Machine Learning Accelerates Prediction of Defect Vibrational Properties in Solids

The optical characteristics of imperfections within solid materials underpin a wide range of phenomena, from the vibrant colours of gemstones to the potential for single-photon emission in quantum networks. Accurately modelling these optical transitions requires understanding how electrons interact with atomic vibrations, known as phonons, but calculating these interactions traditionally demands immense computational resources. Mark E. Turiansky, John L. Lyons, and Noam Bernstein, all from the US Naval Research Laboratory, now demonstrate a way to bypass this limitation by employing machine learning to predict phonon spectra. This innovative approach significantly accelerates calculations without sacrificing accuracy, opening new avenues for detailed investigation of defect vibrational properties and enabling the resolution of subtle features, such as the complex vibrational modes influencing luminescence in silicon defects.

However, current methods require computationally expensive evaluation of all phonon modes in simulation cells containing hundreds of atoms. This work demonstrates that this bottleneck can be overcome using machine learning interatomic potentials with negligible accuracy loss. A key finding is that atomic relaxation data from routine first-principles calculations suffice as a dataset for fine-tuning, although additional data can further improve model performance. The efficiency of this approach enables studies of defect vibrational properties with high-level theory, and the team fine-tunes the models to hybrid functional calculations to obtain highly accurate spectra, comparing the results with explicit calculations and experiments for various defects.

Defect Formation Energies via Density Functional Theory

This supplementary material provides a detailed account of the computational methods used to calculate defect properties in materials using density functional theory (DFT). The authors meticulously document their approach, ensuring transparency and reproducibility, specifying the implementation of DFT using the VASP software package, including the choice of exchange-correlation functionals and dispersion corrections. They detail the parameters used for k-point sampling, energy convergence, and force convergence during structural relaxation, employing the supercell method to model defects and utilizing the Doped package to facilitate their creation. The authors address the complexities of charge state ambiguity in defect calculations and explain their method for correcting it, performing excited state calculations using Time-Dependent DFT.

They explain the use of the mean-value point in the Brillouin zone for defect calculations and provide an overview of DFT and the exchange-correlation functionals used, discussing the Jahn-Teller effect and vibronic structure in relation to understanding defect properties. Kullback-Leibler divergence is mentioned as a measure of probability distribution differences, and the performance of the SCAN meta-GGA functional is assessed for defect calculations. The authors carefully consider supercell size and demonstrate convergence with respect to the k-point grid, comparing results obtained with different functionals, including PBE, HSE06, and SCAN. They detail how they determined the most stable charge state of the defects, discussing vibronic coupling in relation to optical properties and describing how they calculated optical absorption spectra. The team’s approach leverages machine learning to model the complex interactions between electrons and atomic vibrations, a computationally intensive process traditionally requiring extensive calculations. This new technique dramatically reduces the computational burden, enabling detailed studies of defects that were previously impractical. The core of this innovation lies in the use of “foundation models,” machine learning algorithms pre-trained on existing data and then refined using surprisingly small datasets specific to each material defect.

Initial tests demonstrate that the foundation model can qualitatively predict luminescence, but further refinement is crucial for accurate results. Remarkably, the team found that data from routine calculations already performed to determine a defect’s equilibrium geometry, the atomic relaxation, is sufficient for substantial improvement in predictive power, effectively providing a “free” dataset. To further enhance accuracy, the researchers explored generating small numbers of additional configurations and found that adding as few as ten new data points can significantly improve the model’s performance. In the case of carbon defects in hexagonal boron nitride, this approach yielded a nearly 150-fold speedup compared to traditional methods, while maintaining a high degree of accuracy. The team successfully applied this refined method to several complex materials, achieving quantitative agreement with detailed calculations and opening the door to direct comparisons with experimental data, promising to accelerate the discovery and design of materials with tailored optical properties.

Machine Learning Streamlines Defect Vibrational Analysis

This research demonstrates a new approach to calculating the vibrational properties of defects in solid materials, crucial for understanding their optical behaviour and potential applications in areas like quantum computing. The team successfully applied machine learning interatomic potentials (MLIPs) to predict these properties, achieving accuracy comparable to traditional, computationally expensive methods. By training the MLIPs on data from routine calculations of atomic relaxation, they significantly reduced the computational burden, enabling the study of much larger systems, including an 8000-atom evaluation of a defect in silicon, than previously feasible. The key advancement lies in streamlining the process of calculating how defects interact with vibrations, which directly influences their luminescence spectra. This work establishes a systematic method for developing and refining MLIPs specifically for defect studies and opens the door to applying these techniques to a wider range of materials and defects. While the current study utilized a specific hybrid functional within density functional theory, the authors emphasize the adaptability of their approach to other theoretical levels, acknowledging that further improvements to MLIPs will continue to enhance the ability to accurately analyze and characterize defects from first principles.