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The mean-free path (MFP) accumulation function for the effective thermalconductivity, introduced by Dames and Chen is a compact, universal and highlyuseful summary of the effect of ballistic thermal transport on the effectivethermal conductivity measured by various experiments. The frequency domainthermoreflectance (FDTR) experiment is especially well suited to itsdetermination. Extraction of the accumulation function from this experimentuses the thermal penetration depth (TPD) of phonons at each frequency as acut-off for classifying phonons as ballistic or diffusive at that frequency. Inthis paper, we show that using the TPD as a cut-off is arbitrary and prone toserious error. We report on a new technique to deduce the MFP accumulationfunction from the FDTR experiment by numerical solution of an enhanced Fourierlaw.

Quasi-ballistic phonon transport effects on the determination of the mean-free path accumulation function for the effective thermal conductivity