Role of low-energy phonons with mean-free-paths >0.8 μm in heat conduction in silicon

Jiang, Puqing; Lindsay, Lucas R.; Koh, Yee Kan

doi:10.1063/1.4954674

Title: Role of low-energy phonons with mean-free-paths >0.8 μm in heat conduction in silicon

Journal Article · Thu Jun 30 00:00:00 EDT 2016 · Journal of Applied Physics

DOI:https://doi.org/10.1063/1.4954674· OSTI ID:1271890

Jiang, Puqing ^[1]; Lindsay, Lucas R. ^[2]; Koh, Yee Kan ^[1]

National University of Singapore (Singapore)
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

Despite recent progress in the first-principles calculations and measurements of phonon mean-free-paths (ℓ), contribution of low-energy phonons to heat conduction in silicon is still inconclusive, as exemplified by the discrepancies as large as 30% between different first-principles calculations. In this study, we investigate the contribution of low-energy phonons with ℓ>0.8 μm by accurately measuring the cross-plane thermal conductivity (Λ_cross) of crystalline silicon films by time-domain thermoreflectance (TDTR), over a wide range of film thicknesses 1≤ h_f ≤ 10 μm and temperatures 100 ≤ T ≤ 300 K. We employ a dual-frequency TDTR approach to improve the accuracy of our Λ_cross measurements. We find from our Λ_cross measurements that phonons with ℓ>0.8 μm contribute 53 W m^-1 K^-1 (37%) to heat conduction in natural Si at 300 K while phonons with ℓ>3 μm contribute 523 W m^-1 K^-1 (61%) at 100 K, >20% lower than first-principles predictions of 68 W m^-1 K^-1 (47%) and 717 W m^-1 K^-1 (76%), respectively. Using a relaxation time approximation (RTA) model, we demonstrate that macroscopic damping (e.g., Akhieser s damping) eliminates the contribution of phonons with mean-free-paths >20 μm at 300 K, which contributes 15 W m^-1 K^-1 (10%) to calculated heat conduction in Si. Thus, we propose that omission of the macroscopic damping for low-energy phonons in the first-principles calculations could be one of the possible explanations for the observed differences between our measurements and calculations. Finally, our work provides an important benchmark for future measurements and calculations of the distribution of phonon mean-free-paths in crystalline silicon.

View Accepted Manuscript (DOE)

View Accepted Manuscript (Publisher)

Cite

Export

Save

Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 1271890

Alternate ID(s):: OSTI ID: 1259982

Journal Information:: Journal of Applied Physics, Vol. 119, Issue 24; ISSN 0021-8979

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 26 works

Citation information provided by
Web of Science

References (69)

Determining Phonon Mean Free Paths from Observations of Quasiballistic Thermal Transport Minnich, A. J. Physical Review Letters, Vol. 109, Issue 20 https://doi.org/10.1103/PhysRevLett.109.205901	journal	November 2012
Lattice thermal conductivity of nanostructured thermoelectric materials based on PbTe Koh, Yee Kan; Vineis, C. J.; Calawa, S. D. Applied Physics Letters, Vol. 94, Issue 15 https://doi.org/10.1063/1.3117228	journal	April 2009
Role of Disorder and Anharmonicity in the Thermal Conductivity of Silicon-Germanium Alloys: A First-Principles Study Garg, Jivtesh; Bonini, Nicola; Kozinsky, Boris Physical Review Letters, Vol. 106, Issue 4 https://doi.org/10.1103/PhysRevLett.106.045901	journal	January 2011
Quasi-ballistic thermal transport from nanoscale interfaces observed using ultrafast coherent soft X-ray beams Siemens, Mark E.; Li, Qing; Yang, Ronggui Nature Materials, Vol. 9, Issue 1 https://doi.org/10.1038/nmat2568	journal	November 2009
The mean free path of electrons in metals Sondheimer, E. H. Advances in Physics, Vol. 1, Issue 1 https://doi.org/10.1080/00018735200101151	journal	January 1952
Ab initio thermal transport in compound semiconductors Lindsay, L.; Broido, D. A.; Reinecke, T. L. Physical Review B, Vol. 87, Issue 16 https://doi.org/10.1103/PhysRevB.87.165201	journal	April 2013
Thermal Conductivity Spectroscopy Technique to Measure Phonon Mean Free Paths Minnich, A. J.; Johnson, J. A.; Schmidt, A. J. Physical Review Letters, Vol. 107, Issue 9 https://doi.org/10.1103/PhysRevLett.107.095901	journal	August 2011
Thermal conductivity of diamond nanowires from first principles Li, Wu; Mingo, Natalio; Lindsay, L. Physical Review B, Vol. 85, Issue 19 https://doi.org/10.1103/PhysRevB.85.195436	journal	May 2012
Isotope scattering of dispersive phonons in Ge Tamura, Shin-ichiro Physical Review B, Vol. 27, Issue 2 https://doi.org/10.1103/PhysRevB.27.858	journal	January 1983
An ESCA method for determining the oxide thickness on aluminum alloys Strohmeier, Brian R. Surface and Interface Analysis, Vol. 15, Issue 1 https://doi.org/10.1002/sia.740150109	journal	January 1990
Heat transport in silicon from first-principles calculations Esfarjani, Keivan; Chen, Gang; Stokes, Harold T. Physical Review B, Vol. 84, Issue 8 https://doi.org/10.1103/PhysRevB.84.085204	journal	August 2011
Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density Lee, Chengteh; Yang, Weitao; Parr, Robert G. Physical Review B, Vol. 37, Issue 2 https://doi.org/10.1103/PhysRevB.37.785	journal	January 1988
Thermal conductivity of isotopically enriched ²⁸Si: revisited Kremer, R. K.; Graf, K.; Cardona, M. Solid State Communications, Vol. 131, Issue 8, p. 499-503 https://doi.org/10.1016/j.ssc.2004.06.022	journal	August 2004
Ultrasonic Attenuation in Ge–Si Alloys Keller, K. R. Journal of Applied Physics, Vol. 38, Issue 9 https://doi.org/10.1063/1.1710210	journal	August 1967
Semi-analytical solution to the frequency-dependent Boltzmann transport equation for cross-plane heat conduction in thin films Hua, Chengyun; Minnich, Austin J. Journal of Applied Physics, Vol. 117, Issue 17 https://doi.org/10.1063/1.4919432	journal	May 2015
Density-functional exchange-energy approximation with correct asymptotic behavior Becke, A. D. Physical Review A, Vol. 38, Issue 6 https://doi.org/10.1103/PhysRevA.38.3098	journal	September 1988
Nanoscale thermal transport. II. 2003–2012 Cahill, David G.; Braun, Paul V.; Chen, Gang Applied Physics Reviews, Vol. 1, Issue 1 https://doi.org/10.1063/1.4832615	journal	March 2014
Onset of size effect in lattice thermal conductivity of thin films Maznev, A. A. Journal of Applied Physics, Vol. 113, Issue 11 https://doi.org/10.1063/1.4795601	journal	March 2013
First-Principles Determination of Phonon Lifetimes, Mean Free Paths, and Thermal Conductivities in Crystalline Materials: Pure Silicon and Germanium Garg, Jivtesh; Bonini, Nicola; Marzari, Nicola Topics in Applied Physics https://doi.org/10.1007/978-1-4614-8651-0_4	book	September 2013
Nonlocal theory for heat transport at high frequencies Koh, Yee Kan; Cahill, David G.; Sun, Bo Physical Review B, Vol. 90, Issue 20 https://doi.org/10.1103/PhysRevB.90.205412	journal	November 2014
Thermal conductivity of epitaxial layers of dilute SiGe alloys Cahill, David G.; Watanabe, Fumiya; Rockett, Angus Physical Review B, Vol. 71, Issue 23 https://doi.org/10.1103/PhysRevB.71.235202	journal	June 2005
Frontiers of silicon-on-insulator Celler, G. K.; Cristoloveanu, Sorin Journal of Applied Physics, Vol. 93, Issue 9 https://doi.org/10.1063/1.1558223	journal	May 2003
Thermal Conductivity Measurements of Ultra-Thin Single Crystal Silicon Layers Liu, Wenjun; Asheghi, Mehdi Journal of Heat Transfer, Vol. 128, Issue 1 https://doi.org/10.1115/1.2130403	journal	June 2005
Analysis of heat flow in layered structures for time-domain thermoreflectance Cahill, David G. Review of Scientific Instruments, Vol. 75, Issue 12 https://doi.org/10.1063/1.1819431	journal	December 2004
Cross-plane heat conduction in thin films with ab-initio phonon dispersions and scattering rates Vermeersch, Bjorn; Carrete, Jesús; Mingo, Natalio Applied Physics Letters, Vol. 108, Issue 19 https://doi.org/10.1063/1.4948968	journal	May 2016
Accurate Numerical Method for Calculating Frequency-Distribution Functions in Solids Gilat, G.; Raubenheimer, L. J. Physical Review, Vol. 144, Issue 2 https://doi.org/10.1103/PhysRev.144.390	journal	April 1966
Radial quasiballistic transport in time-domain thermoreflectance studied using Monte Carlo simulations Ding, D.; Chen, X.; Minnich, A. J. Applied Physics Letters, Vol. 104, Issue 14 https://doi.org/10.1063/1.4870811	journal	April 2014
A frequency-domain thermoreflectance method for the characterization of thermal properties Schmidt, Aaron J.; Cheaito, Ramez; Chiesa, Matteo Review of Scientific Instruments, Vol. 80, Issue 9 https://doi.org/10.1063/1.3212673	journal	September 2009
First-Principles Determination of Ultrahigh Thermal Conductivity of Boron Arsenide: A Competitor for Diamond? Lindsay, L.; Broido, D. A.; Reinecke, T. L. Physical Review Letters, Vol. 111, Issue 2, Article No. 025901 https://doi.org/10.1103/PhysRevLett.111.025901	journal	July 2013
Thermal conductivity of bulk and nanowire Mg $_{2}$ Si $_{x}$ Sn $_{1 - x}$ alloys from first principles Li, Wu; Lindsay, L.; Broido, D. A. Physical Review B, Vol. 86, Issue 17 https://doi.org/10.1103/PhysRevB.86.174307	journal	November 2012
Spectral mapping of thermal conductivity through nanoscale ballistic transport Hu, Yongjie; Zeng, Lingping; Minnich, Austin J. Nature Nanotechnology, Vol. 10, Issue 8 https://doi.org/10.1038/nnano.2015.109	journal	June 2015
Mean free path spectra as a tool to understand thermal conductivity in bulk and nanostructures Yang, Fan; Dames, Chris Physical Review B, Vol. 87, Issue 3 https://doi.org/10.1103/PhysRevB.87.035437	journal	January 2013
Dispersion of the long-wavelength phonons in Ge, Si, GaAs, quartz, and sapphire Hao, H. -Y.; Maris, H. J. Physical Review B, Vol. 63, Issue 22 https://doi.org/10.1103/PhysRevB.63.224301	journal	May 2001
Heat-Transport Mechanisms in Superlattices Koh, Yee Kan; Cao, Yu; Cahill, David G. Advanced Functional Materials, Vol. 19, Issue 4 https://doi.org/10.1002/adfm.200800984	journal	February 2009
Effect of exchange–correlation on first-principles-driven lattice thermal conductivity predictions of crystalline silicon Jain, Ankit; McGaughey, Alan J. H. Computational Materials Science, Vol. 110 https://doi.org/10.1016/j.commatsci.2015.08.014	journal	December 2015
Ultrasonic attenuation in pure and doped $n$ -type silicon Kor, S. K.; Mishra, P. K.; Tripathi, N. D. Physical Review B, Vol. 10, Issue 2 https://doi.org/10.1103/PhysRevB.10.775	journal	July 1974
Adiabatic bond charge model for the phonons in diamond, Si, Ge, and $α - Sn$ Weber, Werner Physical Review B, Vol. 15, Issue 10 https://doi.org/10.1103/PhysRevB.15.4789	journal	May 1977
Computational Study of In-Plane Phonon Transport in Si Thin Films Wang, Xinjiang; Huang, Baoling Scientific Reports, Vol. 4, Issue 1 https://doi.org/10.1038/srep06399	journal	September 2014
Transient thermoreflectance from thin metal films Paddock, Carolyn A.; Eesley, Gary L. Journal of Applied Physics, Vol. 60, Issue 1, p. 285-290 https://doi.org/10.1063/1.337642	journal	July 1986
Broadband phonon mean free path contributions to thermal conductivity measured using frequency domain thermoreflectance Regner, Keith T.; Sellan, Daniel P.; Su, Zonghui Nature Communications, Vol. 4, Issue 1 https://doi.org/10.1038/ncomms2630	journal	March 2013
Frequency dependence of the thermal conductivity of semiconductor alloys Koh, Yee Kan; Cahill, David G. Physical Review B, Vol. 76, Issue 7 https://doi.org/10.1103/PhysRevB.76.075207	journal	August 2007
Interpreting picosecond acoustics in the case of low interface stiffness Hohensee, Gregory T.; Hsieh, Wen-Pin; Losego, Mark D. Review of Scientific Instruments, Vol. 83, Issue 11 https://doi.org/10.1063/1.4766957	journal	November 2012
Profiling Nanowire Thermal Resistance with a Spatial Resolution of Nanometers Liu, Dan; Xie, Rongguo; Yang, Nuo Nano Letters, Vol. 14, Issue 2 https://doi.org/10.1021/nl4041516	journal	January 2014
Reconstructing phonon mean-free-path contributions to thermal conductivity using nanoscale membranes Cuffe, John; Eliason, Jeffrey K.; Maznev, A. A. Physical Review B, Vol. 91, Issue 24 https://doi.org/10.1103/PhysRevB.91.245423	journal	June 2015
Anisotropic failure of Fourier theory in time-domain thermoreflectance experiments Wilson, R. B.; Cahill, David G. Nature Communications, Vol. 5, Issue 1 https://doi.org/10.1038/ncomms6075	journal	October 2014
Microscale Heat Conduction in Dielectric Thin Films Majumdar, A. Journal of Heat Transfer, Vol. 115, Issue 1 https://doi.org/10.1115/1.2910673	journal	February 1993
Intrinsic lattice thermal conductivity of semiconductors from first principles Broido, D. A.; Malorny, M.; Birner, G. Applied Physics Letters, Vol. 91, Issue 23 https://doi.org/10.1063/1.2822891	journal	December 2007
Ab initio theory of the lattice thermal conductivity in diamond Ward, A.; Broido, D. A.; Stewart, Derek A. Physical Review B, Vol. 80, Issue 12 https://doi.org/10.1103/PhysRevB.80.125203	journal	September 2009
Gallium arsenide thermal conductivity and optical phonon relaxation times from first-principles calculations Luo, Tengfei; Garg, Jivtesh; Shiomi, Junichiro EPL (Europhysics Letters), Vol. 101, Issue 1 https://doi.org/10.1209/0295-5075/101/16001	journal	January 2013
Picosecond ultrasonic measurements of attenuation of longitudinal acoustic phonons in silicon Daly, B. C.; Kang, K.; Wang, Y. Physical Review B, Vol. 80, Issue 17 https://doi.org/10.1103/PhysRevB.80.174112	journal	November 2009
Ultrasonic attenuation in a quasicrystal studied by picosecond acoustics as a function of temperature and frequency Duquesne, J. -Y.; Perrin, B. Physical Review B, Vol. 68, Issue 13 https://doi.org/10.1103/PhysRevB.68.134205	journal	October 2003
Phonon scattering in silicon films with thickness of order 100 nm Ju, Y. S.; Goodson, K. E. Applied Physics Letters, Vol. 74, Issue 20 https://doi.org/10.1063/1.123994	journal	May 1999
Phonon–boundary scattering in ultrathin single-crystal silicon layers Liu, W.; Asheghi, M. Applied Physics Letters, Vol. 84, Issue 19 https://doi.org/10.1063/1.1741039	journal	May 2004
Direct Measurement of Room-Temperature Nondiffusive Thermal Transport Over Micron Distances in a Silicon Membrane Johnson, Jeremy A.; Maznev, A. A.; Cuffe, John Physical Review Letters, Vol. 110, Issue 2 https://doi.org/10.1103/PhysRevLett.110.025901	journal	January 2013
Accurate measurements of cross-plane thermal conductivity of thin films by dual-frequency time-domain thermoreflectance (TDTR) Jiang, Puqing; Huang, Bin; Koh, Yee Kan Review of Scientific Instruments, Vol. 87, Issue 7 https://doi.org/10.1063/1.4954969	journal	July 2016
Thermal conductivity of individual silicon nanowires Li, Deyu; Wu, Yiying; Kim, Philip Applied Physics Letters, Vol. 83, Issue 14, p. 2934-2936 https://doi.org/10.1063/1.1616981	journal	October 2003
Single Nanowire Thermal Conductivity Measurements by Raman Thermography Doerk, Gregory S.; Carraro, Carlo; Maboudian, Roya ACS Nano, Vol. 4, Issue 8 https://doi.org/10.1021/nn1012429	journal	July 2010
Analytical interpretation of nondiffusive phonon transport in thermoreflectance thermal conductivity measurements Regner, K. T.; McGaughey, A. J. H.; Malen, J. A. Physical Review B, Vol. 90, Issue 6 https://doi.org/10.1103/PhysRevB.90.064302	journal	August 2014
Ultrasonic‐Wave Propagation in Pure Silicon and Germanium Mason, Warren P.; Bateman, T. B. The Journal of the Acoustical Society of America, Vol. 36, Issue 4 https://doi.org/10.1121/1.1919031	journal	April 1964
Temperature Dependence of Microwave Phonon Attenuation Pomerantz, M. Physical Review, Vol. 139, Issue 2A https://doi.org/10.1103/PhysRev.139.A501	journal	July 1965
Accurate Numerical Method for Calculating Frequency Distribution Functions in Solids Gilat, G.; Raubenheimer, L. J. Physical Review, Vol. 147, Issue 2 https://doi.org/10.1103/physrev.147.670.2	journal	July 1966
The mean free path of electrons in metals Sondheimer, E. H. Advances in Physics, Vol. 50, Issue 6 https://doi.org/10.1080/00018730110102187	journal	September 2001
Quasi-ballistic thermal transport from nanoscale interfaces observed using ultrafast coherent soft x-ray beams Siemens, Mark E.; Li, Qing; Yang, Ronggui SPIE OPTO, SPIE Proceedings https://doi.org/10.1117/12.871455	conference	February 2011
Analytical interpretation of nondiffusive phonon transport in thermoreflectance thermal conductivity measurements Regner, K. T.; McGaughey, Alan J. H.; Malen, Jonathan Carnegie Mellon University https://doi.org/10.1184/r1/6489731	text	January 2014
Analytical interpretation of nondiffusive phonon transport in thermoreflectance thermal conductivity measurements Regner, K. T.; McGaughey, Alan J. H.; Malen, Jonathan Carnegie Mellon University https://doi.org/10.1184/r1/6489731.v1	text	January 2014
Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density Robert, Parr,; Chengteh, Lee,; Weitao, Yang, The University of North Carolina at Chapel Hill University Libraries https://doi.org/10.17615/zrp0-ry04	text	January 1988
Ab initio theory of the lattice thermal conductivity in diamond Ward, Alister; Broido, David; Stewart, Derek A. Universität Regensburg https://doi.org/10.5283/epub.9466	text	January 2009
Heat transport in silicon from first principles calculations Esfarjani, Keivan; Chen, Gang; Stokes, Harold T. arXiv https://doi.org/10.48550/arxiv.1107.5288	text	January 2011
Direct Measurement of Room Temperature Non-diffusive Thermal Transport Over Micron Distances in a Silicon Membrane Johnson, Jeremy A.; Maznev, A. A.; Cuffe, John arXiv https://doi.org/10.48550/arxiv.1204.4735	text	January 2012

Cited By (12)

Phonon Spectrum and Transient Regimes in the KCM Torres Alvarez, Pol Thermal Transport in Semiconductors https://doi.org/10.1007/978-3-319-94983-3_6	book	January 2018
Phonon Scattering in Silicon by Multiple Morphological Defects: A Multiscale Analysis Lorenzi, Bruno; Dettori, Riccardo; Dunham, Marc T. Journal of Electronic Materials, Vol. 47, Issue 9 https://doi.org/10.1007/s11664-018-6337-z	journal	May 2018
Heat guiding and focusing using ballistic phonon transport in phononic nanostructures Anufriev, Roman; Ramiere, Aymeric; Maire, Jeremie Nature Communications, Vol. 8, Issue 1 https://doi.org/10.1038/ncomms15505	journal	May 2017
Dislocation-induced thermal transport anisotropy in single-crystal group-III nitride films Sun, Bo; Haunschild, Georg; Polanco, Carlos Nature Materials, Vol. 18, Issue 2 https://doi.org/10.1038/s41563-018-0250-y	journal	December 2018
Probing ballistic thermal conduction in segmented silicon nanowires Anufriev, Roman; Gluchko, Sergei; Volz, Sebastian Nanoscale, Vol. 11, Issue 28 https://doi.org/10.1039/c9nr03863a	journal	January 2019
A new elliptical-beam method based on time-domain thermoreflectance (TDTR) to measure the in-plane anisotropic thermal conductivity and its comparison with the beam-offset method Jiang, Puqing; Qian, Xin; Yang, Ronggui Review of Scientific Instruments, Vol. 89, Issue 9 https://doi.org/10.1063/1.5029971	journal	September 2018
Tutorial: Time-domain thermoreflectance (TDTR) for thermal property characterization of bulk and thin film materials Jiang, Puqing; Qian, Xin; Yang, Ronggui Journal of Applied Physics, Vol. 124, Issue 16 https://doi.org/10.1063/1.5046944	journal	October 2018
Modeling ballistic phonon transport from a cylindrical electron beam heat source Wehmeyer, Geoff Journal of Applied Physics, Vol. 126, Issue 12 https://doi.org/10.1063/1.5115165	journal	September 2019
Highly anisotropic thermoelectric properties of black phosphorus crystals Zeng, Qingsheng; Sun, Bo; Du, Kezhao 2D Materials, Vol. 6, Issue 4 https://doi.org/10.1088/2053-1583/ab2816	journal	July 2019
First principles kinetic-collective thermal conductivity of semiconductors Torres, P.; Torelló, A.; Bafaluy, J. Physical Review B, Vol. 95, Issue 16 https://doi.org/10.1103/physrevb.95.165407	journal	April 2017
A new elliptical-beam method based on time-domain thermoreflectance (TDTR) to measure the in-plane anisotropic thermal conductivity and its comparison with the beam-offset method Jiang, Puqing; Qian, Xin; Yang, Ronggui arXiv https://doi.org/10.48550/arxiv.1803.06551	text	January 2018
Dislocation-induced thermal transport anisotropy in single-crystal group-III nitride films Sun, Bo; Haunschild, Georg; Polanco, Carlos arXiv https://doi.org/10.48550/arxiv.1804.02825	text	January 2018

Similar Records

Thermal conductivity of GaN, ⁷¹GaN, and SiC from 150 K to 850 K

Journal Article · Thu Jan 03 00:00:00 EST 2019 · Physical Review Materials · OSTI ID:1271890

Zheng, Qiye; Li, Chunhua; Rai, Akash; +3 more

Quantifying the Uncertainty in Deterministic Phonon Transport Calculations of Thermal Conductivity using Polynomial Chaos Expansions

Journal Article · Fri Jul 01 00:00:00 EDT 2016 · Transactions of the American Nuclear Society · OSTI ID:1271890

Harter, Jackson R.; Palmer, Todd S.; Greaney, P. Alex

Quasi-Ballistic Thermal Transport Across MoS₂ Thin Films

Journal Article · Wed Feb 27 00:00:00 EST 2019 · Nano Letters · OSTI ID:1271890

Sood, Aditya; Xiong, Feng; Chen, Shunda; +7 more

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
36 MATERIALS SCIENCE

Title: Role of low-energy phonons with mean-free-paths >0.8 μm in heat conduction in silicon

Citation Formats

References (69)

Cited By (12)

Similar Records

Related Subjects