Monte Carlo method for modeling of small signal response including the Pauli exclusion principle

Abstract

A Monte Carlo method for small signal analysis of degenerate semiconductors is presented. The response to an electric field impulse parallel to the stationary electric field is obtained using the nonlinear Boltzmann kinetic equation with the Pauli exclusion principle in the scattering operator. After linearization of the Boltzmann equation a new Monte Carlo algorithm for small signal analysis of the nonlinear Boltzmann kinetic equation is constructed using an integral representation of the first order equation. The generation of initial distributions for two carrier ensembles which arise in the method is performed by simulating a main trajectory to solve the zero order equation. The normalization of the static distribution function is discussed. To clarify the physical interpretation of our algorithm we consider the limiting case of vanishing electric field and show that in this case kinetic processes are determined by a linear combination of forward and backward scattering rates. It is shown that at high degeneracy backward scattering processes are dominant, while forward transitions are quantum mechanically forbidden under such conditions due to the Pauli exclusion principle. Finally, the small signal Monte Carlo algorithm is formulated and the results obtained for degenerate semiconductors are discussed.