Theoretical results in inverse problems for size, solvability, and uniqueness in the p-n junction and doping profile of semiconductors

Abstract

We present an overview of mathematical models for electrons and holes in semiconductors. We use these to pose some inverse problems for determining the doping profile of a semiconductor. We establish the solvability of the equilibrium equation λ²∆u = e^u−e^(-u)–C in Ω. We also obtain information about the conductivity coefficient in the important case when it is piecewise constant and discontinuous.