On inverse doping profile problems for the stationary voltage-current map

TL;DR

This paper addresses the inverse problem of identifying discontinuous doping profiles in semiconductors from stationary voltage-current data, introducing a level set method approach and comparing it with existing techniques.

Contribution

It presents a novel numerical method using level set techniques for inverse doping profile identification and relates it to diffusion tomography theory.

Findings

The level set method effectively identifies discontinuous doping profiles.

The approach outperforms previous Landweber-Kaczmarz methods in certain scenarios.

The method is validated through numerical experiments.

Abstract

We consider the problem of identifying possibly discontinuous doping profiles in semiconductor devices from data obtained by\,stationary voltage-current maps. In particular, we focus on the so-called unipolar case, a system of PDE's derived directly from the drift diffusion equations. The related inverse problem corresponds to an inverse conductivity problem with partial data. The identification issue for this inverse problem is considered. In particular, for a discretized version of the problem, we derive a result connected to diffusion tomography theory. A numerical approach for the identification problem using level set methods is presented. Our method is compared with previous results in the literature, where Landweber-Kaczmarz type methods were used to solve a similar problem.