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Cited by 759Thermal properties of materialsThermoelastic and Magnetoelastic PhenomenaThermodynamic and Structural Properties of Metals and Alloys

Heat transport in silicon from first-principles calculations

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Esfarjani, Keivan, Chen, Gang, Stokes, Harold T.·2011·Physical Review B
DOI 10.1103/physrevb.84.085204
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Abstract

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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Crossref · 10.1103/physrevb.84.085204

Cites

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  • The long mean free path phonons probed by BB-FDTR contribute substantially to thermal conductivity, but not to heat capacity (less than 1%).

    “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]

    Section E, “Thermal conductivity from lattice dynamics” (page not available), reports that phonons with mean free paths longer than 1 micron contribute almost half of silicon’s thermal conductivity. The cited paper does not establish that those phonons contribute less than 1% of heat capacity or identify them as phonons probed by BB-FDTR. (LLM, conf=0.86)

    Experimental — accuracy not yet measured

  • The 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 [187]

    Section E, “Thermal conductivity from lattice dynamics” (page unavailable), supports the cited point that pure crystalline silicon has very long phonon mean free paths: nearly half its thermal conductivity comes from phonons with MFPs above 1 µm. The paper does not establish that the Λ > dp interpretation works only for semiconductor alloys, or report the stated TDTR frequency-dependence result. (LLM, conf=0.86)

    Experimental — accuracy not yet measured

  • Our data compare favourably with the first principles predictions by Esfarjani and coworkers at all temperatures.

    “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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Cites

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Research works printed but not linked: 3

  1. A. Henry and G. Chen, J. Comput. Theor. Nanosci. 5, 141 (2008).
  2. R. Prado, Time Series: Modeling, Computation, and Inference, CRC Texts in Statistical Science (Chapman and Hall, London, 2010), Vol. 86.
  3. P. G. Klemens, in Thermal Conductivity, edited by R. P. Tve (Academic, London, 1969), Vol. 1.

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Authors
Esfarjani, K., Chen, G., & Stokes, H. T.
Affiliations
  • Massachusetts Institute of Technology (US)
  • Brigham Young University (US)
ORCID
Venue
Physical Review B
Publisher
American Physical Society (APS)
Published
2011-08-23
Volume
84
Issue
8
ISSN
  • 1098-0121 (ISSN-L)
  • 1550-235X
DOI
10.1103/physrevb.84.085204
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
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 › Engineering › Mechanical Engineering › 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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