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Microscopic Mechanisms of Low Lattice Thermal Conductivity in AlxGa1−xN Alloys Revealed by Neuroevolution Machine-Learning Potential

Yuwen Zhang1,2, Tao Ouyang3, Zheyong Fan4, and Wu Li1,5,*

  • *Contact author: wu.li.phys2011@gmail.com

PRX Energy 5, 023013 – Published 18 June, 2026

DOI: https://doi.org/10.1103/df1n-9bll

Abstract

Understanding thermal transport in AlxGa1−xN alloys is critical for the reliable thermal management of high-power electronic devices. However, theoretical predictions of lattice thermal conductivity κℓ based on the traditional Abele’s virtual crystal approximation (VCA) significantly deviate from experimental measurements, and these discrepancies have long been attributed to finite-size effects. Unlike the traditional VCA, which homogenizes atomic masses and bonding environments, we explicitly incorporate both mass disorder and interatomic force constant (IFC) disorder by directly performing Boltzmann transport equation calculations on large special quasirandom structures, aiming to uncover their impact on lattice thermal transport. Our results show that mass disorder plays a dominant role in suppressing κℓ by significantly enhancing the anharmonic scattering of low-frequency phonons, whereas the heat-carrying capacity of high-frequency phonons is completely eliminated due to substantially reduced group velocities and strong harmonic scattering. In comparison, IFC disorder mainly increases anharmonic scattering rates but has negligible influence on the group velocities of low-frequency phonons. When both disorder types are accounted for, the predicted thermal conductivities align closely with experimental observations. This indicates that the previously reported overestimations from VCA are not due to finite-size effects. We also find that the alloy scattering model based on perturbation theory significantly overestimates the harmonic scattering rates of high-frequency phonons, despite their negligible contribution to thermal conductivity. These findings highlight the necessity of atomistic disorder modeling in wide-bandgap alloys and provide critical insights for thermal design in AlxGa1−xN-based electronics.

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References (81)

  1. J. Piprek, Ultra-violet light-emitting diodes with quasi acceptor-free AlGaN polarization doping, Opt. Quantum Electron. 44, 67 (2012).
  2. C.-P. Wang and Y.-R. Wu, Study of optical anisotropy in nonpolar and semipolar AlGaN quantum well deep ultraviolet light emission diode, J. Appl. Phys. 112, 033104 (2012).
  3. I. Omura, W. Saito, T. Domon, and K. Tsuda, Gallium Nitride power HEMT for high switching frequency power electronics, in 2007 International Workshop on Physics of Semiconductor Devices (2007), p. 781.
  4. A. S. A. Fletcher and D. Nirmal, A survey of gallium nitride HEMT for RF and high power applications, Superlattices. Microstruct. 109, 519 (2017).
  5. J. Zhang and N. Tansu, Engineering of AlGaN-Delta-GaN quantum-well gain media for mid- and deep-ultraviolet lasers, IEEE Photonics J. 5, 2600209 (2013).
  6. S. Ali and M. Usman, Performance enhancement of ultraviolet-C AlGaN laser diode, Eur. Phys. J. Plus 137, 771 (2022).
  7. A. G. Baca, A. M. Armstrong, B. A. Klein, A. A. Allerman, E. A. Douglas, and R. J. Kaplar, Al-rich AlGaN based transistors, J. Vac. Sci. Technol. A 38, 020803 (2020).
  8. D. Q. Tran, R. D. Carrascon, M. Iwaya, B. Monemar, V. Darakchieva, and P. P. Paskov, Thermal conductivity of AlxGa1−xN (0≤x≤1) epitaxial layers, Phys. Rev. Mater. 6, 104602 (2022).
  9. T.-L. Luo, Y.-F. Ding, B.-J. Wei, J.-Y. Du, X.-Y. Shen, G.-M. Zhu, and B.-W. Li, Phononic thermal conduction and thermal regulation in low-dimensional micro-nano scale systems: Nonequilibrium statistical physics problems from chip heat dissipation, Acta Phys. Sin. 72, 234401 (2023).
  10. Z. Qi, W. Shen, R. Li, X. Sun, L. Li, Q. Wang, G. Wu, and K. Liang, AlN/diamond interface nanoengineering for reducing thermal boundary resistance by molecular dynamics simulations, Appl. Surf. Sci. 615, 156419 (2023).
  11. A. Chen, D. Wei, J. Xu, A. Li, H. Wang, Z. Qin, and G. Qin, Alloying reversed anisotropy of thermal transport in bulk Al0.5Ga0.5N, J. Phys. Chem. Lett. 14, 9746 (2023).
  12. W. Liu and A. A. Balandin, Temperature dependence of thermal conductivity of AlxGa1−xN thin films measured by the differential 3ω technique, Appl. Phys. Lett. 85, 5230 (2004).
  13. W. Liu and A. A. Balandin, Thermal conduction in AlxGa1−xN alloys and thin films, J. Appl. Phys. 97, 073710 (2005).
  14. D. Q. Tran, R. Delgado-Carrascon, J. F. Muth, T. Paskova, M. Nawaz, V. Darakchieva, and P. P. Paskov, Phonon-boundary scattering and thermal transport in AlxGa1−xN: Effect of layer thickness, Appl. Phys. Lett. 117, 252102 (2020).
  15. D. G. Cahill, Thermal conductivity measurement from 30 to 750 K: The 3ω method, Rev. Sci. Instrum. 61, 802 (1990).
  16. J. Ma, W. Li, and X. Luo, Intrinsic thermal conductivities and size effect of alloys of wurtzite AlN, GaN, and InN from first-principles, J. Appl. Phys. 119, 125702 (2016).
  17. B. Abeles, Lattice thermal conductivity of disordered semiconductor alloys at high temperatures, Phys. Rev. 131, 1906 (1963).
  18. J. Garg, N. Bonini, B. Kozinsky, and N. Marzari, Role of disorder and anharmonicity in the thermal conductivity of silicon-germanium alloys: A first-principles study, Phys. Rev. Lett. 106, 045901 (2011).
  19. T. Dao-Sheng, H. Yu-Chao, Z. Yan-Guang, and C. Bing-Yang, Thermal conductivity modeling of GaN films, Acta Phys. Sin. 70, 045101 (2021).
  20. G. Yang, Y.-B. Liu, L. Yang, and B.-Y. Cao, Machine-learned atomic cluster expansion potentials for fast and quantum-accurate thermal simulations of wurtzite AlN, J. Appl. Phys. 135, 085105 (2024).
  21. A. Ward, D. A. Broido, D. A. Stewart, and G. Deinzer, Ab initio theory of the lattice thermal conductivity in diamond, Phys. Rev. B 80, 125203 (2009).
  22. R. Drautz, Atomic cluster expansion for accurate and transferable interatomic potentials, Phys. Rev. B 99, 014104 (2019).
  23. Z. Fan, Y. Wang, P. Ying, K. Song, J. Wang, Y. Wang, Z. Zeng, K. Xu, E. Lindgren, J. M. Rahm, A. J. Gabourie, J. Liu, H. Dong, J. Wu, Y. Chen, Z. Zhong, J. Sun, P. Erhart, Y. Su, and T. Ala-Nissila, GPUMD: A package for constructing accurate machine-learned potentials and performing highly efficient atomistic simulations, J. Chem. Phys. 157, 114801 (2022).
  24. Z. Fan, Z. Zeng, C. Zhang, Y. Wang, K. Song, H. Dong, Y. Chen, and T. Ala-Nissila, Neuroevolution machine learning potentials: Combining high accuracy and low cost in atomistic simulations and application to heat transport, Phys. Rev. B 104, 104309 (2021).
  25. Z. Fan, Improving the accuracy of the neuroevolution machine learning potential for multi-component systems, J. Phys.: Condens. Matter 34, 125902 (2022).
  26. L. Dai, M. Li, and Y. Hu, Machine learning for thermal transport and phonon high-order anharmonicity in high thermal conductivity materials: A case study in boron arsenide, Phys. Rev. Mater. 9, 045403 (2025).
  27. I. S. Novikov, K. Gubaev, E. V. Podryabinkin, and A. V. Shapeev, The MLIP package: Moment tensor potentials with MPI and active learning, Mach. Learn.: Sci. Technol. 2, 025002 (2021).
  28. J. Tiwari and T. Feng, Accurate prediction of thermal conductivity of Al2O3 at ultrahigh temperatures, Phys. Rev. B 109, 075201 (2024).
  29. L. Zhang, J. Han, H. Wang, R. Car, and W. E, Deep potential molecular dynamics: A scalable model with the accuracy of quantum mechanics, Phys. Rev. Lett. 120, 143001 (2018).
  30. H. Dong, Z. Li, B. Sun, Y. Zhou, L. Liu, and J.-Y. Yang, Thermal transport in disordered wurtzite ScAlN alloys using machine learning interatomic potentials, Mater. Today Commun. 39, 109213 (2024).
  31. Z. Sun, X. Sun, Z. Qi, Q. Wang, R. Li, L. Li, G. Wu, W. Shen, and S. Liu, Investigating thermal transport across the AlN/diamond interface via the machine learning potential, Diamond Relat. Mater. 147, 111303 (2024).
  32. K. Song et al., General-purpose machine-learned potential for 16 elemental metals and their alloys, Nat. Commun. 15, 10208 (2024).
  33. 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).
  34. P. E. Blöchl, Projector augmented-wave method, Phys. Rev. B 50, 17953 (1994).
  35. G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59, 1758 (1999).
  36. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  37. H. J. Monkhorst and J. D. Pack, Special points for Brillouin-zone integrations, Phys. Rev. B 13, 5188 (1976).
  38. X. Z. Shi, C. Y. He, C. J. Pickard, C. Tang, and J. X. Zhong, Stochastic generation of complex crystal structures combining group and graph theory with application to carbon, Phys. Rev. B 97, 014104 (2018).
  39. A. Jain, S. P. Ong, G. Hautier, W. Chen, W. D. Richards, S. Dacek, S. Cholia, D. Gunter, D. Skinner, G. Ceder, and K. A. Persson, Commentary: The Materials Project: A materials genome approach to accelerating materials innovation, APL Mater. 1, 011002 (2013).
  40. W. Li, J. Carrete, N. A. Katcho, and N. Mingo, ShengBTE: A solver of the Boltzmann transport equation for phonons, Comput. Phys. Commun. 185, 1747 (2014).
  41. Z. Han, X. Yang, W. Li, T. Feng, and X. Ruan, FourPhonon: An extension module to ShengBTE for computing four-phonon scattering rates and thermal conductivity, Comput. Phys. Commun. 270, 108179 (2022).
  42. S. Grimme, J. Antony, S. Ehrlich, and H. Krieg, A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu, J. Chem. Phys. 132, 154104 (2010).
  43. S. Grimme, S. Ehrlich, and L. Goerigk, Effect of the damping function in dispersion corrected density functional theory, J. Comput. Chem. 32, 1456 (2011).
  44. A. Togo and I. Tanaka, First principles phonon calculations in materials science, Scr. Mater. 108, 1 (2015).
  45. A. Sztein, J. Haberstroh, J. E. Bowers, S. P. DenBaars, and S. Nakamura, Calculated thermoelectric properties of InxGa1−xN, InxAl1−xN, and AlxGa1−xN, J. Appl. Phys. 113, 183707 (2013).
  46. A. Zunger, S. H. Wei, L. G. Ferreira, and J. E. Bernard, Special quasirandom structures, Phys. Rev. Lett. 65, 353 (1990).
  47. M. Ångqvist, W. A. Muñoz, J. M. Rahm, E. Fransson, C. Durniak, P. Rozyczko, T. H. Rod, and P. Erhart, ICET – A Python library for constructing and sampling alloy cluster expansions, Adv. Theory Simul. 2, 1900015 (2019).
  48. See Supplemental Material at http://link.aps.org/supplemental/10.1103/df1n-9bll for additional results and validations, including convergence tests of lattice thermal conductivity with respect to q-point sampling, supercell size, and the sampling method; validation of the NEP model against DFT for crystalline phases, heterostructures, and out-of-sample alloy compositions; representative SQS configurations of AlxGa1−xN alloys used in this work; and a comparison of anharmonic scattering rates of the Al0.5Ga0.5N alloy at different temperatures.
  49. W. Li, L. Lindsay, D. A. Broido, D. A. Stewart, and N. Mingo, Thermal conductivity of bulk and nanowire Mg2SixSn1−x alloys from first principles, Phys. Rev. B 86, 174307 (2012).
  50. S.-I. Tamura, Isotope scattering of dispersive phonons in Ge, Phys. Rev. B 27, 858 (1983).
  51. A. Katre, J. Carrete, B. Dongre, G. K. H. Madsen, and N. Mingo, Exceptionally strong phonon scattering by B substitution in cubic SiC, Phys. Rev. Lett. 119, 075902 (2017).
  52. Z. Fan, H. Dong, A. Harju, and T. Ala-Nissila, Homogeneous nonequilibrium molecular dynamics method for heat transport and spectral decomposition with many-body potentials, Phys. Rev. B 99, 064308 (2019).
  53. D. J. Evans, Homogeneous nemd algorithm for thermal conductivity—Application of non-canonical linear response theory, Phys. Lett. A 91, 457 (1982).
  54. K. K. Mandadapu, R. E. Jones, and P. Papadopoulos, A homogeneous nonequilibrium molecular dynamics method for calculating thermal conductivity with a three-body potential, J. Chem. Phys. 130, 204106 (2009).
  55. T. Ruf, J. Serrano, M. Cardona, P. Pavone, M. Pabst, M. Krisch, M. D’Astuto, T. Suski, I. Grzegory, and M. Leszczynski, Phonon dispersion curves in wurtzite-structure GaN determined by inelastic X-ray scattering, Phys. Rev. Lett. 86, 906 (2001).
  56. M. Schwoerer-Böhning, A. T. Macrander, M. Pabst, and P. Pavone, Phonons in wurtzite aluminum nitride, Phys. Status Solidi (b) 215, 177 (1999).
  57. J. M. Zhang, T. Ruf, M. Cardona, O. Ambacher, M. Stutzmann, J. M. Wagner, and F. Bechstedt, Raman spectra of isotopic GaN, Phys. Rev. B 56, 14399 (1997).
  58. Z. Cheng, Y. R. Koh, A. Mamun, J. Shi, T. Bai, K. Huynh, L. Yates, Z. Liu, R. Li, E. Lee, M. E. Liao, Y. Wang, H. M. Yu, M. Kushimoto, T. Luo, M. S. Goorsky, P. E. Hopkins, H. Amano, A. Khan, and S. Graham, Experimental observation of high intrinsic thermal conductivity of AlN, Phys. Rev. Mater. 4, 044602 (2020).
  59. A. V. Inyushkin, A. N. Taldenkov, D. A. Chernodubov, E. N. Mokhov, S. S. Nagalyuk, V. G. Ralchenko, and A. A. Khomich, On the thermal conductivity of single crystal AlN, J. Appl. Phys. 127, 205109 (2020).
  60. L. Lindsay, D. A. Broido, and T. L. Reinecke, Thermal conductivity and large isotope effect in GaN from first principles, Phys. Rev. Lett. 109, 095901 (2012).
  61. G. A. Slack, R. A. Tanzilli, R. O. Pohl, and J. W. Vandersande, The intrinsic thermal conductivity of AlN, J. Phys. Chem. Solids 48, 641 (1987).
  62. Q. Zheng, C. Li, A. Rai, J. H. Leach, D. A. Broido, and D. G. Cahill, Thermal conductivity of GaN, 71GaN, and SiC from 150 K to 850 K, Phys. Rev. Mater. 3, 014601 (2019).
  63. H. Shibata, Y. Waseda, H. Ohta, K. Kiyomi, K. Shimoyama, K. Fujito, H. Nagaoka, Y. Kagamitani, R. Simura, and T. Fukuda, High thermal conductivity of gallium nitride (GaN) crystals grown by HVPE process, Mater. Trans. 48, 2782 (2007).
  64. L. Lindsay, D. A. Broido, and T. L. Reinecke, Ab initio thermal transport in compound semiconductors, Phys. Rev. B 87, 165201 (2013).
  65. W. Li and N. Mingo, Thermal conductivity of bulk and nanowire InAs, AlN, and BeO polymorphs from first principles, J. Appl. Phys. 114, 183505 (2013).
  66. R. Wu, R. Hu, and X. Luo, First-principle-based full-dispersion Monte Carlo simulation of the anisotropic phonon transport in the wurtzite GaN thin film, J. Appl. Phys. 119, 145706 (2016).
  67. J. Garg, T. Luo, and G. Chen, Spectral concentration of thermal conductivity in GaN—A first-principles study, Appl. Phys. Lett. 112, 252101 (2018).
  68. B. C. Daly, H. J. Maris, A. V. Nurmikko, M. Kuball, and J. Han, Optical pump-and-probe measurement of the thermal conductivity of nitride thin films, J. Appl. Phys. 92, 3820 (2002).
  69. A. Filatova-Zalewska, Z. Litwicki, T. Suski, and A. Jeżowski, Thermal conductivity of thin films of gallium nitride, doped with aluminium, measured with 3ω method, Solid State Sci. 101, 106105 (2020).
  70. P. F. de Aguiar, B. Bourguignon, M. S. Khots, D. L. Massart, and R. Phan-Than-Luu, D-optimal designs, Chemometr. Intell. Lab. Syst. 30, 199 (1995).
  71. E. Podryabinkin, K. Garifullin, A. Shapeev, and I. Novikov, MLIP-3: Active learning on atomic environments with moment tensor potentials, J. Chem. Phys. 159, 084112 (2023).
  72. S. A. Goreinov, I. V. Oseledets, D. V. Savostyanov, E. E. Tyrtyshnikov, and N. L. Zamarashkin, How to find a good submatrix, in Matrix Methods: Theory, Algorithms and Applications (World Scientific, Singapore, 2010), p. 247.
  73. https://github.com/psn417/nep_extrapolation.
  74. L. Zhang, H. Yan, G. Zhu, S. Liu, Z. Gan, and Z. Zhang, Effect of substrate surface on deposition of AlGaN: A molecular dynamics simulation, Crystals 8, 279 (2018).
  75. D.-S. Tang and B.-Y. Cao, Phonon thermal transport and its tunability in GaN for near-junction thermal management of electronics: A review, Int. J. Heat Mass Transf. 200, 123497 (2023).
  76. A. Katre, J. Carrete, B. Dongre, G. K. H. Madsen, and N. Mingo, Exceptionally strong phonon scattering by B substitution in cubic SiC, Phys. Rev. Lett. 119, 075902 (2017).
  77. G. Pang, F. Meng, Y. Chen, A. Katre, J. Carrete, B. Dongre, G. K. Madsen, N. Mingo, and W. Li, Thermal conductivity reduction in highly-doped cubic SiC by phonon-defect and phonon-electron scattering, Mater. Today Phys. 41, 101346 (2024).
  78. A. Kundu, N. Mingo, D. A. Broido, and D. A. Stewart, Role of light and heavy embedded nanoparticles on the thermal conductivity of SiGe alloys, Phys. Rev. B 84, 125426 (2011).
  79. H. Wu, Z. Qin, S. Li, L. Lindsay, and Y. Hu, Nonperturbative determination of isotope-induced anomalous vibrational physics, Phys. Rev. B 108, L140302 (2023).
  80. M. Li, K. Pan, Y. Ge, K. Huynh, M. S. Goorsky, T. S. Fisher, and Y. Hu, Wafer-scale bonded GaN–AlN with high interface thermal conductance, Appl. Phys. Lett. 125, 032104 (2024).
  81. E. Fransson, M. Slabanja, P. Erhart, and G. Wahnström, Dynasor—A tool for extracting dynamical structure factors and current correlation functions from molecular dynamics simulations, Adv. Theory Simul. 4, 2000240 (2021).

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