The quasi-neutral limit in optimal semiconductor design
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.
Cite
@article{arxiv.1512.01116,
title = {The quasi-neutral limit in optimal semiconductor design},
author = {Rene Pinnau and Claudia Totzeck and Oliver Tse},
journal= {arXiv preprint arXiv:1512.01116},
year = {2017}
}