Dispersive photoluminescence decay by geminate recombination in amorphous semiconductors

The photoluminescence decay in amorphous semiconductors is described by power-law t^-δ at long times. The power-law decay of photoluminescence at long times is commonly observed but recent experiments have revealed that the exponent δ~1.2--1.3, is smaller than the value 1.5 predicted from a geminate recombination model assuming normal diffusion. Transient currents observed in the time-of-flight experiments are highly dispersive characterized by the disorder parameter α smaller than 1. The geminate recombination rate should be influenced by the dispersive transport of charge carriers. In this paper we derive the simple relation δ=1+α∕2. Not only the exponent but also the amplitude of the decay calculated in this study is consistent with measured photoluminescence in a-Si:H.