CALCULATION OF DISTRIBUTION FUNCTIONS BY EXPLOITING STABILITY OF STEADY STATE

A numerical method is described for calculating distribution functions of free carriers in crystals from a knowledge of the scattering rates and applied fields. The stability of the steady state is exploited to derive an explicit expression for the distribution function without introducing any a priori assumptions about its form. This expression can be evaluated by a convergent iterative process. A rate of scatter leaving the free carrier wave vector unaltered is defined. This scattering process has no physical consequence, but suitable choice of its rate can make the numerical iteration straightforward. The technique is extended to accommodate scattering processes dependent on the distribution function and to analyse time dependent effects. Results are given of numerical calculations of distribution functions for free carriers in electric fields, taking into account scattering processes including polar phonon and impurity scattering. © 1969.