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 which are typically modelled by complex equivalent circuits. This approach can lead to the inclusion of circuit elements without a sensible physical interpretation and can 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 scenarios where large densities of electrons or holes build up within the perovskite bulk, causing the displacement of mobile ions. We create a comprehensive framework that explains the shapes of all previously published spectra. We classify the different spectra 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, we show 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. Finally, best practices for future reporting of impedance measurements are discussed, with the goals of reducing confusion and aiding the meaningful interpretation of the data.