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Research Papers

DSMC Scheme for Phonon Transport in Solid Thin Films

[+] Author and Article Information
Mitsuhiro Matsumoto

Department of Mechanical Engineering and Science,  Graduate School of Engineering,  Kyoto University, Kyoto 606-8501, Japan;matsumoto@kues.kyoto-u.ac.jp Advanced Research Institute of Fluid Science and Engineering,  Kyoto University, Kyoto 615-8530, Japanmatsumoto@kues.kyoto-u.ac.jp

Masaya Okano1

Department of Mechanical Engineering and Science,  Graduate School of Engineering,  Kyoto University, Kyoto 606-8501, Japan

Yusuke Masao

Department of Mechanical Engineering and Science,  Graduate School of Engineering,  Kyoto University, Kyoto 606-8501, Japan

1

Current address: Hitachi, Ltd., Japan

J. Heat Transfer 134(5), 051009 (Apr 13, 2012) (7 pages) doi:10.1115/1.4005639 History: Received April 16, 2010; Revised October 01, 2010; Published April 11, 2012; Online April 13, 2012

Analysis of phonon dynamics based on a linearized Boltzmann transport equation is widely used for thermal analysis of solid thin films, but couplings among various phonon modes appear in some situations. We propose a direct simulation Monte Carlo (DSMC) scheme to simulate the phonon gas starting without the conventional linearization approximation. This requires no relaxation time as an input parameter, and we can investigate the couplings among phonons with different modes. A prototype code based on a simple phonon model was developed, and energy flux was evaluated for thin films of various thickness as a test calculation.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic temperature profile in solid thin films, for three typical conditions of Kn = l/L (l: phonon mean free path, L: film thickness)

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Figure 2

Example of mode–mode couplings in phonon dynamics observed in nonequilibrium MD simulations [21]. As the excited region of 0.9 × 1012 ≤ω [rad/s] ≤ 1.1 × 1012 relaxes, other regions gradually develop.

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Figure 3

Density of state D(ω) and the number density of phonons f(ω;T)D(ω) in the frequency domain

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Figure 4

Temperature dependence of phonon properties at thermal equilibrium; (a) mean energy per phonon, (b) number of phonons per unit volume, (c) total energy per unit volume, and (d) heat capacity per unit volume. The unit volume in this calculation contains 3 × 106 atoms, which means that 3 × 106 samplings were taken. For the unit of each property, see Sec. 2.

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Figure 5

Ratio of successful collisions (filled square) and ratio of umklapp processes (open square) to collision trials

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Figure 6

Schematic view of the three-dimensional DSMC simulation system, a cuboid contacting with two heat baths

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Figure 7

Energy flux q calculated with our DSMC code. The Fourier’s law where q is inversely proportional to the film thickness is shown with the dashed line, assuming the bulk value of thermal conductivity λ ∼ 150 Wm−1 K−1 .

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Figure 8

Examples of temperature profile for (top) thin film and (bottom) thick film. The end regions of three layers shown as shaded area are thermal reservoirs.

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Figure 9

Distribution of phonon momentum kz along the temperature gradient

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Figure 10

Temperature profiles, estimated for phonons with different propagating directions; the film thickness is 20. The average (solid line) is the same as the profile in Fig. 8 (top).

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