A Deterministic Particle Method for the Semiconductor Boltzmann Equation

We present a new particle method for the simulation of the semiconductor Boltzmann equiation. It differs from the Monte-Carlo method by the approximation of the collision integral: with each particle, we associate a new degree of freedom, a weight, the time variations of which account for the collision integral by means of a quadrature formula. Linear as well as non-linear collision integrals can be handled the same way by this method. It has been applied to the polar optical scattering in the homogeneous field model. Numerical results are presented with an emphasis on the influence of the Pauli degeneracy terms.