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A Two-Surface Problem of the Electron Flow in a Semiconductor on the Basis of Kinetic Theory

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Abstract

A steady flow of electrons in a semiconductor between two parallel plane Ohmic contacts is studied on the basis of the semiconductor Boltzmann equation, assuming a relaxation-time collision term, and the Poisson equation for the electrostatic potential. A systematic asymptotic analysis of the Boltzmann–Poisson system for small Knudsen numbers (scaled mean free paths) is carried out in the case where the Debye length is of the same order as the distance between the contacts and where the applied potential is of the same order as the thermal potential. A system of drift-diffusion-type equations and their boundary conditions is obtained up to second order in the Knudsen number. A numerical comparison is made between the obtained system and the original Boltzmann–Poisson system.

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Authors and Affiliations

  1. Organization of Advanced Science and Technology, Kobe University, Kobe, 657-8501, Japan

    Satoshi Taguchi

  2. Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstr. 8-10, 1040, Wien, Austria

    Ansgar Jüngel

Authors
  1. Satoshi Taguchi
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  2. Ansgar Jüngel
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Correspondence to Ansgar Jüngel.

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Taguchi, S., Jüngel, A. A Two-Surface Problem of the Electron Flow in a Semiconductor on the Basis of Kinetic Theory. J Stat Phys 130, 313–342 (2008). https://doi.org/10.1007/s10955-007-9426-6

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  • DOI: https://doi.org/10.1007/s10955-007-9426-6

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