Scattering and movement asymmetry in the one-dimensional lucky-drift simulation of the avalanche processes in disordered semiconductors

A lucky-drift model for impact ionization has been recently successfully used to account for avalanche phenomenon in amorphous selenium (a-Se). The model presumed angle symmetry for scattering of charge carriers on disorder potential. We check this model by computer simulations in one-dimensional case and show that the analytical formulation used so far essentially underestimates the ionization rate. Furthermore, the scattering symmetry should lead to the dependence of the impact ionization coefficient on the sample thickness. Such dependence has not been experimentally confirmed in a-Se. Therefore, we modify the model taking into account the scattering and movement asymmetry of charge carriers in the applied electric filed. It is shown that in such formulation the impact ionization rate does not depend on the sample thickness in agreement with experimental data.