Energy transport in semiconductor devices

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, energy-transport models with lattice heating or quantum corrections are reviewed.