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

Journal Article · · Journal of Applied Physics
DOI:https://doi.org/10.1063/1.4955164· OSTI ID:1388413
 [1]; ORCiD logo [1];  [1];  [1];  [1];  [1]
  1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
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The phonon Boltzmann transport equation (BTE) is widely utilized to study non-diffusive thermal transport. We find here 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.

Research Organization:
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
Grant/Contract Number:
SC0001299; FG02-09ER46577
OSTI ID:
1388413
Alternate ID(s):
OSTI ID: 1421258
Journal Information:
Journal of Applied Physics, Vol. 120, Issue 2; ISSN 0021-8979
Publisher:
American Institute of Physics (AIP)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 17 works
Citation information provided by
Web of Science

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Cited By (4)

Thermal transport in suspended silicon membranes measured by laser-induced transient gratings journal December 2016
Achieving high power factor and output power density in p-type half-Heuslers Nb 1-x Ti x FeSb journal November 2016
Unifying first-principles theoretical predictions and experimental measurements of size effects in thermal transport in SiGe alloys journal October 2017
Spectrally Resolved Specular Reflections of Thermal Phonons from Atomically Rough Surfaces journal October 2018

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