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Inverse Doping Problems for Semiconductor Devices

In: Recent Progress in Computational and Applied PDES

Author

Listed:
  • Martin Burger

    (Johannes Kepler Universität Linz, Institut für Industriemathematik)

  • Heinz W. Engl

    (Johannes Kepler Universität Linz, Institut für Industriemathematik)

  • Peter A. Markowich

    (Universität Wien, Institut für Mathematik)

Abstract

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.

Suggested Citation

  • Martin Burger & Heinz W. Engl & Peter A. Markowich, 2002. "Inverse Doping Problems for Semiconductor Devices," Springer Books, in: Tony F. Chan & Yunqing Huang & Tao Tang & Jinchao Xu & Long-An Ying (ed.), Recent Progress in Computational and Applied PDES, pages 39-53, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4615-0113-8_3
    DOI: 10.1007/978-1-4615-0113-8_3
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