Inverse Doping Problems for Semiconductor Devices

  • Martin Burger
  • Heinz W. Engl
  • Peter A. Markowich
Conference paper


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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Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Martin Burger
    • 1
  • Heinz W. Engl
    • 1
  • Peter A. Markowich
    • 2
  1. 1.Institut für IndustriemathematikJohannes Kepler Universität LinzLinzAustria
  2. 2.Institut für MathematikUniversität WienAustria

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