Calculation of High-Field Distribution Functions in Semiconductors

Abstract

The relation between various methods proposed recently for calculating the hot‐carrier distribution function in semiconductors is discussed. In particular, it is shown that the method deduced heuristically by Rees from considerations of the stability of the steady state is an iterative prescription for solving a suitably chosen integral form of the Boltzmann equation. It is shown that this method is essentially an adaptation of Kellogg's method with additional sufficiency conditions imposed to guarantee the existence of a positive solution and the convergence of the iterative process. The essential ingredient of these conditions is that the kernel of the integral equation be positive. It is further pointed out that the self‐scattering process introduced by Rees belongs to a larger class of operators that ensure the required positivity of the kernel.