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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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In the citing paper
“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]
Citations
Cites
Room-Temperature Ultraviolet Nanowire Nanolasers
Huang, M. H., Mao, S. S., Feick, H., Yan, H., Wu, Y., Kind, H., Weber, E. R., Russo, R. E., & Yang, P. (2001) · Science · doi:10.1126/science.1060367 · Cited by 8,922
Numerical Recipes: The Art of Scientific Computing
Ziegel, E. R., Press, W. H., Flannery, B. P., Teukolsky, S. A., & Vetterling, W. T. (1987) · Technometrics · doi:10.2307/1269484 · Cited by 6,704
Nanowire Nanosensors for Highly Sensitive and Selective Detection of Biological and Chemical Species
Cui, Y., Wei, Q., Park, H., & Lieber, C. M. (2001) · Science · doi:10.1126/science.1062711 · Cited by 5,857
High-Thermoelectric Performance of Nanostructured Bismuth Antimony Telluride Bulk Alloys
Poudel, B., Hao, Q., Ma, Y., Lan, Y., Minnich, A. J., Yu, B., Yan, X. X., Wang, D., Muto, A., Vashaee, D., et al. (2008) · Science · doi:10.1126/science.1156446 · Cited by 5,627
Enhanced thermoelectric performance of rough silicon nanowires
Hochbaum, A. I., Chen, R., Delgado, R. D., Liang, W., Garnett, E. C., Najarian, M., Majumdar, A., & Yang, P. (2008) · Nature · doi:10.1038/nature06381 · Cited by 4,109
Model for Lattice Thermal Conductivity at Low Temperatures
Callaway, J. (1959) · Physical Review · doi:10.1103/physrev.113.1046 · Cited by 3,209
Silicon nanowires as efficient thermoelectric materials
Boukai, A. I., Bunimovich, Y. L., Tahir‐Kheli, J., Yu, J.-K., Goddard, W. A., & Heath, J. R. (2008) · Nature · doi:10.1038/nature06458 · Cited by 2,731
The mean free path of electrons in metals
Sondheimer, E. H. (1952) · Advances In Physics · doi:10.1080/00018735200101151 · Cited by 2,650
The conductivity of thin metallic films according to the electron theory of metals
Fuchs, K. P. (1938) · Mathematical Proceedings of the Cambridge Philosophical Society · doi:10.1017/s0305004100019952 · Cited by 2,286
Bulk nanostructured thermoelectric materials: current research and future prospects
Minnich, A. J., Dresselhaus, M. S., Ren, Z., & Chen, G. (2009) · Energy & Environmental Science · doi:10.1039/b822664b · Cited by 2,000
Thermal conductivity of individual silicon nanowires
Li, D., Wu, Y., Kim, P., Shi, L., Yang, P., & Majumdar, A. (2003) · Applied Physics Letters · doi:10.1063/1.1616981 · Cited by 1,791
Thermal Conductivity of Silicon and Germanium from 3°K to the Melting Point
Glassbrenner, C. J., & Slack, G. A. (1964) · Physical Review · doi:10.1103/physrev.134.a1058 · Cited by 1,652
Ziman, J. M. (2001) · Oxford University Press eBooks · doi:10.1093/acprof:oso/9780198507796.001.0001 · Cited by 1,227
Analysis of Lattice Thermal Conductivity
Holland, M. G. (1963) · Physical Review · doi:10.1103/physrev.132.2461 · Cited by 1,165
Thermal conductivity and ballistic-phonon transport in the cross-plane direction of superlattices
Chen, G. (1998) · Physical review. B, Condensed matter · doi:10.1103/physrevb.57.14958 · Cited by 1,099
Intrinsic lattice thermal conductivity of semiconductors from first principles
Broido, D. A., Malorny, M., Birner, G., Mingo, N., & Stewart, D. A. (2007) · Applied Physics Letters · doi:10.1063/1.2822891 · Cited by 978
Note on the conduction of heat in crystals
Casimir, H. B. G. (1938) · Physica · doi:10.1016/s0031-8914(38)80162-2 · Cited by 883
Nanoscale Energy Transport And Conversion
Chen, G. (2005) · doi:10.1093/oso/9780195159424.001.0001 · Cited by 877
Heat transport in silicon from first-principles calculations
Esfarjani, K., Chen, G., & Stokes, H. T. (2011) · Physical Review B · doi:10.1103/physrevb.84.085204 · Cited by 759
Phonon scattering in silicon films with thickness of order 100 nm
Ju, Y. S., & Goodson, K. E. (1999) · Applied Physics Letters · doi:10.1063/1.123994 · Cited by 653
Morelli, D. T., Heremans, J. P., & Slack, G. A. (2002) · Physical Review B · doi:10.1103/physrevb.66.195304 · Cited by 628
Thermal Conductivity Spectroscopy Technique to Measure Phonon Mean Free Paths
Minnich, A. J., Johnson, J. A., Schmidt, A. J., Esfarjani, K., Dresselhaus, M. S., Nelson, K. A., & Chen, G. (2011) · Physical Review Letters · doi:10.1103/physrevlett.107.095901 · Cited by 556
Nanostructured Bulk Silicon as an Effective Thermoelectric Material
Bux, S. K., Blair, R. G., Gogna, P. K., Lee, H., Chen, G., Dresselhaus, M. S., Kaner, R. B., & Fleurial, J. (2009) · Advanced Functional Materials · doi:10.1002/adfm.200900250 · Cited by 515
Size effects in molecular dynamics thermal conductivity predictions
Sellan, D. P., Landry, E. S., Turney, J. E., McGaughey, A. J. H., & Amon, C. H. (2010) · Physical Review B · doi:10.1103/physrevb.81.214305 · Cited by 508
Garg, J., Bonini, N., Kozinsky, B., & Marzari, N. (2011) · Physical Review Letters · doi:10.1103/physrevlett.106.045901 · Cited by 491
Wang, Z., Alaniz, J. E., Jang, W., Garay, J. E., & Dames, C. (2011) · Nano Letters · doi:10.1021/nl1045395 · Cited by 462
Self-citationThermal conductivity of germanium crystals with different isotopic compositions
Asen-Palmer, M., Bartkowski, K., Gmelin, E., Cardona, M., Zhernov, A. P., Inyushkin, A. V., Taldenkov, A. N., Ozhogin, V. I., Itoh, K. M., & Häller, E. E. (1997) · Physical review. B, Condensed matter · doi:10.1103/physrevb.56.9431 · Cited by 415
Mingo, N., & Yang, L. (2003) · Physical review. B, Condensed matter · doi:10.1103/physrevb.68.245406 · Cited by 404
Theoretical phonon thermal conductivity of Si/Ge superlattice nanowires
Dames, C., & Chen, G. (2003) · Journal of Applied Physics · doi:10.1063/1.1631734 · Cited by 401
Self-citationChen, G. (1997) · ASME Journal of Heat and Mass Transfer · doi:10.1115/1.2824212 · Cited by 394
Henry, A. S., & Chen, G. (2008) · Journal of Computational and Theoretical Nanoscience · doi:10.1166/jctn.2008.2454 · Cited by 391
Frequency dependence of the thermal conductivity of semiconductor alloys
Koh, Y. K., & Cahill, D. G. (2007) · Physical Review B · doi:10.1103/physrevb.76.075207 · Cited by 383
Thermal conductivity of diamond nanowires from first principles
Li, W., Mingo, N., Lindsay, L., Broido, D., Stewart, D. A., & Katcho, N. A. (2012) · Physical Review B · doi:10.1103/physrevb.85.195436 · Cited by 380
Thermal Conductivity and Phonon Scattering by Magnetic Impurities in CdTe
Slack, G. A., & Galginaitis, S. V. (1964) · Physical Review · doi:10.1103/physrev.133.a253 · Cited by 368
Temperature-Dependent Thermal Conductivity of Single-Crystal Silicon Layers in SOI Substrates
Asheghi, M., Touzelbaev, M. N., Goodson, K. E., Leung, Y.-K., & Wong, S. S. (1998) · ASME Journal of Heat and Mass Transfer · doi:10.1115/1.2830059 · Cited by 368
The electrical conductivity of thin wires
Dingle, R. (1950) · Proceedings of the Royal Society of London A Mathematical and Physical Sciences · doi:10.1098/rspa.1950.0077 · Cited by 353
Phonon-boundary scattering in thin silicon layers
Asheghi, M., Leung, Y. K., Wong, S. S., & Goodson, K. E. (1997) · Applied Physics Letters · doi:10.1063/1.119402 · Cited by 337
Quantifying Surface Roughness Effects on Phonon Transport in Silicon Nanowires
Lim, J., Hippalgaonkar, K., Andrews, S. C., Majumdar, A., & Yang, P. (2012) · Nano Letters · doi:10.1021/nl3005868 · Cited by 333
Predicting the Thermal Conductivity of Si and Ge Nanowires
Mingo, N., Liu, Y., Li, D., & Majumdar, A. (2003) · Nano Letters · doi:10.1021/nl034721i · Cited by 285
Schelling, P. K., Shi, L., & Goodson, K. E. (2005) · Materials Today · doi:10.1016/s1369-7021(05)70935-4 · Cited by 278
Thermal Conductivity Measurements of Ultra-Thin Single Crystal Silicon Layers
Liu, W., & Asheghi, M. (2005) · ASME Journal of Heat and Mass Transfer · doi:10.1115/1.2130403 · Cited by 261
Thermal conductivity of periodic microporous silicon films
Song, D. W., & Chen, G. (2004) · Applied Physics Letters · doi:10.1063/1.1642753 · Cited by 232
Determining Phonon Mean Free Paths from Observations of Quasiballistic Thermal Transport
Minnich, A. J. (2012) · Physical Review Letters · doi:10.1103/physrevlett.109.205901 · Cited by 196
Effect of Isotopes on Low-Temperature Thermal Conductivity
Slack, G. A. (1957) · Physical Review · doi:10.1103/physrev.105.829 · Cited by 180
Anisotropic Heat Conduction in Cubic Crystals in the Boundary Scattering Regime
McCurdy, A. K., Maris, H. J., & Elbaum, C. (1970) · Physical review. B, Solid state · doi:10.1103/physrevb.2.4077 · Cited by 165
Variational Calculation of the Thermal Conductivity of Germanium
HAMILTON, R. A. H., & Parrott, J. E. (1969) · Physical Review · doi:10.1103/physrev.178.1284 · Cited by 146
Mesoscopic Size Effects on the Thermal Conductance of Silicon Nanowire
Heron, J.-S., Fournier, T., Mingo, N., & Bourgeois, O. (2009) · Nano Letters · doi:10.1021/nl803844j · Cited by 121
Role of Phonon Dispersion in Lattice Thermal Conductivity Modeling
Chung, J. D., McGaughey, A. J. H., & Kaviany, M. (2004) · ASME Journal of Heat and Mass Transfer · doi:10.1115/1.1723469 · Cited by 119
Picosecond ultrasonic measurements of attenuation of longitudinal acoustic phonons in silicon
Daly, B. C., Kang, K., Wang, Y., & Cahill, D. G. (2009) · Physical Review B · doi:10.1103/physrevb.80.174112 · Cited by 112
Size Effect on the Thermal Conductivity of High-Tc Thin-Film Superconductors
Flik, M. I., & Tien, C. L. (1990) · ASME Journal of Heat and Mass Transfer · doi:10.1115/1.2910494 · Cited by 95
Marked Effects of Alloying on the Thermal Conductivity of Nanoporous Materials
Bera, C., Mingo, N., & Volz, S. G. (2010) · Physical Review Letters · doi:10.1103/physrevlett.104.115502 · Cited by 94
Prasher, R., Tong, T., & Majumdar, A. (2007) · Nano Letters · doi:10.1021/nl0721665 · Cited by 52
Micromachined polycrystalline thin film temperature sensors
Jiang, L., Wong, M., & Zohar, Y. (1999) · Measurement Science and Technology · doi:10.1088/0957-0233/10/8/301 · Cited by 29
Transport and boundary scattering in confined geometries: Analytical results
Richardson, R. A., & Nori, F. (1993) · Physical review. B, Condensed matter · doi:10.1103/physrevb.48.15209 · Cited by 13
Research works printed but not linked: 2
- C. Dames, 2006, Thermoelectrics Handbook, Macro to Nano
- C. Dames, 2008, Micro/Nanoscale Heat Transfer International Conference
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Moore, A. L., & Shi, L. (2014) · Materials Today · doi:10.1016/j.mattod.2014.04.003 · Cited by 2,156
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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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