Organic solar cells (OPV) have developed rapidly over the past decade but still lag behind their inorganic counterparts in efficiency due to a combination of low open-circuit voltages and the difficulty of making optically thick cells with high fill factors. In this work we develop a comprehensive framework for understanding and improving the open-circuit voltage (Voc) of organic solar cells based on quasi-equilibrium between Charge Transfer (CT) states and free carriers. We first show that the ubiquitous reduced Langevin recombination observed in organic solar cells implies quasi-equilibrium and then use statistical mechanics to calculate how many CT states will be populated in the solar cell at each voltage. This general result allows us to quantitatively assign the open-circuit voltage losses to a combination of interfacial energetic disorder, high CT state binding energies, large degrees of mixing and fast electron transfer at the donor/acceptor interface. Our work reconciles Langevin recombination with detailed balance calculations of Voc based on the CT state absorption spectrum and gives an intuitive physical explanation for why the open-circuit voltage of organic solar cells is almost always 500 to 700 meV below the measured energy of the CT state.
To quantify the impact of energetic disorder on Voc we develop a new temperature dependent Charge Transfer state absorption measurement. By looking at how the apparent CT state energy (Ect) varies with temperature we can directly extract the degree of interfacial energetic disorder since it causes a characteristic 1/T temperature dependence in Ect. We study five different OPV systems and find between 60 and 105 meV of disorder, contributing an additional 75-225 mV of Voc loss not included in the 500-700 mV recombination loss mentioned above. Our theoretical result shows that disorder happens to affect Ect in precisely the same manner as Voc, which is why it does not affect their difference. Finally, we consider various strategies by which the open-circuit voltage could be improved, quantify their impact and show that the best gains could come from slightly raising the bulk dielectric constant of the active layer and reducing energetic disorder at the donor/acceptor interface.