Abstract
This paper is devoted to the identification of doping profiles in the stationarydrift-diffusion equations modelling carrier and charge transport in semiconductordevices. We develop a framework for these inverse doping problems with differentpossible measurements and discuss mathematical properties of the inverseproblem, such as the identifiability and the type of ill-posedness.In addition, we investigate scaling limits of the drift-diffusion equations, where theinverse doping problem reduces to classical (elliptic) inverse problems. As a firstconcrete application we consider the identification of piecewise constant dopingprofiles in p–n diodes.Finally, we discuss the stable solution of the inverse doping problem byregularization methods and their numerical implementation. The theoreticalstatements are tested in a numerical example for a p–n diode.
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