The cross-plane and in-plane phonon thermal conductivities of Stillinger-Weber (SW) silicon thin films are predicted using the Boltzmann transport equation under the relaxation time approximation. We model the thin films using bulk phonon properties obtained from harmonic and anharmonic lattice dynamics calculations. The cross-plane and in-plane thermal conductivities are reduced from the corresponding bulk value. This reduction is more severe for the cross-plane direction than for the in-plane direction. For the in-plane direction, we find that the predicted reduction in thermal conductivity gives a good lower bound to available experimental results. Including the effects of boundary scattering using the Matthiessen rule, which assumes that scattering mechanisms are independent, yields thermal conductivity predictions that are at most 12% lower than our more accurate results. Neglecting optical phonon modes, while valid for bulk systems, introduces 22.5% error when modeling thin films. Using phonon properties along the  direction (i.e., the isotropic approximation) yields bulk predictions that are 15% lower than that when all of the phonon modes are considered. For thin films, this deviation increases to 25%. Our results show that a single bulk phonon mean free path is an inadequate metric for predicting the thermal conductivity reduction in thin films.
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Phonon Transport in Thin Films: A Lattice Dynamics/Boltzmann Transport Equation Study
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Sellan, DP, Turney, JE, Landry, ES, McGaughey, AJH, & Amon, CH. "Phonon Transport in Thin Films: A Lattice Dynamics/Boltzmann Transport Equation Study." Proceedings of the 2010 14th International Heat Transfer Conference. 2010 14th International Heat Transfer Conference, Volume 6. Washington, DC, USA. August 8–13, 2010. pp. 393-402. ASME. https://doi.org/10.1115/IHTC14-22623
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