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

Perovskite solarcells show a number of internal electronic-ioniceffects that produce hysteresis in the current-voltage curvesand a dependence of the temporal response on the conditions of theprevious stimulus applied to the sample. There are many models andexplanations in the literature, but predictive methods that may leadto an assessment of the solar cell behavior based on independent measurementsare needed. Here, we develop a method to predict time domain responsestarting from the frequency domain response measured by impedancespectroscopy over a collection of steady states. The rationale ofthe method is to convert the impedance response into a set of differentialequations, in which the internal state variables emerge naturallyand need not be predefined in terms of a physical (drift/diffusion/interfaces)model. Then, one solves (integrates) the evolution for a requiredexternal perturbation such as voltage sweep at a constant rate (cyclicvoltammetry). Using this method, we solve two elementary but relevantequivalent circuit models for perovskite solar cells and memristors,and we show the emergence of hysteresis in terms of the relevant timeand energy constants that can be fully obtained from impedance spectroscopy.We demonstrate quantitatively a central insight in agreement withmany observations: regular hysteresis is capacitive, and invertedhysteresis is inductive. Analysis of several types of perovskite solarcells shows excellent correlation of the type of equivalent circuitand the observed hysteresis. A new phenomenon of transformation fromcapacitive to inductive hysteresis in the course of the current-voltagecurve is reported.