Diffusion and Homogenization approximation for semiconductor Boltzmann-Poisson system
نویسندگان
چکیده
We are concerned with the study of the diffusion and homogenization approximation of the Boltzmann-Poisson system in presence of a spatially oscillating electrostatic potential. By analyzing the relative entropy, we prove uniform energy estimate for well prepared boundary data. An averaging lemma and two scale convergence techniques are used to prove rigorously the convergence of the scaled Boltzmann equation (coupled to Poisson) to a homogenized Drift-Diffusion-Poisson system.
منابع مشابه
Diffusion Approximation and Homogenization of the Semiconductor Boltzmann Equation
Abstract. The paper deals with the diffusion approximation of the Boltzmann equation for semiconductors in the presence of spatially oscillating electrostatic potential. When the oscillation period is of the same order of magnitude as the mean free path, the asymptotics leads to the Drift-Diffusion equation with a homogenized electrostatic potential and a diffusion matrix involving the small sc...
متن کاملOn the Diffusion limit of a semiconductor Boltzmann-Poisson system without micro-reversible process
This paper deals with the diffusion approximation of a semiconductor BoltzmannPoisson system. The statistics of collisions we are considering here, is the Fermi-Dirac operator with the Pauli exclusion term and without the detailed balance principle. Our study generalizes, the result of Goudon and Mellet [14], to the multi-dimensional case. keywords: Semiconductor, Boltzmann-Poisson, diffusion a...
متن کاملDiffusion Limit of a Semiconductor Boltzmann-Poisson System
The paper deals with the diffusion limit of the initial-boundary value problem for the multi-dimensional semiconductor Boltzmann-Poisson system. Here, we generalize the one dimensional results obtained in [6] to the case of several dimensions using global renormalized solutions. The method of moments and a velocity averaging lemma are used to prove the convergence of the renormalized solutions ...
متن کاملDiffusion models for spin transport derived from the spinor Boltzmann equation
The aim of this paper is to derive and analyse diffusion models for semiconductor spintronics. We begin by presenting and studying the so called ”spinor” Boltzmann equation. Starting then from a rescaled version of linear Boltzmann equation with different spin-flip and non spin-flip collision operators, different continuum (drift-diffusion) models are derived. By comparing the strength of the s...
متن کاملHigh Field Mobility and Diffusivity of Electron Gas in Silicon Devices
Abstract. In this paper the Boltzmann equation describing the carrier transport in a semiconductor is considered. A modified Chapman-Enskog method is used, in order to find approximate solutions in the weakly non-homogeneous case. These solutions allow to calculate the mobility and diffusion coefficients as function of the electric field. The integral-differential equations derived by the above...
متن کامل