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