Abstract
In ballistic thermal conduction, the wave characteristics of phonons allow the transmission of energy without dissipation. However, the observation of ballistic heat transport at room temperature is challenging because of the short phonon mean free path. Here we show that ballistic thermal conduction persisting over 8.3 µm can be observed in SiGe nanowires with low thermal conductivity for a wide range of structural variations and alloy concentrations. We find that an unexpectedly low percentage (∼0.04%) of phonons carry out the heat conduction process in SiGe nanowires, and that the ballistic phonons display properties including non-additive thermal resistances in series, unconventional contact thermal resistance, and unusual robustness against external perturbations. These results, obtained in a model semiconductor, could enable wave-engineering of phonons and help to realize heat waveguides, terahertz phononic crystals and quantum phononic/thermoelectric devices ready to be integrated into existing silicon-based electronics.
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References
Balandin, A. A. Thermal properties of graphene and nanostructured carbon materials. Nature Mater. 10, 569–581 (2011).
Chiu, H. Y. et al. Ballistic phonon thermal transport in multiwalled carbon nanotubes. Phys. Rev. Lett. 95, 226101 (2005).
Zhu, G. H. et al. Increased phonon scattering by nanograins and point defects in nanostructured silicon with a low concentration of germanium. Phys. Rev. Lett. 102, 196803 (2009).
Bera, C., Mingo, N. & Volz, S. Marked effects of alloying on the thermal conductivity of nanoporous materials. Phys. Rev. Lett. 104, 115502 (2010).
Garg, J., Bonini, N., Kozinsky, B. & Marzari, N. Role of disorder and anharmonicity in the thermal conductivity of silicon–germanium alloys: a first-principles study. Phys. Rev. Lett. 106, 045901 (2011).
Hu, M., Giapis, K. P., Goicochea, J. V., Zhang, X. & Poulikakos, D. Significant reduction of thermal conductivity in Si/Ge core–shell nanowires. Nano Lett. 11, 618–623 (2011).
Yang, J. E., Jin, C. B., Kim, C. J. & Jo, M. H. Band-gap modulation in single-crystalline Si1–xGex nanowires. Nano Lett. 6, 2679–2684 (2006).
Chang, H-K. & Lee, S-C. The growth and radial analysis of Si/Ge core–shell nanowires. Appl. Phys. Lett. 97, 251912 (2010).
Rego, L. G. C. & Kirczenow, G. Quantized thermal conductance of dielectric quantum wires. Phys. Rev. Lett. 81, 232–235 (1998).
Steele, M. C. & Rosi, F. D. Thermal conductivity and thermoelectric power of germanium–silicon alloys. J. Appl. Phys. 29, 1517–1520 (1958).
Koh, Y. K. & Cahill, D. G. Frequency dependence of the thermal conductivity of semiconductor alloys. Phys. Rev. B 76, 075207 (2007).
Bolotin, K. I., Ghahari, F., Shulman, M. D., Stormer, H. L. & Kim, P. Observation of the fractional quantum Hall effect in graphene. Nature 462, 196–199 (2009).
Du, X., Skachko, I., Duerr, F., Luican, A. & Andrei, E. Y. Fractional quantum Hall effect and insulating phase of Dirac electrons in graphene. Nature 462, 192–195 (2009).
Prasher, R. Predicting the thermal resistance of nanosized constrictions. Nano Lett. 5, 2155–2159 (2005).
Slack, G. A. & Hussain, M. A. The maximum possible conversion efficiency of silicon-germanium thermoelectric generators. J. Appl. Phys. 70, 2694–2718 (1991).
Liu, C-K. et al. Thermal conductivity of Si/SiGe superlattice films. J. Appl. Phys. 104, 114301 (2008).
Minnich, A. J. et al. Modeling study of thermoelectric SiGe nanocomposites. Phys. Rev. B 80, 155327 (2009).
Meddins, H. R. & Parrott, J. E. Thermal and thermoelectric properties of sintered germanium–silicon alloys. J. Phys. C 9, 1263–1276 (1976).
Lu, Q. et al. Raman scattering from Si1–xGex alloy nanowires. J. Phys. Chem. C 112, 3209–3215 (2008).
Ju, Y. S. & Goodson, K. E. Phonon scattering in silicon films with thickness of order 100 nm. Appl. Phys. Lett. 74, 3005–3007 (1999).
Alvarez-Quintana, J., Rodriguez-Viejo, J., Alvarez, F. X. & Jou, D. Thermal conductivity of thin single-crystalline germanium-on-insulator structures. Int. J. Heat Mass Transf. 54, 1959–1962 (2011).
Smith, C. G. Low-dimensional quantum devices. Rep. Prog. Phys. 59, 235–282 (1996).
Li, D. Y. et al. Thermal conductivity of individual silicon nanowires. Appl. Phys. Lett. 83, 2934–2936 (2003).
Chen, R. K. et al. Thermal conductance of thin silicon nanowires. Phys. Rev. Lett. 101, 105501 (2008).
Hochbaum, A. I. et al. Enhanced thermoelectric performance of rough silicon nanowires. Nature 451, 163–165 (2008).
Wingert, M. C. et al. Thermal conductivity of Ge and Ge–Si core–shell nanowires in the phonon confinement regime. Nano Lett. 11, 5507–5513 (2011).
Rowe, D. M., Shukla, V. S. & Savvides, N. Phonon-scattering at grain-boundaries in heavily doped fine-grained silicon–germanium alloys. Nature 290, 765–766 (1981).
Lee, E. K. et al. Large thermoelectric figure-of-merits from SiGe nanowires by simultaneously measuring electrical and thermal transport properties. Nano Lett. 12, 2918–2923 (2012).
Yin, L. et al. The influence of phonon scatterings on the thermal conductivity of SiGe nanowires. Appl. Phys. Lett. 101, 043114 (2012).
Acknowledgements
This work was supported by the National Science Council of Taiwan (NSC101-2112-M-002-014-MY3) and Academia Sinica (AS-101-TP2-A01).
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T.K.H. conducted the thermal conductivity measurements and analysed the data. H.K.C. and S.C.L. contributed the nanowires. S.C.L. and M.W.C. performed the TEM characterizations. C.W.C. initiated the project, supervised it, and wrote the paper. All authors discussed the results and commented on the manuscript.
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Hsiao, TK., Chang, HK., Liou, SC. et al. Observation of room-temperature ballistic thermal conduction persisting over 8.3 µm in SiGe nanowires. Nature Nanotech 8, 534–538 (2013). https://doi.org/10.1038/nnano.2013.121
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DOI: https://doi.org/10.1038/nnano.2013.121
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