Analysis of a diffusive effective mass model for nanowires

TL;DR

This paper develops and analyzes a self-consistent drift-diffusion model for electron transport in nanowires, incorporating quantum confinement and phonon interactions, and proves its existence in bounded domains.

Contribution

It derives a nanowire drift-diffusion Poisson model from kinetic theory and establishes an existence result for the model.

Findings

Model accurately describes diffusive transport in nanowires.

Existence of solutions to the coupled PDE system is proven.

Provides a rigorous foundation for numerical simulations.

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 in 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.