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Mean free path spectra as a tool to understand thermal conductivity in bulk and nanostructures
Abstract
A rigorous derivation is given for the thermal conductivity accumulation function and mean free path (MFP) spectrum of an isotropic bulk material. The key physical insight is to express the kinetic theory integral in terms of MFP rather than frequency. Extending this framework to incorporate boundary scattering in nanostructures leads to an integral equation that transforms a material's bulk MFP spectrum into the size-dependent thermal conductivity of the nanostructure. The kernel of this transform represents the boundary scattering rule for the particular type of nanostructure. The principal benefit of this transform is that it requires only a single function, the material's bulk MFP spectrum, or equivalently its accumulation function. Explicit knowledge of the material's dispersion relation and frequency-dependent bulk MFPs is not needed, nor is a summation over polarizations, because the bulk MFP spectrum already contains this information in exactly the form required to evaluate boundary scattering. The utility of this framework is demonstrated through a case study of six models for the phonon thermal conductivity of silicon: three analytical, one gray, and two numerical.
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“Such bulk phonon MFP spectra can be extended to predict the thermal conductivity of thin films and nanostructures using the approaches of Yang and Dames 9 .”
From Broadband phonon mean free path contributions to thermal conductivity measured using frequency domain thermoreflectance (2013) · cites this paper as [9]
In the citing paper
“With the approaches from Ref. 35 the data in Fig. 2 allows for mapping of thermal conductivity suppression in nanostructured materials and devices.”
From Universal phonon mean free path spectra in crystalline semiconductors at high temperature (2013) · cites this paper as [35]
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Metadata
- Authors
- Yang, F., & Dames, C.
- Affiliations
- University of California, Berkeley (US)
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2013-01-31
- Volume
- 87
- Issue
- 3
- ISSN
- 1098-0121 (ISSN-L)
- 1550-235X
- OpenAlex
- W2328394108
- Cited by
- 283
- References
- 54
- Citations by year
- 2026: 13 · 2025: 20 · 2024: 13 · 2023: 18 · 2022: 18 · 2021: 23 · 2020: 17 · 2019: 21 · 2018: 23 · 2017: 32 · 2016: 34 · 2015: 27 · 2014: 14 · 2013: 10
- FWCI
- 12.78
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical Review B (publishedVersion)
- 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
- lattice thermal conductivity, boundary scattering, nanostructures, size-dependent thermal conductivity, silicon, phonon dispersion
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