# American Institute of Mathematical Sciences

September  2011, 4(3): 809-829. doi: 10.3934/krm.2011.4.809

## Properties of the steady state distribution of electrons in semiconductors

 1 Dipartimento di Matematica e Informatica, Università degli Studi di Catania, Viale Andrea Doria 6 - 95125 Catania, Italy, Italy 2 Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39 - 10117 Berlin, Germany

Received  October 2010 Revised  April 2011 Published  August 2011

This paper studies a Boltzmann transport equation with several electron-phonon scattering mechanisms, which describes the charge transport in semiconductors. The electric field is coupled to the electron distribution function via Poisson's equation. Both the parabolic and the quasi-parabolic band approximations are considered. The steady state behaviour of the electron distribution function is investigated by a Monte Carlo algorithm. More precisely, several nonlinear functionals of the solution are calculated that quantify the deviation of the steady state from a Maxwellian distribution with respect to the wave-vector. On the one hand, the numerical results illustrate known theoretical statements about the steady state and indicate directions for further studies. On the other hand, the nonlinear functionals provide tools that can be used in the framework of Monte Carlo algorithms for detecting regions in which the steady state distribution has a relatively simple structure, thus providing a basis for domain decomposition methods.
Citation: Orazio Muscato, Wolfgang Wagner, Vincenza Di Stefano. Properties of the steady state distribution of electrons in semiconductors. Kinetic & Related Models, 2011, 4 (3) : 809-829. doi: 10.3934/krm.2011.4.809
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