A first analysis of a new fixed point iteration of the Boltzmann equation: Application to TCAD

Abstract

This paper presents a first analysis of a new general fixed point iteration of the Boltzmann transport equation. The scheme is based on a recent theory on Inverse Scattering Operators. Due to the fact that the implementation of this scheme is extremely involved, the expansion is truncated after the second iteration as a start. Comparisons with Monte Carlo simulations verify that the second iteration step gives sufficient corrections to the equilibrium distribution in bulk silicon, if the external field is not too large. However, it turns out that the second iteration is not sufficient to address inhomogeneous semiconductors. One reason is that a term containing the built-in electric field is not compensated in this order. Moreover, even in regions with low electric field and with small gradients of the quasi-Fermi level the second-order solution deviates notably from Monte Carlo simulations. Although this scheme has a lot of potential for TCAD applications, the adaptability is not straight-forward and further analysis of higher order terms is necessary.