Beyond Langevin Recombination: How Equilibrium Between Free Carriers and Charge Transfer States Determines the Open-Circuit Voltage of Organic Solar Cells

Organic solar cells lag behind their inorganic counterparts in efficiency due largely to low open-circuit voltages (V-oc). In this work, a comprehensive framework for understanding and improving the open-circuit voltage of organic solar cells is developed based on equilibrium between charge transfer (CT) states and free carriers. It is first shown that the ubiquitous reduced Langevin recombination observed in organic solar cells implies equilibrium and then statistical mechanics is used to calculate the CT state population density at each voltage. This general result permits the quantitative assignment of V-oc losses to a combination of interfacial energetic disorder, non-negligible CT state binding energies, large degrees of mixing, and sub-ns recombination at the donor/acceptor interface. To quantify the impact of energetic disorder, a new temperature-dependent CT state absorption measurement is developed. By analyzing how the apparent CT energy varies with temperature, the interfacial disorder can be directly extracted. 63-104 meV of disorder is found in five systems, contributing 75-210 mV of V-oc loss. This work provides an intuitive explanation for why qV(oc) is almost always 500-700 meV below the energy of the CT state and shows how the voltage can be improved.