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

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 PDEs 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.