Theory of Hysteresis in Halide Perovskites by Integration of the Equivalent Circuit

Perovskite solar cells show a number of internal electronic-ionic effects that produce hysteresis in the current-voltage curves and a dependence of the temporal response on the conditions of the previous stimulus applied to the sample. There are many models and explanations in the literature, but predictive methods that may lead to an assessment of the solar cell behavior based on independent measurements are needed. Here, we develop a method to predict time domain response starting from the frequency domain response measured by impedance spectroscopy over a collection of steady states. The rationale of the method is to convert the impedance response into a set of differential equations, in which the internal state variables emerge naturally and need not be predefined in terms of a physical (drift/diffusion/interfaces) model. Then, one solves (integrates) the evolution for a required external perturbation such as voltage sweep at a constant rate (cyclic voltammetry). Using this method, we solve two elementary but relevant equivalent circuit models for perovskite solar cells and memristors, and we show the emergence of hysteresis in terms of the relevant time and energy constants that can be fully obtained from impedance spectroscopy. We demonstrate quantitatively a central insight in agreement with many observations: regular hysteresis is capacitive, and inverted hysteresis is inductive. Analysis of several types of perovskite solar cells shows excellent correlation of the type of equivalent circuit and the observed hysteresis. A new phenomenon of transformation from capacitive to inductive hysteresis in the course of the current-voltage curve is reported.