A Hierarchy of Diffusion Higher-Order Moment Equations for Semiconductors.
by Ansgar Jüngel, Stefan Krause and Paola Pietra
SIAM J. Appl. Math. 68, 171-198, (2007).
ABSTRACT
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 elastic
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 from nonequilibrium
thermodynamics. An entropy inequality (or H-theorem) follows from
the latter formulation.
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