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RESEARCH PAPERS: Micro/Nanoscale Heat Transfer

In-Plane and Out-Of-Plane Thermal Conductivity of Silicon Thin Films Predicted by Molecular Dynamics

[+] Author and Article Information
Carlos J. Gomes, Javier V. Goicochea

Department of Mechanical Engineering and Institute for Complex Engineered Systems, Carnegie Mellon University, Pittsburgh, PA 15213-3890

Marcela Madrid

Pittsburgh Supercomputing Center and Institute for Complex Engineered Systems, Carnegie Mellon University, Pittsburgh, PA 15213-3890

Cristina H. Amon1

Raymond Lane Distinguished Professor, Department of Mechanical Engineering and Institute for Complex Engineered Systems, Carnegie Mellon University, Pittsburgh, PA 15213-3890camon@cmu.edu

1

Current address: University of Toronto, Department of Mechanical and Industrial Engineering.

J. Heat Transfer 128(11), 1114-1121 (Apr 06, 2006) (8 pages) doi:10.1115/1.2352781 History: Received June 22, 2005; Revised April 06, 2006

The thermal conductivity of silicon thin films is predicted in the directions parallel and perpendicular to the film surfaces (in-plane and out-of-plane, respectively) using equilibrium molecular dynamics, the Green-Kubo relation, and the Stillinger-Weber interatomic potential. Three different boundary conditions are considered along the film surfaces: frozen atoms, surface potential, and free boundaries. Film thicknesses range from 2to217nm and temperatures from 300to1000K. The relation between the bulk phonon mean free path (Λ) and the film thickness (ds) spans from the ballistic regime (Λds) at 300K to the diffusive, bulk-like regime (Λds) at 1000K. When the film is thin enough, the in-plane and out-of-plane thermal conductivity differ from each other and decrease with decreasing film thickness, as a consequence of the scattering of phonons with the film boundaries. The in-plane thermal conductivity follows the trend observed experimentally at 300K. In the ballistic limit, in accordance with the kinetic and phonon radiative transfer theories, the predicted out-of-plane thermal conductivity varies linearly with the film thickness, and is temperature-independent for temperatures near or above the Debye’s temperature.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

(a) Sketch of a thin film defining the in-plane and out-of-plane directions. (b) Simulation domain consisting of 4×4×8 silicon lattice constants and film thickness ds.

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Figure 2

(a) Starting configuration of the atoms located on the surface of a film consisting of 10×10 lattice constants in the cross-section, and eight lattice constants (4.34nm) thickness. (b) Surface reconstruction after 100,000 steps of molecular dynamics, showing the individual dimes oriented in the [110] crystallographic direction and the group of dimes aligned in the [11¯0] direction.

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Figure 3

Radial distribution functions of the atoms located on the first four layers of a film consisting of 7×7×8 lattice constants, for the different boundary conditions used

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Figure 4

MD predicted in-plane thermal conductivity at TMD=400K as a function of film thickness, for the three boundary conditions simulated: Addition of a surface potential (◻), frozen atoms (엯), and free boundaries (▵)

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Figure 5

MD predicted thermal conductivities: In-plane (∎) and out-of-plane (◻) at TMD=400K, and in-plane (●) and out-of-plane (엯) at TMD=1000K, as a function of film thickness ds. Experimental bulk silicon thermal conductivities at 375 and 1000K are shown as dashed lines (67).

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Figure 6

In-plane silicon thermal conductivity predicted by molecular dynamics at TMD=400K (∎), and experimental data at 300K: (◻) (12), (▵) (13), and (엯) (14)

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Figure 7

Out-of-plane thermal conductivity versus film thickness at different temperatures TMD, for film thicknesses up to 217nm, and in the insert, for film thicknesses up to 14nm

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