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

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, whichmore » 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.« less
Authors:
 [1] ;  [2] ;  [1]
  1. National University of Singapore (Singapore)
  2. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Publication Date:
Grant/Contract Number:
AC05-00OR22725
Type:
Accepted Manuscript
Journal Name:
Journal of Applied Physics
Additional Journal Information:
Journal Volume: 119; Journal Issue: 24; Journal ID: ISSN 0021-8979
Publisher:
American Institute of Physics (AIP)
Research Org:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org:
USDOE Office of Science (SC)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 36 MATERIALS SCIENCE
OSTI Identifier:
1271890
Alternate Identifier(s):
OSTI ID: 1259982

Jiang, Puqing, Lindsay, Lucas R., and Koh, Yee Kan. Role of low-energy phonons with mean-free-paths >0.8 μm in heat conduction in silicon. United States: N. p., Web. doi:10.1063/1.4954674.
Jiang, Puqing, Lindsay, Lucas R., & Koh, Yee Kan. Role of low-energy phonons with mean-free-paths >0.8 μm in heat conduction in silicon. United States. doi:10.1063/1.4954674.
Jiang, Puqing, Lindsay, Lucas R., and Koh, Yee Kan. 2016. "Role of low-energy phonons with mean-free-paths >0.8 μm in heat conduction in silicon". United States. doi:10.1063/1.4954674. https://www.osti.gov/servlets/purl/1271890.
@article{osti_1271890,
title = {Role of low-energy phonons with mean-free-paths >0.8 μm in heat conduction in silicon},
author = {Jiang, Puqing and Lindsay, Lucas R. and Koh, Yee Kan},
abstractNote = {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 (Λcross) of crystalline silicon films by time-domain thermoreflectance (TDTR), over a wide range of film thicknesses 1≤ hf ≤ 10 μm and temperatures 100 ≤ T ≤ 300 K. We employ a dual-frequency TDTR approach to improve the accuracy of our Λcross measurements. We find from our Λcross 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.},
doi = {10.1063/1.4954674},
journal = {Journal of Applied Physics},
number = 24,
volume = 119,
place = {United States},
year = {2016},
month = {6}
}

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