MEMS技术 第四讲 电子零件原理(2)PPT课件

MEMS和微系统设计,课程内容,MEMS概述及MEMS设计的概述工艺简要回顾系统设计、工艺设计及版图设计主要的机械、电子元件及其设计基础多域耦合设计：以机电耦合为例子器件性能的估计简单的其他域的元件及其简要设计要点设计实例,第4讲主要内容(3),1、弹簧设计原理及计算例子2、薄膜设计原理及计算例子3、电容设计原理及计算例子4、电阻设计原理及计算例子5、压电模型,电容变化静电力,图2-17电容式微传感器的基本结构,平行板电容器的电容为,电容敏感原理,式中A为极板面积为真空介电常数为极板间介质的相对介电常数当介质为空气时，；为两极板间距离,间隙变化型：改变两极板间隙面积变化型：改变形成电容的有效面积A介质变化型：改变两极间介质的介电常数,间隙变化型电容式微传感器,利用泰勒级数展开，由麦克劳林公式可得,略除高阶无穷小项，得,这时传感器的灵敏度和非线性误差分别为：,采用差动电容结构可以大大减小传感器输出的非线性：,(2-12),(2-13),(2-14),(2-15),在小位移情况下，外加作用和成比例关系，可见电容的倒数差及电容的差除和都与输入作用力成线性关系。式(2-14)表明，用电容的差除和表达传感器的性能，其输出还要受到介质介电常数的影响。式(2-15)表明电容差除和只受电容极板间隙和间隙变化的影响。目前，硅电容变送器普遍采取式(2-15)的方法来描述传感器的性能。,其他的电容变化形式,变面积电容器,Aexample:calculatetoCandtheshiftofC,两种电容变化形式的变化量对比（电容原值、导线的电容值、电容变化值）,Wire：L=1m,r=0.2mm,d=1mm,gap=g=1Thickness=t=2fingerlength=L=100overlaplengthx=75,电容readout位置检测和速度检测,Whymodulatev(t)?Idealbuffer:cin=0,MatchedAir-GapReferenceCapacitors,SimpleCapacitorDivider(con.),matchedair-gapreferencecapacitor,offset,signal,CapacitorDividerWithDifferentialExcitation,Whymodulatev+andv-?Idealbuffer:cin=0,Impedancedividerwithsuperposition:,ImprovedCapacitiveDivider(cont.),nooffset!,distortion,ThecapacitiveHalf-Bridge,Impedancedividerwithsuperposition:,ThecapacitiveHalfBridge(cont.),Simplifyexpression:,Nooffset，2xsignalincrease,ParasiticCapacitances,Surfacemicromachinedz-axisparallel-platecapacitor,Equivalentcircuit,Cpp(x):nominal|platesensecapacitorCf1(x):fringecapacitance(varieswithplatedisplacement)Cf2:fringecapacitancebetweenupperplate(connectedtoanchorplane)andlowerplateslightdependenceonxCpu:parasiticcapacitancefromupperplatetosubstrateCpl:parasiticcapacitancefromlowerplatetosubstrate,VelocitySensing,Fundamentalcurrent-voltagerelationshipforatime-varyingcapacitor:Considerspecialcase:v=vp=constantusedinhigh-qualitycapacitancemicrophones,VelocitySensing(cont.),Sensecapacitorstimevariation:Parallel-platesensecapacitorwithgapgo:Harmonicmotion:,SomeNumbers,Surfacemicromachinedcapacitor:,Isthisreal?,noiseinbufferamp,WorldRecordCapacitivePosition-SenseResolution*AnalogDevicesADRS-150vibratoryrategyroscopeJohnGeen,SteveSherman,JohnChang,andSteveLewis,IEEEJ.Solid-StateCircuits,37,Dec.2002,1860-1866,FullscaleCorillis-induceddisplacement=20Sensecapacitance1000fFMinimumdetectablecapacitancechange12zF=0.012aFNominalsensegap=1.6mMinimumdisplacement:16fm!*Surfacemicromachiningclassaudiofrequencyband,EEC245-MEC218Fall2003Lecture12,IsADLSplittingElectrons?,AtV+=5V,thechargeonthesensecapacitoris:qs=c+v+=(1000fF)(5V)=5000fCNumberofelectronsatMinimumdetectablechangeinsensecharge:Minimumdetectedchangeinnumberofelectrons:,电容变化静电力,变间隙电容驱动器的基本理论BasicphysicsofElectrostaticActuation,Twowaystochangetheenergy:1.Changethechargeq2.changetheseparationxNote:weassumethattheplatesaresupportedelastically,sotheydontcollapse.,Charge-ControlCase(cont.),Storedenergy:,Force(attractive,internal):,Voltage:,Independentofthegap!,constant,ElectrostaticForce(VoltageControl),Findco-energyintermsofvoltage,Variationofco-energywithrespecttogapyieldsv.s.force:,Variationofco-energywithrespecttovoltageyieldscharge,asexpected,LinearizingtheVoltageSquare-Law,PolarizethecapacitorbyapplyingaDCoffsetvoltageVPtogetherwitha(small)signalvoltageVsig(t)VP,DCoffset,neglect(small),TheDifferentialElectrostaticActuator,Netforceonsuspendedcenterelectrodeisthedifference,ParallelPlateCapacitiveNonlinearity,Example:laterallydrivenspringsuspendedplate(eventuallywithbalancedelectrodes)Nomenclature,Conductivestructure,electrode,Value,ACorsignalcomponent(lowercasevariablesubscript),DCComponent(uppercasevariable:uppercasesubscript),ParallelPlateCapacitiveNonlinearity,Example:clamped-clampedlaterallydrivenbeamwithbalancedelectrodesExpressionfor,ExpandtheTaylorSeriesfurther,Conductivestructure,electrode,ParallelplateCapacitiveNonlinearity,ParallelPlateCapacitiveNonlinearity,Retainingonlytermsatthedrivefrequency:Thesetwotogethermeanthatthisforceactsagainstthespringrestoringforce!AnegativespringconstantsinceitderivesfromVPwecallittheelectricalstiffness,givenby:,Driveforcearisingfromtheinputexcitationvoltageatthefrequencyofthisvoltage,Proportionaltodisplacement,900phase-shiftedfromdrive,soinphasewithdisplacement,Electricalstiffness,Ke,TheelectricalstiffnesskebehaveslikeanyotherstiffnessItaffectsresonancefrequency:,Frequencyisnowafunctionofdc-biasVp1,CanOneCancelKewithTwoElectrodes?,WhatifwedontlikethedependenceoffrequencyonVP?CanwecancelKCviaadifferentialinputelectrodeconfiguration?IfwedoasimilaranalysisforFd2atElectrode2:,SubtractsfromtheFd1term,asexpected,AddtothequadraturetermKcsadd,nomattertheelectrodeconfiguration!,.,ThecapacitiveHalf-Bridge,Impedancedividerwithsuperposition:,.,ThecapacitiveHalfBridge(cont.),Simplifyexpression:,Electrostaticforce:,.,ElectrostaticForce(Cont.),Outputvoltageisproportionaltothedisplacement(forxa,theelectricfieldatthepointPis:Thepotentialandelectricfieldappearasifthechargesarecoincidentattheircenterofgravity(pointO),OriginofPiezoelectricEffect,AssumetheappliedforceFcausesthelineODtorotatecounterclockwisebyasmallangleThisstrainshiftsthecenterofgravityofthethreepositiveandnegativechargestotheleftandright,respectivelyAdipolemoment,p=qr,iscreatedwhichhasanarm(r)of:p=qrqa33/2AssumingthecrystalcontainsNsuchmoleculesperunitvolume,eachsubjecttothesamestrain,thepolarization(ordipolemomentperunitvolume)is:,polarization,strain,OriginofPiezoelectricEffect,Forsufficientlysmalldeformations,polarization(p)islinearlyrelatedtothestrain(s)by:p=gswheregisthepiezoelectricvoltagecoefficient.ConversePiezoelectricEffectWhenapiezoelectriccrystalisplacedinanelectricfield,positiveandnegativeionsarepushedinoppositedirectionsandadipoletendstorotatetoalignitselfwiththeelectricfield.TheresultingmotiongivesrisetostrainsthatisproportionaltoelectricfieldES=dEwheredisthepiezoelectricchargecoefficient.,AnisotropicCrystalProperties:GeneralizedStress-Strain,Inanisotropicmaterialsatensilestresscanproducebothaxialandshearstrain.Forexample,athin,x-cutrodofquartzsubjecttoatensileforcewillnotonlybecomelongerandthinner,longitudinalaxis.Sincewehave6componentsofstress(T)and6componentsofstrain(S),36constantsmustbeusedtodescribebehaviorinthegeneralcase.Crystalsymmetry(e.g.trigonal,hexagonal)greatlyreducesthenumberofindependentconstants.,AnisotropicCrystalProperties:GeneralizedStress-Strain,Forsmalldeformations,stress(T)andstrain(S)arerelatedthoughthecompliancematrix(s)Conservationofenergyrequiressij=sji.Performingrotationsbasedupontrigonalsymmetryconsiderations,thecompliancematrixreducesto6independentcoefficients:,Quartzhasthreefoldsymmetry,physicalpropertiesrepeatevery1200.Quartzisalsosymmetricaboutthex-axis,AnisotropicCrystalProperties:GeneralizedStress-Strain,Recallthatthestrain(S)isrelatedtotheelectric(E)bythepiezoelectricchargecoefficientmatrix(d),Applyingthesymmetryconditionsforquartz,thepiezoelectricstrainmatrix(d)simplifiesto:,AnistropicCrystalProperties,ElasticmodulusandcomplianceThermalconductivityElectricalconductivityCoefficientofthermalexpansionDielectricconstantsPiezoelectriccontantsOpticalindexofrefractionVelocityofpropagationofshearwaves,ConstitutiveEquationsforPiezoelectricMaterials,Superscriptedmaterialconstants(e.g.sE)arethosevaluesobtainedwhensuperscriptedquantityisheldconstant.,PiezoelectricstrainCoefficients(transpose),Dielectricpermittivity,PropertiesCommonPiezoelectrics,SAWDevices,Thestress-freeboundaryconditionimposedb