MEMS技术 第六讲 噪声与器件的性能

MEMS和微系统设计

课程的基本目的掌握MEMS设计的基本过程掌握mems机电及其耦合分析的基本理论掌握机电结构微器件的性能分析方法了解热、流体的基本理论了解MEMS的发展前沿知识培养对MEMS的兴趣课程内容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本章提纲噪声处理的基本知识和类型器件的分辨率系统的分辨率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噪声源干扰噪声（理论可消除：隔离和共地）机械噪声（thermalnoise:browniannoise）电噪声thermalnoise(johnsonnoise)shotnoise(散粒噪声）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!本章提纲噪声处理的基本知识和类型器件的分辨率系统的分辨率对简单模型加速度计噪声的估计WhereVout-n=[(Vs-n+Ve1-n)A1+Ve2-n]*A2

Vout-n是电路最终输出的噪声；

Vs-n是sensor-noise;Ve1-n,Ve2-n是一级放大器和二级放大器的电噪声；

A1和A2是一级和二级放大器的放大倍数。按照等效噪声的功率谱计算办法，这些信号将成平方关系，这也解释了为什么放大器一般采用二级放大，而且第一级一般采用低噪声低倍数放大的缘故。上式还可以看出传感器的灵敏度是可以放大的，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）由于原子的热运动，1/2KT的随机能量噪声在任意地方任何静止时刻都是存在的，可以用能量的观点来进行静态估计；由于电子的热运动形成了电流，电流随机存在，均值为零，动态随机存在，功率随温度可变，从频率域看来，其功率在频率上保持4KT，只对电阻有效；类似的，对应于机械系统，4KT只对应阻尼有效；对于二阶机械系统：4KT*df*c（此处，df是带宽，c是阻尼，不是阻尼比什么的，即F=c*v）就是系统的扰动功率（即1/2m*v*v/t,也可写作F*v，此处，F是扰动力，v是速度，其大小可以用F/c算出来），相当于二阶电子系统的V*V/R，F相当于R。11233:Areviewtolastlesson.:usingpiezoresistorasexampleCapacitorsensor:sameStonebridgeasusedinpiezoresistor,inputaVininputpositivecurveandanegativecurvevoltage(V+-V-):aexampleisgiventocaculatesensitivity\noise\resolutionanasys(withconsiderationwithamplifycircuit)noisecamefromthedistributecapacitancewhichinfluencecapacitormuchmorethanpiezoresistor112334:capacitorsensor:acalculationtohowf,andresolutionofaaccerameteraredesignedduetonoise.(1kHzfrequencyrequirementandnoiseexistingaretranferedintoaresolutionof0.1mg)distributedcapacitorandamplifiercircuitnoise,andhowtogetridofthosenoisesExample:GyroMDSCalculation根据下图，画出压阻加速度计的噪声模型，途中的Cp需要改成R和Cp的并联。计算方式可参考陀螺的计算过程。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：压力-电容的例子以差压（电压）电源供电来检查电容的变化，需要后接放大电路。放大电路的输入电容Cp对被测电容的影响较大（Cp通常比参考电容C0要大的多），而且传感器的输入电容还包括：引线电容（10pf/m).解决问题的办法包括：第一个放大器是1：1的放大器，放大器的输出反馈到放大器输入电容的一端(输入电容的另一端接放大器的输入），这样输入电容处于V=0的状态。本章提纲噪声处理的基本知识和类型器件的分辨率系统的分辨率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