Electromechanics and MEMS

582 Pages·2013·15.813 MB·English

by  Jones T.B., Nenadic N.G.

more information - www.cambridge.org/9780521764834

ElectromechanicsandMEMS
Offering a consistent, systematic approach to capacitive, piezoelectric, and magnetic
MEMS, this textbook equips students to design and develop practical, system-level
MEMSmodels.
(cid:2)
Includesaconciseyetthoroughtreatmentoftheunderlyingprinciplesofelectrome-
chanicaltransduction.
(cid:2)
Makesextensiveuseofeasy-to-interpretelectricalandmechanicalanalogs,suchas
electricalcircuits,electromechanicaltwo-portmodels,andthecascadeparadigm.
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Each chapter features extensive worked examples, and numerous homework
problems.
ThomasB.JonesisProfessorofElectricalEngineeringattheUniversityofRochester.
Anexperiencededucatorinvolvedinteachingforover40years,hisresearchhasfocused
onelectricfield-mediatedmanipulationandtransportofparticlesandliquids.Heholds
aPh.D.fromMIT,istheauthorofElectromechanicsofParticles(CambridgeUniversity
Press,1995)andisaFellowoftheIEEE.
Nenad G. Nenadic is a Research Associate Professor at the Rochester Institute of
Technology. His career, spanning both industry and academia, has involved him in
many aspects of MEMS, including design and analysis, system-level simulation, test
development,andmarketing.HeholdsaPh.D.fromtheUniversityofRochester,where
heassistedintheteachingofgraduate-levelMEMScourses.
“Thisisanexcellenttextbookpresentingthefundamentalsofelectromechanicsrequiredbyevery
practicing MEMS engineer. The authors treat the arduous concepts of coupled electrical and
mechanical systems simultaneously with lucidity and a thorough pedagogical rigor that comes
fromdeepappreciationofthefieldandthelovetoimpartthatknowledgeasateacher.Thebook
elucidatestheconceptswithverytopicalexamplesofmicroelectromechanicalsystemssuchas
MEMSmicrophones,combdriveactuators,gyroscopes,energyharvesters,andpiezoelectricand
magneticdevices,includingMATLABmodelsandacomprehensivesetofproblemsattheendof
eachchapter.”
SrinivasTadigadapa,ThePennsylvaniaStateUniversity
“Afantasticbookforthestudentseekingasolidfoundationinelectromechanicaldevicedesign
andanessentialreferencefortheexpertMEMSengineer.JonesandNenadicpresentthefunda-
mentaltheorybehindelectromechanicaltransduction,withafocusoncapacitivedriveandsense
microsystems.Theauthorssystematicallyframethedevicefundamentalsintorealworldmicro
scaledeviceapplicationsthatproviderelevancetotheunderlyingphysics.Thisbookcapturesand
dutifullyexplainsthefoundationalphysicsatworkintheMEMSdevicesweoftenunknowingly
usedailyinourautomobiles,mobilephonesandelectronicdevices.”
ChrisKeimel,GEGlobalResearch
“ElectromechanicsandMEMSisathoroughtreatmentoffundamentalMEMSanalysisforboth
thestudentandthepractitioner.Thereadersarepresentedwiththetoolstomethodicallybuild
systemmodelsthatarecomprehensiveyetmanageable.”
EricChojnacki,MEMSIC,Inc.
Electromechanics and MEMS
THOMAS B. JONES
UniversityofRochester,NewYork
NENAD G. NENADIC
RochesterInstituteofTechnology,NewYork
CAMBRIDGEUNIVERSITYPRESS
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Informationonthistitle:www.cambridge.org/9780521764834
(cid:2)C CambridgeUniversityPress2013
Thispublicationisincopyright.Subjecttostatutoryexception
andtotheprovisionsofrelevantcollectivelicensingagreements,
noreproductionofanypartmaytakeplacewithoutthewritten
permissionofCambridgeUniversityPress.
Firstpublished2013
PrintedandboundintheUnitedKingdombytheMPGBooksGroup
AcatalogrecordforthispublicationisavailablefromtheBritishLibrary
LibraryofCongressCataloginginPublicationdata
Jones,T.B.(ThomasByron),1944–
ElectromechanicsandMEMS/ThomasB.Jones,UniversityofRochester,NewYork,
NenadG.Nenadic,RochesterInstituteofTechnology.
pages cm
Includesbibliographicalreferences.
ISBN978-0-521-76483-4(hardback)
1.Microelectromechanicalsystems. I.Nenadic,NenadG. II.Title.
TK7875.J66 2012
621.381–dc23 2012021830
ISBN978-0-521-76483-4Hardback
Additionalresourcesforthispublicationatwww.cambridge.org/mems
CambridgeUniversityPresshasnoresponsibilityforthepersistenceor
accuracyofURLsforexternalorthird-partyinternetwebsitesreferredto
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Contents
Preface pagexiii
1 Introduction 1
1.1 Background 1
1.2 Someterminology 2
1.3 Electromechanicalsystems 3
1.4 Conclusion 7
Problems 7
Reference 9
2 Circuit-basedmodeling 10
2.1 Fundamentalsofcircuittheory 10
2.1.1 Motivation 10
2.1.2 Kirchhoff’scurrentandvoltagelaws 11
2.1.3 Circuitelements 12
2.1.4 Tellegen’stheorem:powerandenergy 12
2.1.5 ACcircuits,impedance,andadmittance 14
2.2 Circuitmodelsforcapacitivedevices 15
2.2.1 BasicRCcircuitbuildingblock 16
2.2.2 Theseriescapacitivecircuit 17
2.2.3 Theparallelcapacitivecircuit 18
2.2.4 Specialcases:seriesandparallelcapacitance 20
2.2.5 Summary 20
2.3 Two-portnetworks 22
2.3.1 Impedanceandadmittancematrices 22
2.3.2 Thetransmissionmatrix 24
2.3.3 Cascadedtwo-portnetworks 25
2.3.4 Someimportanttwo-portnetworks 27
2.3.5 Thegyratorandthetransformer 29
2.3.6 Embeddednetworks 30
2.3.7 Sourceandimpedancereflection 32
2.4 Summary 34
Problems 34
References 43
vi Contents
3 Capacitivelumpedparameterelectromechanics 44
3.1 Basicassumptionsandconcepts 44
3.1.1 Thelosslesselectromechanicalcoupling 45
3.1.2 Statevariablesandconservativesystems 46
3.1.3 Evaluationofenergyfunction 46
3.1.4 Forceofelectricalorigin 48
3.2 Coenergy–analternateenergyfunction 49
3.2.1 Definitionofcoenergy 49
3.2.2 Integralevaluationofcoenergy 50
3.2.3 Evaluationofforceofelectricalorigin 51
3.3 Couplingswithmultipleports 52
3.3.1 Energyconservationrelation 53
3.3.2 Systemwithtwoelectricalandtwomechanicalports 54
3.4 Basiccapacitivetransducertypes 56
3.4.1 Variable-gapcapacitors 56
3.4.2 Variable-areacapacitors 58
3.4.3 Comparisonofvariable-gapandvariable-areaactuators 60
3.4.4 Transducerstroke 62
3.4.5 Thecomb-drivegeometry 64
3.4.6 Anothervariable-areacapacitor 65
3.5 Rotationaltransducers 66
3.5.1 Modelingrotationalelectromechanics 67
3.5.2 Torqueofelectricalorigin 68
3.5.3 Anexample 68
3.6 Electrets 71
3.7 Non-linearconservativeelectromechanicalsystems 75
3.7.1 Conservationlawsforcapacitivedevices 75
3.7.2 Non-linearoscillationsandstability 77
3.7.3 Numericalsolutions 79
3.7.4 Constantchargeconstraint 80
3.7.5 Discussion 83
3.8 Summary 83
Problems 84
References 96
4 Small-signalcapacitiveelectromechanicalsystems 97
4.1 Background 97
4.2 Linearizedelectromechanicaltransducers 98
4.2.1 Somepreliminaries 98
4.2.2 Linearizationintermsofenergyandcoenergy 99
4.3 Electromechanicaltwo-portnetworks 101
4.3.1 Thetransducermatrix 101
4.3.2 Thelinearcapacitivetransducer 103
Contents vii
4.3.3 Importantspecialcases 105
4.3.4 Transducerswithangulardisplacement 105
4.3.5 Multiportelectromechanicaltransducers 107
4.4 Electromechanicalcircuitmodels 109
4.4.1 Analogousvariables 109
4.4.2 M-formequivalentelectromechanicalcircuit 110
4.4.3 N-formequivalentelectromechanicalcircuit 112
4.4.4 Moreaboutthecascadeparadigm 113
4.5 ReconciliationwithNeubert 113
4.6 Externalconstraints 114
4.6.1 Mechanicalconstraints 115
4.6.2 Electricalconstraints 118
4.6.3 Fullyconstrainedelectromechanicaltransducers 118
4.6.4 Otherusefulmatrixforms 120
4.7 Applicationsofelectromechanicaltwo-porttheory 121
4.7.1 Applicationofsourceandimpedancereflection 121
4.7.2 Acapacitivemicrophone 123
4.7.3 Electromechanicaltransferfunctions 125
4.7.4 Acomb-driveactuator 126
4.7.5 Thethree-platecapacitivesensor 127
4.7.6 Linearmodelforelectrettransducer 130
4.8 Stabilityconsiderations 132
4.8.1 Preliminarylookatstability 132
4.8.2 Generalstabilitycriteria 133
4.8.3 Thepull-ininstabilitythreshold 137
4.8.4 Aphysicalinterpretationofinstability 138
4.9 Summary 140
Problems 141
References 149
5 Capacitivesensingandresonantdrivecircuits 150
5.1 Introduction 150
5.2 Basicsofoperationalamplifiers 151
5.3 Invertingamplifiersandcapacitivesensing 152
5.3.1 Basicinvertingconfiguration 153
5.3.2 One-sidedhigh-impedance(charge)amplifier 154
5.3.3 Variable-gapandvariable-areacapacitors 157
5.3.4 Effectofop-ampleakagecurrent 157
5.4 Differential(three-plate)capacitancesensing 163
5.4.1 DCfeedbackforthedifferentialconfiguration 165
5.5 AC(modulated)sensing 166
5.5.1 Capacitivesensorexcitedbyzero-meansinusoidalvoltage 167
5.5.2 Two-platecapacitivesensingwithACexcitation 169
viii Contents
5.5.3 AnalysisincludingthefeedbackresistanceR 170
f
5.5.4 AMsignaldemodulation 172
5.5.5 DifferentialACsensing 173
5.5.6 Synchronousdemodulation 174
5.6 ACsensorsusingsymmetricsquare-waveexcitation 175
5.6.1 Transducersusingsquare-waveexcitation 175
5.6.2 Three-platesensingusingsquare-waveexcitation 176
5.7 Switchedcapacitancesensorcircuits 178
5.7.1 Basicsofswitched-capacitorcircuits 178
5.7.2 Simplesensorbasedonswitchedcapacitance 179
5.7.3 Half-wavebridgesensorusingswitchedcapacitance 180
5.8 NoiseincapacitiveMEMS 183
5.8.1 Commonnoisecharacteristics 184
5.8.2 Filterednoise 185
5.8.3 Noisytwo-ports 186
5.8.4 Electricalthermalnoise 186
5.8.5 Mechanicalthermalnoise 189
5.8.6 1/famplifiernoise 191
5.8.7 Effectofmodulationon1/fnoise 192
5.9 ElectrostaticdrivesforMEMSresonators 193
5.9.1 Mechanicalresonators 194
5.9.2 Driveelectrodeswithsinusoidaldrive 194
5.9.3 Non-harmonicdrives 197
5.9.4 Senseelectrodes 200
5.9.5 HarmonicoscillatorsbasedonMEMSresonators 200
5.9.6 Phase-lockedloopdrives 208
5.9.7 PLLsystemlinearization 210
5.10 Summary 213
Problems 214
References 222
6 Distributed1-Dand2-Dcapacitiveelectromechanicalstructures 223
6.1 Introduction 223
6.2 Amotivatingexample–electrostaticactuationofacantilevered
beam 224
6.2.1 Problemdescription 224
6.2.2 Derivationofthelumpedparametermodel 225
6.2.3 Evaluationofequivalentspringconstant,mass,andmechanical
damping 228
6.2.4 Resonanceofacantileveredbeam 229
6.2.5 Recapitulationoflumpedparametermodelidentification
procedure 233