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 $\left(\alpha \right)$ versus the reciprocal field $(1∕F)$ for holes in $\mathrm{a}\text{-}\mathrm{Se}$ and electrons in $\mathrm{a}\text{-}\mathrm{Se}$ and $\mathrm{a}\text{-}\mathrm{Si}:\mathrm{H}$ 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 $\mathrm{a}\text{-}\mathrm{Se}$ 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 $\left(\mathrm{LD}\right)$ 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 $\mathrm{a}\text{-}\mathrm{Se}$ and electrons in $\mathrm{a}\text{-}\mathrm{Si}:\mathrm{H}$ . We have extracted the electron impact ionization coefficient versus field (${\alpha }_e$ vs $F$ ) data for $\mathrm{a}\text{-}\mathrm{Si}:\mathrm{H}$ 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 $\mathrm{LD}$ 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, $E_I=E_g$ . If $\lambda$ is the mean free path associated with momentum relaxing collisions and ${\lambda }_E$ is the energy relaxation length associated with energy relaxing collisions, than the $\mathrm{LD}$ model requires ${\lambda }_E>\lambda$ . The application of the $\mathrm{LD}$ model with energy and field independent ${\lambda }_E$ to $\mathrm{a}\text{-}\mathrm{Se}$ leads to ionization threshold energies $E_I$ that are quite small, less than $E_g∕2$ , and requires the possible but improbable ionization of localized states. By making ${\lambda }_E={\lambda }_E(E,F)$ energy and field dependent,...