Role of low-energy phonons with mean-free-paths >0.8 μ m in heat conduction in silicon
Open accessAbstract
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.
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For the Al/Si sample, the cumulative thermal conductivity data at room temperature agree remarkably with the first-principles calculation by Esfarjani et al.
“For the Al/Si sample, our data exhibit remarkable agreement with the first-principles calculation by Esfarjani et al. [19] at RT.”
From Boundary conditions dictate frequency dependence of thermal conductivity in silicon (2025) · cites this paper as [19]
Figure 3(d) (Additional information, p. 17) compares room-temperature Si measurements with a prediction derived from Esfarjani et al.’s first-principles calculation. The paper does not describe remarkable agreement between its measurements and that calculation; Results and discussions (pp. 10–11) instead selects Lindsay et al. for direct comparison and reports differences beyond experimental uncertainty. (LLM, conf=0.82)
Experimental — accuracy not yet measuredAt 80 K, phonon mean free paths are approximately an order of magnitude longer than at room temperature.
“Secondly, the phonon MFPs at 80 K are approximately an order of magnitude longer than those at RT [14, 19, 28].”
From Boundary conditions dictate frequency dependence of thermal conductivity in silicon (2025) · cites this paper as [19]
The Results and discussions (p. 11) report heat-conduction contributions from phonons with mean free paths above 3 µm at 100 K and above 0.8 µm at 300 K, consistent with longer relevant paths at lower temperature. The paper reports measurements from 100 to 300 K, however, and does not establish an approximately tenfold difference at 80 K. (LLM, conf=0.78)
Experimental — accuracy not yet measuredThe simple interpretation that phonons with Λ > dp do not contribute to the apparent thermal conductivity works as a good approximation only for semiconductor alloys due to their extremely broad MFP distributions but not for pure crystals.
“This simple interpretation, however, works as a good approximation only for semiconductor alloys due to their extremely broad MFP distributions 209 but not for pure crystals, as frequency dependence was not observed in TDTR measurements of crystalline Si despite its very long MFPs of phonons 185, 187 .”
From Tutorial: Time-domain thermoreflectance (TDTR) for thermal property characterization of bulk and thin film materials (2018) · cites this paper as [185]
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Hong, S.-N., Kim, R.-J., Jong, U.-G., Han, J.-M., Pak, Y.-S., & Yu, C. (2025) · Applied Physics Letters · doi:10.1063/5.0302051
- Authors
- Jiang, P., Lindsay, L., & Koh, Y. K.
- Affiliations
- National University of Singapore (SG)
- Oak Ridge National Laboratory (US)
- ORCID
- Lindsay, Lucas
- Venue
- Journal of Applied Physics
- Publisher
- AIP Publishing
- Published
- 2016-06-28
- Volume
- 119
- Issue
- 24
- ISSN
- 0021-8979 (ISSN-L)
- 1089-7550
- OpenAlex
- W2224375005
- Cited by
- 42
- References
- 62
- Citations by year
- 2025: 6 · 2024: 2 · 2023: 2 · 2022: 3 · 2021: 2 · 2020: 7 · 2019: 4 · 2018: 8 · 2017: 4 · 2016: 4
- FWCI
- 2.97
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Journal of Applied Physics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Ministry of Education - Singapore (MOE2013-T2-2-147, R-265-000-364-133)
- U.S. Department of Energy
- Topics
- Physical Sciences › Materials Science › Materials Chemistry › Thermal properties of materials
- Physical Sciences › Engineering › Mechanics of Materials › Thermoelastic and Magnetoelastic Phenomena
- Physical Sciences › Engineering › Civil and Structural Engineering › Thermal Radiation and Cooling Technologies
- Keywords
- phonon mean free path, low-energy phonons, thermal conductivity, silicon, through-plane thermal conductivity, time-domain thermoreflectance, phonon transport, film thickness dependence
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