A Unified Description of the Electrical Properties with Complex Dynamical Patterns in Metal Halide Perovskite Photovoltaics

One of the most promising emerging photovoltaic technologies is represented by perovskite materials essentially due to their outstanding performance. However, the complex fundamental understanding of relevant device physics is challenging, making it harder to obtain correlations with efficiency and long-term stability, and thus definitely transforming the landscape of solar energy. In electrical terms, perovskite solar cells often show different types of experimental behaviors at long timescales (light-enhanced capacitance and chemical inductor) in separate voltage domains, but with permanent deviations from the ideal pattern (Cole-Cole relaxation processes, fractional dynamics, and beyond). Here, we reevaluate the dynamical behavior of a photovoltaic perovskite model that leads to the two versions of constant-phase element behavior in the impedance response. Our general theory is, therefore, able to explain naturally the vast majority of results concerning the nonlinear polarization mechanisms of perovskite solar cells, extending the mathematical framework from the perspective of fractional-order electrical circuits. In this context, we discover a novel property that reveals the anomalous electrical coupling of memory effects in photovoltaic perovskites. We hope that this work can provide a useful tool for modeling experts and device physicists belonging to the photovoltaic community, moving forward toward addressing the outstanding challenges in this fast-developing field.