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arXiv · 1605.08007

Variational Approach to Solving the Spectral Boltzmann Transport Equation in Transient Thermal Grating for Thin Films

Vazrik Chiloyan·Lingping Zeng·Samuel Huberman·Alexei A. Maznev·Keith A. Nelson·Gang Chen
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Abstract

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 (MFP) distribution of materials via transient grating experiments.

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Vazrik Chiloyan, Lingping Zeng, Samuel Huberman, Alexei A. Maznev, Keith A. Nelson, Gang Chen. 2016-05-25. Variational Approach to Solving the Spectral Boltzmann Transport Equation in Transient Thermal Grating for Thin Films. https://doi.org/10.1063/1.4955164

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