While current-voltage hysteresis in perovskite solar cells has been the subject of significant modelling efforts, identifying the cause as mobile halide vacancies, a complete description of the phenomena known as inverted hysteresis (in which current density is greater on the forward sweep than on the reverse) has not yet been proposed. Although some studies have successfully reproduced inverted hysteresis in numerical simulations, the underlying mechanism is difficult to infer, due to the complexity of the drift-diffusion model. The cause has usually been attributed to ionic extraction barriers created by large preconditioning voltages [1] or asymmetric transport layer band offsets [2]. Here we reconcile the differing interpretations of simulations by providing an asymptotic analysis of the drift-diffusion model that resolves the underlying causes of inverted hysteresis.

The model is based on an adaption of the surface polarisation model by Courtier et al. [3], with the additional assumption of a significant imbalance in the carrier population in the perovskite after preconditioning, induced by large preconditioning voltages, asymmetric band offsets, or, possibly, some as yet unidentified mechanism. We identify the hole-rich scenario as being more likely than the electron-rich. Steady state solutions reveal that the hole population causes halide vacancies to migrate out of the perovskite bulk and into both Debye layers near the transport layer interfaces, contrary to previous descriptions of the model, in which the ionic Debye layers were though to be net neutral. Solutions during the reverse sweep show that the electric potential in the perovskite bulk forms a wavefront, moving from the ETL interface toward the HTL, dividing the perovskite into a region of strong electric field and a diffusion-limited region. When bulk recombination is strongly hole-limited, recombination losses are high in the latter region, but reduced once the wavefront traverses the entire layer, explaining the initial inhibition of current density that manifests as inverted hysteresis. By identifying the speed of this wavefront, we show that the timescale and magnitude of inverted hysteresis are particularly sensitive to a small number of material parameters, including the transport layer band offsets, preconditioning voltage, and transport layer doping levels.