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Research Papers: Micro/Nanoscale Heat Transfer

Monte Carlo Study of Phonon Heat Conduction in Silicon Thin Films Including Contributions of Optical Phonons

[+] Author and Article Information
Arpit Mittal

Department of Mechanical Engineering, Ohio State University, 201 West 19th Avenue, Columbus, OH 43210

Sandip Mazumder1

Department of Mechanical Engineering, Ohio State University, 201 West 19th Avenue, Columbus, OH 43210mazumder.2@osu.edu

1

Corresponding author.

J. Heat Transfer 132(5), 052402 (Mar 08, 2010) (11 pages) doi:10.1115/1.4000447 History: Received March 24, 2009; Revised September 23, 2009; Published March 08, 2010; Online March 08, 2010

Abstract

The Monte Carlo method has found prolific use in the solution of the Boltzmann transport equation for phonons for the prediction of nonequilibrium heat conduction in crystalline thin films. This paper contributes to the state-of-the-art by performing a systematic study of the role of the various phonon modes on thermal conductivity predictions, in particular, optical phonons. A procedure to calculate three-phonon scattering time-scales with the inclusion of optical phonons is described and implemented. The roles of various phonon modes are assessed. It is found that transverse acoustic (TA) phonons are the primary carriers of energy at low temperatures. At high temperatures $(T>200 K)$, longitudinal acoustic (LA) phonons carry more energy than TA phonons. When optical phonons are included, there is a significant change in the amount of energy carried by various phonons modes, especially at room temperature, where optical modes are found to carry about 25% of the energy at steady state in silicon thin films. Most importantly, it is found that inclusion of optical phonons results in better match with experimental observations for silicon thin-film thermal conductivity. The inclusion of optical phonons is found to decrease the thermal conductivity at intermediate temperatures (50–200 K) and to increase it at high temperature $(>200 K)$, especially when the film is thin. The effect of number of stochastic samples, the dimensionality of the computational domain (two-dimensional versus three-dimensional), and the lateral (in-plane) dimension of the film on the statistical accuracy and computational efficiency is systematically studied and elucidated for all temperatures.

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Figures

Figure 1

Computational domain (a) 3D and (b) 2D

Figure 2

Curve-fit data for dispersion curves for silicon in [100] direction

Figure 3

Group velocity of the various phonon modes

Figure 4

Normalized cumulative distribution function: (a) without optical phonons and (b) with optical phonons

Figure 5

Phonon-phonon scattering time-scales computed using the present hybrid approach and Holland’s model at (a) 100 K and (b) 300 K

Figure 6

Comparison of mean free paths of all four phonon modes at 300 K computed using the present hybrid approach, and data obtained using molecular dynamics by Henry and Chen (31)

Figure 7

Predicted and measured (16) through-plane thermal conductivity for a 0.42 μm silicon film

Figure 8

Predicted and measured (16) through-plane thermal conductivity for a 1.6 μm silicon film

Figure 9

Predicted and measured (16) through-plane thermal conductivity for a 3 μm silicon film

Figure 10

Predicted thermal conductivity using 2D versus 3D computational domains

Figure 11

CPU time taken for 2D versus 3D simulations with Nprescribed=50,000

Figure 12

Time-dependent energy flux at the boundaries for a 0.42 μm thin film with (a) Nprescribed=50,000 and (b) Nprescribed=500,000

Figure 13

Time averaged energy flux (average of data presented in Fig. 1) at the boundaries for a 0.42 μm thin film computed using Nprescribed=50,000

Figure 14

Energy flux at the boundaries for a 0.42 μm film with (a) Nprescribed=50,000 and (b) flux time averaged over 1000 time steps

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