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Despite recent progress in the first-principles calculations and measurements of phonon mean-free-paths (ℓ), contribution of low-energy phonons to heat conduction in silicon is still inconclusive, as exemplified by the discrepancies as large as 30% between different first-principles calculations. Here, we investigate the contribution of low-energy phonons with ℓ?>?0.8?μm by accurately measuring the cross-plane thermal conductivity (Λcross) of crystalline silicon films by time-domain thermoreflectance (TDTR), over a wide range of film thicknesses 1?≤?hf?≤?10?μm and temperatures 100?≤?T?≤?300?K. We employ a dual-frequency TDTR approach to improve the accuracy of our Λcross measurements. We find from our Λcross measurements that phonons with ℓ?>?0.8?μm contribute 53?W?m-1?K-1 (37%) to heat conduction in natural Si at 300?K, while phonons with ℓ?>?3 μm contribute 523?W?m-1?K-1 (61%) at 100?K, >20% lower than first-principles predictions of 68?W?m-1?K-1 (47%) and 717?W?m-1?K-1 (76%), respectively. Using a relaxation time approximation model, we demonstrate that macroscopic damping (e.g., Akhieser's damping) eliminates the contribution of phonons with mean-free-paths >20?μm at 300?K, which contributes 15?W?m-1?K-1 (10%) to calculated heat conduction in Si. 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 differences between our measurements and calculations. Our work provides an important benchmark for future measurements and calculations of the distribution of phonon mean-free-paths in crystalline silicon. [ABSTRACT FROM AUTHOR]

It is challenging to characterize thermal conductivity of materials with strong anisotropy. In this work, we extend the time-domain thermoreflectance (TDTR) method with a variable spot size approach to simultaneously measure the in-plane (Kr) and the through-plane (Kz) thermal conductivity of materials with strong anisotropy. We first determine Kz from the measurement using a larger spot size, when the heat flow is mainly one-dimensional along the through-plane direction, and the measured signals are only sensitive to Kz. We then extract the in-plane thermal conductivity Kr from a second measurement using the same modulation frequency but with a smaller spot size, when the heat flow becomes three-dimensional, and the signal is sensitive to both Kr and Kz. By choosing the same modulation frequency for the two sets of measurements, we can avoid potential artifacts introduced by the frequency-dependent Kz, which we have found to be non-negligible, especially for some two-dimensional layered materials like MoS2. After careful evaluation of the sensitivity of a series of hypothetical samples, we provided guidelines on choosing the most appropriate laser spot size and modulation frequency that yield the smallest uncertainty, and established a criterion for the range of thermal conductivity that can be measured reliably using our proposed variable spot size TDTR approach. We have demonstrated this variable spot size TDTR approach on samples with a wide range of in-plane thermal conductivity, including fused silica, rutile titania (TiO2 [001]), zinc oxide (ZnO [0001]), molybdenum disulfide (MoS2), hexagonal boron nitride (h-BN), and highly ordered pyrolytic graphite. [ABSTRACT FROM AUTHOR]

Accurate measurements of the cross-plane thermal conductivity Λcross of a high-thermal-conductivity thin film on a low-thermal-conductivity (Λs) substrate (e.g., Λcross/Λs > 20) are challenging, due to the low thermal resistance of the thin film compared with that of the substrate. In principle, Λcross could be measured by time-domain thermoreflectance (TDTR), using a high modulation frequency fh and a large laser spot size. However, with one TDTR measurement at fh, the uncertainty of the TDTR measurement is usually high due to low sensitivity of TDTR signals to Λcross and high sensitivity to the thickness hAl of Al transducer deposited on the sample for TDTR measurements. We observe that in most TDTR measurements, the sensitivity to hAl only depends weakly on the modulation frequency f . Thus, we performed an additional TDTR measurement at a low modulation frequency f0, such that the sensitivity to hAl is comparable but the sensitivity to Λcross is near zero. We then analyze the ratio of the TDTR signals at fh to that at f0, and thus significantly improve the accuracy of our Λcross measurements. As a demonstration of the dual-frequency approach, we measured the cross-plane thermal conductivity of a 400-nm-thick nickel-iron alloy film and a 3-μm-thick Cu film, both with an accuracy of ∼10%. The dual-frequency TDTR approach is useful for future studies of thin films. [ABSTRACT FROM AUTHOR]