Dispersive-diffusion-controlled distance-dependent recombination in amorphous semiconductors

The photoluminescence in amorphous semiconductors decays according to the power law t(-delta) at long times. The photoluminescence is controlled by dispersive transport of electrons. The latter is usually characterized by the power alpha of the transient current observed in the time-of-flight experiments. Geminate recombination occurs by radiative tunneling which has a distance dependence. In this paper, we formulate ways to calculate reaction rates and survival probabilities in the case carriers execute dispersive diffusion with long-range reactivity. The method is applied to obtain tunneling recombination rates under dispersive diffusion. The theoretical condition of observing the relation delta=alpha/2+1 is obtained and theoretical recombination rates are compared to the kinetics of observed photoluminescence decay in the whole time range measured.