The issue of hysteresis in perovskite solar cells has now been convincingly linked to the presence of mobile ions within the perovskite layer. Here we test the limits of the ionic theory by attempting to account for a number of exotic characterization results using a detailed numerical device model that incorporates ionic charge accumulation at the perovskite interfaces. Our experimental observations include a temporary enhancement in open-circuit voltage following prolonged periods of negative bias, dramatically S-shaped current-voltage sweeps, decreased current extraction following positive biasing or "inverted hysteresis", and non-monotonic transient behaviours in the dark and the light. Each one of these phenomena can be reproduced and ultimately explained by our models, providing further evidence for the ionic theory of hysteresis as well as valuable physical insight into the factors that coincide to bring these phenomena about. In particular we find that both interfacial recombination and carrier injection from the selective contacts are heavily affected by ionic accumulation, and are essential to explaining the non-monotonic voltage transients and S-shaped J-V curves. Inverted hysteresis is attributed to the occurrence of "positive" ionic accumulation, which may also be responsible for enhancing the stabilized open-circuit voltage in some perovskite cells.
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