We examine the voltage and energy loss in methyl-ammonium lead-halide perovskite solar cells in comparison to crystalline silicon (c-Si) and polymer:fullerene systems. The contributions to voltage and energy loss can be interpreted either in terms of a balance of generation and recombination events or in terms of energy levels. Using the principles of detailed balance, combined with electroluminescence spectroscopy (EL) and sub-bandgap quantum efficiency measurements, we derive the theoretical upper limit of the open-circuit voltage (Voc,rad), when only radiative recombination occurs. The voltage difference ΔVoc,nr between the actual Voc and Voc,rad is attributed to non-radiative recombination.
We show that pervoskite solar cells have a slightly larger non-radiative voltage loss (0.28 V) than c-Si (0.22 V) but smaller than the best organic system (0.35 V). The voltage drop between optical bandgap (Eopt/q) and Voc,rad for perovskite and c-Si are similar, at about 0.26 V for both, whilst the organic devices investigated exhibit a much larger voltage drop due to the need for a heterojunction to separate excitons. The voltage loss can, alternatively, be divided into components representing geminate and non-geminate recombination. The results show that recombination losses in perovskite devices are dominated by non-geminate processes in contrast to c-Si and organic solar cells which show a higher proportion of geminate loss.
We also show that radiative recombination in perovskite devices is independent of the hysteresis behavior that is often observed in these devices. The hysteresis behavior can strongly affect the non-radiative recombination process. Also, a correlation is seen between the photocurrent, photovoltage, photoluminescence and electroluminescence during the time dependent relaxation due to the hysteresis effects. The magnitudes and relaxation times of these measurements vary with temperature from 90K to 330K in perovskite devices, with less hysteresis observed at lower temperatures.
The understanding of different factors contributing to recombination and limitingVoc in the different material systems can be used in future research to minimize energetic losses and increase stability in perovskite solar cells.