Markowich, Peter A.; Schmeiser, Christian Relaxation time approximation for electron-phonon interaction in semiconductors. (English) Zbl 0832.65142 Math. Models Methods Appl. Sci. 5, No. 4, 519-527 (1995). The subject of this paper is the derivation of hydrodynamic limits of kinetic models for the transport of electrons in a semiconductor crystal, with the scattering mechanism being modelled mathematically by an integral operator on \(\mathbb{R}^3\). Physical assumptions include the parabolic band approximation and a new relaxation time model for electron-phonon interaction. The relaxation time approximation is based on the projection of an appropriately chosen weighted \(L^2\)-space onto the null space of the collision operator. Thermal equilibrium distributions for this scattering mechanisms are products of Maxwellian distributions with periodic functions of energy, where the period is the energy of a photon. The hydrodynamics limit is considered, and a drift- diffusion model is derived by formal asymptotic methods. Reviewer: H.Brunner (St.John’s) Cited in 6 Documents MSC: 65R20 Numerical methods for integral equations 45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) 45K05 Integro-partial differential equations 78A55 Technical applications of optics and electromagnetic theory Keywords:Boltzmann equation; thermal equilibrium; hydrodynamic limits; kinetic models; transport of electrons; semiconductor crystal; scattering; integral operator; parabolic band approximation; relaxation time model; electron-phonon interaction; Maxwellian distributions; periodic functions; drift-diffusion model PDFBibTeX XMLCite \textit{P. A. Markowich} and \textit{C. Schmeiser}, Math. Models Methods Appl. Sci. 5, No. 4, 519--527 (1995; Zbl 0832.65142) Full Text: DOI