Research Papers: Micro/Nanoscale Heat Transfer

Modeling the Thermal Conductivity and Phonon Transport in Nanoparticle Composites Using Monte Carlo Simulation

[+] Author and Article Information
Ming-Shan Jeng2

Mechanical Engineering Department, Massachusetts Institute of Technology, Cambridge, MA 02139msjeng@itri.org.tw

Ronggui Yang3

Mechanical Engineering Department, Massachusetts Institute of Technology, Cambridge, MA 02139ronggui.yang@colorado.edu

David Song

 Intel Corporation, Chandler, AZ 85226

Gang Chen

Mechanical Engineering Department, Massachusetts Institute of Technology, Cambridge, MA 02139gchen2@mit.edu


On leave from the Industrial Technology Research Institute, Chutung, Hsinchu, Taiwan 310, R.O.C.


Present address: Department of Mechanical Engineering, University of Colorado, Boulder, CO.

J. Heat Transfer 130(4), 042410 (Mar 19, 2008) (11 pages) doi:10.1115/1.2818765 History: Received October 23, 2006; Revised June 04, 2007; Published March 19, 2008

This paper presents a Monte Carlo simulation scheme to study the phonon transport and the thermal conductivity of nanocomposites. Special attention has been paid to the implementation of periodic boundary condition in Monte Carlo simulation. The scheme is applied to study the thermal conductivity of silicon germanium (Si–Ge) nanocomposites, which are of great interest for high-efficiency thermoelectric material development. The Monte Carlo simulation was first validated by successfully reproducing the results of (two-dimensional) nanowire composites using the deterministic solution of the phonon Boltzmann transport equation reported earlier and the experimental thermal conductivity of bulk germanium, and then the validated simulation method was used to study (three-dimensional) nanoparticle composites, where Si nanoparticles are embedded in Ge host. The size effects of phonon transport in nanoparticle composites were studied, and the results show that the thermal conductivity of nanoparticle composites can be lower than that of the minimum alloy value, which is of great interest to thermoelectric energy conversion. It was also found that randomly distributed nanopaticles in nanocomposites rendered the thermal conductivity values close to that of periodic aligned patterns. We show that interfacial area per unit volume is a useful parameter to correlate the size effect of thermal conductivity in nanocomposites. The key for the thermal conductivity reduction is to have a high interface density where nanoparticle composites can have a much higher interface density than the simple 1D stacks, such as superlattices. Thus, nanocomposites further benefit the enhancement of thermoelectric performance in terms of thermal conductivity reduction. The thermal conductivity values calculated by this work qualitatively agrees with a recent experimental measurement of Si–Ge nanocomposites.

Copyright © 2008 by American Society of Mechanical Engineers
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Figure 2

The schematic process flow of the MC simulation algorithm. The MC simulation starts with the initialization step. After the initialization step, phonons experience the moving and scattering in each time step.

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Figure 3

Typical variation of thermal conductivity values with respect to calculation time. The case shown is a 2D nanocomposite with 10nm Si nanowire embedded in Ge host. The result is converged after 10ns simulation, corresponding to 10,000 time steps, with a variation of less than 0.1% afterward.

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Figure 4

Comparison of the thermal conductivity value from the gray-medium MC simulation conducted in this work with the experimental thermal conductivity value of a bulk germanium sample. The experimental Ge value is taken from Ref. 44. The circular symbols indicate the results of simulating a solid bulk material without any particle inside. The triangle symbol represents the simulation of a pseudocomposite when both the particle and the host material are Ge. When the two sides of the interface both have transmissivity values of 1, the simulation should equal that of a solid bulk material without any particles. This pseudocomposite simulation served to validate the MC coding.

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Figure 5

Comparison of the temperature (energy density) distributions inside a nanowire composite obtained, respectively, by the deterministic solution of the phonon BTE and MC method. (a) Geometric dimensions of the unit cell for a Si0.2–Ge0.8 nanowire composite with a 10×10nm2 nanowire inclusion with z along the wire direction. (b) Temperature distribution along the x direction at various y positions assuming heat flows in the x direction.

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Figure 6

Comparison of thermal conductivity values for the 2D nanowire composites obtained by a MC simulation and by a deterministic solution of the BTE. The relative percentage deviation is less than 8%.

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Figure 7

Sketch of nanoparticle composites with silicon cubic nanoparticles distributed (a) in an aligned pattern, (b) in a staggered pattern, and, randomly, (c) in a germanium matrix for MC simulation conducted in this work. Even in (c), the cubic nanoparticles are aligned parallel to each other. The thermal conductivity calculated in this work are all in the direction normal to the cubic nanoparticles.

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Figure 8

Temperature distribution inside an aligned periodic nanoparticle composite in the middle plane in the z direction. The dimension of the nanoparticle is 10×10×10nm3. The volume fraction of Si particles is 3.7%, corresponding to a Si0.04–Ge0.96 atomic composition.

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Figure 9

Comparison of the heat flux at the hot (x=0) and cold (x=Lx)x boundaries in (a) A periodic aligned nanoparticle composite, i.e., with one 10nm cubic particle inside a 14nm cubic unit cell. (b) A random nanoparticle composite, i.e., with ten nanoparticles, each of which is a 10nm cube randomly distributed inside a 40×40×40nm3unit cell. The comparison demonstrates the periodicity of local heat flux in the x direction.

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Figure 10

The effects of silicon nanoparticle size and distribution on the thermal conductivity of nanoparticle composites: (a) Comparison of the thermal conductivity of composites with 10nm and 50nm silicon cubic particles distributed in a simple periodic pattern in a germanium host and that of a Si–Ge alloy as a function of atomic composition. (b) The effect of the distribution pattern on the thermal conductivity of composites with 10nm silicon particle inclusions. Also shown in (b) is the thermal conductivity of a Si–Ge alloy.

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Figure 11

Thermal conductivity of nanoparticle composites predicted by the MC simulation conducted in this work and that predicted by the EMA proposed by Nan in Ref. 18. The EMA based on incorporating the thermal boundary resistance into the solutions of the Fourier heat conduction law underpredicts the size effects.

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Figure 13

The thermal conductivity of nanoparticle composites as a function of the interfacial area per unit volume (interface density). The thermal conductivity data of nanoparticle composites falls on to a single curve nicely as a function of interfacial area per unit volume. The randomness either in particle size or position distribution causes slight fluctuations. However, these fluctuations are not a dominant factor for the reduction in the thermal conductivity. The effective thermal conductivity of 2D nanowire composites is lower than that of 3D nanoparticle composites for the same interface area per unit volume since the effectiveness of interface scattering on the thermal conductivity reduction is different when the interface is perpendicular to the applied temperature difference direction and when the interface is parallel to the applied temperature difference direction.

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Figure 14

(a) The temperature-dependent thermal conductivity of nanoparticle composites. (b) Comparison of the simulated thermal conductivity with recent experimental results from the Jet Propulsion Laboratory (50).

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Figure 1

(a) Periodic nanocomposite with cubic silicon nanoparticles dispersed periodically in a germanium matrix. (b) With the periodic boundary condition dictated in Sec. 2, the MC simulation of phonon transport in the computational domain (unit cell) represents phonon transport in the whole structure shown in (a). The unit cell (computational domain) is further divided into subcells.

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Figure 12

Comparison of the thermal conductivity of a periodically aligned nanocomposite with 50nm cubic silicon particles distributed in a germanium matrix and that of a random composite with silicon nanoparticles having a size range from 10nmto100nm distributed randomly in a germanium matrix as a function of germanium atomic composition.



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