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Thermal Conductivity Spectroscopy Technique to Measure Phonon Mean Free Paths
Open accessAbstract
Size effects in heat conduction, which occur when phonon mean free paths (MFPs) are comparable to characteristic lengths, are being extensively explored in many nanoscale systems for energy applications. Knowledge of MFPs is essential to understanding size effects, yet MFPs are largely unknown for most materials. Here, we introduce the first experimental technique which can measure MFP distributions over a wide range of length scales and materials. Using this technique, we measure the MFP distribution of silicon for the first time and obtain good agreement with first-principles calculations.
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“our calculation overpredicts the effective thermal conductivity for all pump diameters below T ¼ 150 K”
From Radial quasiballistic transport in time-domain thermoreflectance studied using Monte Carlo simulations (2014) · cites this paper as [14]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“Similarly, while TDTR can be used to study non-equilibrium phenomena such as quasi-ballistic phonon transport 90, 91, 109-111 and electronphonon coupling 55 due to its ability to detect temperature evolutions at micrometer-scale and picosecond-scale resolutions, the majority of the experimental work in the literature deduced thermal properties based on Fourier's”
From Tutorial: Time-domain thermoreflectance (TDTR) for thermal property characterization of bulk and thin film materials (2018) · cites this paper as [91]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
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“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 [14]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“At 80 K, our measurements align closely with first-principles results, calculated through interpolation of calculations by Minnich et al. at 100 K and 60 K [14], with a slight deviation for phonons with short MFPs.”
From Boundary conditions dictate frequency dependence of thermal conductivity in silicon (2025) · cites this paper as [14]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“These findings are consistent with the conclusion that the ballistic thermal resistance effects found in TDTR measurements in both this and previous [39] works can contribute over a wide temperature range extending from cryogenic up to even room temperatures.”
From Mean Free Path Effects on the Experimentally Measured Thermal Conductivity of Single-Crystal Silicon Microbridges (2013) · cites this paper as [39]
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“This interpretation is the same as that of Koh and Cahill 16 , and consistent with Minnich et al. 1 and Johnson et al. 19,20 who instead used the laser spot diameter and transient grating period as the cutoff dimensions.”
From Broadband phonon mean free path contributions to thermal conductivity measured using frequency domain thermoreflectance (2013) · cites this paper as [1]
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“Although our data compare favourably with the first principles predictions by Esfarjani and coworkers 1,2,41 at all temperatures”
From Broadband phonon mean free path contributions to thermal conductivity measured using frequency domain thermoreflectance (2013) · cites this paper as [1]
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“The diameter dependence of the radial heat flux demonstrates that the pump size is a key variable that sets the thermal length scale for radial transport, confirming previous explanations for observations of a pump-beam size dependent thermal conductivity.14”
From Radial quasiballistic transport in time-domain thermoreflectance studied using Monte Carlo simulations (2014) · cites this paper as [14]
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“The results show the experimentally observed trend of decreasing effective thermal conductivity with decreasing pump beam size.14”
From Radial quasiballistic transport in time-domain thermoreflectance studied using Monte Carlo simulations (2014) · cites this paper as [14]
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“At these temperatures, our result predicts a similar trend in thermal conductivity versus pump size”
From Radial quasiballistic transport in time-domain thermoreflectance studied using Monte Carlo simulations (2014) · cites this paper as [14]
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In the citing paper
“Recent studies have shown that it is possible to experimentally measure the MFP dependent contributions of phonons to thermal conductivity–the phonon MFP spectrum12345.”
From Universal phonon mean free path spectra in crystalline semiconductors at high temperature (2013) · cites this paper as [3]
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In the citing paper
“Further studies using TDTR have equated l* to the laser spot size on Si3 and the dimensions of nano-patterned heaters on sapphire26.”
From Universal phonon mean free path spectra in crystalline semiconductors at high temperature (2013) · cites this paper as [3]
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In the citing paper
“Heat sources with dimensions smaller than phonon MFPs also perceive a locally suppressed thermal conductivity323.”
From Universal phonon mean free path spectra in crystalline semiconductors at high temperature (2013) · cites this paper as [3]
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“However, care should be taken when applying a diffusive thermal transport model to systems where a significant fraction of heat is carried by phonons with long mean-free paths (MFPs). 90-92, 112”
From Tutorial: Time-domain thermoreflectance (TDTR) for thermal property characterization of bulk and thin film materials (2018) · cites this paper as [91]
The cited source says what the claim attributes to it.
In the citing paper
“Furthermore, the thermal conductivity reductions reported by Minnich et al. [39] for comparable pump diameters in natural silicon agree in trend over the reported temperature range, as shown in Fig. 7.”
From Mean Free Path Effects on the Experimentally Measured Thermal Conductivity of Single-Crystal Silicon Microbridges (2013) · cites this paper as [39]
The cited source says what the claim attributes to it.
In the citing paper
“This is consistent with the results of Minnich et al. whose measurements were independent of modulation frequency (i.e., varying thermal penetration depth), but instead showed a pump diameter dependence.”
From Mean Free Path Effects on the Experimentally Measured Thermal Conductivity of Single-Crystal Silicon Microbridges (2013) · cites this paper as [39]
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Metadata
- Authors
- Minnich, A. J., Johnson, J. A., Schmidt, A. J., Esfarjani, K., Dresselhaus, M. S., Nelson, K. A., & Chen, G.
- Affiliations
- Massachusetts Institute of Technology (US)
- Boston University (US)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2011-08-25
- Volume
- 107
- Issue
- 9
- Pages
- 095901-095901
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2019490594
- Cited by
- 556
- References
- 21
- Citations by year
- 2026: 24 · 2025: 42 · 2024: 25 · 2023: 23 · 2022: 33 · 2021: 48 · 2020: 38 · 2019: 40 · 2018: 35 · 2017: 34 · 2016: 66 · 2015: 54 · 2014: 34 · 2013: 34 · 2012: 20
- FWCI
- 14.77
- Type
- journal article
- Language
- en
- Open access
- green
- www.osti.gov
- Licence
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
- DSpace@MIT (Massachusetts Institute of Technology) (submittedVersion, cc-by-nc)
- APS
- Funders
- U.S. Department of Energy
- National Science Foundation
- 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, phonon transport, silicon, nanoscale heat conduction, thermal conductivity measurement
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