MEMS技術-第四講-電子零件原理

MEMS和微系統(tǒng)設計

MEMS和微系統(tǒng)設計

1課程內(nèi)容MEMS概述及MEMS設計的概述工藝簡要回顧系統(tǒng)設計、工藝設計及版圖設計主要的機械、電子元件及其設計基礎多域耦合設計：以機電耦合為例子器件性能的估計簡單的其他域的元件及其簡要設計要點設計實例課程內(nèi)容MEMS概述及MEMS設計的概述2第4講主要內(nèi)容(3)1、彈簧設計原理及計算例子2、薄膜設計原理及計算例子3、電容設計原理及計算例子4、電阻設計原理及計算例子5、壓電模型第4講主要內(nèi)容(3)1、彈簧設計原理及計算例子3電容變化靜電力電容變化4圖2-17電容式微傳感器的基本結構

平行板電容器的電容為電容敏感原理

圖2-17電容式微傳感器的基本結構平行板電容器的電容為電容5

式中A為極板面積為真空介電常數(shù)為極板間介質的相對介電常數(shù)當介質為空氣時，；為兩極板間距離間隙變化型：改變兩極板間隙面積變化型：改變形成電容的有效面積A介質變化型：改變兩極間介質的介電常數(shù)

式中間隙變化型：改變兩極板間隙6間隙變化型電容式微傳感器利用泰勒級數(shù)展開，由麥克勞林公式可得間隙變化型電容式微傳感器利用泰勒級數(shù)展開，由麥克7略除高階無窮小項，得這時傳感器的靈敏度和非線性誤差分別為：略除高階無窮小項，得這時傳感器的靈敏度和非線性誤差分別為：8采用差動電容結構可以大大減小傳感器輸出的非線性：

(2-12)

(2-13)

(2-14)

(2-15)采用差動電容結構可以大大減小傳感器輸出的非線 (29

在小位移情況下，外加作用和成比例關系，可見電容的倒數(shù)差及電容的差除和都與輸入作用力成線性關系。

式(2-14)表明，用電容的差除和表達傳感器的性能，其輸出還要受到介質介電常數(shù)的影響。

式(2-15)表明電容差除和只受電容極板間隙和間隙變化的影響。目前，硅電容變送器普遍采取式(2-15)的方法來描述傳感器的性能。

在小位移情況下，外加作用和成比例關系，可見電容的10其他的電容變化形式變面積電容器其他的電容變化形式變面積電容器11Aexample:calculatetoCandtheshiftofC兩種電容變化形式的變化量對比

（電容原值、導線的電容值、電容變化值）Wire：L=1m,r=0.2mm,d=1mmgap=g=1Thickness=t=2fingerlength=L=100overlaplengthx=75Aexample:calculatetoCan12電容readout—位置檢測和速度檢測Whymodulatev(t)?Idealbuffer:cin=0電容readout—位置檢測和速度檢測Whymodulat13MatchedAir-GapReferenceCapacitors

MatchedAir-GapReferenceCapa14SimpleCapacitorDivider(con.)matchedair-gapreferencecapacitoroffsetsignalSimpleCapacitorDivider(con.15CapacitorDividerWithDifferentialExcitationWhymodulatev+andv-?Idealbuffer:cin=0Impedancedividerwithsuperposition:CapacitorDividerWithDiffere16ImprovedCapacitiveDivider(cont.)nooffset!distortionImprovedCapacitiveDivider(c17ThecapacitiveHalf-BridgeImpedancedividerwithsuperposition:ThecapacitiveHalf-BridgeImp18ThecapacitiveHalf–Bridge(cont.)Simplifyexpression:Nooffset，2xsignalincreaseThecapacitiveHalf–Bridge(c19ParasiticCapacitancesSurfacemicromachinedz-axisparallel-platecapacitorParasiticCapacitancesSurface20EquivalentcircuitCpp(x):nominal||platesensecapacitorCf1(x):fringecapacitance(varieswithplatedisplacement)Cf2:fringecapacitancebetweenupperplate(connectedtoanchorplane)andlowerplate…slightdependenceonxCpu:parasiticcapacitancefromupperplatetosubstrateCpl:parasiticcapacitancefromlowerplatetosubstrateEquivalentcircuitCpp(x):nom21VelocitySensingFundamentalcurrent-voltagerelationshipforatime-varyingcapacitor:Considerspecialcase:v=vp=constant…usedinhigh-qualitycapacitancemicrophonesVelocitySensingFundamentalcu22VelocitySensing(cont.)Sensecapacitor’stimevariation:Parallel-platesensecapacitorwithgapgo:Harmonicmotion:VelocitySensing(cont.)Sense23SomeNumbersSurfacemicromachinedcapacitor:

Isthisreal?…noiseinbufferampSomeNumbersSurfacemicromachi24WorldRecordCapacitivePosition-SenseResolution*AnalogDevicesADRS-150vibratoryrategyroscopeJohnGeen,SteveSherman,JohnChang,andSteveLewis,IEEEJ.Solid-StateCircuits,37,Dec.2002,1860-1866FullscaleCorillis-induceddisplacement=20?Sensecapacitance≈1000fFMinimumdetectablecapacitancechange≈12zF=0.012aFNominalsensegap=1.6

m

Minimumdisplacement:16fm!*Surfacemicromachiningclassaudiofrequencyband

EEC245-MEC218Fall2003Lecture12WorldRecordCapacitiveFullsc25IsADLSplittingElectrons?AtV+=5V,thechargeonthesensecapacitoris:qs=c+v+=(1000fF)(5V)=5000fCNumberofelectronsatMinimumdetectablechangeinsensecharge:Minimumdetectedchangeinnumberofelectrons:IsADLSplittingElectrons?At26電容變化靜電力電容變化27變間隙電容驅動器的基本理論

BasicphysicsofElectrostaticActuation

Twowaystochangetheenergy:

1.Changethechargeq2.changetheseparationxNote:weassumethattheplatesaresupportedelastically,sotheydon’tcollapse.

變間隙電容驅動器的基本理論

Basicphysicsof28Charge-ControlCase(cont.)Storedenergy:Force(attractive,internal):Voltage:Independentofthegap!constantCharge-ControlCase(cont.)Sto29ElectrostaticForce(VoltageControl)Findco-energyintermsofvoltageVariationofco-energywithrespecttogapyieldsv.s.force:Variationofco-energywithrespecttovoltageyieldschargeasexpectedElectrostaticForce(VoltageC30LinearizingtheVoltageSquare-LawPolarizethecapacitorbyapplyingaDCoffsetvoltageVPtogetherwitha(small)signalvoltageVsig(t)<<VPDCoffsetneglect(small)LinearizingtheVoltageSquare31TheDifferentialElectrostaticActuatorNetforceonsuspendedcenterelectrodeisthedifferenceTheDifferentialElectrostatic32Parallel–PlateCapacitiveNonlinearityExample:laterallydrivenspringsuspendedplate(eventuallywithbalancedelectrodes)NomenclatureConductivestructureelectrodeValueACorsignalcomponent(lowercasevariablesubscript)DCComponent(uppercasevariable:uppercasesubscript)Parallel–PlateCapacitiveNon33Parallel–PlateCapacitiveNonlinearityExample:clamped-clampedlaterallydrivenbeam

withbalancedelectrodesExpressionfor

ExpandtheTaylorSeriesfurtherConductivestructureelectrodeParallel–PlateCapacitiveNon34Parallel–plateCapacitiveNonlinearityParallel–plateCapacitiveNon35Parallel–PlateCapacitiveNonlinearityRetainingonlytermsatthedrivefrequency:Thesetwotogethermeanthatthisforceactsagainstthespringrestoringforce!AnegativespringconstantsinceitderivesfromVPwecallittheelectricalstiffness,givenby:DriveforcearisingfromtheinputexcitationvoltageatthefrequencyofthisvoltageProportionaltodisplacement900phase-shiftedfromdrive,soinphasewithdisplacementParallel–PlateCapacitiveNon36Electricalstiffness,KeTheelectricalstiffnesskebehaveslikeanyotherstiffnessItaffectsresonancefrequency:Frequencyisnowafunctionofdc-biasVp1Electricalstiffness,KeTheel37CanOneCancelKewithTwoElectrodes?Whatifwedon’tlikethedependenceoffrequencyonVP?CanwecancelKCviaadifferentialinputelectrodeconfiguration?IfwedoasimilaranalysisforFd2atElectrode2:

SubtractsfromtheFd1term,asexpectedAddtothequadraturetermKc’sadd,nomattertheelectrodeconfiguration!CanOneCancelKewithTwoE38ThecapacitiveHalf-BridgeImpedancedividerwithsuperposition:ThecapacitiveHalf-BridgeImp39ThecapacitiveHalf–Bridge(cont.)Simplifyexpression:Electrostaticforce:ThecapacitiveHalf–Bridge(c40ElectrostaticForce(Cont.)Outputvoltageisproportionaltothedisplacement(forx<<go)DCand2wtermsElectrostaticForce(Cont.)Out41ElectrostaticSpringConstantkenotedirection:springappliesforceoppositetodisplacement

BothDCand2wcomponents:usesquarewaveexcitationtoyieldconstantkeElectrostaticSpringConstant42GraphicalSolutionforPlateStability

Plotnormalizedelectrostaticandspringforcesvs.normalizeddisplacement1-(g/go)GraphicalSolutionforPlateS43SowhyareelectrostaticactuatorsimportantinMEMS,anyway?Easytomakeinmicromachiningprocesses,sinceconductorsandairgapsallthat’sneededEnergy–conserving

onlyparasiticenergylossthroughi2RlossesinconductorsandinterconnectsPull-inphenomenoncanbeexploitedtomakeahystereticactuatorsimplifiescontrolMultipleplatestructures(combs,3D)canbeusedtotailortheforce(displacementvoltage)functionScalingoftheelectrostaticforceisfavorableduetoPaschen’scurveSamestructurecanbeusedforpositionsensingSowhyareelectrostaticactua44Paschen’sCurvePaschen’sCurve45叉指驅動器的理論模型(Electrostaticcombdrive)Useofcomb-capacitivetranducersbringsmanybenefits

．Linearizesvoltage-generatedinputforces

．(Ideally)eliminatesdependenceoffrequencyondc-bias．Allowalargerangeofmotion叉指驅動器的理論模型(Electrostaticcomb46ElectrostaticForce:aFirstPassStator(fixedelectrode)Rotor(not…butmoving)Gap=g,thickness=tL=fingerlengthX=overlaplengthElectrostaticForce:aFirstP47First-PassElectrostaticForce(cont.)NeglectfringingfieldsParallel-platecapacitancebetweenstatorandrotorIndependentofx！First-PassElectrostaticForce48RelativeForceforSurfaceMicrostructuresCombdrive(x-direction)(V1=V2=VS=1V)Differential||plate(y-direction)(V1=0V,V2=1V)||platewinsbig…forsurfaceMEMSGap=g=1Thickness=t=2Fingerlength=L=100Overlaplengthx=75RelativeForceforSurfaceMic49CombDriveForce:aSecondPassEnergymustincludecapacitancebetweenthestatorandrotorandunderlyinggroundplane,whichistypicallybiasedatthestatorvoltageVs…why？CombDriveForce:aSecondPa50CombDriveForcewithGroundplaneCorrectionFingerdisplacementchangescapacitancesfromstatorandrotortothegroundplanemodifiestheelectrostaticenergy

CombDriveForcewithGroundp51CapacitanceExpressionsConsidercasewhereVr=VP=0VCsp=dependsonwhetherornotfingersareengagedCapacitanceperlengthunitCapacitanceExpressionsConside52Simulation(2DFiniteElement)20-40%reductionofFeSimulation(2DFiniteElement)53VerticalForce(Levitation)

considerVr=0Vasshown:VerticalForce(Levitation)co54LevitationForce“electricalspringconst.”constantLevitationforceaddstothemechanicalspringconstantinthezdirectionincreasestheresonantfrequencyLevitationForce“electricalsp55VerticalResonantFrequencyMustaccountforelectricalspringsinfindingMEMSresonantfrequenciesComb(x-axis)Ke=0Comb(z-axis)Ke>0ParallelplateKe<0VerticalResonantFrequencyMus56第4講主要內(nèi)容(3)1、彈簧設計原理及計算例子2、薄膜設計原理及計算例子3、電容設計原理及計算例子4、電阻設計原理及計算例子5、壓電模型第4講主要內(nèi)容(3)1、彈簧設計原理及計算例子57MEMS技術-第四講-電子零件原理58

1、金屬的電阻改變：由材料幾何尺寸的變化引起的；與相關

2、半導體的電阻改變：由材料受力后電阻率的變化引起，與相關；

3、半導體的靈敏度因子比金屬的高得多，一般在70-170之間

59當電阻為立體結構時，有立體單元電阻的應力圖當電阻為立體結構時，有立體單元電阻的應力圖60(7-6)其中{ΔR}=代表與應力分量{σ}=（如圖7.13）相對應的一個無限小的立方壓電電阻晶體單元的電阻變化。(7-6)其中{ΔR}=61式7-6、7-7立體電阻的壓阻系數(shù)(7-7)式7-6、7-7立體電阻的壓阻系數(shù)(7-7)62得出：得出：63若電阻為薄膜電阻，在正交坐標系中，當坐標軸與晶軸一致時，電阻的相對變化與應力的關系為若電阻為薄膜電阻，在正交坐標系中，當坐標軸與64

表示縱向應力

為橫向應力表示、垂直方向上的應力，它比和小很多，一般都略去。、、分別為、、相對應的壓阻系數(shù)，為縱向壓阻系數(shù)，為橫向壓阻系數(shù)。表示縱向應力65

當電阻處于任意晶向P時，如果有縱向應力沿此方向作用在單晶硅電阻上，則會引起縱向壓阻系數(shù)，如果電阻上同時作用有和電阻方向垂直的橫向應力，則會引起橫向壓阻系數(shù)，那么任意晶向的壓阻系數(shù)為（2-6）當電阻處于任意晶向P時，如果有縱向應力66（2-7）式中，、、分別為單晶硅晶軸上的縱向壓阻系數(shù)、橫向壓阻系數(shù)和剪切壓阻系數(shù)；、、分別為電阻的縱向應力相對于晶體主軸坐標系中的方向余弦；、、分別為電阻的橫向應力相對于晶體主軸系中的方向余弦。（2-7）式中，、、分別為單晶硅晶軸上的縱向67RelativeresistancechangecanbeexpressedbythelongitudinalandtransversepiezoresistivecoefficientsPiezoresistorsareoftenalignedtothewaferflatof(100)wafers,whichisinthe[110]direction.Senturia,p.473providestheresultofcoordinatetransformations:

Relativeresistancechangecan68SiliconpiezoresistivecoefficientsFunctionoftype,doping,andtemperatureLongitudinalandtransversecoefficientsin[110]directionn-type11.7-102.253.4-13.6P-type7.86.6-1.1138.1Units[-cm],10-1Pa-1valuesareatT=250Cn-type

P-typeSiliconpiezoresistivecoeffic69一般地，當晶面為(100)時，有表7-9P型壓電阻在各方向的壓阻系數(shù)晶面取向<x>取向<y>πLπT(100)<111><211>+0.66π44-0.33π44(100)<110><100>+0.5π44~0(100)<110><110>+0.5π44-0.5π44(100)<100><100>+0.02π440.02π44一般地，當晶面為(100)時，有表7-9P型壓電阻在各70PiezoresistorPlacementBulkmicromachineddiaphragmpressuresensorPiezoresistorPlacementBulkmi71電阻變化的read-out公式?電阻變化的read-out公式?72舉例計算電阻的變化導致電壓的變化舉例計算電阻的變化導致電壓的變化73第4講主要內(nèi)容(3)1、彈簧設計原理及計算例子2、薄膜設計原理及計算例子3、電容設計原理及計算例子4、電阻設計原理及計算例子5、壓電模型第4講主要內(nèi)容(3)1、彈簧設計原理及計算例子74OriginofPiezoelectricEffectSeveralviewsofanα-quartzcrystalOriginofPiezoelectricEffect75OriginofPiezoelectricEffectForr>>a,theelectricfieldatthepointPis:Thepotentialandelectricfieldappearasifthechargesarecoincidentattheircenterofgravity(pointO)OriginofPiezoelectricEffect76OriginofPiezoelectricEffectAssumetheappliedforceFcausesthelineODtorotatecounterclockwisebyasmallangleThisstrainshiftsthecenterofgravityofthethreepositiveandnegativechargestotheleftandright,respectivelyAdipolemoment,p=qr,iscreatedwhichhasanarm(r)of:p=qrqa33/2AssumingthecrystalcontainsNsuchmoleculesperunitvolume,eachsubjecttothesamestrain,thepolarization(ordipolemomentperunitvolume)is:

polarizationstrainOriginofPiezoelectricEffect77OriginofPiezoelectricEffectForsufficientlysmalldeformations,polarization(p)islinearlyrelatedtothestrain(s)by:p=gswheregisthepiezoelectricvoltagecoefficient.ConversePiezoelectricEffectWhenapiezoelectriccrystalisplacedinanelectricfield,positiveandnegativeionsarepushedinoppositedirectionsandadipoletendstorotatetoalignitselfwiththeelectricfield.TheresultingmotiongivesrisetostrainsthatisproportionaltoelectricfieldES=dEwheredisthepiezoelectricchargecoefficient.OriginofPiezoelectricEffect78AnisotropicCrystalProperties:GeneralizedStress-StrainIn

anisotropicmaterialsatensilestresscanproducebothaxialandshearstrain.Forexample,athin,x-cutrodofquartzsubjecttoatensileforcewillnotonlybecomelongerandthinner,longitudinalaxis.Sincewehave6componentsofstress(T)and6componentsofstrain(S),36constantsmustbeusedtodescribebehaviorinthegeneralcase.Crystalsymmetry(e.g.trigonal,hexagonal)greatlyreducesthenumberofindependentconstants.AnisotropicCrystalProperties79AnisotropicCrystalProperties:GeneralizedStress-StrainForsmalldeformations,stress(T)andstrain(S)arerelatedthoughthecompliancematrix(s)Conservationofenergyrequiressij=sji.Performingrotationsbasedupontrigonalsymmetryconsiderations,thecompliancematrixreducesto6independentcoefficients:Quartzhasthreefoldsymmetry,physical

propertiesrepeatevery1200.Quartzisalsosymmetricaboutthex-axisAnisotropicCrystalProperties80AnisotropicCrystalProperties:GeneralizedStress-StrainRecallthat

thestrain(S)isrelatedtotheelectric

(E)bythepiezoelectricchargecoefficientmatrix(d)Applyingthesymmetryconditionsforquartz,thepiezoelectricstrainmatrix(d)simplifiesto:AnisotropicCrystalProperties81AnistropicCrystalPropertiesElasticmodulusandcomplianceThermalconductivityE