Existence of solutions and uniform bounds for the stationary semiconductor equations with generation and ionic carriers

TL;DR

This paper proves the existence of solutions and establishes uniform bounds for a stationary semiconductor model with ionic carriers and generation, relevant for perovskite solar cells, using truncation and energy estimates.

Contribution

It introduces new mathematical techniques to prove solution existence and bounds for a complex drift-diffusion system with ionic charge carriers.

Findings

Existence of solutions is established.

Uniform bounds on solutions are derived.

Numerical analysis of bounds' dependency on model parameters.

Abstract

We consider a stationary drift-diffusion system with ionic charge carriers and external generation of electron and hole charge carriers. This system arises, among other applications, in the context of semiconductor modeling for perovskite solar cells. Thanks to truncation techniques and iterative energy estimates, we show the existence and uniform upper and lower bounds on the solutions. The dependency of the bounds on the various parameters of the model is investigated numerically on physically relevant test cases.