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Semi-Analy6calModelforLeakageCurrentinUltra-ShortDGMOSFETBasedonNEGFFormalism

FabianHosenfeld1,2MichaelGraef1,2,FabianHorst1,2,BenjaminIniguez2,FrancoisLime2,AlexanderKloes1

1CompetenceCentreforNanotechnologyandPhotonics,TechnischeHochschuleMiQelhessen,Gießen,Germany

2UniversitatRoviraiVirgili,Tarragona,Spain

MOS-AK,March18th,2016

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Mul$scaleSimula$on-  Semi-analy6cal-  Closedformsolu6onofPoisson->NEGF

FabianHosenfeld 1

Introduc$onGa

p

DeviceSimula$on-  Atomicscale-  Numericalsolu6on

CircuitSimula$on-  Terminalvoltages/currents-  Analy6calsolu6on

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Advantages

Advantage-  Quantumeffectsintransport

direc6onincluded-  SourcetoDraintunneling-  Fasterthanclassicaldevice

simula6on

Disadvantage-  Notselfconsistent(tobeshownifsufficient)-  Slowerthancompactmodel

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ConceptoftheModelingApproach

Electrosta$cs:2Dclosed-formpoten$alsolu$on

Devicecurrent

One-dimensionalNEGF

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M.Graef,T.Hol6j,F.Hain,A.Kloes,andB.Iniguez,“ImprovedAnaly6calPoten6alModelinginDouble-GateTunnel-FETs.”inMixedDesignofIntegratedCircuitsSystems(MIXDES),2014Proceedingsofthe21stInterna6onalConference,pp.49–53,June2014.

S.DaQa,“NanoscaleDeviceModeling:theGreen’sFunc6onMethod.”SuperlalcesandMicrostructures,vol.28,no.4,pp.253–278,2000.

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Electrosta$cs

4FabianHosenfeld

-  2Dclosed-formsolu6onofPoisson‘sequa6on

-  Basedoncomformalmapping-  Mobilechargeneglected

(subthreshold)-  Effec6vebuilt-inpoten6almodel

One-dimensionalconduc6onbands(slicesfromsourcetodrain)

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NEGF–WithoutScaEering

5

Green‘sfunc$on:

Integra$onoverenergy:

Electrondensity:

1DCurrentinoneslice:

Hamiltonian:

FabianHosenfeld

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DeviceCurrent

6FabianHosenfeld

•  Surfacecurrent

•  Centercurrent

•  Parabolicfunc$on(GatetoGate)

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Results

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•  ComparedagainstTCAD2DNanoMOSZhibinRenetal.,(2014),"NanoMOS,"hQps://nanohub.org/resources/nanomos.

•  Deviceparameters:–  tch=2nm–  lch=6-10nm–  lsd=10nm–  tox=2.4nm–  Nsd=2*1020cm3–  ɛox=16*ɛ0–  m=0.19*m0–  Vds=0.4V–  ϑ=300K

•  FiPngofVR(quantumconfinement)DaliaSelimetal.,“RapidandEfficientMethodforNumericalQuantumMechanicalSimula6onofGate-All-AroundNanowireTransistors,“Proceedingsofthe28thINTERNATIONALCONFERENCEONMICROELECTRONICS,MAY,2012.

•  FiPngofeffec$vemassm=0.29*m0fortch=1nm

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ElectronDensity

8FabianHosenfeld

tch=2nm,lch=6nm,Vds=0.4V

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Modelvs.TCAD:DrainCurrent

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tch=2nm,lch=6nm-10nm,Vds=0.4V

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Modelvs.TCAD:DrainCurrent

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tch=1nm,lch=6nm-10nm,Vds=0.4V

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Modelvs.TCAD:DrainCurrent

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tch=2nm,lch=6nm,10nm,Vds=0.4V,ϑ=75K,300K

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Modelvs.TCAD:SubthresholdSlope

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tch=2nm,lch=6nm,10nm,Vds=0.4V,ϑ=75K-300K

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FutureWork

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tch=2nm,Vds=0.4V

•  Speedupapproachbyavoidingnumericalintegra6onoverenergy:–  Calculatecurrentonlyatsignificantpointsinenergyspectrum–  Defineempiricalanaly6calfunc6onwhichallowsforintegra6onoverenergyin

closedform

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Acknowledgements

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Thisprojectwassupportedby:

•  GermanFederalMinistryofEduca6onandResearchundercontractNo.03FH001I3

•  WewouldliketothankKeysightTechnologiesandAdMOSforsupportandsoywaredona6onofIC-CAP.

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F O R S C H U N G A N F A C H H O C H S C H U L E N