Separation of geminate electron-hole pairs, which are formed as a result of exciton dissociation, is one of the fundamental physical processes taking place in organic photovoltaic devices. Despite significant research, we still lack a reliable and convenient theory that describes the expected electron-hole escape probability in terms of known parameters of the cell medium, such as the molecular size or charge mobility. The well-known Onsager theory [1] and its extensions [2,3] are based on the continuous diffusion model and, as such, are not directly applicable to discrete media. The presence of a donor-acceptor heterojunction in the solar cell systems is another complicating issue that further limits the applicability of the classical recombination theories.

In this study, we attempt to build a useful empirical theory of geminate electron-hole recombination based on computer simulation results obtained for various lattice models of the medium, different charge transport mechanisms, and different heterojunction topologies. By analyzing a wide range of simulation data, we show that the electron-hole escape probability can be conveniently described by an analytical formula derived from the extended Onsager model with an additional empirical factor S. For homogeneous systems, this factor is mostly determined by the lattice structure of the medium, very weakly depends on the particular form of the charge transport mechanism, and is independent of many physical parameters of the medium, such as the dielectric constant, molecular size, or charge mobility. In the presence of a donor-acceptor heterojunction, the empirical factor S is no longer independent of the medium parameters, but shows a simple power-law dependence on the product εd, where ε is the dielectric constant and d is the molecular size. The effect of heterojunction topology on the electron-hole escape probability is found to be only moderate. We also study the geminate recombination in the presence of an applied electric field. In all cases the field effect on the electron-hole escape probability is found to be well described by the functional form used in the Onsager-Braun model. The validity ranges of various series expansions of this dependence are also determined.

This work was supported by the National Science Centre of Poland (Grant No. DEC-2013/09/B/ST4/02956).

[1] L. Onsager, Phys. Rev. 54, 554 (1938).

[2] C. L. Braun, J. Chem. Phys. 80, 4157 (1984).

[3] M. Wojcik and M. Tachiya, J. Chem. Phys. 130, 104107 (2009).