Identification of doping profiles in semiconductor devices

Martin Burger*, Heinz W. Engl, Peter Markowich, Paola Pietra

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

30 Scopus citations

Abstract

This paper is devoted to the identification of doping profiles in the stationary drift-diffusion equations modelling 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 the identifiability and the type of ill-posedness. In addition, we investigate scaling limits of the drift-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.

Original languageEnglish (US)
Pages (from-to)1765-1795
Number of pages31
JournalInverse Problems
Volume17
Issue number6
DOIs
StatePublished - Dec 1 2001

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Signal Processing
  • Mathematical Physics
  • Computer Science Applications
  • Applied Mathematics

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