Mobility dependent recombination models for organic solar cells

Modern solar cell technologies are driven by the effort to enhance power conversion efficiencies. A main mechanism limiting power conversion efficiencies is charge carrier recombination which is a direct function of the encounter probability of both recombination partners. In inorganic solar cells with rather high charge carrier mobilities, charge carrier recombination is often dominated by energetic states which subsequently trap both recombination partners for recombination. Free charge carriers move fast enough for Coulomb attraction to be irrelevant for the encounter probability. Thus, charge carrier recombination is independent of charge carrier mobilities. In organic semiconductors charge carrier mobilities are much lower. Therefore, electrons and holes have more time react to mutual Coulomb-forces. This results in the strong charge carrier mobility dependencies of the observed charge carrier recombination rates. In 1903 Paul Langevin published a fundamental model to describe the recombination of ions in gas-phase or aqueous solutions, known today as Langevin recombination. During the last decades this model was used to interpret and model recombination in organic semiconductors. However, certain experiments especially with bulk-heterojunction solar cells reveal much lower recombination rates than predicted by Langevin. In search of an explanation, many material and device properties such as morphology and energetic properties have been examined in order to extend the validity of the Langevin model. A key argument for most of these extended models is, that electron and hole must find each other at a mutual spatial location. This encounter may be limited for instance by trapping of charges in trap states, by selective electrodes separating electrons and holes, or simply by the morphology of the involved semiconductors, making it impossible for electrons and holes to recombine at high rates. In this review, we discuss the development of mobility limited recombination models from the early Langevin theory to state-of-the art models for charge carrier recombination in organic solar cells.