Interpreting Spectroscopic Data in Halide Perovskites using Bayesian Inference

The characterization of recombination processes is a crucial step in the development of solar cells. TRPL is a traditional characterization method for observing recombination mechanisms, frequently used for instance in the field of lead-halide perovskites for photovoltaic and optoelectronic applications. However, especially in the fairly intrinsic lead-halide perovskites, the interpretation of data is complicated because many processes, such as different recombination mechanisms and charge transport, occur at similar time scales. While it is reasonably straightforward to solve the forward problem of simulating TRPL transients for a given set of material parameters, the inverse problem of inferring the material parameters from measured transients is difficult. Fitting analytical models typically leads to an oversimplified model while fitting numerical simulations is very time consuming.<br/>In this study, we propose a novel approach that combines Bayesian inference with surrogate models to increase computational speed. Using our approach, we obtained results from a typical TRPL dataset in less than an hour on an ordinary desktop PC. Instead of using the drift-diffusion simulations during fitting, we used ~10⁶ simulations to train a convolutional neural network which works as a surrogate model. Reading out the surrogate model for a certain material parameter combination is approximately as fast as the evaluation of an analytical equation but allows the inclusion of significantly more complexity in the choice of model. Given the speed of comparing the output of the surrogate model with the experimental data, it becomes feasible to evaluate the physically plausible parameter space by slow methods such as grid search. This approach allows us to obtain a profound understanding of parameter correlations and can estimate fitting errors.<br/>Conventional methods used to experimentally determine TRPL transients such as TCSPC suffer from a limited dynamic range. However, the recombination parameters only become visible in data that covers several orders (&gt;4) of magnitude in PL intensity and time. Thus, we used a gated CCD setup to measure TRPL over a wide dynamic range of up to eight orders of magnitude. This provides insights into the recombination processes that would be difficult to obtain otherwise. A noteworthy result in the context of lead-halide perovskite thin films is the predominance of recombination via shallow defects and the apparent complete absence of deep defect recombination in the data that we observe over a wide range of compositions. We can infer important parameters, such as trap depths, trap density, and capture cross-sections from the TRPL data. Our method offers rapid and comprehensive insights into the parameters governing the recombination process in solar cells.