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S. Taguchi, A. Jüngel:
"A two-surface problem of the electron flow in a semiconductor on the basis of kinetic theory";
Journal of Statistical Physics, 130 (2007), 313 - 342.

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.

Siehe englisches Abstract.

Drift-diffusion equations, semiconductors, boundary conditions

http://dx.doi.org/10.1007/s10955-007-9426-6