MEMS技術(shù) 第六講 噪聲與器件的性能

MEMS和微系統(tǒng)設(shè)計(jì)

課程的基本目的掌握MEMS設(shè)計(jì)的基本過(guò)程掌握mems機(jī)電及其耦合分析的基本理論掌握機(jī)電結(jié)構(gòu)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(fā)展前沿知識(shí)培養(yǎng)對(duì)MEMS的興趣課程內(nèi)容MEMS概述及MEMS設(shè)計(jì)的概述工藝簡(jiǎn)要回顧系統(tǒng)設(shè)計(jì)、工藝設(shè)計(jì)及版圖設(shè)計(jì)主要的機(jī)械、電子元件及其設(shè)計(jì)基礎(chǔ)多域耦合設(shè)計(jì)：以機(jī)電耦合為例子器件性能的估計(jì)簡(jiǎn)單的其他域的元件及其簡(jiǎn)要設(shè)計(jì)要點(diǎn)設(shè)計(jì)實(shí)例本章提綱噪聲處理的基本知識(shí)和類型器件的分辨率系統(tǒng)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(jī)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(shí)和類型器件的分辨率系統(tǒng)的分辨率對(duì)簡(jiǎn)單模型加速度計(jì)噪聲的估計(jì)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(jí)放大器和二級(jí)放大器的電噪聲；

A1和A2是一級(jí)和二級(jí)放大器的放大倍數(shù)。按照等效噪聲的功率譜計(jì)算辦法，這些信號(hào)將成平方關(guān)系，這也解釋了為什么放大器一般采用二級(jí)放大，而且第一級(jí)一般采用低噪聲低倍數(shù)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(yùn)動(dòng)，1/2KT的隨機(jī)能量噪聲在任意地方任何靜止時(shí)刻都是存在的，可以用能量的觀點(diǎn)來(lái)進(jìn)行靜態(tài)估計(jì)；由于電子的熱運(yùn)動(dòng)形成了電流，電流隨機(jī)存在，均值為零，動(dòng)態(tài)隨機(jī)存在，功率隨溫度可變，從頻率域看來(lái)，其功率在頻率上保持4KT，只對(duì)電阻有效；類似的，對(duì)應(yīng)于機(jī)械系統(tǒng)，4KT只對(duì)應(yīng)阻尼有效；對(duì)于二階機(jī)械系統(tǒng)：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(tǒng)的擾動(dòng)功率（即1/2m*v*v/t,也可寫作F*v，此處，F(xiàn)是擾動(dòng)力，v是速度，其大小可以用F/c算出來(lái)），相當(dāng)于二階電子系統(tǒng)的V*V/R，F(xiàn)相當(dāng)于R。11233:Areviewtolastlesson.:usingpiezoresistorasexampleCapacitorsensor:sameStonebridgeasusedinpiezoresistor,inputaVininputpositivecurveandanegativecurvevoltage(V+-V-):aexampleisgiventocaculatesensitivity\noise\resolutionanasys(withconsiderationwithamplifycircuit)noisecamefromthedistributecapacitancewhichinfluencecapacitormuchmorethanpiezoresistor112334:capacitorsensor:acalculationtohowf,andresolutionofaaccerameteraredesignedduetonoise.(1kHzfrequencyrequirementandnoiseexistingaretranferedintoaresolutionof0.1mg)distributedcapacitorandamplifiercircuitnoise,andhowtogetridofthosenoisesExample:GyroMDSCalculation根據(jù)下圖，畫出壓阻加速度計(jì)的噪聲模型，途中的Cp需要改成R和Cp的并聯(lián)。計(jì)算方式可參考陀螺的計(jì)算過(guò)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(lái)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(duì)被測(cè)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(wèn)題的辦法包括：第一個(gè)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(tài)。本章提綱噪聲處理的基本知識(shí)和類型器件的分辨率系統(tǒng)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