Uniform L $\infty$ estimates for approximate solutions of the bipolar drift-diffusion system

TL;DR

This paper proves uniform L-infinity bounds for approximate solutions of the bipolar drift-diffusion system in semiconductors, using a discrete Moser iteration technique applied to Scharfetter-Gummel finite-volume scheme.

Contribution

It introduces a novel discrete Moser iteration method to establish uniform bounds for numerical solutions of the bipolar drift-diffusion system.

Findings

Established uniform L-infinity bounds for approximate solutions

Applied the method to Scharfetter-Gummel finite-volume scheme

Provided a new analytical tool for semiconductor device modeling

Abstract

We establish uniform L $\infty$ bounds for approximate solutions of the drift-diffusion system for electrons and holes in semiconductor devices, computed with the Schar-fetter-Gummel finite-volume scheme. The proof is based on a Moser iteration technique adapted to the discrete case.