2013, Wagner, Wolfgang

The paper studies the kinetic equation for electron transport in semiconductors. New formulas for the heat generation rate are derived by analyzing the basic scattering mechanisms. In addition, properties of the steady state distribution are discussed and possible extensions of the deviational particle Monte Carlo method to the area of electron transport are proposed.

2013, Farshbaf-Shaker, Mohammad Hassan, Hecht, Claudia

In this paper we consider a elastic vector-valued AllenCahn MPCC (Mathematical Programs with Complementarity Constraints) problem. We use a regularization approach to get the optimality system for the subproblems. By passing to the limit in the optimality conditions for the regularized subproblems, we derive certain generalized first-order necessary optimality conditions for the original problem.

2010, Muscato, Orazio, Wagner, Wolfgang, Di Stefano, Vincenza

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 possible directions for future 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