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# Monte Carlo Simulation of Silicon Nanowire Thermal Conductivity

[+] Author and Article Information
Yunfei Chen1

Department of Mechanical Engineering and China Education Council Key Laboratory of MEMS,  Southeast University, Nanjing, 210096, People's Republic of China

Deyu Li

Department of Mechanical Engineering,  Vanderbilt University, Nashville, TN, 37235-1592

Jennifer R. Lukes

Department of Mechanical Engineering and Applied Mechanics,  University of Pennsylvania, Philadelphia, PA 19104-6315

Arun Majumdar

Department of Mechanical Engineering,  University of CA, Berkeley, California, 94720 Materials Science Division,  Lawrence Berkeley National Lab, Berkeley, CA, 94720

1

Electronic mail: yunfeichen@yahoo.com

J. Heat Transfer 127(10), 1129-1137 (May 18, 2005) (9 pages) doi:10.1115/1.2035114 History: Received September 28, 2004; Revised May 18, 2005

## Abstract

Monte Carlo simulation is applied to investigate phonon transport in single crystalline Si nanowires. Phonon-phonon normal $(N)$ and Umklapp $(U)$ scattering processes are modeled with a genetic algorithm to satisfy energy and momentum conservation. The scattering rates of N and U scattering processes are found from first-order perturbation theory. The thermal conductivity of Si nanowires is simulated and good agreement is achieved with recent experimental data. In order to study the confinement effects on phonon transport in nanowires, two different phonon dispersions, one from experimental measurements on bulk Si and the other solved from elastic wave theory, are adopted in the simulation. The discrepancy between simulations using different phonon dispersions increases as the nanowire diameter decreases, which suggests that the confinement effect is significant when the nanowire diameter approaches tens of nanometers. It is found that the U scattering probability in Si nanowires is higher than that in bulk Si due to the decrease of the frequency gap between different modes and the reduced phonon group velocity. Simulation results suggest that the dispersion relation for nanowires obtained from elasticity theory should be used to evaluate nanowire thermal conductivity as the nanowire diameter is reduced to the sub-100 nm scale.

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## Figures

Figure 1

Longitudinal phonon dispersion relations for 10 nm diameter Si nanowire

Figure 2

Flexural phonon dispersion relations for 10 nm diameter Si nanowire

Figure 3

Torsional phonon dispersion relations for 10 nm diameter Si nanowire

Figure 4

Dispersion relation for the lowest longitudinal, flexural, and torsional branches of a 10 nm diameter Si nanowire

Figure 5

“Temperature” distribution along the Si nanowire under ballistic transport condition. TL, TR correspond to the temperatures on the left and right ends of the nanowire.

Figure 6

Temperature dependence of bulk Si thermal conductivity from MC simulation results

Figure 7

Thermal conductivity of Si nanowires with different diameters: MC simulation with bulk dispersion relation (lines) and experiment (symbols)

Figure 8

Nanowire thermal conductivity versus diameter at T=300K

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