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Mathematical theory of kinetic equations for transport modelling in semiconductors. (English) Zbl 0863.76075

Perthame, B. (ed.), Advances in kinetic theory and computing: selected papers. Singapore: World Scientific. Ser. Adv. Math. Appl. Sci. 22, 141-168 (1994).
Summary: We present a review of mathematical results available for kinetic models for semiconductors. These models are mainly based on Vlasov-Poisson-Boltzmann system of equations. However, the transport of particles (electrons and holes) is not purely classical but takes into account quantum effects due to the periodicity of the semiconductor lattice. Although the mathematical analysis is almost complete from the point of view of existence and uniqueness of solutions, it remains a lot of open problems concerning the connection between quantum, kinetic and fluid levels of modelling.
For the entire collection see [Zbl 0830.00019].

MSC:

76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
82D99 Applications of statistical mechanics to specific types of physical systems
82C70 Transport processes in time-dependent statistical mechanics
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