Simulating photoconductive atomic-force microscopy on disordered photovoltaic materials

We present a tool for simulating photoconductive atomic-force microscopy (Pc-AFM) on bulk heterojunction (BHJ) materials with a minimal set of empirical parameters. The simulation is a master-equation solution of a three-dimensional hopping charge transport model which includes donor-acceptor domain morphology, energetic and spatial disorder, exciton transport and splitting, charge-pair generation and recombination, and tip-substrate electrostatics. A simplifying aspect of the model is that electron transport, hole transport, and electron-hole recombination are treated as the same electron-transfer process. The model recreates realistic bulk recombination rates, without requiring short-range Coulombic effects to be calculated. We demonstrate the tool by simulating line scans of a Pc-AFM tip passing over the surface of a buried or exposed acceptor cluster in a BHJ film. The simulations confirm experimental observations that such defects can be detected by open-circuit mode Pc-AFM imaging, even when the clusters are buried below the surface.