Exploring the impact of fractional-order capacitive behavior on the hysteresis effects of perovskite solar cells: A theoretical perspective

Abstract

Perovskite-based solar cells are devices of increasing interest among new generation of photovoltaic technologies due to the outstanding power conversion efficiency (PCE) achieved in the last few years, and the favorable fabrication conditions. Among all these excellent photovoltaic properties, perovskite light-harvesting devices also show relevant issues such as the hysteresis mechanisms in the current density-voltage (J-V) characteristics, whose underlying origins have not yet been clarified from a single and universally accepted point of view. Here, we focus our attention on the ideal capacitive mechanisms which, on the other hand, are often modeled using fractional-order capacitors in the equivalent circuits used to fit impedance measurements. In particular, we provide the theoretical framework for the transient-photocurrent analysis described by fractional-order responses which involve the generalized Mittag-Leffler function. Importantly, the model introduces a connection between perovskite traps and defects, memory processes, fractional dynamics, and Cole-Cole behavior. Crucial dependences of non-ideal capacitive dynamics on fractional-order α and the selected scan rate were found in the J-V hysteresis behavior from the perspective of the non-integer order calculus. In this sense, it is necessary to point out that our numerical simulations of dark J-V curves by considering non-ideal capacitive effects reveal more prominent distortions than those of the ideal case, leading from free-hysteretic influences (α = 1) to significant hysteresis distortions (0<α<1) under certain voltage rates. Thus, this study can help to advance in the origin and the understanding of the experimental hysteresis mechanisms under pristine conditions or during degradation processes (α value decreases indicating a highly disordered morphology).