Approximate Analytical Models for Phonon Specific Heat and Ballistic Thermal Conductance of Nanowires (original) (raw)
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International Journal of Heat and Mass Transfer, 2018
A mathematical model is presented for thermal transport in nanowires with rectangular cross sections. Expressions for the effective thermal conductivity of the nanowire across a range of temperatures and cross-sectional aspect ratios are obtained by solving the Guyer-Krumhansl hydrodynamic equation for the thermal flux with a slip boundary condition. Our results show that square nanowires transport thermal energy more efficiently than rectangular nanowires due to optimal separation between the boundaries. However, circular nanowires are found to be even more efficient than square nanowires due to the lack of corners in the cross section, which locally reduce the thermal flux and inhibit the conduction of heat. By using a temperature-dependent slip coefficient, we show that the model is able to accurately capture experimental data of the effective thermal conductivity obtained from Si nanowires, demonstrating that phonon hydrodynamics is a powerful framework that can be applied in nanosystems even at room temperature.
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Journal of Applied Physics, 2011
Phonon-wall collisions (with smooth or rough walls) have a deep influence on the thermal conductivity of nanowires. Usually this influence is analyzed in the steady-state thermal conductivity. Here, by using a phonon-hydrodynamic model with slip heat flow along the walls, we explore the influence of phonon-wall collisions on frequency-dependent thermal conductivity, which imply a reduction of it with increasing frequency. Understanding of this dependence would allow one to obtain information on the collisions complementary to that of the steady states.
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Thermal conductivity of a model nanowire, composed of Zr-Ti-Cu-Ni-Be amorphous alloy, has been studied by computer simulations and theoretical calculations. The results from the molecular dynamics simulations are compared to predictions from Fourier continuum mechanics theory, and with published experimental data. Analysis of the theoretical phonon thermal conductivity follows the previously published incoherent particle model. The novelty of this study is in the employment of amorphous structure, lacking any order or superlattice. The simulated thermal conductivity is significantly lower than that measured by experiments on bulk alloy. It appears that amorphous structure and side-wall scattering reduce thermal diffusivity significantly. Velocity auto correlation time constant increases during heating cycle in proportion to the ratio of atomic weight divided by atomic scattering cross-sectional area.
The lattice thermal conductivity of a semiconductor nanowire
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It has been found experimentally as well as theoretically that the lattice thermal conductivity can be largely reduced by the size confinement effect. The significant boundary scattering effect is one of the dominant factors. In most existing lattice thermal conductivity models, an empirical relation is used for this scattering rate. An unconfined or confined phonon distribution obtained based on the phonon Boltzmann equation and the relaxation time approximation is then employed to calculate the lattice thermal conductivity. In this work, we first attempt to derive an analytical form of the boundary scattering rate for phonon conduction in a semiconductor nanowire and then claim two reasonable ways to take it into account correctly. Consistent mathematical models in the sense that the effects of the size confinement on (i) the phonon dispersion relation, (ii) the phonon distribution, (iii) the phonon group and phase velocities, and (iv) the Debye temperature are finally proposed.
Journal of Applied Physics, 2011
The effect of geometrical confinement, atomic position and orientation of Silicon nanowires (SiNWs) on their thermal properties are investigated using the phonon dispersion obtained using a Modified Valence Force Field (MVFF) model. The specific heat (C v) and the ballistic thermal conductance (κ bal l) shows anisotropic variation with changing cross-section shape and size of the SiNWs. The C v increases with decreasing cross-section size for all the wires. The triangular wires show the largest C v due to their highest surface-to-volume ratio. The square wires with [110] orientation show the maximum κ bal l since they have the highest number of conducting phonon modes. At the nano-scale a universal scaling law for both C v and κ bal l are obtained with respect to the number of atoms in the unit cell. This scaling is independent of the shape, size and orientation of the SiNWs revealing a direct correlation of the lattice thermal properties to the atomistic properties of the nanowires. Thus, engineering the SiNW cross-section shape, size and orientation open up new ways of tuning the thermal properties at the nanometer regime.
Prediction of thermal conductivity of nanostructures: Influence of phonon dispersion approximation
International Journal of Heat and Mass Transfer, 2009
In this study, the influence of phonon dispersion approximation on the prediction of in-plane and out-ofplane thermal conductivity of thin films and nanowires is shown. Results obtained using the famous Holland dispersion approximation and the Brillouin zone boundary condition (BZBC) dispersion curves are compared. For (in-plane and out-of-plane) thermal conductivity predictions based on BZBC dispersion curves, new relaxation time parameters fitted from experimental data of bulk silicon thermal conductivity are reported. The in-plane thermal conductivity of nanostructures (films of thicknesses 20 nm, 100 nm, and 420 nm and nanowires of widths 22 nm, 37 nm, and 100 nm) in the temperature range 20-1000 K is calculated from the modified bulk thermal conductivity model by scaling the bulk phonon mean free path (MFP) by the Fuch-Sondheimer factor of boundary scattering developed for nanostructures with rectangular cross-section. The pseudo out-of-plane thermal conductivity of films of thicknesses 20 nm, 100 nm, and 420 nm and in the temperature range 150-1000 K is calculated from the solution of the Boltzmann transport equation (BTE) for phonons by using the Discrete ordinate method (DOM), and the Monte Carlo (MC) simulation. In order to confirm the current results, the calculated in-plane thermal conductivity of silicon thin films and silicon nanowires are compared with existing experimental data. Moreover, due to lack of experimental and theoretical data of out-of-plane thermal conductivity of thin films, comparison of the DOM and MC simulation is performed. The current work shows that a drastic simplification of dispersion curves can lead to wrong prediction of both in-plane and out-of-plane thermal conductivities of nanostructures, especially for ultra thin nanostructures and/or at high temperatures. Comparison with experimental data of in-plane thermal conductivity of silicon thin films and silicon nanowires proves that more refined dispersion approximation such as the BZBC is well adequate for phonon transport calculations when confinement has negligible effect. Moreover, the comparison between the thermal conductivity in the out-of-plane direction and that in the inplane direction enables one to quantify the anisotropy of thermal conductivity of the film.