Analysis of a diffusive effective mass model for nanowires

Clément Jourdana; Nicolas Vauchelet

doi:10.3934/krm.2011.4.1121

Article Contents

2011, Volume 4, Issue 4: 1121-1142. Doi: 10.3934/krm.2011.4.1121

This issue Previous Article A hybrid Schrödinger/Gaussian beam solver for quantum barriers and surface hopping Next Article A problem of moment realizability in quantum statistical physics

Analysis of a diffusive effective mass model for nanowires

Clément Jourdana^1, and
Nicolas Vauchelet^2,

1.
Istituto di Matematica Applicata e Tecnologie Informatiche CNR, via Ferrata 1, 27100 Pavia
2.
UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, CNRS, UMR 7598, Laboratoire Jacques-Louis Lions, INRIA Paris-Rocquencourt, EPI MAMBA, F-75005, Paris

Received: April 30, 2011

Revised: July 31, 2011

Published: November 2011

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Abstract

We propose in this paper to derive and analyze a self-consistent model describing the diffusive transport in a nanowire. From a physical point of view, it describes the electron transport in an ultra-scaled confined structure, taking into account the interactions of charged particles with phonons. The transport direction is assumed to be large compared to the wire section and is described by a drift-diffusion equation including effective quantities computed from a Bloch problem in the crystal lattice. The electrostatic potential solves a Poisson equation where the particle density couples on each energy band a two dimensional confinement density with the monodimensional transport density given by the Boltzmann statistics. On the one hand, we study the derivation of this Nanowire Drift-Diffusion Poisson model from a kinetic level description. On the other hand, we present an existence result for this model in a bounded domain.

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Mathematics Subject Classification: Primary: 35Q40, 76R99, 49K20, 82D80; Secondary: 81Q10.

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