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

• Main Authors: Chiloyan, Vazrik (Contributor), Zeng, Lingping (Contributor), Huberman, Samuel C. (Contributor), Maznev, Alexei (Contributor), Nelson, Keith Adam (Contributor), Chen, Gang (Contributor)
• Other Authors: Massachusetts Institute of Technology. Department of Chemistry (Contributor), Massachusetts Institute of Technology. Department of Mechanical Engineering (Contributor)
• Format: Article
• Language: English
• Published: American Institute of Physics (AIP), 2018-02-02T14:23:36Z.
• Subjects: Article
• Online Access: Get fulltext

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.