On inverse problems for semiconductor equations

TL;DR

This paper investigates inverse problems for stationary drift-diffusion equations in semiconductors, focusing on reconstructing doping profiles from various measurements, including a case reducing to an inverse conductivity problem, supported by a numerical experiment.

Contribution

It analyzes different inverse problems for semiconductor equations and connects some cases to classical inverse conductivity problems, providing both theoretical insights and a numerical example.

Findings

Inverse problems for doping profile reconstruction are analyzed.

Special cases reduce to classical inverse conductivity problems.

Numerical experiment demonstrates the approach in a linearized unipolar case.

Abstract

This paper is devoted to the investigation of inverse problems related to stationary drift-diffusion equations modeling semiconductor devices. In this context we analyze several identification problems corresponding to different types of measurements, where the parameter to be reconstructed is an inhomogeneity in the PDE model (doping profile). For a particular type of measurement (related to the voltage-current map) we consider special cases of drift-diffusion equations, where the inverse problems reduces to a classical inverse conductivity problem. A numerical experiment is presented for one of these special situations (linearized unipolar case).