Perovskites represent promising new-generation solar cell materials with high photovoltaic conversion efficiencies. The development of lead-free perovskite materials, such as GeSn-based perovskites, necessitates the prediction of various material properties and analysis of the factors influencing these properties.

The optimal band gap required for the best performing perovskite single layer cell materials is estimated to be within the range of 1.53 eV to 1.56 eV. A typical perovskite such as methylammonium lead iodide (MAPbI₃) has a band gap of 1.56 eV and exhibits high stability and efficiency. MASnI₃, in which the B site is substituted with Sn²⁺, the same divalent transition metal as Pb²⁺, has a narrow band gap of 1.30 eV, which is conducive to tuning the band gap for enhanced efficiency. In addition, atomic substitution has a significant impact on structural stability. Many experimental and theoretical studies have been published on tuning the band gap and improving stability by compositional approaches such as implanting Ge into Sn-based perovskites or using mixed halides. [1]

According to molecular orbital theory, the conduction band is mainly contributed by the bonding orbitals of the B-site atoms, and the valence band is mainly contributed by the antibonding orbitals of the X-site atoms. However, first-principles calculations must be performed to accurately estimate the orbital energy of the new composition. On the other hand, the tolerance factors have mainly been used to evaluate perovskite structures. The tolerance factor requires only the ionic radius to estimate the stability, but its accuracy is often insufficient.

To overcome these complex situations, machine learning (ML) has become popular in recent years. A Crystal Graph Convolutional Neural Network (CGCNN) [2] can incorporate the local structure effects, making it a model suitable for a wide range of molecules and crystals.

In this study, we first predicted the band gap using CGCNN for a dataset containing double perovskites with optimized structures [3] and evaluated the prediction performance. Second, even if there are only unoptimized structures, we would like to predict the bandgap of systems with subtle atomic ratios without the computational cost of first-principles calculations. Therefore, we train a model to predict the changing pattern of the band gap when the B-site atom mixing ratio is 0, 0.5, and 1. By analyzing this model, the factors that are important for the bandgap are identified and the model is used as a preliminary bandgap prediction model, which will improve the accuracy of bandgap prediction.