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Based on the reaction of electron-hole separation in perovskite solar cells, we derived the mathematical relationship between current and voltage from the viewpoint of electrochemical kinetics and, moreover, by using this relation, we successfully fitted the i–E curves. We found that the nonlinear relationships between the activation energy and the potential of the recombination reaction are the fundamental reason for the appearance of the hysteresis loop.

A oversimplified physical model has been constructed and then the mathematical model of electrochemical impedance of relative diffusion of two ions has been obtained. And the corresponding spectrum has been drawn from the model, which fills up the blank of the electrochemical impedance (EIS) theory in the field of multi-ion diffusion impedance. It is shown that the reaction order, surface concentration and diffusion coefficient are the three principle factors influencing the diffusion impedance, among which, the diffusion coefficient has the greatest influence. By controlling the relative value of the diffusion coefficient of the two ions, finally a series of regular EIS spectra has been got.