Kinetics of Distance-Dependent Recombination between Geminate Charge Carriers by Diffusion under Coulomb Interaction

The survival probability of electron–hole pairs decays following a power law given by t –1/2 at long times when geminate recombination proceeds under diffusion and Coulomb interaction. Although the power law decay was known, the dependence of the decay amplitude on the strength of the Coulomb interaction, distance dependence of the intrinsic recombination rate, and the diffusion coefficient has not yet been fully understood. In this manuscript, we show analytical expressions on the amplitude of the asymptotic decay and compare the results with the overall kinetics obtained by numerical calculations. The results were applied to the measured data on the kinetics of carriers in LaTiO 2 N (LTON) solid photocatalyst measured using time-resolved diffuse reflectance spectroscopy (TRDR). The kinetic parameters of carriers were estimated and the presence of trap states was suggested. We also discuss the generalization of the results to the case that the diffusion is dispersive. The dispersive transport of carriers is considered to originate from the carrier transport by successive transitions among trap states with various release times.