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A. Jüngel, S. Krause, P. Pietra:
"A hierarchy of diffusive higher-order moment equation for semiconductors";
in: "ASC Report 13/2007", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2007, ISBN: 978-3-902627-00-1, '?.

A hierarchy of diffusive partial differential equations is derived by a moment method
and a Chapman-Enskog expansion from the semiconductor Boltzmann equation assuming dominant
collisions. The moment equations are closed by employing the entropy maximization principle of
Levermore. The new hierarchy contains the well-known drift-diffusion model, the energy-transport
equations, and the six-moments model of Grasser et al. It is shown that the diffusive models are of
parabolic type. Two different formulations of the models are derived: a drift-diffusion formulation,
allowing for a numerical decoupling, and a symmetric formulation in generalized dual entropy variables,
inspired by nonequilibrium thermodynamics. An entropy inequality (or H-theorem) follows
from the latter formulation.

Semiconductor Boltzmann equation, moment method, Chapman-Enskog expansion,

http://www.asc.tuwien.ac.at/preprint/2007/asc13x2007.pdf