Inverse Doping Problems for Semiconductor Devices
This paper is devoted to a class of inverse problems arising in the testing of semiconductor devices, namely the identification of doping profiles from indirect measurements of the current or the voltage on a contact. In mathematical terms, this can be modeled by an inverse source problem for the drift-diffusion equations, which are a coupled system of elliptic or parabolic partial differential equations.
We discuss these inverse problems in a stationary and a transient setting and compare these two cases with respect to their mathematical properties. In particular , we discuss the identifiability of doping profiles in the model problem of the unipolar drift-diffusion system. Finally, we investigate the important special case of a piecewise constant doping profile, where the aim is to identify the p-n junctions, i.e., the curves between regions where the doping profile takes positive and negative values.
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