Avoiding Ionic Interference in Computing the Ideality Factor for Perovskite Solar Cells and an Analytical Theory of Their Impedance-Spectroscopy Response

Impedance spectroscopy (IS) is a straightforward experimental technique that is commonly used to obtain information about the physical and chemical characteristics of photovoltaic devices. However, the nonstandard physical behavior of perovskite solar cells (PSCs), which are heavily influenced by the motion of mobile ion vacancies, has hindered efforts to obtain a consistent theory of PSC impedance. This work rectifies this omission by deriving a simple analytic model of the impedance response of a PSC from the underlying drift-diffusion model of charge-carrier dynamics and ion-vacancy motion, via an intermediate model that shows extremely good agreement with the drift-diffusion model in the relevant parameter regimes. Excellent agreement is demonstrated between the analytic impedance model and the much more complex drift-diffusion model for applied biases (including both open circuit and the maximum power point at 0.1 and 1 Sun) close to the cell's built-in voltage ${V}_{\mathrm{bi}}$. Both models show good qualitative agreement to experimental IS data in the literature and predict many of the observed anomalous features found in impedance measurements on PSCs. The analytic model provides a practical and useful tool with which to interpret PSC impedance data and extract physical parameters from IS experiments. We define a physical parameter, ${n}_{\mathrm{el}}$ (the electronic ideality factor), that is of particular significance to PSC physics, since, in contrast to the apparent ideality factor, the value of ${n}_{\mathrm{el}}$ can be used to identify the dominant source of recombination in the cell independent of its ionic properties.