On the Analysis of Parasitic Quantum Effects in Classical MOS Circuits

MOS-AK ESSCIRC 2004 20.09. Leuven (Belgium)

On the Analysis of Parasitic On the Analysis of Parasitic QuantumQuantum

Effects in Classical MOS CircuitsEffects in Classical MOS CircuitsFrank FelgenhauerFrank Felgenhauer, ,

Simon Fabel, Wolfgang MathisSimon Fabel, Wolfgang Mathis

Institute of Electromagnetic Theory Institute of Electromagnetic Theory and Microwave Techniqueand Microwave Technique

University of Hannover, GermanyUniversity of Hannover, Germany

Felgenhauer Uni Hannover20.09.2004

MOS-AK ESSCIRC 2004

OutlineOutline

IntroductionIntroduction

Simulation StrategySimulation Strategy

SummarySummary



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Exponential increase in gate leakageExponential increase in gate leakage– increased power consumptionincreased power consumption– degraded device performancedegraded device performance

Charge carrier quantization in the Charge carrier quantization in the channelchannel– loss of inversion chargeloss of inversion charge– loss of transconductanceloss of transconductance

Polysilicon-gate depletion effectsPolysilicon-gate depletion effects


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Scaling into mesoscopic regimeScaling into mesoscopic regime– Increasing influence of qm-effectsIncreasing influence of qm-effects– Changing of device behaviorChanging of device behavior

Question:Question:– Validity of device modelsValidity of device models– Influence in classical circuitsInfluence in classical circuits


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Quantum InterferenceQuantum Interference

Classical Classical CircuitCircuit

Including Including

qm-Effectsqm-Effects


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OutlineOutline



SummarySummary


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Spice circuit modelsSpice circuit models

Circuit SimulationCircuit Simulation

Quantum-mechanical modeling Quantum-mechanical modeling and numerical simulationand numerical simulation

Qm-Effects in MOS devicesQm-Effects in MOS devicesQm-Effects in MOS devicesQm-Effects in MOS devices


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QM-Effects in MOS DevicesQM-Effects in MOS Devices

Tunneling currentsTunneling currents Charge quantizationCharge quantization

Oxide

n+ Gatep Substrate

(or Soure/Drain extension)

EC

EC

TunnelingCurrent

a)

n(x)

b)

quantumclassical

Oxide p Substrate

Gate

Source Drain

Itc

Its Itd


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MOSFETMOSFET– Tunneling Currents (channel – gate, edge Tunneling Currents (channel – gate, edge

direct tunneling)direct tunneling)– Charge quantizationCharge quantization

MOS CapacitorMOS Capacitor– Channel – gate tunnelingChannel – gate tunneling– Charge quantizationCharge quantization


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Qm-Effects in MOS devicesQm-Effects in MOS devices


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Quantum-mechanical Quantum-mechanical ModelingModeling

and Numerical Simulationand Numerical Simulation

Quantum mechanical descriptionsQuantum mechanical descriptions

–Transmission formalismTransmission formalism

–Scattering matrixScattering matrix

–NNon-on-eequilibrium quilibrium GGreen‘s reen‘s ffunction unction formalism (NEGF)formalism (NEGF)


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Non-equilibrium, open boundary conditionsNon-equilibrium, open boundary conditions

1-d MOS-structure1-d MOS-structure Time invariant systemTime invariant system Spatial dependent effective mass and Spatial dependent effective mass and

permittivitypermittivity ScatteringScattering

Poisson self-consistencyPoisson self-consistency


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Selfconsistent Selfconsistent potentialpotential Tunneling currentTunneling current


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Qm-Effects in MOS devicesQm-Effects in MOS devices


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Spice Circuit ModelsSpice Circuit Models

1-d qm simulation1-d qm simulation look-up table modellook-up table model non-linear elements (black box)non-linear elements (black box)

– non-linear current source non-linear current source

tunnelingtunneling– non-linear capacitor non-linear capacitor

MOS C-V, charge quantizationMOS C-V, charge quantization


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Parasitic effect identificationParasitic effect identification

Spice circuit modelSpice circuit model




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(Choi et al, Transaction on Electron Devices ´01)


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VVoutout

VVinin


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(Choi et al, Transaction on Electron Devices ´01)

VxVxVoutVout

VaVa

VbVb

ClockClock


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ClockClock

VaVa

VbVb

VxVx

VouVoutt


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(Nii et al, IEEE Journal of Solid States ´04)


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Leakage CurrentsLeakage Currents

3.6296

9.1743

0

2

4

6

8

10

12

14

Standby leakage (pA/cell)

1.2

Supply Voltage (V)

Ioff

Ig


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OutlineOutline



SummarySummary


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SummarySummary Numerical simulationNumerical simulation

Spice modelsSpice models

Circuit simulationCircuit simulation

Circuit functionality – quantum effectsCircuit functionality – quantum effects


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Classical descriptionClassical description– Drift-DiffusionDrift-Diffusion– Hydrodynamic transport equationHydrodynamic transport equation– Boltzmann transport equationBoltzmann transport equation

Semi-classical description (QM-Semi-classical description (QM-corrections)corrections)– Density GradientDensity Gradient– Quantum hydrodynamic equationQuantum hydrodynamic equation


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Poisson equation

Schrödinger equation

Electron density n Potential U


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Schrödinger equationSchrödinger equation

Density matrixDensity matrix

Electron densityElectron density

Poisson equationPoisson equation 2DU q N n

*

',

( ) ( ) ( ')r r

n r r r

0

1( )

2F E A E dE

( ) ( )H U r E r


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Impact in CircuitsImpact in Circuits

Static CMOSStatic CMOS– Off-state power dissipationOff-state power dissipation

Dynamic CMOSDynamic CMOS– Off-state power dissipationOff-state power dissipation– Discharge breakdown, parasitic currentsDischarge breakdown, parasitic currents

Analog – mixed Signal Analog – mixed Signal – Discharge breakdown, parasitic currentsDischarge breakdown, parasitic currents– Magnitude variationMagnitude variation


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QM transport processQM transport process

Integral Integral valuesvalues

I,UI,U

Integral Integral valuesvalues

I,UI,U

Circuit Circuit modelingmodeling

Circuit Circuit modelingmodelingPhysical Physical

LayerLayer

On the Analysis of Parasitic Quantum Effects in Classical MOS Circuits

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