Matrix quantum kinetic treatment of impact ionization in avalanche photodiodes

Matrix-based quantum kinetic simulations have been widely used for the predictive modeling of electronic devices. Inelastic scattering from phonons and electrons are typically treated as higher-order processes in these treatments, captured using mean-field approximations. Carrier multiplication in avalanche photo-diodes (APDs), however, relies entirely on strongly inelastic impact ionization, making electron-electron scattering the dominant term requiring a rigorous, microscopic treatment. We go well beyond the conventional Born approximation for scattering to develop a matrix-based quantum kinetic theory for impact ionization, involving products of multiple Green's functions. Using a model semiconductor in a reverse-biased p-i-n configuration, we show how its calculated nonequilibrium charge distributions show multiplication at dead-space values consistent with energy-momentum conservation. Our matrix approach can be readily generalized to more sophisticated atomistic Hamiltonians, setting the stage for a fully predictive, first-principles theory of APDs.