In low dielectric materials, photo-generated electron-hole pairs are bound by Coulombic interaction. The separated electron-hole pairs will recombine or ultimately separate by diffusion. The probability of ultimate separation (separation to an infinite distance apart) is called the escape probability. An important length scale inherent in the system is the Onsager length where the thermal energy of diffusion becomes comparable to the Coulombic interaction.The escape probability and its kinetics depend on the intrinsic recombination rates and the dependence is largely affected by the Onsager length. Although the power law decay of the survival probability was known, the interference between the distance dependence of the intrinsic recombination rate and diffusion has not yet been fully investigated in relation with the Onsager length. We obtained 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 inorganic semiconductors when an external electric field is not applied. ¹⁾

 The charge separation efficiency can be increased by applying external electric fields. The field dependence of the escape probability is important to know the charge separation efficiency and to obtain current voltage characteristic of the organic photo-voltaic materials. In organic materials, the initial charge separation occurs between molecules and the distance is much smaller than the Onsager length. The escape probability of the initially closed pair of an electron and a hole has been widely studied even when an external electric field is applied. For a certain situation, where recombination is assumed to proceed at a certain rate at a certain distance, exact methods to calculate the escape probability have been developed. However, the calculation involves solving infinite dimensional linear equations. For this reason, we have derived approximate expressions by noticing low values of the relative dielectric constants in organic materials. The approximate results were compared to the exact result. We show that within a practical range of field strength the approximation is reasonable when the Onsager length is much larger than the typical recombination distance.

1) Y. Suzuki, A. Furube, R. B. Singh, H. Matsuzaki, T. Minegishi, T. Hisatomi, K. Domen, and K. Seki, Kinetics of Distance-Dependent Recombination between Geminate Charge Carriers by Diffusion under Coulomb Interaction , J. Phys. Chem. C, 119 (10), pp 5364-5373 (2015)