MEMS和微系統設計

課程的基本目的掌握MEMS設計的基本過程掌握mems機電及其耦合分析的基本理論掌握機電結構微器件的性能分析方法了解熱、流體的基本理論了解MEMS的發展前沿知識培養對MEMS的興趣課程內容MEMS概述及MEMS設計的概述工藝簡要回顧系統設計、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本章提綱噪聲處理的基本知識和類型器件的分辨率系統的分辨率NoiseNoise:RandomfluctuationofagivenparameterI(t)Inaddition,anoisewaveformhasazeroaveragevalueWecan’thandlenoiseatinstantaneoustimesButwecanhandlesomeoftheaveragedeffectsofrandomfluctuationsbygivingnoiseapowerspectraldensityrepresentationThus,representnoisebyitsmean-squarevalue:NoiseSpectralDensityWecanplotthespectraldensityofthismean-squarevalue:CircuitNoiseCalculationsDeterministic:Random:HandlingNoiseDeterministicallyCandothisfornoiseinatinybandwidth(e.g.,1Hz)Canapproximatethisbyasimusoidalvoltagegenerator(especiallyforsmallB,say1Hz)[Thisisactuallytheprinciplebywhichoscillatorsworkoscillatorsarejustnoisegoingthroughatinybandwidthfilter]Why?Neithertheamplitudenorthephaseofasignalcanchangeappreciablywithinatimeperiod1/B.SystematicNoisecalculationprocedureGeneralCircuitwithSeveralNoiseSourceAssumenoisesourcesareuncorrelated1.Forreplacew/adeterministicsourceofvalueSystematicNoiseCalculationProcedure2.Calculate (treatingitlikeadeterministicsignal)3.Determine4.Repeatforeachnoisesource:5.Addnoisepower(meansquarevalues)TotalRMSvalue噪聲源干擾噪聲（理論可消除：隔離和共地）機械噪聲（thermalnoise:browniannoise）電噪聲thermalnoise(johnsonnoise)shotnoise(散粒噪聲）1/fnoiseMechanical(Brownian)NoiseImpingingmoleculesgiverisetoaBrowniannoiseforce:NoiseforceappliedtoM-k-bsystemresultsinrandomBrownianmotionwithafrequency-depenndentpowerspectrum:Implications:f<<f1

ElectronicNoiseSourcesThermalnoiseinresistors generatedbyrandommotionofelectronsorholeswhitespectraldensity(upto10THz) spectraldensity Example:R=1kΩ,T=300KThermalNoise(cont.)Thermalnoisecurrent:findNortonequivalent Example:R=1kΩ,T=300K,BW=1MHzResistorNoiseinMEMSInterconnectresistanceRinttocapacitivepositionsensors >routinginpolySi0canleadtoahighresistances, duetorelativelyhighsheetresistanceofthislayer >inertialMEMSoftenhavecompliantsuspensionslargenumberofsquaresinpolySi1andsignificantcontributiontoRintFlicker(1/f)NoiseNoisemechanismrequireaaDCcurrent,incontrasttothermalnoiseOriginof1/fnoiseinMOSFETs:surfacestatesNearDC,thenoisecurrentdiverges!MOSFETNoisesourcesWhenbiasedinsaturation,(VDS>VDS,sat),thenoisecanberepresentedbyaninputnoisevoltageandaninputnoisecurrentOriginof1/fnoiseinMOSFETs:surfacestateschannelresistanceinsaturationinversedependenceongatearealargetransistorshavelower1/fnoise(neglectingDCgatecurrentandit’sshotnoiseMOSFETNoisesource(cont.)EquivalentMOSFETsmall-signalmodelwithinput-referrednoisesourcesCrossoverfrequencybetweenthermalandflickernoisecanrangefrom1kHzto1MHzSNRandDR,DefinedSignal-to-noiseratio=SNRNote1:Pnoise

iscalculatedoveralimitedbandwidthNote2:Vn,rmsistakenastheminimumdetectablesignal,intheabsenceofspecialcodingorsignalprocessingDynamicrange=DRSignalandNoisewaveformsSinusoidwithamplitudenormalizedto1Gaussiannoisewithrmslevelnormalizedto1;notethatpeak-peaknoiselevelisoccasionallyashighas6!本章提綱噪聲處理的基本知識和類型器件的分辨率系統的分辨率對簡單模型加速度計噪聲的估計WhereVout-n=[(Vs-n+Ve1-n)A1+Ve2-n]*A2

Vout-n是電路最終輸出的噪聲；

Vs-n是sensor-noise;Ve1-n,Ve2-n是一級放大器和二級放大器的電噪聲；

A1和A2是一級和二級放大器的放大倍數。按照等效噪聲的功率譜計算辦法，這些信號將成平方關系，這也解釋了為什么放大器一般采用二級放大，而且第一級一般采用低噪聲低倍數放大的緣故。上式還可以看出傳感器的靈敏度是可以放大的，但分辨率和信躁比是不可以放大的。例子：Resolution=noise(equivalentoutput)/sensitivity,unitisthesameasinput,amplifywillnotbeusefulfortheresolution,butforsensitivity.(X*A1+Ynoise-equitvalent)*A2+Yele-equitvalent=Y,Xisinput,Yisoutput,A1issensitivityofsensor,A2iselectricalamplifier,Ynoise-equitvalentisnoiseequitavalentY,Yele-equitvalentiselectronic-noiseequitavalent,thewholesensitivityofsystemisY/X=A1*A2,resolutionofthesystemis（A2*Ynoise-equitvalent+Ynoise-equitvalent）/（Y/X）由于原子的熱運動，1/2KT的隨機能量噪聲在任意地方任何靜止時刻都是存在的，可以用能量的觀點來進行靜態估計；由于電子的熱運動形成了電流，電流隨機存在，均值為零，動態隨機存在，功率隨溫度可變，從頻率域看來，其功率在頻率上保持4KT，只對電阻有效；類似的，對應于機械系統，4KT只對應阻尼有效；對于二階機械系統：4KT*df*c（此處，df是帶寬，c是阻尼，不是阻尼比什么的，即F=c*v）就是系統的擾動功率（即1/2m*v*v/t,也可寫作F*v，此處，F是擾動力，v是速度，其大小可以用F/c算出來），相當于二階電子系統的V*V/R，F相當于R。11233:Areviewtolastlesson.:usingpiezoresistorasexampleCapacitorsensor:sameStonebridgeasusedinpiezoresistor,inputaVininputpositivecurveandanegativecurvevoltage(V+-V-):aexampleisgiventocaculatesensitivity\noise\resolutionanasys(withconsiderationwithamplifycircuit)noisecamefromthedistributecapacitancewhichinfluencecapacitormuchmorethanpiezoresistor112334:capacitorsensor:acalculationtohowf,andresolutionofaaccerameteraredesignedduetonoise.(1kHzfrequencyrequirementandnoiseexistingaretranferedintoaresolutionof0.1mg)distributedcapacitorandamplifiercircuitnoise,andhowtogetridofthosenoisesExample:GyroMDSCalculation根據下圖，畫出壓阻加速度計的噪聲模型，途中的Cp需要改成R和Cp的并聯。計算方式可參考陀螺的計算過程。ThegyrosensepresentsalargeeffectivesourceimpedanceCurrentsaretheimprtantvariable;voltagesare“opend”outMustcomparei0withthetotalcurrentnoiseieqTOTgoingintotheamplifiercircuitB.ThesimplePressuresnesorInthesimplepressuresnesor,themovingmassisdirectlyexposedtotheincidentacousticpressureandthedisplacementofthismassismeasured.SuchasensorisshownschematicallyinFig.3.ForanarbitraryforceF,thedisplacementresponseZisIEEETRANSACTIONSONELECTRONDEVICES,VOL.40,NO.5.MAY1993Mechanical-ThermalNoiseinMicromachinedAcousticandVibrationSensorsForsignal,theforceF=psS,whereSistheareaofthetransducerfaceandpsisthespectraldensityofthesignalpressure;fornoise,theforce ,sothesignal-to-noiseratiois例子：壓力-電容的例子以差壓（電壓）電源供電來檢查電容的變化，需要后接放大電路。放大電路的輸入電容Cp對被測電容的影響較大（Cp通常比參考電容C0要大的多），而且傳感器的輸入電容還包括：引線電容（10pf/m).解決問題的辦法包括：第一個放大器是1：1的放大器，放大器的輸出反饋到放大器輸入電容的一端(輸入電容的另一端接放大器的輸入），這樣輸入電容處于V=0的狀態。本章提綱噪聲處理的基本知識和類型器件的分辨率系統的分辨率IEEESENSORSJOURNAL,VOL.5,NO.3.JUNE2005Mechanical-ThermalNoiseinMEMSGyroscopesVibratoryGyroscopesGeneratemomentumbyvibratingstructuresAgain,conservationofmomentumleadstomechanismsformeasuringrotationrateandorentationExample:vibratingmassinarotatingframeBasicVibratoryGyroscopeOperationPrincipleofOperation

Drive/SenseReponsespectra:TuningForkGyroscopeMEMS-BasedTuningForkGyroscopeIn-planedriveandsensemodespickupz-axisrotationsMode-matchingformaxmumoutputsensitivityFrom[Zaman,Ayazi,etal,MEMS’06]MEMS-BasedTuningForkGyroscopeDriveAxisEquivalentCircuitGeneratesdrivedisplacementvelocityxdtowhichtheCoriolisforceisproportionalToSenseAmplifer(forsynchronization)Drive-to-SenseTransferFunctionGyroRedoutEquivalentCircuit

(forasingletine)GyroSenseElementOutputCircuitGyroSenseElementOutputCircuitEasiesttoanalyzeifallnoisesourcearesummedatcommonnodeGyroRedoutEquivalentCircuit

(forasingl