Prediction of thermal conductivity of nanostructures: Influence of phonon dispersion approximation

Baillis, Dominique; Randrianalisoa, Jaona

doi:10.1016/j.ijheatmasstransfer.2009.01.017

Cited by 40 publications

(34 citation statements)

References 34 publications

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“…͑10͒ and ͑11͒. [35][36][37] In contrast to previous work, however, our expressions for F and b do not use the isotropic approximation. We instead use our ability to compute the properties of all phonons in the Brillouin zone to differentiate between the in-plane and cross-plane motions of each phonon mode.…”

Section: B Implementationmentioning

confidence: 96%

In-plane phonon transport in thin films

Turney

McGaughey

Amón

2010

Journal of Applied Physics

130

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The in-plane phonon thermal conductivities of argon and silicon thin films are predicted from the Boltzmann transport equation under the relaxation time approximation. We model the thin films using bulk phonon properties obtained from harmonic and anharmonic lattice dynamics calculations. The input required for the lattice dynamics calculations is obtained from interatomic potentials: Lennard-Jones for argon and Stillinger-Weber for silicon. The effect of the boundaries is included by considering only phonons with wavelengths that fit within the film and adjusting the relaxation times to account for mode-dependent, diffuse boundary scattering. Our model does not rely on the isotropic approximation or any fitting parameters. For argon films thicker than 4.3 nm and silicon films thicker than 17.4 nm, the use of bulk phonon properties is found to be appropriate and the predicted reduction in the in-plane thermal conductivity is in good agreement with results obtained from molecular dynamics simulation and experiment. We include the effects of boundary scattering without employing the Matthiessen rule. We find that the Matthiessen rule yields thermal conductivity predictions that are at most 12% lower than our more accurate results. Our results show that the average of the bulk phonon mean free path is an inadequate metric to use when modeling the thermal conductivity reduction in thin films.

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Section: B Implementationmentioning

confidence: 96%

In-plane phonon transport in thin films

Turney

McGaughey

Amón

2010

Journal of Applied Physics

130

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“…Graham [57] also has reported similar patterns for temperature and heat flux profiles when the characteristic size of their computational domain was comparable to the phonon mean free path. They compared their LBM predicted results against those obtained from the discrete ordinate method (DOM) [58,59], and observed that the DOM also yields a very coarse temperature profile in ballistic regime, if the number of propagation directions for phonons are not sufficient. This issue is common in any numerical method when a limited number of discrete propagation directions are selected to represent a continuous scattering process.…”

Section: Thermal Wave Propagation In An Infinite Mediummentioning

confidence: 99%

On the lattice Boltzmann method for phonon transport

Nabovati

Sellan

Amón

2011

Journal of Computational Physics

113

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“…(23) is a good approximation with relatively high accuracy, but this model is a solution to the phonon Boltzmann equation with Gray model (single mean free path), and the localized atomic vibrations and hopping are not considered. Therefore, more accurate solutions to the backbone thermal conductivity can be obtained by the nanoscale numerical methods, such as the Molecular Dynamics simulation [126e128], Monte Carlo method [129e133] and solving the phonon Boltzmann equation[133,134]. In addition, such numerical solutions can also be employed to improve the prediction accuracy of the numerical model described in Section 3.2.4, i.e., act as the thermal conductivity of solid phase in Eq (62)…”

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confidence: 99%