Generalized lucky-drift model for impact ionization in semiconductors with disorder

An extension of an original lucky-drift model to the case of disordered semiconductors is proposed, motivated by experimental observations of an avalanche phenomenon in amorphous semiconductors. The generalization encompasses two scattering mechanisms: an inelastic one due to optical phonons and an elastic one due to a disorder potential. An obtained analytical solution is verified by a kinetic Monte Carlo simulation. Eventually, experimental data on a field dependence of the impact ionization coefficient in amorphous selenium are interpreted using reasonable material parameters.