Publication date: 15th December 2025
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, 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.
A modified drift-diffusion model, which captures degradation via an increasing recombination rate during the course of characterization experiments, is then used to investigate the effect of device degradation on current−voltage and impedance measurements of perovskite solar cells (PSCs). Numerical solutions of this model are obtained with the open-source drift-diffusion software IonMonger. These show that impedance spectroscopy is significantly more sensitive measure of degradation than current−voltage curves, reliably detecting a power conversion efficiency drop of as little as 0.06% over a 4 h measurement. Furthermore, it is found that fast degradation occurring during impedance spectroscopy can induce loops lying above the axis in the Nyquist plot, the first time this experimentally observed phenomenon has been replicated in a physics-based model.
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