Correlation functions from multiple solution of the transient Boltzmann equation in semiconductors: Application to noise temperature of holes in silicon

Abstract

We present a new numerical method to calculate the correlation functions in semiconductor materials by a direct solution of the Boltzmann equation. The correlation function is calculated solving a set of time-dependent Boltzmann equations corresponding to different initial conditions. As application, we present the calculation of the correlation function of velocity fluctuations and the noise temperature for holes in silicon at T=300 K. The results are in good agreement with Monte Carlo calculation as well as with experimental data.

An iterative matrix solution of the Boltzmann equation for the calculation of diffusion and noise in semiconductors

“…To adapt this method to the calculation of the correlation function, we have adopted the same procedure as the one used in the scattered packet method and in direct methods [8]. We have replaced the Dirac distribution by a Gaussian distribution centred in k = k M and weighted by a factor G according to:…”