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High field approximations of the spherical harmonics expansion model for semiconductors

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

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.

Key words. Semiconductors, spherical-harmonics expansion model, high field asymptotics, Chapman-Enskog expansion. 

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Copyright information

© Birkhäuser Verlag, Basel, 2001

Authors and Affiliations

  • N. Ben Abdallah
    • 1
  • P. Degond
    • 1
  • P. Markowich
    • 2
  • C. Schmeiser
    • 3
  1. 1.Mathématiques pour l'Industrie et la Physique, UMR CNRS 9974, Université Paul Sabatier, 118 rue de Narbonne, 31062 Toulouse Cedex, FranceFR
  2. 2.Institut für Mathematik, Universität Wien, Boltzmanngasse 9, 1090 Wien, AustriaAT
  3. 3.Institut fü Angewandte und Numerische Mathematik, TU Wien, Wiedner Hauptstraße 8-10, 1040 Wien, AustriaAT

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