A Legendre Polynomial Solver for the Langevin Boltzmann Equation

摘要

The first numerical solver for the Langevin-type Boltzmann transport equation is presented and it is based on a Legendre Polynomial expansion. In contrast to the well-known Monte Carlo method, this new approach allows the direct calculation of noise in the frequency domain. This makes it for the first time possible to access the RF and low frequency range without prohibitive CPU times. It is shown that for most noise calculations a Legendre Polynomial expansion up to the third order is required and that, on the other hand, terms higher than third order yield only negligible improvements. Excellent agreement with MC results verifies the implementation of the new solver.