High field approximations of the spherical harmonics expansion model for semiconductors

N. Ben Abdallah, P. Degond, P. Markowich, C. Schmeiser

Research output: Contribution to journalArticlepeer-review

26 Scopus citations

Abstract

We present an asymptotic analysis (with the scaled mean free path as small parameter) of the spherical-harmonics expansion (SHE-) model for semiconductors in the case of a large electric field. The Hilbert and Chapman-Enskog expansions are performed and the dependence of macroscopic parameter-functions such as the mobility and the diffusivity on the details of the considered elastic and inelastic scattering processes are investigated. For example, we verify so called velocity-saturation mobility models, so far obtained by heuristic considerations, by means of an asymptotic analysis for certain scattering processes.

Original languageEnglish (US)
Pages (from-to)201-230
Number of pages30
JournalZeitschrift fur Angewandte Mathematik und Physik
Volume52
Issue number2
DOIs
StatePublished - Jan 1 2001

Keywords

  • Chapman-Enskog expansion
  • High field asymptotics
  • Semiconductors
  • Spherical-harmonics expansion model

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)
  • Applied Mathematics

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