The quasi-neutral limit in optimal semiconductor design

TL;DR

This paper investigates the quasi-neutral limit in an optimal semiconductor design problem, establishing a rigorous mathematical framework and validating it with numerical experiments to improve computational efficiency.

Contribution

It introduces a variational approach and Gamma-convergence analysis for the quasi-neutral limit in semiconductor optimization, providing a foundation for fast algorithms.

Findings

Gamma-convergence of minima and minimizers established

Quasi-neutral limit justified for optimization problems

Numerical experiments confirm approach feasibility

Abstract

We study the quasi-neutral limit in an optimal semiconductor design problem constrained by a nonlinear, nonlocal Poisson equation modelling the drift diffusion equations in thermal equilibrium. While a broad knowledge on the asymptotic links between the different models in the semiconductor model hierarchy exists, there are so far no results on the corresponding optimization problems available. Using a variational approach we end up with a bi-level optimization problem, which is thoroughly analysed. Further, we exploit the concept of Gamma-convergence to perform the quasi-neutral limit for the minima and minimizers. This justifies the construction of fast optimization algorithms based on the zero space charge approximation of the drift-diffusion model. The analytical results are underlined by numerical experiments confirming the feasibility of our approach.