A cellular-automaton method for solving the Boltzmann equation for semiclassical transport is presented and applied to nonlinear transport in semiconductors. It is shown that the Boltzmann equation for semiconductor transport can be transformed into a Boolean master equation, which represents a cellular automaton with nearest-neighbor interaction in position space. The resulting numerical algorithm is physically equivalent to the ensemble Monte Carlo method and tailored to modern vector or parallel processing. The algorithm is well suited for carrier systems with pronounced spatial inhomogeneities, large density variations, and scattering kernels involving single- and more-particle interactions. Several tests of the cellular-automaton technique for nonlinear transport in Si and GaAs are presented. The results agree very well with published Monte Carlo calculations.

• Received 3 February 1992

DOI:https://doi.org/10.1103/PhysRevB.46.1382