Journal of Statistical Physics

, Volume 130, Issue 2, pp 313–342 | Cite as

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

  • Satoshi Taguchi
  • Ansgar Jüngel


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.


Semiconductor Boltzmann equation Hilbert expansion Drift-diffusion equations Second-order boundary conditions 


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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Organization of Advanced Science and TechnologyKobe UniversityKobeJapan
  2. 2.Institute for Analysis and Scientific ComputingVienna University of TechnologyWienAustria

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