Impact of Elastic and Inelastic Scrattering

8/14/2019 Impact of Elastic and Inelastic Scrattering

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3D simulation of Si nanowire FETs:

impact of elastic and inelastic scattering

Marco Pala

IMEP-LAHC, Grenoble, France

Main collaboration withS. Poli, ARCES Bologna

C. Buran, IMEP-LAHCM. Mouis, IMEP-LAHC


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Outline

Introduction

Models and methods

Transport properties of Silicon nanowire FETs atroom temperature

Surface roughness scattering

Remote Coulomb scattering Electron-phonon scattering


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Semiconductor nanowire FET

Important for scaling of nanoelectronics

Optimal electrostatic control

Specific transport properties due to 1D geometry

Accurate modeling requires:

Quantum confinement

Interference effects

Spatial fluctuations

3D description

Inelastic scattering due to phonons or othermechanisms (e-e, )


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3D NE Greens functions

Goal: Schrdinger equation with open-boundaryconditions at the contacts (out-of equilibrium)

Tight-binding Hamiltonian On-site Greens functions

connected via the Dyson equation

Recursive strategy to compute thetotal Greens function

Meier-Wingreen formalism validalso for inelastic transport

n n+1

nL ,G 1,G +nR

00 GGGG U+=

( )


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Surface roughness in SiNWs

Examples:

We consider devices with 20nm gate length. Quasi-ballistic regime: a proper statistical treatment isadopted

Potential profiles and electron densitiesfor two different slices

mL

r

merC

2

2)(

=

S. Poli et al., IEEE-TED 55, 2968 (2008)


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Size effect: effective mobility

D

eff

qN

GL

1

=

Small wire section: 3x3 nm2

Different behaviour depending on the SR realization

Effective mobility can even increase with Vgs


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Different overdrive regimes

Possible localization phenomena at low Vgs-Vt

LOW BIAS HIGH BIAS


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Large section: more than 25 nm2

We recover a standard picture: the effective mobilitydecreases with Vgs

Predominance of the mode-mixing with respect to the

potential-fluctuations mechanism


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Lateral charge distribution

Size effect: for nanowires with large section theelectron density distribute towards the surface at highbias

Such effect is less efficient in narrow nanowires wherequantum confinement dominates with respect to theelectrostatic control of the gate

HIGH BIAS

3x3 nm2 7x7 nm25x5 nm2


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Effect of SR on the current on SiNWs

Varying RMS of roughness Unchanged sub-threshold voltage slope

Threshold voltage shift

C. Buran et al., IEEE-TED 57 (2009)


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SR-limited mobility

Extracted after subtraction of the ballisticcomponent from the effective mobility

( ) 1

11 = baleffSR


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Remote Coulomb scattering

Charged defects at the interface of differentmaterials like in high-k gate stacks

Random distribution of point-like defects at theinterfaces

Main parameters are NFix and tIL

S. Poli et al., IEEE-TED 56, 1191 (2009)


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1D subband profiles

Subband for different overdrive regimes

Influence of screening effects

Possibility of cluster formation


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Effects on the current

Current detrimental in the subthreshold regime

Larger sub-threshold voltage slope


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Increase of tunneling current

Transmission probability for different densities offixed charges


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Effective mobility

Importance of screening effects

Strong variation between different realizations

due to the presence of clusters


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RCS-limited mobility

Extracted via the Mathiessen rule

Almost linear dependence on the linear density


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Parameters

Influence of fixed-charge density

Influence of interfacial layer thickness

Inefficiency of screening at short distances


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Electron-phonon scattering

Elastic scattering: Acoustic phonons

Inelastic scattering: Optical phonons

Both g-type and f-type for Si are considered Self-energies within self-consistent Born approx

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Impact of Elastic and Inelastic Scrattering

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