The global pursuit of sustainable energy necessitates the development of efficient photocatalysts for water splitting. This process uses sunlight to generate hydrogen, a clean fuel source. Semiconductor photocatalysts are key to this process, requiring specific band properties: appropriate band edge positions relative to water-splitting redox potentials (to minimize overpotential) and a suitable bandgap (1.6-2.1 eV) for efficient visible light absorption. Current materials meeting these criteria are limited. Solid-solution alloying offers a promising route for band engineering, but the vast compositional space of multicomponent alloys presents a significant challenge for experimental screening. High-throughput Density Functional Theory (DFT) calculations can aid material discovery, but their computational cost increases exponentially with system complexity. This research addresses this limitation by employing machine learning (ML) to efficiently explore the compositional space of ZnTe-based alloys, leveraging a small dataset to minimize the need for extensive DFT calculations. The goal is to identify optimal ZnTe-based high-entropy alloys with desirable band properties for photocatalytic water splitting. The study's importance lies in its potential to accelerate the discovery of novel multicomponent alloy materials with tailored properties for various applications, not just water splitting.

Extensive research focuses on designing efficient photocatalysts for water splitting, aiming to harness solar energy for clean fuel production. Studies highlight the importance of precise bandgap and band edge alignment for optimal catalytic performance. The literature emphasizes the need for materials with bandgaps within the visible light spectrum (1.65-3.26 eV) and band edges strategically positioned relative to water reduction and oxidation potentials. Several promising materials have been identified, including GaN:ZnO solid solutions, β-Ge₃N₄, Al-doped SrTiO₃, and Ta₃N₅. However, the current material palette is limited. High-throughput DFT calculations have proven effective in material discovery for photocatalysis, frequently combined with ML models to accelerate the search. Existing ML approaches often rely on large datasets primarily focusing on simple stoichiometric compounds, overlooking the potential of solid-solution alloys. The authors' previous work demonstrated the effectiveness of combining SISSO with the α-method in reducing the need for extensive datasets. Cation/anion exchange provides a route to explore wide variations in material properties, leveraging composition-property relationships and high-entropy stabilization to fine-tune band properties. The challenges of creating comprehensive databases for multicomponent alloys, especially at very dilute compositions, are also highlighted.

This study employs a combined computational and machine learning approach. First, density functional theory (DFT) calculations were performed using the Vienna Ab initio Simulation Package (VASP) with the projector augmented wave (PAW) method. The generalized gradient approximation (GGA) attributed to Perdew, Burke, and Ernzerhof (PBE) was used for structural relaxations, and the Heyd-Scuseria-Ernzerhof (HSE06) hybrid functional was used for accurate bandgap and band edge calculations. Special quasi-random structures (SQS) were generated using the integrated cluster expansion toolkit (ICET) to model the solid solutions. A total of 109 ternary and binary ZnTe-based alloy configurations were generated and their properties calculated. This data comprised the training set for the machine-learning model. The Sure Independence Screening and Sparsifying Operator (SISSO) was used to discover descriptors (mathematical functions) correlating with the conduction band minimum (CBM) and valence band maximum (VBM) . The SISSO algorithm uses symbolic regression and compressed sensing to efficiently identify these descriptors, making it suitable for small datasets. The agreement method (α-method) was integrated with SISSO to improve model accuracy and generalizability to higher-order systems. The model's performance was evaluated using RMSE and Pearson correlation on the training, testing and validation datasets. The validation set contained quaternary compounds. The robustness of the model was assessed by training with different dataset sizes (13 to 85 data points). Finally, the trained model, using just 13 data points, was used to explore the hexanary compositional space, focusing on combinations of Zn, Mg, Ca, Te, Se, and S. Candidate hexanary alloy configurations were identified based on bandgap, band alignment, and thermodynamic stability, and further validated using DFT calculations. Absorption coefficients were calculated to assess solar spectrum absorption efficiency.

The study successfully demonstrates that the SISSO+α-method can effectively predict the CBM and VBM of ZnTe-based alloys with remarkable accuracy, even when trained on a very small dataset (13 data points). The α-method significantly improves the model's performance compared to SISSO alone, mitigating overfitting and enabling accurate predictions for higher-order systems (quaternary and hexanary). The analysis of RMSE and Pearson correlation coefficients across different data sizes showed consistent performance of the SISSO+α-method, highlighting its suitability for small data applications. The model revealed a clear relationship between atomic features (covalent radius, ionic radius, ionization energy, and electronegativity) and band edge positions. Based on the model, several promising hexanary ZnTe-based alloys for water splitting were identified, exhibiting desirable bandgaps and band edge alignments. Importantly, these candidates demonstrate sufficient thermodynamic stability at near room temperature and optimal absorption in the visible light region of the solar spectrum. The study shows the potential of combining machine learning and high-throughput calculations for materials discovery.

The key finding that the SISSO+α-method achieves high accuracy with a minimal training dataset is significant. This drastically reduces the computational cost and time required for materials discovery, enabling high-throughput screening of a much larger compositional space. The identified hexanary alloys represent promising candidates for water-splitting photocatalysts due to their electronic structure and thermodynamic stability. The established correlation between atomic features and electronic properties provides valuable insights for rational material design and for predicting the effect of compositional changes on band properties. This strategy has potential applications beyond water splitting, offering a generalizable approach for designing multicomponent alloys with tailored functionalities for various applications.

This study successfully demonstrated a highly efficient machine learning approach, utilizing SISSO and the α-method, to predict the band edge positions of ZnTe-based multicomponent alloys using a remarkably small training dataset. The method proved effective in identifying promising hexanary alloy compositions for water-splitting photocatalysis, showing significant advantages in computational cost and efficiency. The interpretable descriptors generated by the model provide valuable insights for guiding future materials design and optimization. Future research could explore other multicomponent alloy systems and expand the types of material properties predicted by the model. Integrating experimental validation of the predicted materials would further enhance the reliability and impact of this approach.

The study's reliance on DFT calculations introduces inherent limitations related to the approximations within DFT, particularly for strongly correlated systems. The accuracy of the predicted properties depends on the accuracy of the DFT calculations used to generate the training dataset. The generalizability of the model to other alloy systems beyond ZnTe-based chalcogenides needs further investigation. While the thermodynamic stability of the proposed hexanary alloys was assessed, the actual synthesis and characterization of these materials are needed to confirm the model’s predictions experimentally.