Lattice thermal conductivity calculation using machine learning potential

The thermal conductivity of semiconductor materials was evaluated through phonon analysis using a machine learning potential. For the diamond structure of silicon, the phonon dispersion relation and the temperature dependence of thermal conductivity were compared with experimental values, confirming good agreement. Furthermore, cumulative thermal conductivity as a function of frequency was analyzed, showing that low-frequency phonons contribute to heat transport.

Use Cases Highlights

Phonon analysis-based thermal conductivity evaluation
Utilization of machine learning potentials
Analysis of frequency dependence of cumulative thermal conductivity

Silicon crystal model

The computational model used was a 3×3×3 supercell (216 atoms) of a silicon crystal. Phonon analysis was performed using a machine learning potential to estimate interatomic force constants and evaluate thermal conductivity. By calculating the phonon dispersion relation and density of states, agreement with experimental values was confirmed, demonstrating the validity of the model.

Supercell of silicon (3×3×3) used in the calculation

Phonon dispersion and density of states

The phonon dispersion relation showed good agreement with experimental values, and the calculated phonon density of states also confirmed validity. The comparison with experimental values of the phonon dispersion relation is shown on the left, and the calculated phonon density of states is shown on the right, demonstrating high accuracy and reliability of the analysis. It was shown that phonon analysis using a machine learning potential is effective.

Phonon dispersion relation and density of states

Thermal conductivity and cumulative contributions

The temperature dependence of thermal conductivity and the cumulative thermal conductivity as a function of mean free path and phonon frequency are shown. The left panel compares thermal conductivity with experimental values, the middle panel shows cumulative thermal conductivity with respect to mean free path, and the right panel shows cumulative thermal conductivity with respect to phonon frequency. These analyses reveal that low-frequency phonons contribute significantly to heat transport.

Thermal conductivity and cumulative thermal conductivity

Reference

[1] Tadano, T., Gohda, Y., & Tsuneyuki, S. (2014). Anharmonic force constants extracted from first-principles Molecular Dynamics: applications to heat transfer simulations. Journal of Physics Condensed Matter, 26(22), 225402.
[2] Batatia, I., Kovacs, D. P., Simm, G. N. C., Ortner, C., & Csanyi, G. (2022, October 31). MACE: Higher order equivariant message passing neural networks for fast and accurate force fields. OpenReview.
[3] Bartók, A. P., Payne, M. C., Kondor, R., & Csányi, G. (2010). Gaussian Approximation Potentials: The Accuracy of Quantum Mechanics, without the Electrons. Physical Review Letters, 104(13).
[4] Kulda, J., Strauch, D., Pavone, P., & Ishii, Y. (1994). Inelastic-neutron-scattering study of phonon eigenvectors and frequencies in Si. Physical Review. B, Condensed Matter, 50(18), 13347-13354.
[5] Inyushkin, A. V., Taldenkov, A. N., Gibin, A. M., Gusev, A. V., & Pohl, H. (2004). On the isotope effect in thermal conductivity of silicon. Physica Status Solidi. C, Conferences and Critical Reviews/Physica Status Solidi. C, Current Topics in Solid State Physics, 1(11), 2995-2998.AA5

Details of analysis