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A. Jüngel:
"Energy transport in semiconductor devices";
Mathematical and Computer Modelling of Dynamical Systems, 16 (2010), 1; 1 - 22.

The modelling, analysis and numerical approximation of energy-transport models for
semiconductor devices are reviewed. The derivation of the partial differential equations
from the semiconductor Boltzmann equation is sketched. Furthermore, the main ideas for
the analytical treatment of the equations, employing thermodynamic principles, are given.
A new result is the proof of the weak sequential stability of approximate solutions to some
time-dependent energy-transport equations with physical transport coefficients. The
discretization of the stationary model using mixed finite elements is explained, and some
numerical results in two and three space dimensions are presented. Finally, energytransport
models with lattice heating or quantum corrections are reviewed.

Siehe englischen Abstract.

energy-transport equations; semiconductors; existence analysis