A new ideality factor for perovskite solar cells and an analytical theory for their impedance spectroscopy response

Impedance spectroscopy (IS) is a relatively straightforward experimental technique that is commonly used to obtain information about the physical and chemical characteristics of photovoltaic devices. However, the non-standard physical behaviour of perovskite solar cells (PSC), which are heavily influenced by the motion of mobile ion vacancies, has hindered efforts to obtain a consistent theory to interpret PSC impedance data. 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. Extremely good agreement is shown between the analytic model and the much more complex drift-diffusion model in regimes (including maximum power point) where the applied voltage is close to the open circuit voltage $V_{oc}$. 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, such as `the giant low frequency capacitance` and `inductive arcs' in the Nyquist plots. Where the physical properties of the PSC are already known the analytic model can be used to predict the recombination current $j_{rec}$ and the high and low frequency resistances and capacitances of the cell, $R_{HF}$, $C_{HF}$, $R_{LF}$ and $C_{LF}$. In scenarios where the physical properties of the cell are unknown the analytic model can also used to extract physical parameters from experimental PSC impedance data. {A novel physical parameter of particular significance to PSC physics is identified. This is termed the electronic ideality factor, $n_{el}$, and (as opposed to the standard ideality factor) can be used to deduce the dominant source of recombination in a PSC, independent of its ionic properties.