Identification of Doping Profiles in Semiconductor Devices
by Martin Burger, Heinz W. Engl, Peter A. Markowich, Paola Pietra,
in Inverse Problems, 17 (2001), 1765-1795.
ABSTRACT
This paper is devoted to the identification of doping profiles in the
stationary
drift-diffusion equations modeling 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 identificability and the type of ill-posedness.
In addition, we investigate scaling limits of the drft-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.
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