Derivation of the open-circuit voltage of organic solar cells

Organic photovoltaic cells have improved in efficiency from 1% two decades ago to over 10% today. Continued improvement necessitates a theoretical understanding of the factors determining efficiency. Organic photovoltaic efficiency can be parameterized in terms of open-circuit voltage, short-circuit current, and fill factor. Here we present a theory that explains the dependencies of open-circuit voltage on semiconductor energy levels, light intensity, solar cell and light-source temperatures, charge-carrier recombination, and external fluorescence efficiency. The present theory also explains why recombination at the donor-acceptor heterointerface is a dominant process in heterojunction-based cells. Furthermore, the Carnot efficiency appears, highlighting the connection to basic thermodynamics. The theory presented here is consistent with and builds on the experimental and theoretical observations already in the literature. Crucially, the present theory can be straightforwardly derived in a line-by-line fashion using standard tools from statistical physics.