined with photolithographyClosure

79818282838385868888899091939395102102103105106109110112113114115117

Chapter 5 SYNTHESIS WITH PIEZOELECTRIC ACTUATION 121

1.2.3.4.4.14.24.34.44.54.5.14.5.24.65.

IntroductionBackground Theory for PiezoelectricityFEM Applied to PiezoelectricityFlextensional Actuator DesignMean TransductionMaterial ModelFormulation of Optimization ProblemSensitivity AnalysisExamplesAMultilayer ActuatorA Flextensional GripperManufactured PrototypesConclusion

121124129131133136138141142143145148149

Chapter 6 SYNTHESIS OF PIEZOCOMPOSITES 155

1.1.11.1.11.1.22.3.3.14.4.14.1.14.1.24.25.

Piezocomposite DesignPerformance Characteristics of Piezocomposite MaterialsLow-Frequency ApplicationsHigh-Frequency ApplicationsHomogenization MethodPiezocomposite Design ProblemFormulation ofOptimization ProblemExamplesPiezocomposite ManufacturingMicrofabrication by Coextrusion TechniqueStereolithography TechniqueExperimental ResultsConclusions

155157158160160170173177182183185186188

Chapter 7 SYNTHESIS OF PERIODIC MICRO MECHANISMS

1. Introduction2. Numerical homogenization, FE modeling, and sensitivity analysis3. Formulation ofthe problem4. Numerical implementation5. Examples5.1 Shearing materials5.2 Negative Poisson's ratio matrials5.3 Extremal thermal expansion coefficient5.4 Piezoelectric transducers6. Wave propagation6.1 Modeling of wave propagation7. Concluding remarks

Chapter 8 PROCESS SYNTHESIS1. Introduction2. State-space representation3. Planar devi

4.24.34.44.54.65.6.

EtchesDopingGenerating potential mask openingsSubdivision of mask openingsValidating Mask OpeningsExamplesConclusions

281281284285286290292

Chapter 10 SYSTEM·LEVEL SYNTHESIS 297

1.2.2.12.22.2.12.2.22.32.43.4.4.14.25.

Index

MEMS Design representationsSynthesis MethodologyDesign VariablesConstraintsGeometric ConstraintsFunctional ConstraintsSynthesis FormulationLayout GenerationPerformance ModelsSynthesis ResultsSynthesis with In-plane Mode Separation ConstraintsSynthesis with Out-of-plane Mode Separation ConstraintsSummary

297300300302302304306308308311311312313

317

FOREWORD

The field of "microelectromechanical systems," or "MEMS," hasgradually evolved from a "discipline" populated by a small group ofresearchers to an "enabling technology" supporting a variety of products insuch diverse areas as mechanical and inertial sensors, optical projectiondisplays, telecommunications equipment, and biology and medicine. Criticalto the success of these products is the ability to design them, and thisinvariably involves detailed modeling of proposed designs. Over the pasttwenty years, such modeling has become increasingly sophisticated, with fullsuites of MEMS-oriented computer-aided-design tools now availableworldwide.

But there is another equally important side to the design process -figuring out what to build in the first place. In my own book, MicrosystemDesign, I chose to emphasize the modeling aspect of design. The task offiguring out what to build was defined by a vague step called "creativethinking." I used practical product examples to illustrate the many subtlecharacteristics of successful designs, but I made no attempt to systematizethe generation of design proposals or optimized designs. That systemizationis called "synthesis," which is the subject of this book.

On a personal note, I have long recognized the need for progress on thesynthesis problem. In fact, when I heard a graduate student from theUniversity of Michigan present a paper on the constrained optimization ofcompliant microstructures at the 1994 Solid-State Sensors and ActuatorsWorkshop at Hilton Head, I immediately offered that graduate student apostdoc position in my group. The name of that student was G. K.Ananthasuresh. Clearly, his interest in the synthesis problem has beenmaintained since that time, and, in putting together this volume ofcontributions from leaders in the field, he is making an important resourceavailable to the MEMS designer. I am pleased to recommend this book tothe MEMS community.

Stephen D. SenturiaBrookline, Massachusetts, U. S. A.April 9, 2003

CONTRIBUTING AUTHORS

G. K. AnanthasureshAssociate Professor of Mechanical Engineering and Applied Mechanics,University of Pennsylvania, Philadelphia, PA 19104-6315, U.S.A.gksuresh@seas.upenn.edu

Edwin. T. CarlenMEMS Development EngineerComing Intellisense, Wilmington, MA 01887, U. S. A.carlenet@corning.com

Gary K. FedderProfessor of Electrical and Computer Engineering, and RoboticsCarnegie Mellon University, Pittsburgh, PA 15213, U. S. A.fedder@ece.cmu.edu

Carlos. H. MastrangeloVice President of EngineeringComing Intellisense, Wilmington, MA 01887, U. S. A.mastrangch@corning.com

Subrata MukherjeeProfessor of Theoretical and Applied Mechanics and Mechanical andAerospace Engineering, Cornell University, Ithaca, NY 14853, U.S.A.Sm85@cornell.edu

Tarnal MukherjeeSenior Research Scientist, Electrical and Computer EngineeringCarnegie Mellon University, Pittsburgh, PA 15213, U. S. A.tarnal@ece.cmu.edu

RadhaSarrnaAdjunct Associate Professor of Mechanical EngineeringUniversity of Michigan, Ann Arbor, MI 48109, U. S. A.radha@umich.edu

Anuparn SaxenaAssistant Professor of Mechanical EngineeringIndian Institute of Technology, Kanpur, Indiaanupams@iitk.ac.in

Ole SigmundProfessor, Dr. Techn., of Department of Mechanical EngineeringTechnical University of Denmark, Lyngby, DenmarkSigmund@mek.dtu.dk

Emilio Carlos Nelli SilvaAssistant Professor of Mechatronics and Mechanical Systems Engineering,Polytechnic School from University of Sao Paulo, SP 05508-900, Brazil.ecnsilva@usp.br

WenjingYeAssistant Professor of Woodruff School of Mechanical EngineeringGeorgia Institute of Technology, Atlanta, GA 30332-0405, U.S.A.wenjing.ye@me.gatech.edu

PREFACE

A new technology usually begins with experimentation-the process ofbuilding prototypes to demonstrate the feasibility of a novel concept or anew technique. This is immediately followed by modeling as one wants toknow how well the device works before it is built so that expensiveexperimentation can be reduced. These two stages have already been passedby the microsystems technology as is evident from the variety of devices andthe number of modeling software companies that exist today. Modelingtechniques and tools enable analysis of an existing design. The design itselfis largely dependent on the experience, expertise, and the creativity of thedesigner. Synthesis techniques have the potential to reduce this reliance onthe human designer by automatically generating designs for user-specifiedrequirements. Synthesis methods are especially useful for a MEMS designergiven the multi-disciplinary nature of an integrated MEMS device. Softwaretools based on synthesis techniques enable even a novice designer createnew solutions. They also aid the creativity of even experienced designers.This book is a compilation of some of the synthesis efforts in the MEMSarea. It is by no means an exhaustive collection and any omissions areinadvertent.This book is a result of the group effort by many colleagues who have

generously contributed their time to write the chapters. I thank all of themfor their valuable part in this effort. Several others who have madesignificant contributions, as well as the sources of funding are acknowledgedin each chapter. I am grateful to Professor Stephen D. Senturia for his adviceand encouragement over the years, and for suggesting the idea of bringingout a book on the synthesis methods for MEMS.As can be seen in all the chapters, the authors have built prototypes based

on their synthesis solutions. This shows their commitment and enthusiasm tosee these techniques used in real applications. Considerable details ofimplementation are included in all the chapters to facilitate easy application.Interested readers may contact the authors or the editor for further details orto report comments, suggestions, and errors. The methods described here canbe enhanced to include many more practical constraints. Thesedevelopments will be expedited as MEMS designers begin to use them inpractice. Therefore, I close with the slogan-DESIGNERS WANTED.

G. K. AnanthasureshPhiladelphia, Pennsylvania, U. S. A.