Variational approach to solving the spectral Boltzmann transport equation in transient thermal grating for thin films

The phonon Boltzmann transport equation (BTE) is widely utilized to study non-diffusive thermal transport. We find a solution of the BTE in the thin film transient thermal grating (TTG) experimental geometry by using a recently developed variational approach with a trial solution supplied by the Fou...

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Veröffentlicht in:Journal of applied physics 2016-07, Vol.120 (2)
Hauptverfasser: Chiloyan, Vazrik, Zeng, Lingping, Huberman, Samuel, Maznev, Alexei A., Nelson, Keith A., Chen, Gang
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Sprache:eng
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Zusammenfassung:The phonon Boltzmann transport equation (BTE) is widely utilized to study non-diffusive thermal transport. We find a solution of the BTE in the thin film transient thermal grating (TTG) experimental geometry by using a recently developed variational approach with a trial solution supplied by the Fourier heat conduction equation. We obtain an analytical expression for the thermal decay rate that shows excellent agreement with Monte Carlo simulations. We also obtain a closed form expression for the effective thermal conductivity that demonstrates the full material property and heat transfer geometry dependence, and recovers the limits of the one-dimensional TTG expression for very thick films and the Fuchs-Sondheimer expression for very large grating spacings. The results demonstrate the utility of the variational technique for analyzing non-diffusive phonon-mediated heat transport for nanostructures in multi-dimensional transport geometries, and will assist the probing of the mean free path distribution of materials via transient grating experiments.
ISSN:0021-8979
1089-7550
DOI:10.1063/1.4955164