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

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

doi:10.1063/1.4954674

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)

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

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

Country of Publication:: United States

Language:: English

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