MEMS技術(shù)-第四講-電子零件原理

MEMS和微系統(tǒng)設(shè)計

MEMS和微系統(tǒng)設(shè)計

1課程內(nèi)容MEMS概述及MEMS設(shè)計的概述工藝簡要回顧系統(tǒng)設(shè)計、工藝設(shè)計及版圖設(shè)計主要的機(jī)械、電子元件及其設(shè)計基礎(chǔ)多域耦合設(shè)計：以機(jī)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(shè)計要點(diǎn)設(shè)計實(shí)例課程內(nèi)容MEMS概述及MEMS設(shè)計的概述2第4講主要內(nèi)容(3)1、彈簧設(shè)計原理及計算例子2、薄膜設(shè)計原理及計算例子3、電容設(shè)計原理及計算例子4、電阻設(shè)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(shè)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(jié)構(gòu)

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(jié)構(gòu)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(zhì)的相對介電常數(shù)當(dāng)介質(zhì)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(zhì)變化型：改變兩極間介質(zhì)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(xiàng)，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(xiàng)，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(jié)構(gòu)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(jié)構(gòu)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(guān)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(guān)系。

式(2-14)表明，用電容的差除和表達(dá)傳感器的性能，其輸出還要受到介質(zhì)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(guān)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(dǎo)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(qū)動器的基本理論

BasicphysicsofElectrostaticActuation

Twowaystochangetheenergy:

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

變間隙電容驅(qū)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(qū)動器的理論模型(Electrostaticcombdrive)Useofcomb-capacitivetranducersbringsmanybenefits

．Linearizesvoltage-generatedinputforces

．(Ideally)eliminatesdependenceoffrequencyondc-bias．Allowalargerangeofmotion叉指驅(qū)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(shè)計原理及計算例子2、薄膜設(shè)計原理及計算例子3、電容設(shè)計原理及計算例子4、電阻設(shè)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(shè)計原理及計算例子57MEMS技術(shù)-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(guān)

2、半導(dǎo)體的電阻改變：由材料受力后電阻率的變化引起，與相關(guān)；

3、半導(dǎo)體的靈敏度因子比金屬的高得多，一般在70-170之間

59當(dāng)電阻為立體結(jié)構(gòu)時，有立體單元電阻的應(yīng)力圖當(dāng)電阻為立體結(jié)構(gòu)時，有立體單元電阻的應(yīng)力圖60(7-6)其中{ΔR}=代表與應(yīng)力分量{σ}=（如圖7.13）相對應(yīng)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(biāo)系中，當(dāng)坐標(biāo)軸與晶軸一致時，電阻的相對變化與應(yīng)力的關(guān)系為若電阻為薄膜電阻，在正交坐標(biāo)系中，當(dāng)坐標(biāo)軸與64

表示縱向應(yīng)力

為橫向應(yīng)力表示、垂直方向上的應(yīng)力，它比和小很多，一般都略去。、、分別為、、相對應(yīng)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(yīng)力65

當(dāng)電阻處于任意晶向P時，如果有縱向應(yīng)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(yīng)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(dāng)電阻處于任意晶向P時，如果有縱向應(yīng)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(yīng)力相對于晶體主軸坐標(biāo)系中的方向余弦；、、分別為電阻的橫向應(yīng)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(dāng)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(dāng)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(dǎo)致電壓的變化舉例計算電阻的變化導(dǎo)致電壓的變化73第4講主要內(nèi)容(3)1、彈簧設(shè)計原理及計算例子2、薄膜設(shè)計原理及計算例子3、電容設(shè)計原理及計算例子4、電阻設(shè)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(shè)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