The paper deals with the diffusion limit of the initial-boundary value problem for the multi-dimensional semiconductor Boltzmann-Poisson system. Here, we generalize the one dimensional results obtained in  to the case of several dimensions using global renormalized solutions. The method of moments and a velocity averaging lemma are used to prove the… (More)
The paper deals with the diffusion approximation of the Boltzmann equation for semiconductors in the presence of spatially oscillating electrostatic potential. When the oscillation period is of the same order of magnitude as the mean free path, the asymptotics leads to the Drift-Diffusion equation with a homogenized electrostatic potential and a diffusion… (More)
This paper deals with the diffusion approximation of a semiconductor Boltzmann-Poisson system. The statistics of collisions we are considering here, is the Fermi-Dirac operator with the Pauli exclusion term and without the detailed balance principle. Our study generalizes, the result of Goudon and Mellet , to the multi-dimensional case.
The Spherical Harmonics Expansion (SHE) assumes a momentum distribution function only depending on the microscopic kinetic energy. The SHE-Poisson system describes carrier transport in semiconductors with self-induced electrostatic potential. Existence of weak solutions to the SHE-Poisson system subject to periodic boundary conditions is established, based… (More)
We are concerned with the study of the diffusion and homogenization approximation of the Boltzmann-Poisson system in presence of a spatially oscillating electrostatic potential. By analyzing the relative entropy, we prove uniform energy estimate for well prepared boundary data. An averaging lemma and two scale convergence techniques are used to prove… (More)