CryogenicandRFPerformanceofNegativeCapacitance

Field-EffectTransistors

AdityaVarma

ElectricalEngineeringandComputerSciencesUniversityofCalifornia,Berkeley

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CryogenicandRFPerformanceofNegativeCapacitanceField-EffectTransistors

by

AdityaDevVarma

Athesissubmittedinpartialsatisfactionofthe

requirementsforthedegreeof

MasterofScience

in

ElectricalEngineeringandComputerSciences

inthe

GraduateDivision

ofthe

UniversityofCalifornia,Berkeley

Committeeincharge:

ProfessorSayeefSalahuddin,Chair

ProfessorAliNiknejad

Spring2024

ThethesisofAdityaDevVarma,titledCryogenicandRFPerformanceofNegativeCapac-itanceField-EfectTransistors,isapproved:

Chair

Date

Date

Date

5.10.2024

5/10/2024

UniversityofCalifornia,Berkeley

CryogenicandRFPerformanceofNegativeCapacitanceField-EffectTransistors

Copyright2024

by

AdityaDevVarma

1

Abstract

CryogenicandRFPerformanceofNegativeCapacitanceField-EffectTransistors

by

AdityaDevVarma

MasterofScienceinElectricalEngineeringandComputerSciences

UniversityofCalifornia,Berkeley

ProfessorSayeefSalahuddin,Chair

Negativecapacitance(NC)fieldeffecttransistorshavereceivedsignificantresearchinterestinCMOSelectronicsfortheirabilitytoincreasetheintrinsicdevicecapacitance(Cgg)andtransconductance(gm)withoutdegradationtocarriertransport,whilemaintainingahighdegreeofCMOScompatibilityduetotheuseofHfO2andZrO2thin-filmdielectrics.Inthisthesis,weexpandupontwoaspectsofthecurrentresearchonthisemergingdevicetechnology.First,cryogenicRFandDCmeasurementsareperformedonp-typeNCFETsonasilicon-on-insulator(SOI)platform.ThemaintenanceofNCperformanceenhancementsat77Kinp-typedevicesisconfirmed,alongwithsubstantialincreasesingm,indicatingtheattractivenessofNCFETsforfullycomplimentary,low-temperaturelogicandmixed-signalcircuitdesign.Furthermore,anin-depthanalyticalstudyoftheRFnoiseperformanceofnegativecapacitanceFETsisperformed,inordertounderstandhowtherecoveryofthecutofffrequency(fT)fromparasiticcapacitancesuppressionaffectsRFnoise.WefindfavorablescalingtrendsintheminimumnoisefigureNFmin,noisemeasureNM,andnoisesensitivityRnwhencomparedtothescalingperformanceofinterfaciallythinneddielectrics.FutureworkandapplicationsofNCFETsinintegratedcircuitdesignarediscussedinclosing.

i

????????f??????????????f?????????f?

????????↑?????????????????:????????:||17||

BhagawanSriKrishna,BhagavadGita,Chapter12Verse17

ThisthesisisdedicatedwithlovetoRameshK.Verma.

1937-2021

ii

Contents

Contents

ii

ListofFigures

iii

ListofTables

v

1IntroductiontoHfO2-ZrO2(HZH)NegativeCapacitanceFETs

1

1.1LandauTheoryofNegativeCapacitance

2

1.2PriorWorkandTransistor-LevelIntegration

4

1.3ThesisOutline

5

2RFMeasurementandParameterExtractionofNCFETDevices

6

2.1ExperimentalMeasurementSetup

6

2.2RFSmall-SignalModeling

7

2.3ExtrinsicElementDe-EmbeddingandExtraction

8

2.4IntrinsicDeviceElementExtraction

17

3CryogenicMeasurementandCharacterizationofPMOSNCFETDevices

24

3.1RFC-VExtractionat77K

25

3.2DCDeviceCharacterization

26

3.3RFSmall-SignalCharacterizationandBenchmarking

28

4AnalyticalRFNoiseModelingofLow-EOTFieldEffectTransistors

31

4.1NoiseParametersandEOTScaling

32

4.2ModelingusingtheNoiseCorrelationMatrixMethod

35

4.3ProjectionResults

37

5Conclusion

43

Bibliography

44

iii

ListofFigures

1.1Scalingtrendofeffectiveoxidethickness(EOT)vspowersupplyVdd.Figure

Credit:[34]

1

1.2Cross-sectionalschematicofasilicon-on-insulator(SOI)gate-stacktransistor

withanegativecapacitance(NC)dielectric

3

1.3Freeenergylandscapeofamixedorderferroelectric-antiferroelectric(FE-AFE)

system.FigureCredit:[39]

4

2.1ExperimentalsetupforRFMeasurements

7

2.2Small-signalequivalentcircuitusedforRFparameterextraction

8

2.3Open/Shortde-embeddingstructurediagram

9

2.4SeriesandShuntNetworkConnections

10

2.5De-embeddingprocedurediagram

11

2.6IntrinsicandExtrinsicMOSFETdevicemodel(Vgs>Vt)

12

2.7IntrinsicandExtrinsicMOSFETdevicemodelintheoff-state(Vgs<Vt)

12

2.8Extractedgateresistancevs.frequencyviaColdFETmethod

14

2.9ExtractedRsdvs.VovandfrequencyviaColdFETmethod

14

2.10ExtractedLs/Ldvs.VovandfrequencyviaColdFETmethod

15

2.11ExtractedLgvs.VovandfrequencyviaColdFETmethod

16

2.12Capacitiveparasiticsvs.frequencyviaColdFETmethod

17

2.13Cggextractedfor90/120/150nm(left-to-right,respectively)NMOSdevices

19

2.14Cgg,iisextractedusingtheslopeofCgg/WversuschannellengthLg.Theeffective

oxidethickness(EOT)isdeterminedviamatchingtheinversioncapacitanceto

SCHREDsimulations

20

2.15Transconductance(gm)increasesasafunctionofthegatevoltageasstrongin-

versionoperationisreached.gm.iandgm,earecalculatedbylinearfitsacross

frequencyforeachVgbiaspoint

21

2.16fTandfMAXextraction.Theremovalofextrinsicparasiticssignificantlyim-

proveshigh-frequencyperformance

22

2.17Modeledvs.MeasuredS-parametersof90nmNMOSdevice;anexcellentfitis

achievedupto40GHz.S21ismultipliedby0.3toensuredepictionwithinthe

Smithradius,andS22ismultipliedby0.4topreventoverlapwithotherparameters.

23

3.1RFC-Vcharacterizationofp-typeNCFETdevicesatlowtemperature

25

iv

3.2DCId-Vg,SS,andVttrendsofPMOSdevicesatlowtemperature

26

3.3DCId-VdcharacteristicsandId-Vgcharacteristicsunderhigh-Vdbiasconditions.

27

3.4(a,b)SmithChartmodelingat300Ktemperatureand77K-theS21parameter

isdecreasedto0.3timesthemeasuredvaluetokeepitinsidetheS-circle.(b)gm

showsminimaldispersionatboth77Kand300K.(d)fT,iisextractedatroom

temperatureand77Kfromthe|H21|parameter

28

3.5gm,iandvinjvstemperature;benchmarkedgmandvinjagainstindustrialMOS

devices

29

3.6fT,ivs.temperatureandpredictedscalingtrendwithasilicon-germanium(SiGe)

channel

30

4.1Thesuperheterodynereceiverarchitecture,withRF,IF,andAUDIOcompo-

nents.LNAsheadthereceiverchainafteraninitialfilterstage

31

4.2ScalingofNFminunderhighandlowRgassumptions,andvaryingcorrelation.

Insetsarefrequencybehaviorat5angstromEOT

37

4.3Scalingofthenoisesensitivityparameter(Rn)andthenoisepowerspectral

densitiesSiDandSiG.4(c)Inset:5AEOTsimulation

39

4.4NoisemeasureduetoNCEOTscalingandinterfaciallayerthinning.Extrinsic

andintrinsicfT/fMAXvs.EOTexplainthebehaviorinNM

40

4.5NoiseFigurevs.Gaincontoursandscalingtrendvs.literaturereports

41

v

ListofTables

4.1ExtractedRFParametersforLg=90nmNCFET

.................33

vi

Acknowledgments

Firstandforemost,Iwouldliketothankmyadvisor,ProfessorSayeefSalahuddin,forhisguidance,encouragement,andfullsupportofmyresearchintereststhroughoutthedurationofmyundergraduateandmastersstudies.Ihavehadthebenefitoflearningfromhisexpansiveknowledgeandimpact-drivenapproachtosemiconductordeviceresearch,andIammostgratefulfortheopportunitytoworkoncutting-edgenegativecapacitanceFETsinhislaboratory.IamalsogratefultoProfessorAliNiknejadforservingassecondreaderonthisthesis,andforhisinstructivecourses-EE105(MicroelectronicDevices)andEE242A(RFIntegratedCircuits)-whichcontributedtofosteringmyinterestintheapplicationsofsemiconductordevices.

IammostgratefulforthementorshipandcollaborationIreceivedfromNirmaanShanker,whotaughtmehowtoconductRF/cryogenicmeasurementsandofferedsignificantamountsofhistimetoassistmyresearch.Inaddition,IwouldliketothankSurajCheema,whoseencouragementtoexplorenewapplicationsofNCFETsservedasinspirationtofollownovellinesofresearchandinquiry.IwouldalsoliketoextendmysincereappreciationtoMohamedMohamed,whosupervisedmyinternshipatMITLincolnLaboratoryinthesummerof2023,andwhowentoutofhiswaytosupportmyresearch.IwouldalsoliketohighlightthemembersoftheNCsubgroup-JongHo,Chirag,Koushik,Chia-Chun,Junhao,Urmita,Yejin,andSophia-formakingthegroupawelcomingandexcitingplacetobeagraduatestudent.AthanksisalsoduetomypeersKevinLu(withwhomIhavesurvivedmuchoftheBerkeleyEECScurriculum)andAshwinRammohanforseveralhelpfulexchangesregardingRFmodeling.

Finally,IwouldliketoespeciallythankmyfamilyfortheirunconditionalloveandsupportthroughoutfiveoftentumultuousyearsattheUniversityofCalifornia,Berkeley.Theirencouragement,patience,andfullfaithhasbeeninstrumentaltothecompletionofthisthesis.

1

Chapter1

IntroductiontoHfO2-ZrO2(HZH)NegativeCapacitanceFETs

Intherelentlessmarchtowardslow-power,highdensityelectronics,theinsulatinglayerinmoderntransistors-oftenreferredtoasthe’gatedielectric’or’gatestack’-hasbeenacru-cialdriverofimprovedelectronicsperformance.ThegatedielectricfunctionsasacapacitorwithintheMOSFETdevicestructure,allowingavoltageappliedtothegateterminaltomodulatetheamountofchargeinthechannel[

36

].Forlogicapplications,theMOSFETisoperatedasadigitalswitch,withconductingandinsulatingchannelstatesallowingimple-mentationofcomplexlogicfunctionality[

46

].ThesetwostatesoftheMOSdevicecanbeindicatedbyanabsolutecurrentlevel,sometimesreferredtoasIonandIoff.

Figure1.1:Scalingtrendofeffectiveoxidethickness(EOT)vspowersupplyVdd.Figure

Credit:[

34

]

CHAPTER1.INTRODUCTIONTOHFO2-ZRO2(HZH)NEGATIVECAPACITANCE

FETS2

Fromfirstprinciples,currentisproportionaltocharge,andthechannelchargeisdeter-minedbythegatedielectriccapacitorviaQ=C×V[

36

,

54

].Thismeansthatimprovingtheabilityofthecapacitortocontrolthechannelcharge(e.g.itspermittivity,ordielectricstrengthκ)canreducetheneededgatevoltageVovtoachieveacurrentofIon.SincethepowersupplyislowerboundedbyamultipleofVov[

46

],reducingthegatevoltageshowsapathtoreducetheoveralloperatingvoltage,thusloweringCMOSpowerconsumption.Figure1.1showsthehistoricale?icacyofthistrend.

Inthe1990s,Intelandothersemiconductormanufacturersbegantolookbeyondsilicon’snaturaldielectric-SiO2-andexamineddifferentmaterialssystemsforbetterdielectricperformance[

7

].Ofparticularpromiseweretwobinaryoxides-HfO2andZrO2-thatcouldbeintegratedinaCMOS-compatiblefashiontoincreasetheeffectivedielectricconstant(κ).SincecapacitanceisgivenasκE0,usingamaterialwithahigherκthanSiO2canimprovethecapacitance.Thisideahasledtothenotionofeffectiveoxidethickness(EOT).Foragivennon-SiO2material,theEOTstateshowthickanSiO2layerneedstobetoproduceanequivalentcapacitance.TheCMOS-compatibilityofHfO2andZrO2hasledtotheintegrationofthehigh-κmetalgate(HKMG)intomoderntransistors,whichhasbeenaprimarymechanismofMOSFETimprovementinthe2000s.Thishasenabledmoderntransistorswithhigh-κdielectricstoachieveanultrathin9.5?EOT[

41

,

13

],whereithasremainedforseveralyears.

Intheyears2011-2012,itwasdiscoveredthatHfO2[

8

]andZrO2[

43

]filmsexhibitferroelectricity.Ferroelectricitydescribesamaterial’stendencytospontaneouslypolarizeinresponsetoanelectricfield;twokeypropertiesincludethatthispolarizationisswitcheablebyapplyinganelectricfieldintheoppositediection,andthataferroelectricmaterialwillremainpolarizedevenaftertheremovaloftheexternalelectricfield.Thediscoveryofferroelectricityinthismaterialssystemenabledthepossibilityofnegativecapacitance(NC)transistorsinsiliconCMOS,whichwillbeexplainedbelow.

1.1LandauTheoryofNegativeCapacitance

Thecentralideabehindnegativecapacitanceinatransistorisasfollows:supposewehavetheMOSdevicestructureinFigure1.2.

CHAPTER1.INTRODUCTIONTOHFO2-ZRO2(HZH)NEGATIVECAPACITANCE

FETS3

Figure1.2:Cross-sectionalschematicofasilicon-on-insulator(SOI)gate-stacktransistorwithanegativecapacitance(NC)dielectric.

Thetotalcapacitanceofthedielectriclayers(theNClayerplustheSiO2layer)isgivenbyaseriescapacitorequation:

(1.1)

Thecorrespondingeffectiveoxidethickness(EOT)equationis:

EOTtotal=EOTSiO2+EOTNC(1.2)

Now,supposethatthecapacitanceCNC<0orequivalentlyEOTNC<0.Thenequation1.1implies:

(1.3)

wherethemorenegativeCNCis,thelargerthecapacitance.Similarly,equation1.2wouldread[

29

]:

EOTtotal=EOTSiO2-|EOTNC|(1.4)

whichsuggeststheeffectiveoxidethicknesscanbereducedwithoutanyphysicalthinningoftheoveralldielectriclayer.Thisbegsthequestion-howcanwerealizeadielectriclayerwithanegativeEOT?Onemeansofdoingsoisbymanipulatingamaterial’sferroelectricity

1

.

1TheoriginaltheoryofnegativecapacitanceinaferroelectricmaterialcanbeattributedtoRolfLandauerinthe1960s[

38

];thefirstpresentationofadaptingthisideaforintegrationintoaMOSFETwaspresentedbySalahuddinandDattain[

47

].

CHAPTER1.INTRODUCTIONTOHFO2-ZRO2(HZH)NEGATIVECAPACITANCE

FETS4

WewilladopttheLandaufreeenergylandscapeviewinordertoexplainhowtorealizesuchaneffect(Figure1.3).

Figure1.3:Freeenergylandscapeofamixedorderferroelectric-antiferroelectric(FE-AFE)

system.FigureCredit:[

39

]

.

Theenergylandscapeofaferroelectricmaterialisinblue.Thetwominimalenergystatescorrespondtothepolarizedstatesoftheferroelectricmaterial,whichexplainswhythematerialsremainpolarizedevenwithoutanexternallyappliedelectricfield(i.e.thesestatesareenergeticallystable).Capacitanceisrelatedtotheconcavity/convexityofthesefreeenergycurves-aconvexenergylandscapes(likethetwopolarizedstates)representpositivecapacitance.However,thetransitionregionbetweenthetwostablestateshasaconcavecharacteristic–indicatinganegativecapacitance.However,thisregionisveryenergeticallyunstable,andthepresenceofanychargewillshiftthematerialintooneofitstwostablestates.

Nowwecanconsiderwhathappensifweaddasecondmaterialthathasantiferroelec-tricproperties(essentially,amaterialthatstronglydisfavorsthetwostablestatesoftheferroelectricmaterial).AsshowninFigure1.3,theoverallenergylandscapecanbeflat-tened,asrepresentedbythegreencurve.Thiscompositecurvemanagestostabilizetheferroelectriclayerintheotherwiseunstablenegativecapacitanceoperatingstate,leadingtoanenhancementinpermittivityandcapacitance.

1.2PriorWorkandTransistor-LevelIntegration

AlthoughferroelectricitywasdemonstratedinHfO2andZrO2in[

8

,

43

],thethicknesslimitsofthisbehaviorinthesefilmswasnotwellknown.Inordertobeintegratedintomodern

CHAPTER1.INTRODUCTIONTOHFO2-ZRO2(HZH)NEGATIVECAPACITANCE

FETS5

transistorgatestacks,thedielectricisgenerallynothickerthan2-3nanometers[

41

],whereasferroelectricityistypicallyaneffectthatweakenswhenthematerialthicknessisreduced.Contrarytothisgeneralexpectation,emergentferroelectricityinultrathinfilmsofZrO2-downto5?thickness-wasdemonstratedin[

15

],andferroelectricityin1nanometerdopedHfO2filmswasconfirmedin[

16

]duetosizeeffectscounterintuitivelystabilizingthematerialpolarization.In[

17

],a1.8nanometertrilayergatestackcomposedofHfO2-ZrO2-HfO2(HZH)filmswasdemonstratedforadvancedtransistorapplications,witharemarkablyloweffectiveoxidethickness(EOT)of6.5?-particularlynotableastheHZHdielectricwasdepositedontopof8?ofSiO2,confirmingthattheEOTprovidedbytheHZHlayerisindeednegative.

IntegrationoftheHZHgatestackinto90nmNMOSSOItransistorswasdemonstratedin[

39

],showingsubstantiallyhighertransconductance(gm)thanindustrybenchmarks.Repro-ductionofthegatestackprocessinMITLincolnLaboratory’sMicroelectronicsLaboratorywasannouncedin[

52

],notablyincludingPMOSdevices.CryogeniccharacterizationofnFETdeviceswasperformedin[

40

],demonstratingthepotentialofNCFETsforlow-temperaturehigh-performancecomputing,andETSOIdevicesinashort-channelplatformwerereportedin[

61

].Reliabilitystudies,suchas[

52

]showedthatend-of-lifetime(EOL)characteristicsarenotdegradedbythepresenceoftheNCgatedielectric,andcarriermobilitywaslikewiseunaffectedcomparedtohigh-κHfO2control.ThemostrecentstudiesoftheHZHmateri-alssystemhavefocusedontransport-relatedeffects;namely,increasesincarrierinjectionvelocityduetoelectrostaticconfinementeffects[

29

].

1.3ThesisOutline

Thisthesismakestwomaincontributionsinviewoftheexistingliterature-confirmationofthenegativecapacitanceeffectinp-typeMOSFETsatlowtemperature,andastudyoftheRFnoiseperformanceofnegativecapacitanceFETs.

AsmuchofthisthesisdrawsuponRFmeasurementandcharacterization,thesecondchapteraddressesthesefundamentalsasabasisfortheremainderofthethesis.Next,cryo-genicmeasurementandcharacterizationofp-typeNCFETsonanSOIplatformisperformedtoconfirmthestabilityoftheHZHgatedielectricatlowtemperatureforhigh-performancecomputingapplications.Inthefourthchapter,theeffectofEOTscalingontheRFnoiseperformanceofshort-channelMOSdevicesisexploredviaanalyticalnoisemodeling.Thefinalchaptersummarizesthecontributionsofthisthesiswithaviewtofuturework.

6

Chapter2

RFMeasurementandParameterExtractionofNCFETDevices

Twoimportantexperimentalsignaturesofnegative-capacitance(NC)inaMOSstructureareahysteresis-freeenhancementintotalgatecapacitance,duetoimprovementintheeffectiveoxidethickness(EOT),andenhancementsintransconductance(gm)onaccountofincreasedQinu[

51

].Inthenanoscaleregime,seriesresistances,tracecapacitanceandinductancefromexternalpadstructures,andfabrication-relatedparasiticcomponentsdistortthequalityofsemiconductordeviceperformance,necessitatingRFmeasurementsforaccuratedevicecharacterization[

9

].RFmeasurementsareespeciallypowerfulinthisregard,astheyallowanalyticalcorrectionsforseriesimpedanceandpadparasiticsviamethodsfromtwo-portlinearsystemstheory.Inthissection,wedescribeameasurementandanalysisprotocolthatenableshigh-qualitydeviceparameterextractionupto40GHz,emphasizingtheroleoftwo-portnetworktheoryinthecalculations.RFmeasurementsareperformedon90nmnFETSOIdevicesfromMITLincolnLaboratory[

51

]harnessinganegativecapacitance(NC)dielectricgatestacktoillustratethemeasurementandextractionprocedure.

2.1ExperimentalMeasurementSetup

AllmeasurementsinthisthesiswereconductedusingaLakeshoreTTPXCryogenicProbeStationwithLakeshore’sGSG-100-40A-26U-EGSGmicrowaveprobes(Kconnector,40GHz,100μmpitch)asshowninFigure2.1.AnHP8720(40GHz)VectorNetworkAnalyzerisusedtoprovideRFsignals,andDCbiasisprovidedbyaKeysightB1500SemiconductorDeviceAnalyzer,whoseSMUportsareconnectedtotheDCbiasportsoftheVNA.MeasurementcontrolisconductedviaKeysight’sIC-CAPtool,andcalibrationismanagedviaWinCALcalibrationsoftware.

Priortobeginningallmeasurements,calibrationofthenetworkanalyzerisperformedusingtheshort-open-load-through(SOLT)techniquewithaFormFactor(Cascade)GSG101-190ImpedanceStandardSubstrate(100-250umpitch).Forthelow-temperature

CHAPTER2.RFMEASUREMENTANDPARAMETEREXTRACTIONOFNCFET

DEVICES7

measurementsreportedinthispaper,aliquidnitrogentankisconnectedtothecryogenicflowportoftheprobestation,withprobearm,radiationshield,andsubstratechucktemperaturesmonitoredbyvarioustemperaturesensorsinstalledwithintheprobestation.

Figure2.1:ExperimentalsetupforRFMeasurements.

2.2RFSmall-SignalModeling

Theliteratureisexhaustiveonsmall-signalmodelsforRFsemiconductordevices[

9

].Mostsmall-signalcircuitsvaryonlyslightlyinmodelingofspecificphysicalphenomena,asthegeneralmodelhasprovenpowerfulenoughtodescribedevicesasdiverseasGaNtransistors,III-VHEMTs,planarSiFETs,andadvancedgeometrystructuressuchasFinFETs[

22

].Inthissection,wewillreviewtheparameterextractionmethodologyusedinthisthesis(drawnfrom[

9

]),withanemphasisonleveragingtwo-portlinearnetworktheory.

Allextractedresultsarefromasoftwaretool(rfu5.py)thatIdevelopedinmysenioryearofundergraduatestudy.rfu5utilizesPython3.9withamatplotlibandJupyter-Notebookintegratedfront-end,leveragingtheexcellentscikit-RFmicrowaveengineeringpackagefornumerouscomputations[

3

].IamindebtedtoMATLABanalysisscriptsbyWenshenLiforservingasavaluablereferenceforconstructingseveralfeaturesinrfu.

CHAPTER2.RFMEASUREMENTANDPARAMETEREXTRACTIONOFNCFET

DEVICES8

MOSFETSmall-SignalEquivalentCircuit

Thesmall-signalequivalentcircuitmodelusedforRFanalysisisdepictedinFigure2.2.TheelementsgmandRdsrepresenttheclassicquasi-staticsmall-signalparameters-namelythe

devicetransconductance(gm纟)andoutputresistance(Rds=r0纟()-1).The

capacitanceelementsCgsandCgdrepresentapartitionofthetotalgatecapacitance,andsatisfyCgg=Cgs+Cgd.Cdsmodelscapacitiveeffectsbetweenthesourceanddrainterminals.CdsistypicallymuchsmallerthanCgsorCgd,thoughitisimportanttoincludeinRFmodelsasitcanshunttheeffectiveoutputimpedancer0.

TheremainingelementsLs,Rs,Ld,Rd,Lg,Rgrepresentseriesinductanceandresistance,andcanbeseenasafrequency-dependentextensionofthecommonlydiscussedRgateandRsdparameters.Itisimportanttonotethatalloftheseparametersrepresentphysicalquantitiesassociatedwiththedevice-noelementsfullyexternaltotheMOSFETitselfhavebeenintroducedyet.

Figure2.2:Small-signalequivalentcircuitusedforRFparameterextraction.

Theresistancesrgs,rgdmodelnon-quasi-static(NQS)effects,whicharemostlyrelevantwhenthedeviceoperatingfrequencyapproachesthatoftheintrinsiccarriertransittimeτ.gmisadditionallymodeledwithaphasefactore-jωτwhenconsideringNQSeffects.Thisdevicemodelwillbereferredtoasthe’DUT’(DeviceUnderTest)fortheremainderofthissection.

2.3ExtrinsicElementDe-EmbeddingandExtraction

Open-ShortStructureDe-Embedding

CalibrationbringsthereferenceplaneoftheVNArighttotheprobetip(theVNAseestheimpedancethattheprobetipsees,withoutresistancesandlossesthroughtheconnecting

CHAPTER2.RFMEASUREMENTANDPARAMETEREXTRACTIONOFNCFET

DEVICES