A Monte Carlo solution to hole transport processes in avalanche selenium semiconductors

Amorphous selenium is a unique wide-bandgap disordered material, that shows a deterministic single-carrier hole impact ionization process which results in a very low excess noise factor. A key feature of the avalanche phenomenon in amorphous selenium is that transport at high electric fields shifts to non-activated extended states and this necessitates the need to obtain microscopic access into the relaxation dynamics of non-equilibrium 'hot' holes in extended states. Another interesting aspect of elemental selenium is the similarity in short range order that exists across all allotropic forms. Thus, we employ an in-house ensemble Monte Carlo algorithm, in which we take into consideration scattering from acoustic and non-polar optical phonons to describe the general details of the extended-state hole-phonon interaction. The delocalized extended state transport in the amorphous phase is modeled using the band-transport lattice theory of its crystalline counterpart, trigonal selenium. The energy and phonon band structure along with the density of states and acoustic/optical deformation potentials for the crystalline phase was calculated using density functional theory and a parabolic approximation to the density of states function was used in the simulation. We validate our calculated drift mobility with experimental results in the perpendicular and parallel directions to the c-axis, in the unit cell for trigonal selenium. Moreover, in the direction perpendicular to the c-axis we show that acoustic and non-polar optical phonons are able to maintain a stable hole-energy distribution as long as the electric field is lower than the critical value of 650 kV/cm. Beyond a certain critical electric field, holes in selenium can get 'hot' and gain energy at a faster rate than they loose to the lattice.