Prediction of thermal conductivity of nanostructures: Influence of phonon dispersion approximation (original) (raw)
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Journal of Electronic Materials, 2013
We study the thermal properties of ultra-narrow silicon nanowires (NW) with diameters from 3 nm to 12 nm. We use the modified valence-force-field method for computation of phononic dispersion and the Boltzmann transport equation for calculation of phonon transport. Phonon dispersion in ultra-narrow 1D structures differs from dispersion in the bulk and dispersion in thicker NWs, which leads to different thermal properties. We show that as the diameter of the NW is reduced the density of long-wavelength phonons per cross section area increases, which increases their relative importance in carrying heat compared with the rest of the phonon spectrum. This effect, together with the fact that low-frequency, low-wavevector phonons are affected less by scattering and have longer mean-free-paths than phonons in the rest of the spectrum, leads to a counter-intuitive increase in thermal conductivity as the diameter is reduced to the sub-ten-nanometers range. This behavior is retained in the presence of moderate boundary scattering.
An analytical model for the thermal conductivity of silicon nanostructures
Journal of Applied Physics, 2005
A simple model of thermal conductivity, based on the harmonic theory of solids, is used to study the heat transfer in nanostructures. The thermal conductivity is obtained by summing the contribution of all the vibration modes of the system. All the vibrational properties ͑dispersion curves and relaxation time͒ that are used in the model are obtained using the data for bulk samples. The size effect is taken into account through the sampling of the Brillouin zone and the distance that a wave vector can travel between two boundaries in the structure. The model is used to predict the thermal conductivity of silicon nanowires and nanofilms, and demonstrates a good agreement with experimental results. Finally, using this model, the quality of the silicon interatomic potential, used for molecular-dynamics simulations of heat transfer, is evaluated.
In-Plane and Out-Of-Plane Thermal Conductivity of Silicon Thin Films Predicted by Molecular Dynamics
Journal of Heat Transfer, 2006
The thermal conductivity of silicon thin films is predicted in the directions parallel and perpendicular to the film surfaces (in-plane and out-of-plane, respectively) using equilibrium molecular dynamics, the Green-Kubo relation, and the Stillinger-Weber interatomic potential. Three different boundary conditions are considered along the film surfaces: frozen atoms, surface potential, and free boundaries. Film thicknesses range from 2to217nm and temperatures from 300to1000K. The relation between the bulk phonon mean free path (Λ) and the film thickness (ds) spans from the ballistic regime (Λ⪢ds) at 300K to the diffusive, bulk-like regime (Λ⪡ds) at 1000K. When the film is thin enough, the in-plane and out-of-plane thermal conductivity differ from each other and decrease with decreasing film thickness, as a consequence of the scattering of phonons with the film boundaries. The in-plane thermal conductivity follows the trend observed experimentally at 300K. In the ballistic limit, in a...
International Journal of Heat and Mass Transfer, 2020
As one simple metamaterial, nanopatterns are often fabricated across a thin film so that the thermal transport can be manipulated. The etched sidewalls for these nanostructures are usually rough due to surface defects introduced during the nanofabrication, whereas the top and bottom film surfaces are smoother. In existing analytical models, the contrast between these surfaces has not been addressed and all boundaries are assumed to be diffusive for phonon reflection. In this paper, a new two-step approach to address this issue is proposed for phonon transport modeling of general thin-film-based structures. In this approach, the effective in-plane phonon mean free paths (Λ) are first modified from the bulk phonon MFPs to account for the influence of the top/bottom film surfaces, with possibly enhanced probability of specular phonon reflection at cryogenic temperatures. This Λ is further modified to include the scattering by etched sidewalls with almost completely diffusive phonon scattering. Such a two-step phonon mean free path modification yields almost identical results as frequency-dependent phonon Monte Carlo simulations for etched nanowires and representative nanoporous thin films. This simple yet
Thermal Conductivity in Thin Silicon Nanowires: Phonon Confinement Effect
Nano Letters, 2007
Thermal conductivity of thin silicon nanowires (1.4−8.3 nm) including the realistic crystalline structures and surface reconstruction effects is investigated using direct molecular dynamics simulations with Stillinger−Weber potential for Si−Si interactions. Thermal conductivity as a function of decreasing nanowire diameter shows an expected decrease due to increased surface scattering effects. However, at very small diameter (<1.5 nm), an increase in the thermal conductivity is observed, which is explained by the phonon confinement effect.
Size effect on the phonon heat conduction in semiconductor nanostructures
Lattice thermal conductivity for silicon nanowires and quantum well are theoretically investigated in the temperature range from 2K to 300K. The modified Gallaway method for bulk crystal is used for calculating lattice thermal conductivity. All important phonon relaxation mechanism such as Umklapp scattering, Mass-difference scattering and boundary scattering are calculated at 300K. The result show that the modification of the acoustic phonon modes and phonon group velocities due to spatial confinement of phonons lead to significant increase in the all phonon relaxation rate. From our numerical results, we predicate a significant decrease of the lattice thermal conductivity in cylindrical nanowires with diameter (D=10-nm), and quantum well with thickness of the same size, results compared to that of the reported experimental as well as theoretical values.
Monte Carlo Simulation of Steady-State Microscale Phonon Heat Transport
Journal of Heat Transfer, 2008
Heat conduction in submicron crystalline materials can be well modeled by the Boltzmann transport equation (BTE). The Monte Carlo method is effective in computing the solution of the BTE. These past years, transient Monte Carlo simulations have been developed, but they are generally memory demanding. This paper presents an alternative Monte Carlo method for analyzing heat conduction in such materials. The numerical scheme is derived from past Monte Carlo algorithms for steady-state radiative heat transfer and enables us to understand well the steady-state nature of phonon transport. Moreover, this algorithm is not memory demanding and uses very few iteration to achieve convergence. It could be computationally more advantageous than transient Monte Carlo approaches in certain cases. Similar to the famous Mazumder and Majumdar's transient algorithm (2001, "Monte Carlo Study of Phonon Transport in Solid Thin Films Including Dispersion and Polarization," ASME J. Heat Transfer, 123, pp. 749-759), the dual polarizations of phonon propagation, the nonlinear dispersion relationships, the transition between the two polarization branches, and the nongray treatment of phonon relaxation times are accounted for. Scatterings by different mechanisms are treated individually, and the creation and/or destruction of phonons due to scattering is implicitly taken into account. The proposed method successfully predicts exact solutions of phonon transport across a gallium arsenide film in the ballistic regime and that across a silicon film in the diffusion regime. Its capability to model the phonon scattering by boundaries and impurities on the phonon transport has been verified. The current simulations agree well with the previous predictions and the measurement of thermal conductivity along silicon thin films and along silicon nanowires of widths greater than 22 nm. This study confirms that the dispersion curves and relaxation times of bulk silicon are not appropriate to model phonon propagation along silicon nanowires of 22 nm width.
Numerical simulation of transient phonon heat transfer in silicon nanowires and nanofilms
Journal of Physics: Conference Series, 2007
This work proposes a numerical simulation of heat conduction in silicon nanowires and nanofilms. Boltzmann equation for phonons is solved in the relaxation time approximation. The equation is integrated in an axisymmetric cylindrical two dimensional geometry. Solid angle integration is done by means of Discrete Ordinate Method. Moreover, in contrast to other models published in literature, spectral dependency of relaxation times and acoustic wave dispersion are taken into account in this numerical resolution. Consequently, thermal profiles are obtained for silicon nanowires and nanofilms in steady state allowing computation of thermal conductivity and/or thermal conductance. Besides, we solve the unsteady Boltzmann equation in order to obtain nanosystems temporal evolution. The results obtained with this code match nanofilms and nanowires already predicted thermal profiles in steady state. In unsteady condition, diffusive state (Fourier) is discussed for nanowires and nanofilms. At low temperatures, ballistic phenomenons are seen in nanofilms, whereas, in nanowires, due to boundary scattering, diffusion regime is observed.