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Zbl 0840.45011
Markowich, P.A.; Poupaud, F.; Schmeiser, C.
Diffusion approximation of nonlinear electron phonon collision mechanisms. (English)
[J] RAIRO, Modélisation Math. Anal. Numér. 29, No.7, 857-869 (1995). ISSN 0764-583X

The authors investigate the behaviour of the solutions of the Boltzmann equation of solid state physics when the mean free path tends to zero. The paper begins with the examination of the basic properties of the collision operators and then derives the fluid approximation. The nonlinear Boltzmann operator considered models collisions between electrons and phonons with constant energy.\par Further, the paper studies the perturbation of the operator and recovers the usual drift diffusion model and in the next higher order a relaxation term appears as a source term in the energy dependent drift-diffusion equation. The authors point out that distribution functions relax to local equilibrium functions similar to Fermi-Dirac distribution depending on energy dependent chemical potential.
[N.D.Sengupta (Bombay)]

MSC 2000:: *45K05 Integro-partial differential equations
82D20 Solids

Keywords: nonlinear electron phonon collision mechanisms; mean free path; fluid limit; Boltzmann equation; solid state physics; collision operators; drift diffusion model; Fermi-Dirac distribution

Cited in: Zbl 0962.82031

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