MICROSYSTEM DESIGN

ABOUT THE COVER

The author gratefully acknowledges the cover photograph by Felice Frankel,Artist in Residence at the Massachusetts Institute of Technology and coauthorof On the Surface of Things: Images of the Extraordinary in Science.

This particular image, taken with Nomarski optics, presents a wafer-bondedpiezoresistive pressure sensor. It is fabricated in the sealed-cavity processdeveloped by Professor Martin Schmidt of the Massachusetts Institute of Tech-nology with his graduate students, Lalitha Parameswaran and Charles Hsu.The piezoresistors are clearly visible, and the slight contrast across the centraldiaphragm region shows that the diaphragm is actually slightly bent by thepressure difference between the ambient and the sealed cavity beneath.

MICROSYSTEM DESIGN

Stephen D. SenturiaMassachusetts Institute of Technology

KLUWER ACADEMIC PUBLISHERS NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW

eBook ISBN: 0-306-47601-0Print ISBN: 0-7923-7246-8

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Print ©2001 Kluwer Academic Publishers

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Created in the United States of America

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Dordrecht

To Bart Weller,for his generosity, and

To Angelika Weller,for her indomitable spirit

Contents

ForewordPrefaceAcknowledgments

xviixxixxv

Part I GETTING STARTED

1.

2.

3.

33356789

12

15151516171921222426

2929303034

INTRODUCTION1.1

1.21.31.4

1.1.11.1.21.1.31.1.4

What are they?How are they made?What are they made of?How are they designed?

Microsystems vs. MEMS

Markets for Microsystems and MEMSCase StudiesLooking Ahead

AN APPROACH TO MEMS DESIGN2.1

2.2

2.32.4

Design: The Big Picture2.1.12.1.22.1.3

Device CategoriesHigh-Level Design IssuesThe Design Process

Modeling Levels2.2.12.2.2

Analytical or Numerical?A Closer Look

Example: A Position-Control SystemGoing Forward From Here

MICROFABRICATION3.13.2

OverviewWafer-Level Processes3.2.13.2.2

SubstratesWafer Cleaning

viii MICROSYSTEM DESIGN

3437384247505054555767717477

7979798385858691929798

103103104106106106108109114114116116117118119120

125

3.2.33.2.43.2.53.2.63.2.7

Oxidation of SiliconLocal OxidationDopingThin-Film DepositionWafer Bonding

3.3

3.4

Pattern Transfer3.3.13.3.23.3.33.3.43.3.53.3.63.3.7

Optical LithographyDesign RulesMask MakingWet EtchingDry EtchingAdditive Processes: Lift-OffPlanarization

Conclusion

4. PROCESS INTEGRATION4.1

4.2

4.3

4.4

4.1.14.1.2

4.2.14.2.2

4.3.14.3.2

A Bulk-Micromachined Diaphragm Pressure SensorA Surface-Micromachined Suspended Filament

Moving On

Sample Process Flows

Developing a ProcessA Simple Process FlowThe Self-Aligned Gate: A Paradigm-Shifting Process

Basic Principles of Process DesignFrom Shape to Process and Back AgainProcess Design Issues

Part II MODELING STRATEGIES

LUMPED MODELING5.15.25.3

5.4

5.5

5.6

IntroductionConjugate Power VariablesOne-Port Elements5.3.15.3.25.3.35.3.4

PortsThe Variable-Assignment ConventionsOne-Port Source ElementsOne-Port Circuit Elements

5.4.1 Kirchhoff’s LawsCircuit Connections in the Convention

Formulation of Dynamic Equations5.5.15.5.2

Complex ImpedancesState Equations

Transformers and Gyrators5.6.15.6.2

Impedance TransformationsThe Electrical Inductor

5.

6. ENERGY-CONSERVING TRANSDUCERS

Contents ix

125125126127129130131132134137139142145

149149150151152157158160164164165166169173178178

183183184184185186188189190191193195196196

6.16.2

6.36.4

6.56.66.7

7.17.2

7.3

Part III DOMAIN-SPECIFIC DETAILS

8.

7. DYNAMICS

8.18.2

8.3

8.48.5

6.2.16.2.2

6.4.16.4.26.4.36.4.4

7.2.17.2.27.2.37.2.47.2.5

7.3.17.3.27.3.37.3.47.3.57.3.67.3.7

8.2.18.2.28.2.38.2.48.2.58.2.68.2.7

8.3.1

IntroductionThe Parallel-Plate Capacitor

Charging the Capacitor at Fixed GapCharging the Capacitor at Zero Gap, then Lifting

The Two-Port CapacitorElectrostatic Actuator

Charge ControlVoltage ControlPull-InAdding Dynamics to the Actuator Model

The Magnetic ActuatorEquivalent Circuits for Linear TransducersThe Position Control System – Revisited

IntroductionLinear System Dynamics

Direct IntegrationSystem FunctionsFourier TransformSinusoidal Steady StateEigenfunction Analysis

Nonlinear DynamicsFixed Points of Nonlinear SystemsLinearization About an Operating PointLinearization of the Electrostatic ActuatorTransducer Model for the Linearized ActuatorDirect Integration of State EquationsResonators and OscillatorsAnd Then There’s Chaos...

ELASTICITYIntroductionConstitutive Equations of Linear Elasticity

StressStrainElastic Constants for Isotropic MaterialsOther Elastic ConstantsIsotropic Elasticity in Three DimensionsPlane StressElastic Constants for Anisotropic Materials

Thermal Expansion and Thin-Film StressOther Sources of Residual Thin-Film Stress

Selected Mechanical Property DataMaterial Behavior at Large Strains

x MICROSYSTEM DESIGN

197

201201201203203205207207207208211213216218219220222222226231235237

239240243244247249249253254255256257259260260263

267267267269271

8.5.1 Plastic Deformation

9. STRUCTURES9.19.2

9.3

9.49.5

9.6

9.79.8

9.2.19.2.29.2.3

9.3.19.3.29.3.39.3.49.3.59.3.6

9.5.1

9.6.19.6.29.6.3

10.10.110.210.3

10.4

10.5

10.3.1

10.4.110.4.210.4.310.4.410.4.510.4.610.4.7

10.5.110.5.2

11.111.211.311.4

OverviewAxially Loaded Beams

Beams With Varying Cross-sectionStatically Indeterminate BeamsStresses on Inclined Sections

Bending of BeamsTypes of SupportTypes of LoadsReaction Forces and MomentsPure Bending of a Transversely Loaded BeamDifferential Equation for Beam BendingElementary Solutions of the Beam Equation

Anticlastic CurvatureBending of Plates

Plate in Pure BendingEffects of Residual Stresses and Stress Gradients

Stress Gradients in CantileversResidual Stresses in Doubly-Supported BeamsBuckling of Beams

Plates With In-Plane StressWhat about large deflections?

ENERGY METHODSElastic EnergyThe Principle of Virtual WorkVariational Methods

Properties of the Variational Solution

Rayleigh-Ritz MethodsEstimating Resonant FrequenciesExtracting Lumped-Element Masses

11. DISSIPATION AND THE THERMAL ENERGY DOMAINDissipation is EverywhereElectrical ResistanceCharging a CapacitorDissipative Processes

Large Deflections of Elastic StructuresA Center-Loaded Doubly-Clamped BeamCombining Variational Results with SimulationsThe Uniformly Loaded Doubly-Clamped BeamResidual Stress in Clamped StructuresElastic Energy in Plates and MembranesUniformly Loaded Plates and MembranesMembrane Load-Deflection Behavior

Contents xi

272275275277278279279281282286286287288289290291293295296296

299299299300301303305307307308309311

317317318318319320322323324324325326327

11.5

11.6

11.7

11.8

11.9

13.113.2

13.3

The Thermal Energy Domain11.5.111.5.211.5.3

11.6.111.6.211.6.311.6.4

11.7.111.7.211.7.311.7.411.7.5

11.8.111.8.211.8.3

12.112.212.312.4

12.512.612.712.812.912.10

13.2.113.2.213.2.313.2.413.2.513.2.613.2.713.2.8

13.3.1

The Heat-Flow EquationBasic Thermodynamic IdeasLumped Modeling in the Thermal Domain

Self-Heating of a ResistorTemperature Coefficient of ResistanceCurrent-source driveVoltage-source driveA Self-Heated Silicon Resistor

Other Dissipation MechanismsContact FrictionDielectric lossesViscoelastic lossesMagnetic LossesDiffusion

Irreversible Thermodynamics: Coupled FlowsThermoelectric Power and ThermocouplesThermoelectric Heating and CoolingOther Coupled-Flow Problems

Modeling Time-Dependent Dissipative Processes

12.

13.

LUMPED MODELING OF DISSIPATIVE PROCESSESOverviewThe Generalized Heat-Flow EquationThe DC Steady State: The Poisson EquationFinite-Difference Solution of the Poisson Equation12.4.1 Temperature Distribution in a Self-Heated ResistorEigenfunction Solution of the Poisson EquationTransient Response: Finite-Difference ApproachTransient Response: Eigenfunction MethodOne-Dimensional ExampleEquivalent Circuit for a Single ModeEquivalent Circuit Including All Modes

FLUIDSWhat Makes Fluids Difficult?Basic Fluid Concepts

ViscosityThermophysical PropertiesSurface TensionConservation of MassTime Rate of Change of MomentumThe Navier-Stokes EquationEnergy ConservationReynolds Number and Mach Number

Incompressible Laminar FlowCouette Flow

328331332332334339340343344347348348349

353353353354355357363364365365367371371372373376379381381383384384387387388389390391391393

xii MICROSYSTEM DESIGN

13.3.213.3.313.3.4

Poiseuille FlowDevelopment Lengths and Boundary LayersStokes Flow

13.4

13.5

Squeezed-Film Damping

13.5.113.5.213.5.313.5.413.5.513.5.613.5.7

13.4.1 Rigid Parallel-Plate Small-Amplitude MotionElectrolytes and Electrokinetic Effects

Ionic Double LayersElectroosmotic FlowElectrophoresisDiffusion EffectsPressure EffectsMixingModeling of Electrokinetic Systems

Part IV CIRCUIT AND SYSTEM ISSUES

14. ELECTRONICS14.114.2

14.314.414.514.614.7

14.8

14.9

IntroductionElements of Semiconductor Physics14.2.114.2.2

Equilibrium Carrier ConcentrationsExcess Carriers

The Semiconductor DiodeThe Diffused ResistorThe PhotodiodeThe Bipolar Junction TransistorThe MOSFET14.7.114.7.214.7.3

Large-Signal Characteristics of the MOSFETMOSFET CapacitancesSmall-Signal Model of the MOSFET

MOSFET Amplifiers14.8.114.8.214.8.314.8.4

The CMOS InverterLarge-Signal Switching SpeedThe Linear-Gain RegionOther Amplifier Configurations

Operational AmplifiersDynamic Effects14.10

14.11

14.12

Basic Op-Amp Circuits14.11.114.11.214.11.314.11.414.11.514.11.6

Inverting AmplifierShort Method for Analyzing Op-Amp CircuitsNoninverting AmplifierTransimpedance AmplifierIntegratorDifferentiator

Charge-Measuring Circuits14.12.114.12.2

Differential Charge MeasurementSwitched-Capacitor Circuits

397397397398399400405407408409410411411412413417418420

425425426427428429430431433434434435435436436436438439440441442445446447447

xiiiContents

15.

16.

FEEDBACK SYSTEMS15.115.215.3

IntroductionBasic Feedback ConceptsFeedback in Linear Systems15.3.115.3.215.3.315.3.415.3.515.3.615.3.715.3.8

Feedback AmplifiersExample: The Position ControllerPID ControlThe Effect of Amplifier BandwidthPhase MarginNoise and DisturbancesStabilization of Unstable SystemsControllability and Observability Revisited

15.4 Feedback in Nonlinear Systems15.4.1 Quasi-static Nonlinear Feedback Systems

15.5 Resonators and Oscillators15.5.115.5.215.5.3

Simulink ModelThe (Almost) Sinusoidal OscillatorRelaxation Oscillation

NOISE16.116.2

16.3

16.4

16.5

16.6

16.7

IntroductionThe Interference Problem16.2.116.2.216.2.3

ShieldsGround LoopsGuards

Characterization of Signals16.3.1 Amplitude-Modulated SignalsCharacterization of Random Noise16.4.116.4.216.4.316.4.416.4.5

Mean-Square and Root-Mean-Square NoiseAddition of Uncorrelated SourcesSignal-to-Noise RatioSpectral Density FunctionNoise in Linear Systems

Noise Sources16.5.116.5.216.5.316.5.416.5.5

Thermal NoiseNoise BandwidthShot NoiseFlicker NoiseAmplifier Noise

Example: A Resistance Thermometer16.6.116.6.216.6.3

Using a DC sourceModulation of an AC CarrierCAUTION: Modulation Does Not Always Work

Drifts

xiv MICROSYSTEM DESIGN

453453454455459461461462463467

469469470471472473474477480481481483485488492493494

497497498500502507510511512513516518520523525

531

Part V CASE STUDIES

17.

18.

19.

20.

PACKAGING17.117.217.317.4

17.4.117.4.217.4.317.4.417.4.5

18.118.2

18.3

18.2.118.2.218.2.318.2.418.2.518.2.6

18.3.118.3.218.3.318.3.418.3.518.3.618.3.7

19.119.219.3

19.4

19.5

19.3.119.3.219.3.319.3.419.3.5

19.4.119.4.219.4.319.4.4

Introduction to the Case StudiesPackaging, Test, and CalibrationAn Approach to PackagingA Commercial Pressure-Sensor Case Study

Device ConceptSystem PartitioningInterfacesDetailsA Final Comment

A PIEZORESISTIVE PRESSURE SENSORSensing PressurePiezoresistance

Analytic Formulation in Cubic MaterialsLongitudinal and Transverse PiezoresistancePiezoresistive Coefficients of SiliconStructural ExamplesAveraging over Stress and Doping VariationsA Numerical Example

The Motorola MAP SensorProcess FlowDetails of the Diaphragm and PiezoresistorStress AnalysisSignal-Conditioning and CalibrationDevice NoiseRecent Design ChangesHigher-Order Effects

A CAPACITIVE ACCELEROMETERIntroductionFundamentals of Quasi-Static AccelerometersPosition Measurement With Capacitance

Circuits for Capacitance MeasurementDemodulation MethodsChopper-Stabilized AmplifiersCorrelated Double SamplingSignal-to-Noise Issues

A Capacitive Accelerometer Case StudySpecificationsSensor Design and ModelingFabrication and PackagingNoise and Accuracy

Position Measurement With Tunneling Tips

ELECTROSTATIC PROJECTION DISPLAYS

Contents xv

531536536537541544544544548550558

561561561563565566567567570570571573575577578579582592594595598599602602

605605606606610611611614616618

20.120.2

20.3

20.4

20.5

21.

22.

20.2.120.2.2

20.3.1

20.4.120.4.220.4.3

21.121.221.3

21.4

21.5

21.3.121.3.221.3.321.3.4

21.4.121.4.221.4.321.4.421.4.5

21.5.121.5.221.5.321.5.421.5.521.5.621.5.721.5.821.5.9

22.122.2

22.3

22.4

22.2.122.2.2

22.3.122.3.2

22.4.1

IntroductionElectromechanics of the DMD Device

Electrode StructureTorsional Pull-in

Electromechanics of Electrostatically Actuated BeamsM-Test

The Grating-Light-Valve DisplayDiffraction TheoryDevice Fabrication and PackagingQuantitative Estimates of GLV Device Performance

A Comparison

A PIEZOELECTRIC RATE GYROSCOPEIntroductionKinematics of RotationThe Coriolis Rate Gyroscope

Sinusoidal Response FunctionSteady RotationResponse to Angular AccelerationsGeneralized Gyroscopic Modes

PiezoelectricityThe Origin of PiezoelectricityAnalytical Formulation of PiezoelectricityPiezoelectric MaterialsPiezoelectric ActuationSensing with Piezoelectricity

A Quartz Rate Gyroscope Case StudyElectrode StructuresLumped-Element Modeling of Piezoelectric DevicesQRS Specifications and PerformanceA Quantitative Device ModelThe Drive ModeSense-Mode Displacement of the Drive TinesCoupling to the Sense TinesNoise and Accuracy ConsiderationsClosing Comments

DNA AMPLIFICATIONIntroductionPolymerase Chain Reaction (PCR)

Elements of PCRSpecifications for a PCR System

Microsystem Approaches to PCRBatch SystemPCR Flow System

Thermal Model of the Batch ReactorControl Circuit and Transient Behavior

xvi MICROSYSTEM DESIGN

621625

629629630632632634639639641642643643644645646648

651651657657657657658659663

665

677

22.522.6

Thermal Model of the Continuous Flow ReactorA Comparison

23. A MICROBRIDGE GAS SENSOR23.123.223.3

23.4

23.5

23.623.7

OverviewSystem-Level IssuesFirst-Order Device and System Models23.3.123.3.2

Filament CharacteristicsResistance-Control System

A Practical Device and Fabrication Process23.4.123.4.223.4.3

Creating the FilamentHigh-Temperature Bond PadsCatalyst Coating

Sensor Performance23.5.123.5.223.5.3

Demonstration of Hydrogen DetectionMass-Transport-Limited OperationReaction-Rate-Limited Operation

Advanced ModelingEpilogue

AppendicesA– Glossary of NotationB– Electromagnetic Fields

B.1B.2B.3B.4B.5

IntroductionQuasistatic FieldsElementary LawsElectroquasistatic SystemsMagnetoquasistatic Systems

C– Elastic Constants in Cubic Material

References

Index

Foreword

It is a real pleasure to write the Foreword for this book, both because Ihave known and respected its author for many years and because I expectthis book’s publication will mark an important milestone in the continuingworldwide development of microsystems. By bringing together all aspects ofmicrosystem design, it can be expected to facilitate the training of not only anew generation of engineers, but perhaps a whole new type of engineer – onecapable of addressing the complex range of problems involved in reducing entiresystems to the micro- and nano-domains. This book breaks down disciplinarybarriers to set the stage for systems we do not even dream of today.

Microsystems have a long history, dating back to the earliest days of micro-electronics. While integrated circuits developed in the early 1960s, a numberof laboratories worked to use the same technology base to form integratedsensors. The idea was to reduce cost and perhaps put the sensors and circuitstogether on the same chip. By the late-60s, integrated MOS-photodiode arrayshad been developed for visible imaging, and silicon etching was being used tocreate thin diaphragms that could convert pressure into an electrical signal. By1970, selective anisotropic etching was being used for diaphragm formation,retaining a thick silicon rim to absorb package-induced stresses. Impurity- andelectrochemically-based etch-stops soon emerged, and "bulk micromachining"came into its own. Wafer bonding (especially the electrostatic silicon-glassbond) added additional capability and was applied to many structures, includ-ing efforts to integrate an entire gas chromatography system on a single wafer.Many of these activities took place in university laboratories, where sensorresearch could make important contributions that complemented industry. Thework was carried out primarily by electrical engineers trained in microelectron-ics, who often struggled to understand the mechanical aspects of their devices.There were no textbooks to lead the sensor designer through all the relevantareas, information on which was widely scattered.

xviii MICROSYSTEM DESIGN

The demand for improved automotive fuel economy and reduced emissionsin the late 70s took integrated pressure sensors into high-volume production.By the early 1980s, pressure sensors with on-chip readout electronics werealso in production and bulk micromachining was being applied to flowmeters,accelerometers, inkjet print heads, and other devices. At this point, the field of"integrated sensors" began to organize itself, establishing independent meetingsto complement special sessions at microelectronics conferences.

Surface micromachining came on the scene in the mid-80s and quickly led toapplications in accelerometers, pressure sensors, and other electromechanicalstructures. Microactuators became the focus for considerable work, and thenotion of putting entire closed-loop systems on a chip became a real goal. Thefield needed an acronym, and "MEMS" (MicroElectroMechanical Systems)was gradually adopted, in spite of the fact that many of the devices were notreally mechanical. The term "microsystems" also became increasingly com-mon in referring to the integration of sensors, actuators, and signal-processingelectronics on a common (but not necessarily monolithic) substrate. The fieldat this point began to see the long-needed entry of mechanical engineers, butit was still centered in academia. And there were still few, if any, coursesin sensors or MEMS. It was a research focus for people trained mostly inelectrical engineering and physics, and the mechanics, chemistry, or materialsinformation needed as an adjunct to microelectronics had to be dug out bypeople not primarily trained in those fields. There were still no textbooks onmicrosystems.

Beginning in the late 80s, MEMS received increasing emphasis worldwide.In the US, the Emerging Technologies Program of the National Science Foun-dation selected it as a focal point, and in 1992 the Defense Advanced ResearchProjects Agency (DARPA) did as well; suddenly funding went up dramaticallyand so did the number of players. Similar investments were being made inEurope and Asia, so that after more than 25 years the field finally reached crit-ical mass. The 1990s saw MEMS-based inkjet print heads, pressure sensors,flowmeters, accelerometers, gyros, uncooled infrared imagers, and optical pro-jection displays all enter production. Emphasis on full microsystems increased.More advanced devices are now being developed, including DNA analyzers,integrated gas chromatography systems, and miniature mass spectrometers.

Microsystem design now cuts across most disciplines in engineering and isthe focus for courses, and degree programs, at many major universities. Thesecourses, which must be open to individuals with a wide range of backgrounds,need material covering an equally wide range of subjects in a coherent, unifiedway. This book will be a major help in meeting these challenges. The authorhas been a principal figure guiding the development of microsystems for morethan two decades, through both his research contributions and his leadershipof the conferences and journals that have defined the field. The book itself is

xix

comprehensive, a friendly tutor for those just entering the field and a resourcefor long-time practitioners. It is all here — the technology, the modeling, theanalysis methods, and the structures. The important principles of materials,mechanics, and fluidics are here so that the designer can understand and predictthese aspects of advanced structures. And the electronics is here so that he orshe can also understand the signal readout and processing challenges and theuse of on-chip feedback control. Noise is covered so that the basic limitationsto accuracy and resolution can likewise be anticipated. Finally, case studies tieeverything together, highlighting important devices of current interest.

Because this text brings together all of the topics required for microsystemdesign, it will both accelerate development of the field and give rise to a newtype of engineer, the microsystems engineer, who can combine knowledge frommany disciplines to solve problems at the micro- and nano-levels. Microsys-tems are now much more than a specialized sub-area of microelectronics; insubstantial measure, they are the key to its future, forming the front-ends ofglobal information technology networks and bridges from microelectronics tobiotechnology and the cellular world.

Finding solutions to many of today’s problems will require microsystemsengineers to develop devices that we cannot yet imagine at a scale that we cannotsee. Certainly, many challenges lie ahead, but the basic principles presentedhere for meeting them will remain valid. And as the physicist Richard Feynmansaid in proposing microsystems over forty years ago, there really is plenty ofroom at the bottom!

Kensall D. WiseThe University of Michigan Ann Arbor, MI

Preface

The goal of this book is to bring together into one accessible text the fun-damentals of the many disciplines needed by today’s microsystems engineer.The subject matter is wide ranging: microfabrication, mechanics, heat flow,electronics, noise, and dynamics of systems, with and without feedback. Andbecause it is very difficult to enunciate principles of “good design” in the ab-stract, the book is organized around a set of Case Studies that are based onreal products, or, where appropriately well-documented products could not befound, on thoroughly published prototype work.

This book had its roots in a graduate course on “Design and Fabrication ofMEMS Devices” which my colleague Prof. Martin Schmidt and I co-taughtfor the first time in the Fall of 1997. I then offered it as a solo flight in theSpring of 1999. Our goal was to exploit our highly interdisciplinary studentmix, with students from electrical, mechanical, aeronautical, and chemicalengineering. We used design projects carried out by teams of four students asthe focus of the semester, and with this mix of students, we could assign to eachteam someone experienced in microfabrication, another who really understoodsystem dynamics, another with background in electronics, and so on. Lecturesfor the first two-thirds of the semester presented the material that, now in muchexpanded form, comprises the first sixteen chapters of this book. Then, whilethe teams of students were hard at work on their own design problems (moreon this below), we presented a series of lectures on various case studies fromcurrent MEMS practice.

In creating this “written-down” version of our course, I had to make a numberof changes. First and foremost, I greatly expanded both the depth and breadthof the coverage of fundamental material. In fact, I expanded it to such anextent that it is now unlikely I can cover it all within a one-semester course.Therefore, I expect that teachers will have to make selections of certain topicsto be emphasized and others that must be skipped or left to the students to readon their own.

xxii MICROSYSTEM DESIGN

A second change, and perhaps a more important one for teachers using thisbook, is that I took our collection of homework problems compiled from the1997 and 1999 versions of the course and used them as the worked-out examplesin the text chapters. While this had the effect of greatly enriching the content ofthe book, it created a temporary deficiency in homework problems that has onlybeen partially repaired by the rather modest set of new homework problems thatI created for the printed book. Thanks to the world-wide web, though, we nowhave an efficient mechanism for distributing additional homework problems asthey become available. (See “Note to Teachers” below.)

I am hoping to provide, both by example and by presentation of the under-lying fundamentals, an approach to design and modeling that any engineeringstudent can learn to use. The emphasis is on lumped-element models usingeither a network representation or a block-diagram representation. Critical tothe success of such an approach is the development of methods for creating themodel elements. Thus, there is a chapter on the use of energy methods andvariational methods to form approximate analytical solutions to problems inwhich energy is conserved, and a chapter on two different approaches to cre-ating lumped models for dissipative systems that obey the heat flow equationor its steady-state relative, the Laplace equation. The approach to modeling isbased, first, on the use of analytical methods and, second, on numerical simula-tions using MATLAB, SIMULINK, and occasionally MAPLE. Every numericalexample that appears in this book was done using the Student Edition of Version5 of MATLAB and SIMULINK. In a few places, I provide comparisons to theresults of meshed numerical simulations using finite-element methods, but thatis not the main purpose of the book.

The Case Studies that form Part V of the book were selected to samplea multidimensional space: different manufacturing and fabrication methods,different device applications, different physical effects used for transduction.In making the selection, I had the invaluable assistance of extended discussionswith Dr. Stephen Bart and Dr. Bart Romanowicz of Microcosm Technologies,as well as creative suggestions from Prof. Martin Schmidt. It is well knownin the MEMS world that I emphasize the importance of packaging. It willtherefore come as no surprise that the first chapter in Part V is a Case Studyon packaging, using an automotive pressure sensor as an example. The re-maining Case Studies deal with a piezoresistively-sensed bulk-micromachinedsilicon pressure sensor, a capacitively-sensed surface-micromachined polysili-con accelerometer, a piezoelectrically excited and sensed bulk-micromachinedresonant quartz rate gyro, two types of electrostatically actuated optical pro-jection display, two approaches to the construction of single-chip systems foramplification of DNA, and a surface micromachined catalytic sensor for com-bustible gases.

Preface xxiii

As stated earlier, design problems are an important part of our teaching ofthis material. A good design problem is one that requires the student teamto confront the problem’s specifications and constraints, develop a systemarchitecture for approaching the problem, work through the definition of a mi-crofabrication process, assign device dimensions, and model the device andsystem behavior so as to meet the specifications. Examples have included thedesign of a flow controller, a particular type of pressure sensor or accelerometer,a resonant strain sensor (including the circuit that drives it), a system for poly-merase chain reaction (PCR), a temperature-controlled hot stage for catalyticchemical sensors, and many more. Sample design problems will be postedon the web site. We like problems that involve feedback, because this forcesthe creation of a decent open-loop dynamic device model for insertion into theloop. Our experience has been that it is primarily through the design problemsthat students recognize how truly empowering the mastery of the fundamentalsubject matter is. They also learn a lot about teamwork, successful partitioningof a problem, intra-team communication, and very important realities aboutdesign tradeoffs. Only when the team realizes that by making one part of thejob easier they may be making a different part harder does the true merit of thedesign problem emerge. Our students have benefitted from the volunteer effortof several of our graduate students and post-docs who have served as mentorsto these design teams during the semester, and we recommend that teachersarrange such mentorship when using design problems in their own courses.

If Prof. Schmidt and I had to pick one subject that has been the hardest toteach in the context of our course, it would be process integration: creationof realistic fabrication sequences that produce the desired result with no evilside effects (such as putting on gold at a point in the process where high-temperature steps remain). Students who have already had a laboratory classin microfabrication technology have a huge advantage in this regard, and weencourage students to take such a class before embarking on our design course.

The opportunity to write this book was provided by a sabbatical leave frommy regular duties at M.I.T., somewhat stretched to cover a total of thirteenmonths, from August 1999 through August 2000. Because of the tight timeschedule, a few short-cuts had to be made: First, I did not attempt to providecomprehensive references on the various topics in this book. I have includedbasic recommended reading at the end of each chapter and also citations to keypublished work where appropriate. But citations to the work of many peopleare omitted, not because of any lack of respect for the work, but out of the needto get the job done in a finite time and to have it fit in a finite space. Others,such as Kovacs and Madou, have written books with extensive references tothe published literature, and I urge readers of this book to have these books athand as supplementary references. Second, I did not create a CD-ROM withthe MATLAB, SIMULINK, and MAPLE models on it. My reasoning was that

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the world-wide web now offers a much more efficient way to distribute suchmaterial and that, by using the web, I would have some flexibility in revising,correcting, and improving the models over time. Third, I did not include verymuch data on different material properties and process steps. My hope is thatthere is just enough data to permit some useful examples to be worked out. And,thankfully, additional data is now much easier to find, thanks to the compilationof various on-line databases, such as at the mems.isi.edu web site.

A Note to TeachersAs mentioned above, the supply of homework problems in this book is notwhat I would like it to be, in terms of either quantity or intellectual depth.Rather than delay publication of the book solely for the purpose of creatingnew homework problems, I decided to take advantage of the world-wide webto create a depository for supplementary material. The URL for the web sitefor this book is:

http://web.mit.edu/microsystem-design/www

Posted on this web site will be the inevitable errata that I fail to catch be-fore publication, additional homework and design problems, and MATLAB,SIMULINK and MAPLE models that support both the examples in the variouschapters and the new homework problems.

Anyone using this book is invited to submit materials for posting on thisweb site, using the on-line submission form. This is particularly important ifyou find an error or have an idea about how the index can be improved, butnew homework and design problems and numerical models are also welcome.They will be posted with full attribution of the source.

As this manuscript leaves my hands for the publisher, I still have not decidedhow to handle solutions to homework problems. By the time the book appearsin print, there will be a tentative policy. Teachers using the book are invited tosend me comments at sds@mit.edu on what solution-handling method wouldbe most helpful.

Finally, when you submit something to the web site, the web-site submissionform will request that you grant me permission to publish the material, both onthe web site and in future editions of this book. This will greatly strengthen thebody of material that all future microsystem-design students can access.

Stephen D. SenturiaBrookline, MA

Acknowledgments

A book of this type relies on inputs from many sources. I already mentionedin the Preface the contributions of three key individuals: Martin Schmidt, withwhom I developed the original version of the course on which this book is based;and Stephen Bart and Bart Romanowicz of Microcosm Technologies, withwhom I spent many stimulating hours throughout much of the year discussinghow to present this complex field in a coherent and meaningful way. Steve andBart contributed significantly to the process used to select the Case Studies forthis book and provided many helpful and insightful comments on a variety ofdetails.

The Case Studies of Part V each had a champion who provided materialsand commentary. All of the following individuals were of immense help inenabling what could be presented here: David Monk, William Newton, andAndrew McNeil of the Motorola Sensor Products Division (Chapters 17 and18), Michael Judy of Analog Devices and Tom Kenny of Stanford (Chapter19), Josef Berger, David Amm, and Chris Gudeman of Silicon Light Machines(Chapter 20), Brad Sage of Systron Donner (Chapter 21), Andreas Manz ofImperial College and David Moore of Cambridge University (Chapter 22), andRonald Manginell of Sandia National Laboratories (Chapter 23).

Students and various staff members at MIT have also played a role in thecreation of this book. I particularly want to thank Mathew Varghese, whoworked with me to develop the models used in Chapter 22, and Erik Deutsch,who committed precious time to collecting material data and associated ref-erences. Dr. Arturo Ayon was helpful in providing data and documentationfor several examples in the book. Postdocs Mark Sheplak (now at the Univer-sity of Florida), Reza Ghodssi (now at the University of Maryland) and CarolLivermore served as design-team mentors and helped sharpen our insights intothis aspect of teaching. And there have been about fifty students who havenow completed our MIT course. Their excitement about the field has providedsignificant motivation for getting this book written.

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It is highly desirable to “pre-test” textbook material before committing it topress. My first opportunity for such a pre-test was a two-week short courseon Microsystem Design for engineering students at the Institute of Microtech-nology (IMT) and staff members at the Swiss Center of Electronics and Mi-crotechnologies (CSEM) in Neuchâtel, Switzerland, held during June 1998. Iam indebted to Prof. Nico de Rooij of IMT and Phillipe Fischer of the SwissInstitute for Research in Microtechnology (FSRM) for arranging the course,and to Mark Grétillat for his demonstrations of the MEMCAD system as partof the course. This activity, which took place using terse hand-written notes,helped me learn what would make an effective text that could serve the needsof both students and active professionals.

A more extensive pre-test occurred during the Spring of 2000. ProfessorsMark Sheplak and Toshi Nishida of the University of Florida used the first threeparts of an early draft as the basis for a graduate course on MEMS technologyand devices. Their feedback, and the feedback from their students, has led toa number of improvements in scope and presentation, and their very carefulreading of the text identified many small things that needed correction.

I have benefited from the efforts of many other colleagues who have readsections of the draft and provided comments. I particularly want to mentionProf. Olav Solgaard of Stanford, Prof. G. K. Ananthasuresh of the Universityof Pennsylvania, Dr. Srikar Vengallatore of MIT, and MIT graduate studentsJoel Voldman, Mathew Varghese, and Erik Deutsch.

Perhaps the most significant reader has been my wife, Peg Senturia, who, asa non-engineering writer, is able to see issues about presentation and subjectorder that we more technical types overlook. In particular, her suggestionson chapter order in the first part of the book and her editorial efforts on theintroductory material have greatly improved the clarity and accessibility ofthe design approach presented here. Beyond that, words fail to express thegratitude I feel, first, for her putting up with my preoccupation during what hasbeen an intense thirteen months and, second, for doing so in a shared at-homeworkspace. Our bond of love has deepened through this project.

Finally, I want to thank three of my faculty colleagues at MIT for the classes Itook during the Fall semester of 1993. My department has an Adler Scholarshipwhich allows a faculty member a term off from teaching provided that he or shetakes a course for credit and gets a grade! As an Adler Scholar during the Fallof 1993, I enrolled in Prof. Jacob White’s course on numerical methods, didevery homework problem and got a decent grade. During that same semester, Isat in on two mechanical engineering classes on modeling of dynamic systems,one taught by Prof. Kamal Youcef-Toumi, the other by Prof. Neville Hogan.The experience of that semester of total immersion into modeling and numericsplanted the seeds from which this book has grown.

Stephen D. Senturia