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Research Papers: Micro/Nanoscale Heat Transfer

Thin Film Phonon Heat Conduction by the Dispersion Lattice Boltzmann Method

[+] Author and Article Information
Rodrigo A. Escobar

Departamento de Ingeniería Mecánica y Metalúrgica, Pontificia Universidad Católica de Chile, Vicuña Mackenna 4860, Macul Santiago, Chilerescobar@ing.puc.cl

Cristina H. Amon1

Mechanical Engineering Department, Carnegie Mellon University, Pittsburgh, PA 15213camon@cmu.edu

1

Present address: Faculty of Applied Science and Engineering, 35 St. George Street, Room 170, Toronto, ON M5S 1A4, Canada.

J. Heat Transfer 130(9), 092402 (Jul 10, 2008) (8 pages) doi:10.1115/1.2944249 History: Received May 16, 2007; Revised December 07, 2007; Published July 10, 2008

Numerical simulations of time-dependent thermal energy transport in semiconductor thin films are performed using the lattice Boltzmann method applied to phonon transport. The discrete lattice Boltzmann Method is derived from the continuous Boltzmann transport equation assuming nonlinear, frequency-dependent phonon dispersion for acoustic and optical phonons. Results indicate that the heat conduction in silicon thin films displays a transition from diffusive to ballistic energy transport as the characteristic length of the system becomes comparable to the phonon mean free path and that the thermal energy transport process is characterized by the propagation of multiple superimposed phonon waves. The methodology is used to characterize the time-dependent temperature profiles inside films of decreasing thickness. Thickness-dependent thermal conductivity values are computed based on steady-state temperature distributions obtained from the numerical models. It is found that reducing feature size into the subcontinuum regime decreases thermal conductivity when compared to bulk values, at a higher rate than what was displayed by the Debye-based gray lattice Boltzmann method.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Dimensionless steady-state temperature distributions along a one-dimensional film over different film thicknesses

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Figure 2

Transient temperature profile inside a 300nm thin film

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Figure 3

Transient temperature evolution inside a 30nm thin film

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Figure 4

Transient temperature evolution inside a 3nm thin film

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Figure 5

Frequency-dependent Kn for a film of thickness of 1000nm

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Figure 6

Thermal conductivity as a function of film thickness

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