Understanding the Full Zoo of Perovskite Solar Cell Impedance Spectra with the Standard Drift-Diffusion Model

The impedance spectra of perovskite solar cells frequently exhibit multiple features that are typically modelled by complex equivalent circuits. This approach can lead to the inclusion of circuit elements without a sensible physical interpretation and create confusion where different circuits are adopted to describe similar cells. Spectra showing two distinct features have already been well explained by a drift-diffusion model incorporating a single mobile ionic species but spectra with three features have yet to receive the same treatment and have even been dismissed as anomalous. This omission is rectified here by showing that a third (mid-frequency) impedance feature is a natural consequence of the drift-diffusion model in certain scenarios. Our comprehensive framework explains the shapes of all previously published spectra, which are classified into six generic types, each named for an animal resembling the Nyquist plot, and approximate solutions to the drift-diffusion equations are obtained in order to illustrate the specific conditions required for each of these types of spectra to be observed. Importantly, it is shown that the shape of each Nyquist plot can be linked to specific processes occurring within a cell, allowing useful information to be extracted by a visual examination of the impedance spectra.