Quasi-neutral limit of the drift diffusion models for semiconductors: The case of general sign-changing doping profile

Shu Wang*, Zhouping Xin, Peter Markowich

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

31 Scopus citations

Abstract

In this paper the vanishing Debye length limit (space charge neutral limit) of bipolar time-dependent drift-diffusion models for semiconductors with p-n junctions (i.e., with a fixed bipolar background charge) is studied in one space dimension. For general sign-changing doping profiles, the quasi-neutral limit (zero-Debye-length limit) is justified rigorously in the spatial mean square norm uniformly in time. One main ingredient of our analysis is the construction of a more accurate approximate solution, which takes into account the effects of initial and boundary layers, by using multiple scaling matched asymptotic analysis. Another key point of the proof is the establishment of the structural stability of this approximate solution by an elaborate energy method which yields the uniform estimates with respect to the scaled Debye length.

Original languageEnglish (US)
Pages (from-to)1854-1889
Number of pages36
JournalSIAM Journal on Mathematical Analysis
Volume37
Issue number6
DOIs
StatePublished - Feb 1 2006

Keywords

  • Classical energy methods
  • Drift-diffusion equations
  • Multiple scaling asymptotic expansions
  • Quasi-neutral limit
  • Singular perturbation
  • λ-weighted Liapunov-type functional

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

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