Boundary conditions effects by Discontinuous Galerkin solvers for Boltzmann-Poisson models of electron transport

TL;DR

This paper investigates how different boundary conditions, including specular and diffusive reflections, affect solutions of Boltzmann-Poisson models for electron transport using Discontinuous Galerkin methods, revealing boundary layer effects.

Contribution

It provides a numerical analysis of boundary condition effects on Boltzmann-Poisson models with DG methods, highlighting boundary layer phenomena.

Findings

Boundary layer effects observed for diffusive and mixed reflections

Different boundary conditions significantly influence solution behavior

Numerical simulations clarify boundary condition impacts on kinetic moments

Abstract

In this paper we perform, by means of Discontinuous Galerkin (DG) Finite Element Method (FEM) based numerical solvers for Boltzmann-Poisson (BP) semiclassical models of hot electronic transport in semiconductors, a numerical study of reflective boundary conditions in the BP system, such as specular reflection, diffusive reflection, and a mixed convex combination of these reflections, and their effect on the behavior of the solution. A boundary layer effect is observed in our numerical simulations for the kinetic moments related to diffusive and mixed reflection.