REPRODUCE LONG-TAIL CURRENT HYSTERESIS IN PEROVSKITE SOLAR CELLS BASED ON AN IONIC CAPACITOR MODELLED BY A VOLTAGE-RELATED INITIAL CURRENT TIMES THE LINEAR COMBINATION OF THREE EXPONENTIAL DECAY TERMS

It has been reported that the current-voltage (J-V) hysteresis loop of perovskite solar cells (PSCs) could be reproduced by incorporating extra resistances or capacitors in the equivalent circuits of PSCs. However, the exponential decay long-tail current in the hysteresis phenomenon, lasting about 2-5 seconds, remains inadequately modeled, yet it is crucial for maximum power point tracking in PSCs. We propose an ionic capacitor model to describe the impact of ion migration on the current of PSCs, which is composed of a voltage-related initial current multiplies by the linear combination of three exponential decay terms over time. The initial current term is formulated as the product of the voltage step size and a voltage-related conductance. The three exponential terms, each associated with a specific time constants τ, correspond to the migration of electron, iodine ions, and other ions with lower mobilities, respectively. Based on this model, an equivalent circuit for PSCs is constructed, and corresponding parameters were numerical fitted based on available J-V data and current-time response curves. Numerical simulations demonstrate that the proposed model accurately reproduces both the J-V hysteresis loop and the exponential decay long-tail current. This work lays the foundation for the development of MPPT tracking algorithms tailored for PSCs.