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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
>