A circuit model approach for donor acceptor solar cells exhibiting disorder

The Shockley diode model is often used to extract the shunt resistance, series resistance, and ideality of solar cells from current-voltage (IV) curves, and to model open circuit voltage under illumination. However, in a realistic model for solar cells consisting of materials exhibiting disorder, transport through disordered states does not necessarily follow Ohmic behavior because of the influence of space charge. Mark and Helfrich identified the current through organic crystals to follow a power law with voltage, where the exponent is proportional to the trap depth, but it is not clear if the model applies to amorphous thin film devices or donor-acceptor heterojunctions. Here, we present a new equivalent circuit for the dark IV curves of bilayer organic solar cells, which can accurately fit the IV curve across the entire voltage range, from low voltage through values substantially higher than open circuit. In the proposed circuit model, the dark current is represented by circuit elements that combine transport, shunting, and recombination, described by power laws. We validate the model with simulated data and experimental IV curves from devices with different acceptor layers. By better understanding how individual transport mechanisms combine to assemble into the total IV curve, we can extract information about disorder, energy level offsets, and parasitic effects within the solar cell, suggesting ways to improve future devices including perovskite solar cells.