Geminate electron-hole recombination in organic photovoltaic cells. A semi-empirical theory

We propose a semi-empirical theory which describes the geminate electron-hole separation probability in both homogeneous systems and donor-acceptor heterojunction systems applicable in organic photovoltaics. The theory is based on the results of extensive simulation calculations, which were carried out using various lattice models of the medium and different charge-carrier hopping mechanisms, over the parameter ranges typical for organic solar cells. It is found that the electron-hole separation probability can be conveniently described in terms of measurable parameters by a formula whose functional form is derived from the existing recombination theories, and which contains only one empirical parameter. For homogeneous systems, this parameter is determined by the structure of the medium and only weakly depends on the charge-carrier hopping mechanism. In the case of donor-acceptor heterojunction systems, this empirical parameter shows a simple power-law dependence on the product of the dielectric constant and inter-molecular contact distance. We also study the effect of heterojunction structure on the electron-hole separation probability and show that this probability decreases with increasing roughness of the heterojunction. By analyzing the simulation results obtained for systems under the influence of an external electric field, we find that the field effect on the electron-hole separation probability in donor-acceptor heterojunction systems is weaker than in homogeneous systems. We also describe this field effect by a convenient empirical formula.