拉扎维《模拟集成电路设计》第二版Ch2课件

Chapter2:MOSDevicePhysics2.1GeneralConsiderations2.2MOSI/VCharacteristics2.3Second-OrderEffects2.4MOSDeviceModels2.5AppendixA:FinFETs2.6AppendixB:BehaviorofMOSDeviceasaCapacitor2MOSFETasaSwitchWhengatevoltageishigh,deviceison.Sourceanddrainareinterchangeable.But,-Atwhatgatevoltagedoesthedeviceturnon?-HowmuchistheresistancebetweenSandD?-Whatlimitsthespeedofthedevice?3MOSFETStructuren-typeMOS(NMOS)hasn-dopedsource(S)anddrain(D)onp-typesubstrate(“bulk”or“body”).S/Djunctions“side-diffuse”duringfabricationsothateffectivelengthLeff=Ldrawn−2LD.TypicalvaluesareLeff≈10nmandtox≈15

Å.TheSterminalprovideschargecarriersandtheDterminalcollectsthem.Asvoltagesatthethreeterminalschanges,thesourceanddrainmayexchangeroles.4MOSFETStructureMOSFETsactuallyhavefourterminals.Substratepotentialgreatlyinfluencesdevicecharacteristics.TypicallyS/Djunctiondiodesarereversed-biasedandtheNMOSsubstrateisconnectedtothemostnegativesupplyinthesystem.5MOSFETStructurePMOSisobtainedbyinvertingallofthedopingtypes(includingthesubstrate).6MOSFETStructureIncomplementaryMOS(CMOS)technologiesbothNMOS(NFET)andPMOS(PFET)areneededandfabricatedonthesamewafer.Intoday’sCMOS,thePMOSisfabricatedinann-well,wherethen-wellistiedtothemostpositivesupplyvoltage.7MOSSymbolsSubstrateisdenotedby“B”(bulk).PMOSsourceispositionedontopsinceithasahigherpotentialthanthegate.MostcircuitshaveNMOSandPMOSbulktiedtogroundandVDD,respectively,sowetendtoomittheconnections(b,c).Digitalcircuitstendtoincorporate“switch”symbols(c).8ThresholdVoltageAsVGincreasesfromzero,holesinp-substratearerepelledleavingnegativeionsbehindtoformadepletionregion.Therearenochargecarriers,sonocurrentflow.9ThresholdVoltageIncreasingVGfurtherincreasesthewidthofthedepletionregionandthepotentialattheoxide-siliconinterface.Structureresemblesvoltagedividerconsistingofgate-oxidecapacitoranddepletionregioncapacitorinseries.10ThresholdVoltageWheninterfacepotentialreachessufficientlypositivevalue,electronsflowfromthesourcetotheinterfaceandeventuallytothedrain.Thiscreatesachannelofchargecarriers(inversionlayer)beneaththegateoxide.ThevalueofVGatwhichtheinversionlayeroccursisthethresholdvoltage(VTH).11ThresholdVoltageWhere-ΦMSisthedifferencebetweentheworkfunctionsofthepolysilicongateandthesiliconsubstrate.-kisBoltzmann’sconstant.-qistheelectroncharge.-Nsubisthedopingdensityofthesubstrate.-niisthedensityofelectronsinundopedsilicon.-Qdepisthechargeinthedepletionregion.-Coxisthegateoxidecapacitanceperunitarea.-єsiisthedielectricconstantofsilicon.

12ThresholdVoltageInpractice,thresholdvoltageisadjustedbyimplantingdopantsintothechannelareaduringdevicefabrication.ForNMOS,addingathinsheetofp+increasesthegatevoltagenecessarytodepletetheregion.13ThresholdVoltageTurn-onphenomenainPMOSissimilartothatofNMOSbutwithallpolaritiesreversed.Ifthegate-sourcevoltagebecomessufficientlynegative,aninversionlayerconsistingofholesisformedattheoxide-siliconinterface,providingaconductionpathbetweensourceanddrain.PMOSthresholdvoltageisnegative.14DerivationofI/VCharacteristicsWhere-QdisthemobilechargedensityalongthedirectionofcurrentI.-visthechargevelocity.15DerivationofI/VCharacteristicsOnsetofinversionoccursatVGS=VTH.InversionchargedensityproducedbygateoxidecapacitanceisproportionaltoVGS−VTHsinceforVGS≥VTH,chargeplacedonthegatemustbemirroredbychargeinthechannel,yieldingauniformchannelchargedensity:

WhereWCoxisthetotalcapacitanceperunitlength.16DerivationofI/VCharacteristicsChannelpotentialvariesfromzeroatthesourcetoVDatthedrain.LocalvoltagedifferencebetweenthegateandthechannelvariesfromVGtoVG−VD.Chargedensitynowvarieswithrespecttox:,whereV(x)isthechannelpotentialatx.17DerivationofI/VCharacteristicsSince------

AnegativesignisaddedbecausethechargecarriersarenegativeforNMOS.

18DerivationofI/VCharacteristicsVGS−VTHisknownasthe“overdrivevoltage.”W/Lisknownasthe“aspectratio.”IfVDS≤VGS−VTH,wesaythedeviceisoperatinginthe“trioderegion.”..

19DerivationofI/VCharacteristicsIfVDS<<2(VGS−VTH),then

Inthiscase,thedraincurrentisalinearfunctionofVDSsothepathfromsourcetodraincanberepresentedbyalinearresistor:

20DerivationofI/VCharacteristicsIfVDS<<2(VGS−VTH),thedeviceisoperatingin“deeptrioderegion.”Inthisregion,aMOSFETcanoperateasaresistorwhosevalueiscontrolledbytheoverdrivevoltage.Unlikebipolartransistors,aMOSdevicemaybeonevenifitcarriesnocurrent.Forexample,giventhetopologyontheleftandthat-,-,-,

21DerivationofI/VCharacteristics22DerivationofI/VCharacteristicsInreality,ifVDS>VGS−VTH,IDbecomesrelativelyconstantandwesaythatthedeviceoperatesin“saturationregion.”VD,sat=VGS−VTHdenotestheminimumVDSnecessaryforoperationinsaturation.23DerivationofI/VCharacteristicsIfVDSisslightlylargerthanVGS−VTH,theinversionlayerstopsatx≤L,andthechannelbecomes“pinchedoff.”AsVDSincreases,thepointatwhichQDequalszerograduallymovestowardsthesource.Atsomepointalongthechannel,thelocalpotentialdifferencebetweenthegateandtheoxide-siliconinterfaceisnotsufficienttosupportaninversionlayer.24DerivationofI/VCharacteristicsElectronvelocity()risestremendouslyastheyapproachthepinch-offpoint(where)andshootthroughthedepletionregionnearthedrainjunctionandarriveatthedrainterminal.Sincetheintegralbecomes-

-IDisrelativelyindependentofVDSifL’remainsclosetoL.Thedeviceexhibitsa“square-law”behavior.25DerivationofI/VCharacteristics26DerivationofI/VCharacteristicsForPMOSdevices,theequationsbecomeThenegativesignshowsupduetotheassumptionthatdraincurrentflowsfromdraintosource,whereasholesinaPMOSflowinthereversedirection.VGS,VDS,VTH,andVGS−VTHarenegativeforaPMOStransistorthatisturnedon.Sincethemobilityofholesisabout½themobilityofelectrons,PMOSdevicessufferfromlower“currentdrive”capability.27DerivationofI/VCharacteristicsAsaturatedMOSFETcanbeusedasacurrentsourceconnectedbetweenthedrainandthesource.NMOScurrentsourcesinjectcurrentintogroundwhilePMOScurrentsourcesdrawscurrentfromVDD.28DerivationofI/VCharacteristicsVDS=VGS−VTH=VD,satisthelinebetweensaturationandtrioderegion.ForagivenVDS,thedeviceeventuallyleavessaturationasVGSincreases.Thedrainisdefinedastheterminalwithahigher(lower)voltagethanthesourceforanNMOS(PMOS).29MOSTransconductanceTransconductance(usuallydefinedinthesaturationregion)isdefinedasthechangeindraincurrentdividedbythechangeinthegate-sourcevoltage.gmrepresentsthesensitivityofthedevicesinceahighvalueimpliesasmallchangeinVGSwillresultinalargechangeinID.TransconductanceinsaturationregionisequaltotheinverseofRoninthedeeptrioderegion.30MOSTransconductanceEachexpressionfortransconductanceisusefulinstudyingitsbehavior.Draincurrentandoverdrivevoltagearebiasvalues.Ifasmallsignalisappliedtoadevicewithdefinedbiasvalues,weassumethesignalamplitudeissmallenoughthatthevariationintransconductanceisnegligible.31MOSTransconductanceTofindthetransconductanceforthetopologyontheleftwithrespecttoVDS,-SolongasVDS≥Vb−VTH,M1isinsaturation,soIDisrelativelyconstant,andthereforesoisgm.-WhenM1enterstrioderegion(VDS<Vb−VTH),32MOSTransconductanceForPMOS,

Originally,withthebulkofanNMOStiedtoground,thethresholdvoltagewasdefinedasDecreasingthebulkvoltage(VB)increasesthenumberofholesattractedtothesubstrateconnection,whichleavesalargernegativechargebehindandmakesthedepletionregionwider,increasingQdandthusincreasingVTH.Thisisknownasthe“bodyeffect”or“back-gateeffect.”33Second-OrderEffects

Withbodyeffect,theexpressionwhichcharacterizesthedependenceofthresholdvoltageonthebulkvoltageisWhere,--denotesthebodyeffectcoefficient.34Second-OrderEffects35Second-OrderEffectsForexample,let'sfindthedraincurrentasbulkvoltagevariesfromnegativeinfinityto0giventhetopologyontheleftandthat---

IfVXissufficientlynegative,VTHofM1exceeds1.2Vandthedeviceisoff,therefore,where--Bodyeffectmanifestsitselfwheneverthesourcevoltagevarieswithrespecttothebulkpotential.Giventhetopologyontheleftandfirstignoringbodyeffect,asVinvaries,VoutfollowstheinputbecausethedraincurrentremainsequaltoI1,where36Second-OrderEffectsWithbodyeffect,asVin,outbecomemorepositive,VSBincreases,whichincreasesVTHandthusVin–VoutmustincreasetomaintainaconstantID.Originally,whenthedevicewasinsaturationregion,draincurrentwascharacterizedbyTheactuallengthofthechannel(L’=L−ΔL)isafunctionofVDS,whichisaneffectcalled“channellengthmodulation.”1/L’≈(1+ΔL/L)/L,andΔL/L=λVDS,whereλisthechannel-lengthmodulationcoefficient”givesus37Second-OrderEffectsWiththeeffectofchannellengthmodulation,theexpressionsderivedfortransconductanceofthedevicethatneedmodificationare38Second-OrderEffects39Second-OrderEffectsKnowingthat--andkeepingallotherparametersconstant,wecanseethatifthelengthLisdoubled,theslopeofIDvs.VDSisdividedbyfour.Thisisdueto.40Second-OrderEffectsMOSFETsdonotturnoffabruptlywhenVGS<VTH,butactuallythereisa“weak”inversionlayerthatexistsandfinitecurrentflowsfromdraintosourcewithanexponentialdependenceonVGS.Thiseffectiscalled“subthresholdconduction.”WhenVGS<VTH,whereI0W/L,ξ>1isanonidealityfactor,andVT=kT/q.Herethedeviceoperatesin“weakinversion.”ToexamineMOSFETbehaviorasthedrain“currentdensity,”ID/Wvaries,wemustconsidertheequationsforbothstrongandweakinversion:

ForagivencurrentandW/L,wemustobtainVGSfrombothexpressionsandselectthelowervalue.IfIDremainsconstantandWincreases,VGSfallsandthedevicegoesfromstrongtoweakinversion.41Second-OrderEffects42Second-OrderEffectsMOSFETsexperienceundesirableeffectsifterminalvoltagedifferencesexceedcertainlimits,e.g.-IfVGSistoohigh,thegateoxidebreaksdownirreversibly,damagingthetransistor.-Inshortchanneldevices,excessivelylargeVDSwidensdepletionregionaroundthedrainsothatittouchesthedepletionregionaroundthesource,creatingaverylargedraincurrent(aneffectcalled“punchthrough”).43MOSDeviceLayoutThegatepolysiliconandthesourceanddrainterminalsmustbetiedtometal(aluminum)wiresthatserveasinterconnectswithlowresistanceandcapacitance.Thisisaccomplishedwith“contactwindows”whicharefilledwithmetalandconnectedtotheuppermetalwires.Tominimizethecapacitanceofthesourceanddrain,thetotalareaofeachjunctionmustbeminimized.44MOSDeviceLayoutSinceM1andM2sharethesameS/DjunctionsatnodeCandM2andM3dothesameatnodeN,wecanlaythemoutasshownabove.SincethegatepolysiliconofM3cannotbedirectlytiedtothesourcematerialofM1,ametalinterconnectisnecessary.45MOSDeviceCapacitancesTobetterpredicthigh-frequencybehavior,itisnecessarytoconsiderdevicecapacitances.Capacitanceexistsbetweeneverytwoofthefourterminals,andtheirvaluesdependonthebiasconditionsofthetransistor.46MOSDeviceCapacitancesCapacitancesinclude-TheoxidecapacitancebetweenthegateandthechannelC1.-ThedepletioncapacitancebetweenthechannelandthesubstrateC2.-ThecapacitanceduetotheoverlapofthegatepolywiththesourceanddrainareasC3andC4.-Thejunctioncapacitancebetweenthesource/drainareasandthesubstrateC5andC6.47MOSDeviceCapacitances

Duetofringingelectricfields,C3andC4cannotbewrittenasWLDCox;ratherwemustfindtheoverlapcapacitanceperunitwidth(Cov)andmultiplythatvaluewithW.48MOSDeviceCapacitancesC5andC6aredecomposedintotwocomponents:-Thebottom-platecapacitanceassociatedwiththebottomofthejunction,Cj:whereVRisthereversevoltageacrossthejunction,ΦB

isthejunctionbuilt-inpotential,andmisapowertypicallyintherangeof0.3and0.4.-Thesidewallcapacitanceduetotheperimeterofthejunction,Cjsw.49MOSDeviceCapacitancesForexamplecalculatingthesourceanddrainjunctioncapacitanceofthetopologyontheleft,Calculatingthesourceanddrainjunctioncapacitanceofthesecondtopologyontheleft,Weassumedthetotalsource/drainperimeter2(W+E)ismultipliedbyCjsw.50MOSDeviceCapacitancesConsideringcapacitancevaluesindifferentoperatingregions,ifthedeviceisoff,--whereListheeffectivelength,andєsi=єr,sixє0=11.8x(8.85x10-14)F/cm.-ThevaluesofCSBandCDBareafunctionofthesourceanddrainvoltageswithrespecttothesubstrate.

51MOSDeviceCapacitancesIndeeptrioderegion,thesource/drainhaveapproximatelyequalvoltages,sothegate-channelcapacitanceWLCoxisdividedequallybetweenthegate-sourceterminalsandthegate-drainterminals,whichresultsinCGBisusuallyneglectedintriodeandsaturationregionsbecausetheinversionlayeractsasa“shield”betweenthegateandthebulk,soifVGvaries,thechargeissuppliedbythesource/drainratherthanthebulk.52MOSDeviceCapacitancesIfthedeviceisinsaturationregion,CGDwillberoughlyequaltoWCov.Thevaryingpotentialdifferencebetweengateandchannelcausenonuniformverticalelectricfieldinthegateoxidewhilegoingfromsourcetodrain,whichresultsinCGSbeing53MOSDeviceCapacitancesLetssketchthecapacitanceofM1ontheleftasVXvariesfrom0to3VassumingVTH=0.3Vandλ=γ=0.-ForVX≈0,M1isintrioderegion,soCFBismaximum,and-AsVXexceeds1V,therolesofthesource/drainareexchanged,bringingM1outofthetrioderegionforVX≥2V−0.3V.-CNBisindependentofVX.54MOSSmall-SignalModelIfperturbationinbiasconditionsaresmall,a“small-signal”modelcanbeusedtosimplifycalculations(derivedforsaturationregion).Inordertoderivethesmall-signalmodel,we-Applycertainbiasvoltagestotheterminalsofthedevice.-Incrementthepotentialdifferencebetweentwooftheterminalswhiletheotherterminalvoltagesremainconstant.-Measuretheresultingchangeinallterminalcurrents.55MOSSmall-SignalModelBychangingthevoltagebetweentwoterminalsbyΔV=VGSandthenmeasuringacurrentchangeΔI=gmVGS,wecanmodeltheeffectbyavoltage-dependentcurrentsource.Aboveisthesmall-signalmodelofanidealMOSFET.56MOSSmall-SignalModelDuetochannel-lengthmodulation,draincurrentalsovarieswithVDS,butacurrentsourcewhosevaluelinearlydependsonthevoltageacrossitisequivalenttoalinearresistor:\

ItisassumedthatλVDS<<1.rolimitsthemaximumvoltagegainofmostamplifiers.57MOSSmall-SignalModelDuetobodyeffect,bulkpotentialinfluencesVTHandhencegate-sourceoverdrive.Withallotherterminalsheldataconstantvoltage,thebulkbehavesasasecondgatesincethedraincurrentisafunctionofthebulkvoltagegivenbygmbVBS,where58MOSSmall-SignalModelThesmall-signalmodelaboveisadequateformostlow-frequencysmall-signalanalyses.Inreality,eachterminalexhibitsafiniteohmicresistanceduetoresistivityofthematerial(andcontacts),butproperlayoutcanminimizetheseresistances.-Foldingreducesthegateresistancebyafactoroffour.59MOSSmall-SignalModelThecompleteMOSsmall-signalmodelnotonlyincludeschannel-lengthmodulationandbodyeffect,butalsothecapacitancesbetweeneachterminal.60MOSSmall-SignalModelTosketchgmandgmbofM1ontheleftasafunctionofbiascurrentI1,--gmbdependenceonI1islessstraightforward,butasI1increases,VXdecreasesandsodoesVSB.61MOSSmall-SignalModelThederivationofthesmall-signalmodelforPMOSyieldstheexactsamemodelasforNMOS.Themodelshowsthevoltage-dependentcurrentsourcepointingupward,givingthe(wrong)impressionthatthedirection