Lucky drift impact ionization in amorphous semiconductors

Abstract

The review of avalanche multiplication experiments clearly confirms the existence of the impact ionization effect in this class of semiconductors. The semilogarithmic plot of the impact ionization coefficient (α) versus the reciprocal field (1∕F) for holes in a-Se and electrons in a-Se and a-Si:H places the avalanche multiplication phenomena in amorphous semiconductors at much higher fields than those typically reported for crystalline semiconductors with comparable bandgaps. Furthermore, in contrast to well established concepts for crystalline semiconductors, the impact ionization coefficient in a-Se increases with increasing temperature. The McKenzie and Burt [S. McKenzie and M. G. Burt, J. Phys. C 19, 1959 (1986)] version of Ridley’s lucky drift (LD) model [B. K. Ridley, J. Phys. C 16, 3373 (1988)] has been applied to impact ionization coefficient versus field data for holes and electrons in a-Se and electrons in a-Si:H. We have extracted the electron impact ionization coefficient versus field (αe vs F) data for a-Si:H from the multiplication versus F and photocurrent versus F data recently reported by M. Akiyama, M. Hanada, H. Takao, K. Sawada, and M. Ishida, Jpn. J. Appl. Phys.41, 2552 (2002). Provided that one accepts the basic assumption of the Ridley LD model that the momentum relaxation rate is faster than the energy relaxation rate, the model can satisfactorily account for impact ionization in amorphous semiconductors even with ionizing excitation across the bandgap, EI=Eg. If λ is the mean free path associated with momentum relaxing collisions and λE is the energy relaxation length associated with energy relaxing collisions, than the LD model requires λE>λ. The application of the LD model with energy and field independent λE to a-Se leads to ionization threshold energies EI that are quite small, less than Eg∕2, and requires the possible but improbable ionization of localized states. By making λE=λE(E,F) energy and field dependent, we were able to obtain excellent fits to α vs 1∕F data for both holes and electrons in a-Se for both EI=Eg∕2 and EI=Eg. In the former case, one expects occupied localized states at EF(=Eg∕2) to be ionized and in the second case, one expects excitation across the bandgap. We propose that ionization excitation to localized tail states very close to the transport band can explain the thermally activated α since the release time for the observed activation energies is much shorter than the typical transit times at avalanche fields. For the a-Se case, EI=Eg≈2eV leads to the following conclusions: (a) For holes, λE has negligibly little field dependence but increases with energy. At the ionization threshold energy λE∼4nm. (b) For electrons, λE increases with energy and the field with λE∼2nm at the ionization threshold and at impact ionization fields. For electron impact ionization in a-Si:H, the data can be readily interpreted in terms of near bandgap ionization EI=Eg and a λE that decreases with increasing field, and having very little energy dependence. The energy relaxation length has opposite tendencies in a-Se and a-Si:H, which probably reflects the distinctly different types of behavior of hot carriers in the transport band in these two amorphous semiconductors.