The question of what fraction of the total heat flow is transported by phonons with different mean-free-paths is addressed using a Landauer approach with a full dispersion description of phonons to evaluate the thermal conductivities of bulk and thin film silicon. For bulk Si, the results reproduce those of a recent molecular dynamic treatment showing that about 50% of the heat conduction is carried by phonons with a mean-free-path greater than about 1 μm. For the in-plane thermal conductivity of thin Si films, we find that about 50% of the heat is carried by phonons with mean-free-paths shorter than in the bulk. When the film thickness is smaller than ∼0.2 μm, 50% of the heat is carried by phonons with mean-free-paths longer than the film thickness. The cross-plane thermal conductivity of thin-films, where quasi-ballistic phonontransport becomes important, is also examined. For ballistic transport, the results reduce to the well-known Casimir limit [H. B. G. Casimir, Physica 5, 495–500 (1938)]. These results shed light on phonontransport in bulk and thin-film silicon and demonstrate that the Landauer approach provides a relatively simple but accurate technique to treat phonontransport from the ballistic to diffusive regimes.


Copyright (2012) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in J. Appl. Phys. 111, 093708 (2012) and may be found at http://dx.doi.org/10.1063/1.4710993. The following article has been submitted to/accepted by Journal of Applied Physics. Copyright (2012) Changwook Jeong, Supriyo Datta and Mark Lundstrom. This article is distributed under a Creative Commons Attribution 3.0 Unported License.

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Thermal conductivity of bulk and thin-film silicon: A Landauer approach. Changwook Jeong, Supriyo Datta and Mark Lundstrom. J. Appl. Phys. 111, 093708 (2012)



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