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Despite recent progress in the first-principles calculations and measurementsof phonon mean-free-paths (MFPs), contribution of low-energy phonons to heatconduction in silicon is still inconclusive, as exemplified by thediscrepancies between different first-principles calculations. Here weinvestigate the contribution of low-energy phonons with MFP>0.8 um byaccurately measuring the cross-plane thermal conductivity of crystallinesilicon films by time-domain thermoreflectance (TDTR), over a wide range offilm thickness 1-10 um and temperature 100-300 K. We employ a dual-frequencyTDTR approach to improve the accuracy of our cross-plane thermal conductivitymeasurements. We find from our cross-plane thermal conductivity measurementsthat phonons with MFP>0.8 um contribute 53 W/m-K (37%) to heat conduction in Siat 300 K while phonons with MFP>3 um contribute 523 W/m-K (61%) at 100 K, >20%lower than the first-principles predictions by Lindsay et al. of 68 W/m-K (47%)and 695 W/m-K (77%), respectively. Using a relaxation times approximation (RTA)model, we demonstrate that macroscopic damping (e.g., Akhieser's damping)eliminates the contribution of phonons with mean-free-paths >30 um at 300 K,which contributes 15 W/m-K (10%) to heat conduction in Si according to Lindsayet al. Thus we propose that omission of the macroscopic damping for low-energyphonons in the first-principles calculations could be one of the possibleexplanations for the observed discrepancy between our measurements andcalculations by Lindsay et al. Our work provides an important benchmark forfuture measurements and calculations of the distribution of phononmean-free-paths in crystalline silicon.

The role of low-energy phonons with mean-free-paths >0.8 um in heat conduction in silicon