Coupled Ionic-Electronic Equivalent Circuit to Describe Asymmetric Rise and Decay of Photovoltage Profile in Perovskite Solar Cells

In this research, we employed transient photo-voltage rise and decay measurements to investigate the origin of slow unsymmetrical rise and decay profiles in single and triple cation perovskite solar cells. Drastic changes in photo-voltage decay profile were observed upon insertion of Br-, Cs+ and FA(+) ions into perovskite structures. In order to explain our observations, the activation energy for ionic defects was measured and an equivalent circuit model was proposed containing both electrical and ionic components. The electrical branch consists of a diode, the bulk capacitance and resistances for charge transport and recombination. In parallel we introduced an ionic branch describing the ionic response by a resistance for ionic charge transport and a capacitance describing ion accumulation at the interface to the charge transport layer. To reproduce the asymmetry of photo-voltage rise and decay, a diode with a parallel resistor is introduced leading to a belayed backflow of the accumulated ions. The results revealed that the activation energy of ionic defects became larger upon insertion of either halides or cations. There is larger amount of ionic defects in the case of MAPbI(3) while the de-accumulation process of ions happens in much larger time scale in triple cation perovskite. The presence of ions at the interfaces results in band bending generating a potential barrier restraining electrons and holes from recombination; so the loss of built-in potential is delayed until de-accumulation of ionic double layer happens. Our model proposes that the loss of built-in potential depends on electrostatic potential drop, suggesting coupled electronic-ionic phenomenon in perovskite solar cells.