Abstract
This study presents a comprehensive numerical analysis of a quantum-dot-engineered heterostructure, PbS:$Yb^{3+},Er^{3+}$/CuBiO, optimized for water splitting applications. Using density functional theory (DFT) coupled with machine learning, the study explores the electronic, optical, and catalytic properties of the material. The optimized PbS structure exhibited a direct bandgap of 1.191 eV, while co-doping with Yb and Er transitioned the material to a metallic state, enhancing charge carrier mobility and electron-hole separation. The final heterostructure displayed an indirect bandgap of 0.431 eV, favorable for visible-light absorption. Key findings include an internal electric field strength of 6.3 Debye, efficient charge transfer confirmed by Bader analysis, and strong optical absorption at 2.4 eV. Machine learning models, including DNN and LSTM, were employed to predict photon absorption rates, achieving mean squared errors as low as 0.0004. The synergistic effects of enhanced internal electric fields, optimized band structures, and strong photon absorption underscore the materials' potential for efficient hydrogen production. This study bridges advanced computational methods and machine learning, offering a framework for designing high-performance photocatalysts in renewable energy applications.