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.