Global solution to the drift-diffusion-Poisson system for semiconductors with nonlinear recombination-generation rate

TL;DR

This paper proves the existence, uniqueness, and long-term convergence of solutions to a nonlinear drift-diffusion-Poisson system modeling semiconductors, addressing a complex recombination-generation rate.

Contribution

It establishes the global well-posedness and asymptotic stability of solutions for a nonlinear semiconductor model, which was previously unresolved.

Findings

Global weak solutions exist and are unique

Solutions converge to equilibrium over time

Handles higher-order nonlinear recombination-generation rates

Abstract

In this paper, we study the Cauchy problem of a time-dependent drift-diffusion-Poisson system for semiconductors. Existence and uniqueness of global weak solutions are proven for the system with a higher-order nonlinear recombination-generation rate R. We also show that the global weak solution will converge to a unique equilibrium as time tends to infinity.