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Dislocation-induced thermal transport anisotropy in single-crystal group-III nitride films


Dislocations, one-dimensional lattice imperfections, are common to technologically important materials such as III–V semiconductors, and adversely affect heat dissipation in, for example, nitride-based high-power electronic devices. For decades, conventional nonlinear elasticity models have predicted that this thermal resistance is only appreciable when the heat flux is perpendicular to the dislocations. However, this dislocation-induced anisotropic thermal transport has yet to be seen experimentally. Using time-domain thermoreflectance, we measure strong thermal transport anisotropy governed by highly oriented threading dislocation arrays throughout micrometre-thick, single-crystal indium nitride films. We find that the cross-plane thermal conductivity is almost tenfold higher than the in-plane thermal conductivity at 80 K when the dislocation density is ~3 × 1010 cm−2. This large anisotropy is not predicted by conventional models. With enhanced understanding of dislocation–phonon interactions, our results may allow the tailoring of anisotropic thermal transport with line defects, and could facilitate methods for directed heat dissipation in the thermal management of diverse device applications.

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Fig. 1: InN structure design and characterization.
Fig. 2: Temperature-dependent thermal conductivity of InN films with oriented threading dislocations.
Fig. 3: Dislocation density-dependent thermal transport.

Data availability

The data sets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.


  1. 1.

    Li, D. et al. Thermal conductivity of individual silicon nanowires. Appl. Phys. Lett. 83, 2934–2936 (2003).

    CAS  Article  Google Scholar 

  2. 2.

    Chen, S. et al. Thermal conductivity of isotopically modified graphene. Nat. Mater. 11, 203–207 (2012).

    CAS  Article  Google Scholar 

  3. 3.

    Broido, D. A., Malorny, M., Birner, G., Mingo, N. & Stewart, D. A. Intrinsic lattice thermal conductivity of semiconductors from first principles. Appl. Phys. Lett. 91, 231922 (2007).

    Article  Google Scholar 

  4. 4.

    Ma, J., Li, W. & Luo, X. Intrinsic thermal conductivity and its anisotropy of wurtzite InN. Appl. Phys. Lett. 105, 082103 (2014).

    Article  Google Scholar 

  5. 5.

    Wang, T., Carrete, J., van Roekeghem, A., Mingo, N. & Madsen, G. K. H. Ab initio phonon scattering by dislocations. Phys. Rev. B 95, 245304 (2017).

    Article  Google Scholar 

  6. 6.

    Katre, A., Carrete, J., Dongre, B., Madsen, G. K. H. & Mingo, N. Exceptionally strong phonon scattering by B substitution in cubic SiC. Phys. Rev. Lett. 119, 075902 (2017).

    Article  Google Scholar 

  7. 7.

    Polanco, C. A. & Lindsay, L. Ab initio phonon point defect scattering and thermal transport in graphene. Phys. Rev. B 97, 014303 (2018).

    Article  Google Scholar 

  8. 8.

    Yan, Z., Liu, G., Khan, J. M. & Balandin, A. A. Graphene quilts for thermal management of high-power GaN transistors. Nat. Commun. 3, 827 (2012).

    Article  Google Scholar 

  9. 9.

    Zhang, Q. et al. High thermoelectric performance by resonant dopant indium in nanostructured SnTe. Proc. Natl Acad. Sci. USA 110, 13261–13266 (2013).

    CAS  Article  Google Scholar 

  10. 10.

    Klemens, P. G. The scattering of low-frequency lattice waves by static imperfections. Proc. Phys. Soc. A 68, 1113–1128 (1955).

    Article  Google Scholar 

  11. 11.

    Carruthers, P. Scattering of phonons by elastic strain fields and the thermal resistance of dislocations. Phys. Rev. 114, 995–1001 (1959).

    CAS  Article  Google Scholar 

  12. 12.

    Kogure, Y. & Hiki, Y. Scattering of lattice waves by static strain fields in crystals. J. Phys. Soc. Jpn 36, 1597–1607 (1974).

    Article  Google Scholar 

  13. 13.

    Kneeze, G. A. & Granato, A. V. Effect of independent and coupled vibrations of dislocations on low-temperature thermal conductivity in alkali halides. Phys. Rev. B 25, 2851–2866 (1982).

    Article  Google Scholar 

  14. 14.

    Li, M. et al. Nonperturbative quantum nature of the dislocation–phonon interaction. Nano Lett. 17, 1587–1594 (2017).

    CAS  Article  Google Scholar 

  15. 15.

    O’Hara, S. G. & Anderson, A. C. Scattering of thermal phonons by dislocations in superconducting lead and tantalum. Phys. Rev. B 10, 574–579 (1974).

    Article  Google Scholar 

  16. 16.

    Nihira, T. & Iwata, T. Thermal resistivity changes in electron-irradiated pyrolytic-graphite. Jpn J. Appl. Phys. 14, 1099–1104 (1975).

    CAS  Article  Google Scholar 

  17. 17.

    Jo, I., Pettes, M. T., Ou, E., Wu, W. & Shi, L. Basal-plane thermal conductivity of few-layer molybdenum disulfide. Appl. Phys. Lett. 104, 201902 (2014).

    Article  Google Scholar 

  18. 18.

    Sun, B. et al. Temperature dependence of anisotropic thermal conductivity tensor of bulk black phosphorus. Adv. Mater. 29, 1603297 (2017).

    Article  Google Scholar 

  19. 19.

    Sproull, R. L., Moss, M. & Weinstock, H. Effect of dislocations on the thermal conductivity of lithium fluoride. J. Appl. Phys. 30, 334–337 (1959).

    CAS  Article  Google Scholar 

  20. 20.

    Su, Z. et al. Layer-by-layer thermal conductivities of the Group III nitride films in blue/green light emitting diodes. Appl. Phys. Lett. 100, 201106 (2012).

    Article  Google Scholar 

  21. 21.

    Mion, C., Muth, J. F., Preble, E. A. & Hanser, D. Accurate dependence of gallium nitride thermal conductivity on dislocation density. Appl. Phys. Lett. 89, 092123 (2006).

    Article  Google Scholar 

  22. 22.

    Loitsch, B., Schuster, F., Stutzmann, M. & Koblmüller, G. Reduced threading dislocation densities in high-T/N-rich grown InN films by plasma-assisted molecular beam epitaxy. Appl. Phys. Lett. 102, 051916 (2013).

    Article  Google Scholar 

  23. 23.

    Ju, J. et al. Trade-off between morphology, extended defects, and compositional fluctuation induced carrier localization in high In-content InGaN films. J. Appl. Phys. 116, 053501 (2014).

    Article  Google Scholar 

  24. 24.

    Gallinat, C. S., Koblmüller, G., Wu, F. & Speck, J. S. Evaluation of threading dislocation densities in In- and N-face InN. J. Appl. Phys. 107, 053517 (2010).

    Article  Google Scholar 

  25. 25.

    Cahill, D. G. Analysis of heat flow in layered structures for time-domain thermoreflectance. Rev. Sci. Instrum. 75, 5119–5122 (2004).

    CAS  Article  Google Scholar 

  26. 26.

    Sun, B. & Koh, Y. K. Understanding and eliminating artifact signals from diffusely scattered pump beam in measurements of rough samples by time-domain thermoreflectance (TDTR). Rev. Sci. Instrum. 87, 064901 (2016).

    Article  Google Scholar 

  27. 27.

    Feser, J. P., Liu, J. & Cahill, D. G. Pump–probe measurements of the thermal conductivity tensor for materials lacking in-plane symmetry. Rev. Sci. Instrum. 85, 104903 (2014).

    Article  Google Scholar 

  28. 28.

    Jiang, P., Huang, B. & Koh, Y. K. Accurate measurements of cross-plane thermal conductivity of thin films by dual-frequency time-domain thermoreflectance (TDTR). Rev. Sci. Instrum. 87, 075101 (2016).

    Article  Google Scholar 

  29. 29.

    Luckyanova, M. N. et al. Anisotropy of the thermal conductivity in GaAs/AlAs superlattices. Nano Lett. 13, 3973–3977 (2013).

    CAS  Article  Google Scholar 

  30. 30.

    Kwon, S., Zheng, J., Wingert, M. C., Cui, S. & Chen, R. Unusually high and anisotropic thermal conductivity in amorphous silicon nanostructures. ACS Nano 11, 2470–2476 (2017).

    CAS  Article  Google Scholar 

  31. 31.

    Jiang, P., Lindsay, L., Huang, X. & Koh, Y. K. Interfacial phonon scattering and transmission loss in >1 μm thick silicon-on-insulator thin films. Phys. Rev. B 97, 195308 (2018).

    Article  Google Scholar 

  32. 32.

    Jiang, P., Lindsay, L. & Koh, Y. K. Role of low-energy phonons with mean-free-paths >0.8 μm in heat conduction in silicon. J. Appl. Phys. 119, 245705 (2016).

    Article  Google Scholar 

  33. 33.

    Vermeersch, B., Carrete, J. & Mingo, N. Cross-plane heat conduction in thin films with ab-initio phonon dispersions and scattering rates. Appl. Phys. Lett. 108, 193104 (2016).

    Article  Google Scholar 

  34. 34.

    Dong, Z. S. & Zhao, C. W. Measurement of strain fields in an edge dislocation. Physica B Condens. Matter 405, 171–174 (2010).

    CAS  Article  Google Scholar 

  35. 35.

    Katcho, N. A., Carrete, J., Li, W. & Mingo, N. Effect of nitrogen and vacancy defects on the thermal conductivity of diamond: an ab initio Green’s function approach. Phys. Rev. B 90, 094117 (2014).

    Article  Google Scholar 

  36. 36.

    Masataka, H. & Toshiaki, M. High-quality InN film grown on a low-temperature-grown GaN intermediate layer by plasma-assisted molecular-beam epitaxy. Jpn J. Appl. Phys. 41, L540 (2002).

    Article  Google Scholar 

  37. 37.

    Yoshiki, S., Nobuaki, T., Akira, S., Tsutomu, A. & Yasushi, N. Growth of high-electron-mobility InN by RF molecular beam epitaxy. Jpn J. Appl. Phys. 40, L91 (2001).

    Article  Google Scholar 

  38. 38.

    Gallinat, C. S. et al. In-polar InN grown by plasma-assisted molecular beam epitaxy. Appl. Phys. Lett. 89, 032109 (2006).

    Article  Google Scholar 

  39. 39.

    Romanov, A. E. & Speck, J. S. Stress relaxation in mismatched layers due to threading dislocation inclination. Appl. Phys. Lett. 83, 2569–2571 (2003).

    CAS  Article  Google Scholar 

  40. 40.

    Huang, B. & Koh, Y. K. Improved topological conformity enhances heat conduction across metal contacts on transferred graphene. Carbon 105, 268–274 (2016).

    CAS  Article  Google Scholar 

  41. 41.

    Koh, Y. K. & Cahill, D. G. Frequency dependence of the thermal conductivity of semiconductor alloys. Phys. Rev. B 76, 075207 (2007).

    Article  Google Scholar 

  42. 42.

    Minnich, A. J. et al. Thermal conductivity spectroscopy technique to measure phonon mean free paths. Phys. Rev. Lett. 107, 095901 (2011).

    CAS  Article  Google Scholar 

  43. 43.

    Regner, K. T. et al. Broadband phonon mean free path contributions to thermal conductivity measured using frequency domain thermoreflectance. Nat. Commun. 4, 1640 (2013).

    Article  Google Scholar 

  44. 44.

    Wilson, R. B. & Cahill, D. G. Anisotropic failure of Fourier theory in time-domain thermoreflectance experiments. Nat. Commun. 5, 5075 (2014).

    CAS  Article  Google Scholar 

  45. 45.

    Mohammed, A. M. S. et al. Fractal Lévy heat transport in nanoparticle embedded semiconductor alloys. Nano Lett. 15, 4269–4273 (2015).

    CAS  Article  Google Scholar 

  46. 46.

    Peierls, R. E. Quantum Theory of Solids (Clarendon Press, 1955).

  47. 47.

    Ziman, J. M. Electrons and Phonons. The Theory of Transport Phenomena in Solids (Oxford Univ. Press, Oxford, 1960).

  48. 48.

    Srivastava, G. P. The Physics of Phonons (Taylor & Francis, Abingdon, 1990).

  49. 49.

    Omini, M. & Sparavigna, A. Beyond the isotropic-model approximation in the theory of thermal conductivity. Phys. Rev. B 53, 9064–9073 (1996).

    CAS  Article  Google Scholar 

  50. 50.

    Lindsay, L., Broido, D. A. & Reinecke, T. L. Thermal conductivity and large isotope effect in GaN from first principles. Phys. Rev. Lett. 109, 095901 (2012).

    CAS  Article  Google Scholar 

  51. 51.

    Lindsay, L., Broido, D. A. & Reinecke, T. L. Ab initio thermal transport in compound semiconductors. Phys. Rev. B 87, 165201 (2013).

    Article  Google Scholar 

  52. 52.

    Mingo, N., Stewart, D. A., Broido, D. A., Lindsay, L. & Li, W. in Length-Scale Dependent Phonon Interactions (eds Shindé, S. L. & Srivastava, G. P.) 137–173 (Springer, New York, 2014).

  53. 53.

    Lindsay, L. First principles Peierls–Boltzmann phonon thermal transport: a topical review. Nanosc. Microsc. Therm. 20, 67–84 (2016).

    CAS  Article  Google Scholar 

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The authors thank R. Wang and B. Huang at NUS for help with the thermal evaporation of Al films. The authors thank M. Li at MIT for explanation of his papers. This work was supported by an NUS Start-up Grant, the Singapore Ministry of Education Academic Research Fund Tier 2 under award no. MOE2013-T2–2–147 and Singapore Ministry of Education Academic Research Fund Tier 1 FRC project FY2016. C.P. and L.L. acknowledge support from the US Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division and computational resources from the National Energy Research Scientific Computing Center (NERSC), a DOE Office of Science User Facility supported by the Office of Science of the US Department of Energy under contract no. DE-AC02-05CH11231. G.K. acknowledges support from the excellence program Nanosystems Initiative Munich (NIM) funded by the German Research Foundation (DFG).

Author information




G.K. and Y.K.K. initialized the idea. B.S. and Y.K.K. designed the experiments. B.S. performed the TDTR measurements and analysed the data. G.H., J.Z.J. and G.K. prepared and characterized the InN samples. C.P. and L.L. performed the first-principles and phonon-defect scattering calculations. All authors discussed the results and contributed to the manuscript.

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Correspondence to Yee Kan Koh.

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Supplementary information

Supplementary Notes 1–5, Supplementary Figures 1–16, Supplementary Tables 1–4, Supplementary References 1–30

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Sun, B., Haunschild, G., Polanco, C. et al. Dislocation-induced thermal transport anisotropy in single-crystal group-III nitride films. Nature Mater 18, 136–140 (2019).

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