Analytical Green's function of the multidimensional frequency-dependent phonon Boltzmann equation
Abstract
Thermal phonon transport at length scales comparable to mean free paths is governed by the Boltzmann equation, which is challenging to solve due to its high dimensionality. Here, we present an analytical Green's function for the frequency-dependent, multidimensional Boltzmann equation under the relaxation-time approximation. The new analytical solution is valid from diffusive to ballistic transport regimes and rigorously includes frequency dependence of phonon properties. We demonstrate that our result enables simple closed-form solutions for a number of multidimensional problems for which the only prior solution methods have been computationally expensive numerical simulations.
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Reconstructing the phonon MFP spectrum from the measured KA(Lc) and the derived suppression function is an inverse problem that involves complex optimization.
“Reconstructing the phonon MFP spectrum [ i.e . ߶ ሺΛሻ or ߙ ሺΛሻ ] from the measured ܭ ሺ ܮ ሻ and the derived ܵ ቀ ஃ ቁ is thus an inverse problem of Eq.(4.14) that involves complex optimization. 203-205”
From Tutorial: Time-domain thermoreflectance (TDTR) for thermal property characterization of bulk and thin film materials (2018) · cites this paper as [204]
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- Authors
- Hua, C., & Minnich, A. J.
- Affiliations
- California Institute of Technology (US)
- Corresponding author
- Minnich, Austin J.
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2014-12-31
- Volume
- 90
- Issue
- 21
- ISSN
- 1098-0121 (ISSN-L)
- 1550-235X
- OpenAlex
- W2051291984
- Cited by
- 46
- References
- 44
- Citations by year
- 2026: 4 · 2025: 4 · 2024: 2 · 2023: 3 · 2022: 3 · 2021: 2 · 2020: 6 · 2019: 3 · 2018: 7 · 2017: 3 · 2016: 7 · 2015: 2
- FWCI
- 1.82
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical Review B (publishedVersion)
- CaltechAUTHORS (California Institute of Technology) (submittedVersion)
- Funders
- National Science Foundation (CBET CAREER 1254213)
- Topics
- Physical Sciences › Materials Science › Materials Chemistry › Thermal properties of materials
- Physical Sciences › Engineering › Mechanics of Materials › Thermoelastic and Magnetoelastic Phenomena
- Physical Sciences › Mathematics › Applied Mathematics › Gas Dynamics and Kinetic Theory
- Keywords
- phonon Boltzmann equation, Green's function, relaxation time approximation, multidimensional transport, ballistic transport, diffusive transport, analytical solution
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