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Heat transport in silicon from first-principles calculations
Open accessAbstract
Using harmonic and anharmonic force constants extracted from density functional calculations within a supercell, we have developed a relatively simple but general method to compute thermodynamic and thermal properties of any crystal. First, from the harmonic, cubic, and quartic force constants, we construct a force field for molecular dynamics. It is exact in the limit of small atomic displacements and thus does not suffer from inaccuracies inherent in semiempirical potentials such as Stillinger-Weber's. By using the Green-Kubo formula and molecular dynamics simulations, we extract the bulk thermal conductivity. This method is accurate at high temperatures where three-phonon processes need to be included to higher orders, but may suffer from size scaling issues. Next, we use perturbation theory (Fermi golden rule) to extract the phonon lifetimes and compute the thermal conductivity $\ensuremath{\kappa}$ from the relaxation-time approximation. This method is valid at most temperatures, but will overestimate $\ensuremath{\kappa}$ at very high temperatures, where higher-order processes neglected in our calculations also contribute. As a test, these methods are applied to bulk crystalline silicon, and the results are compared and differences are discussed in more detail. The presented methodology paves the way for a systematic approach to model heat transport in solids using multiscale modeling, in which the relaxation time due to anharmonic three-phonon processes is calculated quantitatively, in addition to the usual harmonic properties such as phonon frequencies and group velocities. It also allows the construction of an accurate bulk interatomic potentials database.
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“Regarding (ii), the long MFP phonons probed by BB-FDTR contribute substantially to thermal conductivity, but not to heat capacity (o1%) 2 .”
From Broadband phonon mean free path contributions to thermal conductivity measured using frequency domain thermoreflectance (2013) · cites this paper as [2]
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“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 [187]
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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 [2]
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Metadata
- Authors
- Esfarjani, K., Chen, G., & Stokes, H. T.
- Affiliations
- Massachusetts Institute of Technology (US)
- Brigham Young University (US)
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2011-08-23
- Volume
- 84
- Issue
- 8
- ISSN
- 1098-0121 (ISSN-L)
- 1550-235X
- OpenAlex
- W1992328011
- Cited by
- 759
- References
- 33
- Citations by year
- 2026: 17 · 2025: 47 · 2024: 41 · 2023: 30 · 2022: 38 · 2021: 53 · 2020: 60 · 2019: 60 · 2018: 75 · 2017: 63 · 2016: 68 · 2015: 73 · 2014: 60 · 2013: 42 · 2012: 25
- FWCI
- 20.89
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Physical Review B (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
- DSpace@MIT (Massachusetts Institute of Technology) (submittedVersion, cc-by-nc)
- arXiv (Cornell University)
- APS
- Funders
- 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 › Materials Science › Metals and Alloys › Thermodynamic and Structural Properties of Metals and Alloys
- Keywords
- heat transport, thermal conductivity, crystalline silicon, anharmonic force constants, harmonic force constants, interatomic potentials, Green-Kubo formula, phonon lifetime, three-phonon processes, relaxation time approximation, Fermi's golden rule, phonon transport, multiscale modeling
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