Physics-driven discovery and bandgap engineering of hybrid perovskites†

The unique aspect of hybrid perovskites is their tunability, allowing the engineering of the bandgap via substitution. From the application viewpoint, this allows creation of tandem cells between perovskites and silicon, or two or more perovskites, with associated increase of efficiency beyond the single-junction Shockley–Queisser limit. However, the concentration dependence of the optical bandgap in hybrid perovskite solid solutions can be non-linear and even non-monotonic, as determined by band alignments between endmembers, presence of defect states and Urbach tails, and phase separation. Exploring new compositions brings forth the joint problem of the discovery of the composition with the desired band gap and establishing the physical model of the band gap concentration dependence. Here we report the development of the experimental workflow based on structured Gaussian Process (sGP) models and custom sGP (c-sGP) that allow the joint discovery of the experimental behavior and the underpinning physical model. This approach is verified with simulated datasets with known ground truth and was found to accelerate the discovery of experimental behavior and the underlying physical model. The d/c-sGP approach utilizes a few calculated thin film bandgap data points to guide targeted explorations, minimizing the number of thin film preparation steps. Through iterative exploration, we demonstrate that the c-sGP algorithm that combined 5 bandgap models converges rapidly, revealing a relationship in the bandgap diagram of MA_1−xGA_xPb(I_1−xBr_x)₃. This approach offers a promising method for efficiently understanding the physical model of band gap concentration dependence in binary systems, and this method can also be extended to ternary or higher dimensional systems.