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Voltage dependence of equivalent circuit parameters of bilayer organic photovoltaics

Despite the very different underlying physics of organic photovoltaics (OPVs), inorganic p-n junction’s Shockley’s diode equation is often applied to describe current density–voltage (JV) curves of OPVs. The model parameters, including the diode saturation current, diode ideality factor, series, and parallel resistances, are usually extracted and treated as constants in JV curve analyses. In this work, we develop a drift-diffusion bilayer interface (DD-BI) model for bilayer OPVs, which treats the donor–acceptor (D–A) heterojunction using the detailed balance between densities of polaron pairs, free electrons, and free holes. From the DD-BI model, we derive a diode equation, which is of Shockley’s equation form, but each parameter is explicitly written in terms of the D–A interface properties. We call this model the self-consistent diode (SCD) model as it is consistent with the DD-BI results provided that the key parameters are from the simulation data. By studying the effects of light intensity and carrier mobility, we find that the Shockley SCD parameters are voltage dependent because of space charge accumulation around the D–A heterojunction. Our models are successful in explaining the common discrepancies in OPV JV curve analyses, such as the validity of fitting for series resistance, deviation of ideality factor from the theoretical values, and different resistance values under light and dark conditions. The results provide a better understanding of OPVs with a D–A heterojunction and how we can capture its physics using the SCD equation.