The classical theories of geminate charge recombination – the Onsager theory [1] and its extensions [2,3] – are based on the continuous diffusion model and are therefore of limited applicability to discrete molecular media. A lattice theory of geminate electron-hole recombination is also available [4], but it does not provide convenient expressions of the recombination probability, and has not been found useful in analyzing experimental data. Moreover, the above theories do not take into account various important factors, such as the possibility of different charge transport mechanisms, the presence of a donor-acceptor heterojunction in photovoltaic systems, or the structure of this heterojunction. In such a situation, we think it is desirable to construct a convenient yet reliable empirical theory of geminate charge recombination that could describe this process, in terms of measurable parameters, in a wide class of systems. We attempt to build such a theory by combining computer simulation results with the predictions of the analytical recombination theories.

In the first stage of our work, we analyzed the geminate recombination process using various lattice models of the medium. We have found that the electron-hole escape probability can be conveniently expressed by an equation obtained from the extended Onsager theory with an added empirical factor. In the case of homogeneous systems, this factor is independent of the dielectric constant, lattice constant, and charge mobility. However, it depends on the lattice coordination number and, to some extent, on the assumed form of the charge transport mechanism. In donor-acceptor heterojunction systems, the introduced empirical factor shows a power-law dependence on the product εd, where ε is the dielectric constant and d is the lattice constant. We have also studied the effect of heterojunction roughness on the electron-hole escape probability, and have found that this effect is not very strong.

In the next stage, we extended our considerations to amorphous systems. We modelled the geminate recombination process by simulating a hopping motion of an electron and a hole on amorphous atomic structures. The latter were obtained from separate Monte Carlo simulations that used model interatomic potentials. We have determined the electron-hole escape probabilities for such structures and have used these results to generalize our empirical theory to amorphous media.

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, M. Tachiya, J. Chem. Phys. 130, 104107 (2009).

[4] H. Scher, S. Rackovsky, J. Chem. Phys. 81, 1994 (1984).