Transition from Capacitive to Inductive Hysteresis: A Neuron-Style Model to Correlate I-V Curves to Impedances of Metal Halide Perovskites

Metal halide perovskite (MHP) devices often show different types of hysteresis in separate voltage domains. At low voltage, the impedance response is capacitive, and the cell gives regular hysteresis. At high voltage, the hysteresis is inverted, corresponding to an inductive response that causes a negative capacitance feature. We calculate the hysteresis current due to a chemical inductor model, and we show that the current is inversely proportional to the voltage scan rate. We formulate a general dynamical model for the solar cell response in the style of neuronal models for the action potential, based on a few differential equations. The model allows us to track the transition from capacitive to inductive properties, both by impedance spectroscopy and current-voltage measurements at different voltage sweep rates. We obtain a correlation of the time constants for the capacitor and the inductor. We interpret the origin of the low-frequency features in terms of ion-controlled surface recombination. This explains the strong correlation of the low-frequency capacitance and inductor, as both originate from the same mechanism. The methodology derived in this paper provides great control over the dynamic properties of metal halide perovskite solar cells, even in cases in which there are qualitative changes of the solar cell current-voltage response over a broad voltage range.