Transient photoluminescence (tr-PL) is a popular contact-less characterization method to study recombination and the properties of defects in halide-perovskite films, layer stacks and devices. Due to their low doping density, many lead-halide perovskite compositions have a complex tr-PL behavior. Here, the recombination dynamics is strongly non-linear with respect to electron density. This non-linear recombination then results in PL decays that cannot be described by either mono-exponential or multi-exponential decays leading to differential decay times that are a function of carrier density [1-2].

Whereas the tr-PL data can provide rich information about capture coefficients and defect energies, the necessary postprocessing and fitting of the data requires numerically solving a series of coupled differential equations which provides an obstacle for widespread adaptation of such models. This leads to a discrepancy in the way how spectroscopy and modeling groups analyze the data vs. how technology-focused groups analyze the data. To accelerate and greatly simplify the tr-PL data analysis while at the same time improving its accuracy, we have developed a workflow for analyzing tr-PL data measured using perovskite absorber layers that incorporates physics informed deep learning in the form of a web application called PLPal.

PLPal has an intuitive and interactive interface. The app initially performs preprocessing on the data (e.g. finding the zero of the time axis), calculates the differential decay time vs. carrier density or Fermi-level splitting automatically and then fits the data. The fitting is done very rapidly by using a convolutional neural network acting as a surrogate model [3] for the solutions of the coupled differential equations for electron and hole capture and emission via several defect states. The neural network surrogate model is combined with the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) fitting algorithm to deliver high quality fits within a couple of minutes if run on a commercial laptop. Furthermore, PLPal allows the user to quantify the uncertainty of the best fit and resolves high-dimensional model parameter correlations. With the obtained tr-PL fit parameters PLPal also analyses the quasi steady-state situation to obtain an implied current-voltage curve. Additionally, we incorporated sliders for all parameters that allows the user to vary parameters of the model (like trap depth & density, capture coefficients, etc…) and see the effect on the PL transient in real time.

[1]       Yuan, Y.; et al. Adv. Energy Mater. 2025, 15 (6), 2403279. DOI: 10.1002/aenm.202403279.

[2]       Yuan, Y.; et al. Nat. Mater. 2024, 23 (3), 391–397. DOI: 10.1038/s41563-023-01771-2.

[3]       Das, B.; et al. Research Square August 11, 2025. DOI: 10.21203/rs.3.rs-7115972/v1.