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

Despite recent progress in the first-principles calculations and measurements of phonon mean-free-paths (MFPs), contribution of low-energy phonons to heat conduction in silicon is still inconclusive, as exemplified by the discrepancies between different first-principles calculations. Here we investigate the contribution of low-energy phonons with MFP>0.8 um by accurately measuring the cross-plane thermal conductivity of crystalline silicon films by time-domain thermoreflectance (TDTR), over a wide range of film thickness 1-10 um and temperature 100-300 K. We employ a dual-frequency TDTR approach to improve the accuracy of our cross-plane thermal conductivity measurements. We find from our cross-plane thermal conductivity measurements that phonons with MFP>0.8 um contribute 53 W/m-K (37%) to heat conduction in Si at 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 Lindsay et al. Thus we propose that omission of the macroscopic damping for low-energy phonons in the first-principles calculations could be one of the possible explanations for the observed discrepancy between our measurements and calculations by Lindsay et al. Our work provides an important benchmark for future measurements and calculations of the distribution of phonon mean-free-paths in crystalline silicon.