lec12.MOSFET Drain Current Modeling

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1、6.012-ElectronicDevicesandCircuitsFall2003MOSFETDrainCurrentModelingIntheGradualChannelModelfortheMOSFETwewritethedraincurrent,i*D,astheproductofqN(y),theinversionlayersheetchargedensityatpositionyalongthechannel;sy(y),thenetdriftvelocityoftheinversionlayercarriersthe

2、re(electronsinthen-channeldevicewearemodeling),andW,thechannelwidth:i*D=-qN(y)sy(y)WwitheoxdvCS(y)q*(y)=-[vGB-VT(y)]andsy(y)=-µeEy=µeNtoxdySubstitutingtheseexpressionsyields:dvCS(y)iD=WµCox*[vGB-VT(y)]dywherewehaveidentifiedthegatecapacitanceperunitarea,C*,aseox/toxan

3、doxwherethethresholdvoltageisgivenby1VT(y)=VFB+

4、2fp

5、+vCB(y)+*2eSiqNA[

6、2fp

7、+vCB(y)CoxDefiningthebodyfactor,g,as2eSiqNA/C*,andwritingvCB(y)asvCS(y)-oxvBS,wecanrewritethisasVT(y)=VFB+

8、2fp

9、+vCS(y)-vBS+g

10、2fp

11、+vCS(y)-vBSandthuswecanwriteiDasdvCS(y)iD=WµeCox*[vGS-VFB-

12、2fp

13、-v

14、CS(y)-g

15、2fp

16、+vCS(y)-vBS]dyToproceedweintegratebothsidesfory=0toy=L,recognizingthattheright-handintegralisequivalenttointegratingwithrespecttovCS(y)from0tovDS:1vDSLÛiÛ*ı[vDıdy=WµeCoxGS-VFB-

17、2fp

18、-vCS-g

19、2fp

20、+vCS-vBS]dvCS00Theleft-handintegralisiDL,sowecanwriteiDasvDSÛiD=

21、Kı[vGS-VFB-

22、2fp

23、-vCS-g

24、2fp

25、+vCS-vBS]dvCS0whereKisdefinedas(W/L)µeC*.oxItisnothardtodotheintegralontheright-handsideofthisequation,andyoumaywanttodoitasanexercise(itisdoneinthetextandtheresultisgiveninEquation10.9).Theresultingexpressionisawkwardand,mostimportantly,the

26、thresholdvoltage,VT,ishardtoidentifyintheexpressionandtheroleitplaysinthecurrent-voltagerelationshipishardtounderstand;theresultisnotveryintuitive.ItwillnotbeobvioustoyouuntilyougetmuchmoreexperiencewithMOSFETs,butitisverydesirablefromamodelingstandpointtodosomethingt

27、osimplifytheresultandtogetanexpressionthatgivesusmoreusefulinsight.ManytextssimplyignorthevCSfactorundertheradicalandwritevDSÛiDKı[vGS-VFB-

28、2fp

29、-vCS-g

30、2fp

31、-vBS]dvCS0whichwecansimplifyasvDSiÛD=Kı[vGS-VT'-vCS]dvCS0withVT'definedtobeVFB+

32、2fp

33、+g

34、2fp

35、-vBS.Doingtheintegralw

36、egetvDS2iD=K[(vGS-VT')vDS-]2AmoresatisfyingapproachistonotignorthevCSfactor,butrathertotrytolinearizethedependanceonit.Thetr