AMaSiS 2018 Workshop: Abstracts

Poster Apparent order of electron–hole recombination in organic photovoltaic materials

Martin Wiemer${}^{\mathbf{\text{(1,2)}}}$, Alexey Nenashev${}^{\mathbf{\text{(3)}}}$, Sergei D. Baranovskii${}^{\mathbf{\text{(2)}}}$, and M. Koch${}^{\mathbf{\text{(2)}}}$

(1) Centre National de la Recherche Scientifique, Laboratoire de l’Intégration du Matériau au Système, Pessac

(2) Philipps–Universität Marburg, Dept. of Physics and Material Sciences Center

(3) Institute of Semiconductor Physics and Novosibirsk State University, Dept. of Physics

Efficient organic active media for photovoltaic applications comprise at minimum two different types of molecules, electron–accepting and electron–donating ones. These molecules may be arranged as a bilayer, or a blend (so–called bulk heterojunction) structure. In either case the result is an electron–attractive acceptor and a hole–attractive donor phase within the medium. The electrons and holes, which are generated by photoabsorption, are therefore spatially separated, and may recombine with one another only at the internal donor–acceptor interfaces. Various experimental studies report on a strong deviation of the kinetics of the recombination process from the law for the conventional bimolecular reactions. The apparent order of recombination $\delta$, which may be defined through

$${\frac{\partial \overline{n}}{\partial t}|}_{\mathrm{rec}.}\propto -{\overline{n}}^{\delta }.$$

($\overline{n}$ being the mean concentration of electrons or holes, and $t$ being the time), is often found to vary between $2.5$ and $7$ rather than being equal to $2$ expected for the conventional bimolecular reaction.

The poster presents three models to account for $\delta >2$. In the first one, trap states are hold responsible for a charge–density or time–dependent mobility of the photo–induced charge carriers similar to dispersive transport in the multiple–trapping charge transport regime [1].

The second and the third model [2, 3], both developed in our research group, take the issue of phase–separation into the focus of the consideration. The ’continents and islands’ model [2] represents a topological equivalent to large percolation clusters (’continent’ and ’ocean’) and isolated domains (’islands’ and ’lakes’). The respective charge concentrations are assumed to be homogeneous within each domain, and recombination rates proportional to the product of electron and hole concentrations at each boundary. If the isolated domains are discharged slower than the percolation clusters, recombination essentially stops at a still rather high over–all charge concentration, and $\delta$ rises formally to infinity on the long time scale under transient conditions.

The latter model [3], on the other hand, allows for a more detailed look at the effect of combined drift and diffusive motion of the charge carriers. Here, the system resembles an ideal bilayer structure with an infinite planar interface. The combined action of drift and diffusion can cause a non–linear relation between the local electron and hole concentrations at the interface, and their mean values. Thus, $\delta$ can reach values of up to $4$ under certain, experimentally realistic, conditions in the transient and steady–state case.

Acknowledgments: Funding from the GRK 1782 of the Deutsche Forschungsgemeinschaft is greatfully acknowledged.