Discerning rise time constants to quantify charge carrier extraction in perovskite solar cells

The small-perturbation analysis of perovskite solar cells (PSCs) highlights a fundamental conundrum - while time domain measurements yield two time constants corresponding to the rise and subsequent decay of the photovoltage or photocurrent, the corresponding frequency domain methods only yield one time constant from the analysis of the negative imaginary part of the transfer function. To solve this problem, we propose a modification of the frequency domain transfer function that focusses on the transition of its real part to negative values at high frequencies. After verification using drift-diffusion simulations and equivalent circuit analysis, the application of the method to experimental intensity-modulated photovoltage spectroscopy data of a PSC allows calculation of the hidden rise time constant, showing a good agreement with rise time constants obtained from transient photovoltage measurements. Combining these measurements with transient photoluminescence measurements allows calculation of the figure of merit (FOM) that determines the charge collection efficiency. We determine large FOM values between 0.7-0.95 at or close to the 1 sun open-circuit voltage, indicating a significant electric field exists in the transport layers that allows fast charge collection in these conditions. A method is developed to extract the rise time constant from frequency domain data of perovskite solar cells, which determines the charge extraction efficiency. The results show a good agreement with those obtained from time domain measurements.