Identification of doping profiles in semiconductor devices

This paper is devoted to the identification of doping profiles in the stationary drift-diffusion equations modelling carrier and charge transport in semiconductor devices. We develop a framework for these inverse doping problems with different possible measurements and discuss mathematical properties of the inverse problem, such as the identifiability and the type of ill-posedness. In addition, we investigate scaling limits of the drift-diffusion equations, where the inverse doping problem reduces to classical (elliptic) inverse problems. As a first concrete application we consider the identification of piecewise constant doping profiles in p-n diodes. Finally, we discuss the stable solution of the inverse doping problem by regularization methods and their numerical implementation. The theoretical statements are tested in a numerical example for a p-n diode.