Two-dimensional electron-hole capture in a disordered hopping system

We model the two-dimensional recombination of electrons and holes in a system where the mean free path is short compared with the thermal capture radius. This recombination mechanism is relevant to the operation of bilayer organic light-emitting diodes (LED's), where electrons and holes accumulate on either side of the internal heterojunction. The electron-hole recombination rate can be limited by the time taken for these charge carriers to drift and diffuse to positions where electrons and holes are directly opposite to each other on either side of the interface, at which point rapid formation of an emissive neutral state can occur. In this paper, we use analytical and numerical techniques to find the rate of this two-dimensional electron-hole capture process. Where one species of carrier is significantly less mobile than the other, we find that the recombination rate depends superlinearly on the density of the less mobile carrier. Numerical simulations allow the effects of disorder to be taken into account in a microscopic hopping model. Direct solution of the master equation for hopping provides more efficient solutions than Monte Carlo simulations. The rate constants extracted from our model are consistent with efficient emission from bilayer LED's without requiring independent hopping of electrons and holes over the internal barrier at the heterojunction.