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Published December 15, 2011 | Published
Journal Article Open

Quasiballistic heat transfer studied using the frequency-dependent Boltzmann transport equation


Quasiballistic heat transfer occurs when there is a temperature gradient over length scales comparable to phonon mean free paths (MFPs). This regime has been of interest recently because observation of quasiballistic transport can lead to useful information about phonon MFPs, knowledge of which is essential for engineering nanoscale thermal effects. Here, we use the Boltzmann transport equation (BTE) to understand how observations of quasiballistic transport can yield information about MFPs. We solve the transient, one-dimensional, frequency-dependent BTE for a double-layer structure of a metal film on a substrate, the same geometry that is used in transient thermoreflectance experiments, using a frequency-dependent interface condition. Our results indicate that phonons with MFPs longer than the thermal penetration depth do not contribute to the measured thermal conductivity, providing a means to probe the MFP distribution. We discuss discrepancies between our simulation and experimental observations which offer opportunities for future investigation.

Additional Information

© 2011 American Physical Society. Received 29 August 2011; revised manuscript received 21 October 2011; published 15 December 2011. The authors would like to thank David Cahill for useful discussions. This material is partially based upon work supported as part of the "Solid State Solar-Thermal Energy Conversion Center (S3TEC)," an Energy Frontier Research Center funded by the US Department of Energy, Office of Science, Office of Basic Energy Sciences under Award No. DE-SC0001299/DE-FG02-09ER46577 (G.C.), by the Center for Clean Water and Clean Energy at MIT and KFUPM (A.M., S.M., B.S.Y.), and by the NSF (A.M.).

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