- Open Access
Machine-Learning Prediction of Charged-Defect Formation Energies from Crystal Structures
Phys. Rev. Lett. 135, 246101 – Published 11 December, 2025
DOI: https://doi.org/10.1103/h66h-y5k6
Abstract
Recent advances in materials informatics have expanded the number of synthesizable materials. However, screening promising candidates, such as semiconductors, based on defect properties remains challenging. This is primarily due to the lack of a general framework for predicting defect formation energies in multiple charge states from structural data. In this Letter, we present a protocol, namely data normalization, Fermi level alignment, and treatment of perturbed host states, and validate it by accurately predicting oxygen vacancy formation energies in three charge states using a single model. We also introduce a joint machine-learning model that integrates defect formation energies and band-edge predictions for virtual screening. Using this framework, we identify 89 hole-dopable oxides, including BaGaSbO, a potential ambipolar photovoltaic material. Our protocol is expected to become a standard approach for machine-learning studies on point defect formation energies.
Physics Subject Headings (PhySH)
Article Text
Supplemental Material
References (39)
- S. Curtarolo, G. L. Hart, M. B. Nardelli, N. Mingo, S. Sanvito, and O. Levy, The high-throughput highway to computational materials design, Nat. Mater. 12, 191 (2013).
- A. Jain et al., Commentary: The materials project: A materials genome approach to accelerating materials innovation, APL Mater. 1, 011002 (2013).
- W. Shockley and W. T. Read, Statistics of the recombinations of holes and electrons, Phys. Rev. 87, 835 (1952).
- S. B. Zhang, S.-H. Wei, and A. Zunger, Overcoming doping bottlenecks in semiconductors and wide-gap materials, Physica B 273, 976 (1999).
- A. M. Deml, A. M. Holder, R. P. O’Hayre, C. B. Musgrave, and V. Stevanović, Intrinsic material properties dictating oxygen vacancy formation energetics in metal oxides, J. Phys. Chem. Lett. 6, 1948 (2015).
- Y. Kumagai, N. Tsunoda, A. Takahashi, and F. Oba, Insights into oxygen vacancies from high-throughput first-principles calculations, Phys. Rev. Mater. 5, 123803 (2021).
- M. D. Witman, A. Goyal, T. Ogitsu, A. H. McDaniel, and S. Lany, Defect graph neural networks for materials discovery in high-temperature clean-energy applications, Nat. Comput. Sci. 3, 675 (2023).
- N. C. Frey, D. Akinwande, D. Jariwala, and V. B. Shenoy, Machine learning-enabled design of point defects in 2D materials for quantum and neuromorphic information processing, ACS Nano 14, 13406 (2020).
- X. Wu, H. Chen, J. Wang, and X. Niu, Machine learning accelerated study of defect energy levels in perovskites, J. Phys. Chem. C 127, 11387 (2023).
- J. B. Varley, A. Samanta, and V. Lordi, Descriptor-based approach for the prediction of cation vacancy formation energies and transition levels, J. Phys. Chem. Lett. 8, 5059 (2017).
- A. Mannodi-Kanakkithodi, X. Xiang, L. Jacoby, R. Biegaj, S. T. Dunham, D. R. Gamelin, and M. K. Y. Chan, Universal machine learning framework for defect predictions in zinc blende semiconductors, Patterns 3, 100450 (2022).
- T. Xie and J. C. Grossman, Crystal graph convolutional neural networks for an accurate and interpretable prediction of material properties, Phys. Rev. Lett. 120, 145301 (2018).
- K. Yim, Y. Youn, M. Lee, D. Yoo, J. Lee, S. H. Cho, and S. Han, Computational discovery of p-type transparent oxide semiconductors using hydrogen descriptor, npj Comput. Mater. 4, 17 (2018).
- Y. Kumagai, Computational screening of p-type transparent conducting oxides using the optical absorption spectra and oxygen-vacancy formation energies, Phys. Rev. Appl. 19, 034063 (2023).
- T. N. H. Vu and Y. Kumagai, Investigation of hole dopability in oxygen-2p-dominated bands, Chem. Mater. (2025), 10.1021/acs.chemmater.5c02032.
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/h66h-y5k6 for providing details of a CGCNN-based model that predicts charged oxygen-vacancy formation energies directly from crystal structures. It also explains how defect energies are aligned across materials (via O core potentials or VBMs) and how a consistent Fermi-level reference is chosen, and presents the model architecture, graph features, and optimized hyperparameters, and documents the DFT workflow used to generate the training data, along with the pruning rules for removing anomalous vacancy relaxations.
- K. Cabello-Solorzano, I. O. de Araujo, M. Peña, L. Correia, and A. J. Tallón-Ballesteros, 18th International Conference on Soft Computing Models in Industrial and Environmental Applications (SOCO 2023), Lect. Notes Netw. Syst. 344 (2023).
- Y. Zhang, A. Mascarenhas, and L.-W. Wang, Systematic approach to distinguishing a perturbed host state from an impurity state in a supercell calculation for a doped semiconductor: Using GaP:N as an example, Phys. Rev. B 74, 041201 (2006).
- N. Tsunoda, Y. Kumagai, A. Takahashi, and F. Oba, Electrically benign defect behavior in zinc tin nitride revealed from first principles, Phys. Rev. Appl. 10, 011001 (2018).
- Y. Kumagai, M. Choi, Y. Nose, and F. Oba, First-principles study of point defects in chalcopyrite , Phys. Rev. B 90, 125202 (2014).
- G. Zhang, A. Canning, N. Gronbech-Jensen, S. Derenzo, and L.-W. Wang, Shallow impurity level calculations in semiconductors using Ab initio methods, Phys. Rev. Lett. 110, 166404 (2013).
- H. R. Gopidi, L. Vashist, and O. I. Malyi, Physics of band-filling correction in defect calculations of solid-state materials, RSC Adv. 14, 17675 (2024).
- S. Lany and A. Zunger, Anion vacancies as a source of persistent photoconductivity in II-VI and chalcopyrite semiconductors, Phys. Rev. B 72, 035215 (2005).
- C. Persson, Y.-J. Zhao, S. Lany, and A. Zunger, n-type doping of and , Phys. Rev. B 72, 035211 (2005).
- Y. Kumagai, S. R. Kavanagh, I. Suzuki, T. Omata, A. Walsh, D. O. Scanlon, and H. Morito, Alkali mono-pnictides: A new class of photovoltaic materials by element mutation, PRX Energy 2, 043002 (2023).
- Y. Kumagai, K. Harada, H. Akamatsu, K. Matsuzaki, and F. Oba, Carrier-induced band-gap variation and point defects in Zn3N2 from first principles, Phys. Rev. Appl. 8, 014015 (2017).
- A. Merchant, S. Batzner, S. S. Schoenholz, M. Aykol, G. Cheon, and E. D. Cubuk, Scaling deep learning for materials discovery, Nature (London) 624, 80 (2023).
- Y. Hinuma, Y. Kumagai, I. Tanaka, and F. Oba, Band alignment of semiconductors and insulators using dielectric-dependent hybrid functionals: Toward high-throughput evaluation, Phys. Rev. B 95, 075302 (2017).
- J. H. Skone, M. Govoni, and G. Galli, Self-consistent hybrid functional for condensed systems, Phys. Rev. B 89, 195112 (2014).
- J. P. Perdew, A. Ruzsinszky, G. I. Csonka, O. A. Vydrov, G. E. Scuseria, L. A. Constantin, X. Zhou, and K. Burke, Restoring the density-gradient expansion for exchange in solids and surfaces, Phys. Rev. Lett. 100, 136406 (2008).
- S. L. Dudarev, S. Y. Savrasov, C. J. Humphreys, and A. P. Sutton, Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA + U study, Phys. Rev. B 57, 1505 (1998).
- A. Teredesai et al., Optuna, Proc. 25th ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. 2623 (2019).
- P. E. Blöchl, Projector augmented-wave method, Phys. Rev. B 50, 17953 (1994).
- G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59, 1758 (1999).
- G. Kresse and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54, 11169 (1996).
- Y. Hinuma, G. Pizzi, Y. Kumagai, F. Oba, and I. Tanaka, Band structure diagram paths based on crystallography, Comput. Mater. Sci. 128, 140 (2017).
- J. Heyd, G. E. Scuseria, and M. Ernzerhof, Hybrid functionals based on a screened Coulomb potential, J. Chem. Phys. 118, 8207 (2003).
- A. V. Krukau, O. A. Vydrov, A. F. Izmaylov, and G. E. Scuseria, Influence of the exchange screening parameter on the performance of screened hybrid functionals, J. Chem. Phys. 125, 224106 (2006).
- https://github.com/kumagai-group/ML_charged_defects.