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.