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.

Impact ionization of holes and domination of p-conductivity in chalcogenide semiconductors are attributed to a weak electron-phonon interaction inherent to lone-pair states. This argument is supported by first-principles calculations of an acoustical deformation potential in trigonal selenium. Results of the calculations reveal a strong dependence of the deformation potential on the excess energy of charge carriers. The latter is interpreted using a simple tight-binding model.