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UniversityofAppliedSciences
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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UniversityofAppliedSciences
Mul$scaleSimula$on- Semi-analy6cal- Closedformsolu6onofPoisson->NEGF
FabianHosenfeld 1
Introduc$onGa
p
DeviceSimula$on- Atomicscale- Numericalsolu6on
CircuitSimula$on- Terminalvoltages/currents- Analy6calsolu6on
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UniversityofAppliedSciences FabianHosenfeld 2
Advantages
Advantage- Quantumeffectsintransport
direc6onincluded- SourcetoDraintunneling- Fasterthanclassicaldevice
simula6on
Disadvantage- Notselfconsistent(tobeshownifsufficient)- Slowerthancompactmodel
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UniversityofAppliedSciences 3
ConceptoftheModelingApproach
Electrosta$cs:2Dclosed-formpoten$alsolu$on
Devicecurrent
One-dimensionalNEGF
FabianHosenfeld
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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UniversityofAppliedSciences
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$onoverenergy:
Electrondensity:
1DCurrentinoneslice:
Hamiltonian:
FabianHosenfeld
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UniversityofAppliedSciences
DeviceCurrent
6FabianHosenfeld
• Surfacecurrent
• Centercurrent
• Parabolicfunc$on(GatetoGate)
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Results
7FabianHosenfeld
• 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
9FabianHosenfeld
tch=2nm,lch=6nm-10nm,Vds=0.4V
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UniversityofAppliedSciences
Modelvs.TCAD:DrainCurrent
10FabianHosenfeld
tch=1nm,lch=6nm-10nm,Vds=0.4V
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UniversityofAppliedSciences
Modelvs.TCAD:DrainCurrent
11FabianHosenfeld
tch=2nm,lch=6nm,10nm,Vds=0.4V,ϑ=75K,300K
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Modelvs.TCAD:SubthresholdSlope
12FabianHosenfeld
tch=2nm,lch=6nm,10nm,Vds=0.4V,ϑ=75K-300K
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UniversityofAppliedSciences
FutureWork
13FabianHosenfeld
tch=2nm,Vds=0.4V
• Speedupapproachbyavoidingnumericalintegra6onoverenergy:– Calculatecurrentonlyatsignificantpointsinenergyspectrum– Defineempiricalanaly6calfunc6onwhichallowsforintegra6onoverenergyin
closedform
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Acknowledgements
14
Thisprojectwassupportedby:
• GermanFederalMinistryofEduca6onandResearchundercontractNo.03FH001I3
• WewouldliketothankKeysightTechnologiesandAdMOSforsupportandsoywaredona6onofIC-CAP.
FabianHosenfeld
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