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Steady-state thermal transport in nanostructures with dimensions comparable to the phonon mean-free-path is examined. Both the case of contacts at different temperatures with no internal heat generation and contacts at the same temperature with internal heat generation are considered. Fourier's Law results are compared to finite volume method solutions of the phonon Boltzmann equation in the gray approximation. When the boundary conditions are properly specified, results obtained using Fourier's Law without modifying the bulk thermal conductivity are in essentially exact quantitative agreement with the phonon Boltzmann equation in the ballistic and diffusive limits. The errors between these two limits are examined in this paper. For the four cases examined, the error in the apparent thermal conductivity as deduced from a correct application of Fourier's Law is less than 6%. We also find that the Fourier's Law results presented here are nearly identical to those obtained from a widely-used ballistic-diffusive approach, but analytically much simpler. Although limited to steady-state conditions with spatial variations in one dimension and to a gray model of phonon transport, the results show that Fourier's Law can be used for linear transport from the diffusive to the ballistic limit. The results also contribute to an understanding of how heat transport at the nanoscale can be understood in terms of the conceptual framework that has been established for electron transport at the nanoscale., 23 pages, 11 figures

This article reviews recent numerical studies of thermal transport in graphene, with a focus on molecular dynamics simulation, the atomistic Green's function method, and the phonon Boltzmann transport equation method. The mode-wise phonon contribution to the intrinsic thermal conductivity (kappa) of graphene and the effects of extrinsic mechanisms-for example, substrate, isotope, impurities, and defects-on kappa are discussed. We also highlight the insights from numerical studies aimed at bridging the gaps between 1D, 2D, and 3D thermal transport in carbon nanotubes/graphene nanoribbons, graphene, and graphite. Numerical studies on thermal transport across the interface between graphene and other materials and nonlinear thermal transport phenomena such as thermal rectification and negative differential thermal resistance are also reviewed.

The author reports an experimental study of electrical and thermal transport in reduced graphene oxide (RGO)/polystyrene (PS) composites. The electrical conductivity (sigma) of RGO/PS composites with different RGO concentrations at room temperature shows a percolation behavior with the percolation threshold of similar to 0.25 vol. %. Their temperature-dependent electrical conductivity follows Efros-Shklovskii variable range hopping conduction in the temperature range of 30-300K. The thermal conductivity (kappa) of composites is enhanced by similar to 90% as the concentration is increased from 0 to 10 vol. %. The thermal conductivity of composites approximately linearly increases with increasing temperature from 150 to 300 K. Composites with a higher concentration show a stronger temperature dependence in the thermal conductivity. (C) 2014 AIP Publishing LLC.

We show that thermal rectification (TR) in asymmetric graphene nanoribbons (GNRs) is originated from phonon confinement in the lateral dimension, which is a fundamentally new mechanism different from that in macroscopic heterojunctions. Our molecular dynamics simulations reveal that, though TR is significant in nanosized asymmetric GNRs, it diminishes at larger width. By solving the heat diffusion equation, we prove that TR is indeed absent in both the total heat transfer rate and local heat flux for bulk-size asymmetric single materials, regardless of the device geometry or the anisotropy of the thermal conductivity. For a deeper understanding of why lateral confinement is needed, we have performed phonon spectra analysis and shown that phonon lateral confinement can enable three possible mechanisms for TR: phonon spectra overlap, inseparable dependence of thermal conductivity on temperature and space, and phonon edge localization, which are essentially related to each other in a complicated manner. Under such guidance, we demonstrate that other asymmetric nanostructures, such as asymmetric nanowires, thin films, and quantum dots, of a single material are potentially high-performance thermal rectifiers.

The effects of CdSe nanocrystal (NC) shape and size on the temperature sensitivity of the Raman shift have been investigated, for the interest of Raman thermometry using NCs. For spherical CdSe NCs of diameters 2.8 nm, 3.6 nm, and 4.4 nm, the temperature sensitivities are -0.0131 cm(-1)/K, -0.0171 cm(-1)/K, and -0.0242 cm(-1)/K, respectively. This trend indicates that as the diameter increases, the effect of increasing phonon anharmonicity dominates over the effect of the decreasing thermal expansion coefficient. On the other hand, triangular NCs with a size of 4.2 nm and elongated NCs of a dimension of 4.6 nm by 14 nm show temperature sensitivities of -0.0182 cm(-1)/K and -0.0176 cm(-1)/K, respectively. This trend indicates that in non-spherical shape NCs, the effect of decreasing thermal expansion coefficient dominates over the effect of slightly increasing phonon anharmonicity. The selection of NCs for Raman thermometry should depend on the specific requirements of temperature sensitivity, spatial resolution, and response time. (C) 2013 AIP Publishing LLC.

Various models were previously used to predict interfacial thermal conductance of vertical carbon nanotube (CNT)-silicon interfaces, but the predicted values were several orders of magnitude off the experimental data. In this work, we show that the CNT filling fraction (the ratio of contact area to the surface area of the substrate) is the key to remedy this discrepancy. Using molecular dynamics, we have identified an upper limit of thermal interface conductance for C-Si interface which is around 1.25GW/m(2)K, corresponding to a 100% filling fraction of carbon nanotube or graphene nanoribbon on substrate. By extrapolating to low filling fraction (similar to 1%) that was measured in experiments, our predicted interfacial thermal conductance agrees with experimental data for vertical CNT arrays grown on silicon substrate (similar to 3MW/m(2) K). Meanwhile, thermal rectification of more than 20% has been found at these C-Si interfaces. We observed that this is strongly dependent on the interfacial temperature drop than the filling fraction. This new effect needs to be considered in future thermal interface materials design. (C) 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4790367]

We have used a two-temperature nonequilibrium molecular dynamics method for predicting interfacial thermal resistance across metal-nonmetal interfaces. This method is an extension of the conventional nonequilibrium molecular dynamics for the dielectric-dielectric interface, where a temperature bias is imposed and the heat current is derived. We have included the electron degree of freedom for the interfacial thermal transport problem by treating the electron-phonon coupling with the two-temperature model. The method is demonstrated on two model systems, that is, silicon-copper interface and carbon-nanotube--copper interface. Temperature nonequilibrium between electrons and phonons in the metal side is quantitatively predicted, and a temperature drop across the interface is observed. The results agree with experimental data better than those obtained from conventional nonequilibrium molecular dynamics simulations where only phonons are considered. Our approach is capable of taking into account both the electron and lattice degrees of freedom in a single molecular dynamics simulation and is a generally useful tool for modeling interfacial thermal transport across metal-nonmetal interfaces.

We have performed molecular dynamics simulations with phonon spectral analysis to predict the mode-wise phonon relaxation times (RT) of suspended and supported graphene at room temperature, and the findings are consistent with recent optical measurements. For acoustic phonons, RTs reduce from up to 50 ps to less than 5 ps when graphene is put on silicon dioxide substrate. Similarly, optical phonon RTs reduce by half when supported. Stronger interfacial bonding is found to result in more RT reduction. Our results provide a fundamental understanding at the spectral phonon property level for the observed thermal conductivity reduction in supported graphene. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4712041]

Using non-equilibrium molecular dynamics, we show that asymmetrically defected graphene nanoribbons (GNR) are promising thermal rectifiers. The optimum conditions for thermal rectification (TR) include low temperature, high temperature bias, similar to 1% concentration of single-vacancy or substitutional silicon defects, and a moderate partition of the pristine and defected regions. TR ratio of similar to 80% is found in a 14-nm long and 4-nm wide GNR at a temperature of 200 K and bias of 90 K, where heat conduction is in the ballistic regime since the bulk effective phonon mean-free-path is around 775 nm. As the GNR length increases towards the diffusive regime, the TR ratio decreases and eventually stabilizes at a length-independent value of about 3%-5%. This work extends defect engineering to 2D materials for achieving TR. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3703756]

We have examined steady-state and time-resolved luminescence properties of CdS:Te quantum dots (QDs). The transient emission spectra have a red shift along the emission process. Using singular value decomposition and multiexponential decay analysis, the luminescence is found to originate from two distinct and parallel channels: band-edge excitonic emission and trapping state emission. With increasing amount of Te, the emission peaks of the QDs show an obvious red shift. Our experimental results suggest that CdS: Te quantum dots have tunable emission spectra and luminescence lifetimes which may have applications in chemical sensing, high throughput screening and other biotechnological applications.

Spectral reflectance of GaAs from infrared (IR) to ultra-violet (UV) bands is predicted using ab initio calculations. We first predict the spectral dielectric function. Two major mechanisms exist for different photon wavelength, namely, photon-electron coupling in the UV to near-IR region and photon-phonon coupling in the far-IR region. For the near-IR to UV band, the electronic band structure of GaAs is calculated, and the imaginary part of the dielectric function is determined from the band structure using the Fermi's golden rule. The real part of spectral dielectric function is then derived from Kramer-Kronig transformation. For the far-IR region, ab initio calculations are used to determine the phonon modes. and the dielectric function is then predicted using the oscillator model. The spectral reflectance for the entire spectrum is then calculated using Fresnel's law for a semi-infinite GaAs slab. The predicted results agree reasonably well with experimental data, demonstrating the capability of ab initio calculations to predict thermal radiative properties of semiconductor materials from their atomic structures. (C) 2009 Elsevier Ltd. All rights reserved.

Two-body interatomic potentials in the Morse potential form have been developed for bismuth telluride, and the potentials are used in molecular dynamics simulations to predict the thermal conductivity. The density-functional theory with local-density approximations is first used to calculate the total energies for many artificially distorted ${\text{Bi}}_{2}{\text{Te}}_{3}$ configurations to produce the energy surface. Then by fitting to this energy surface and other experimental data, the Morse potential form is parameterized. The fitted empirical interatomic potentials are shown to reproduce the elastic and phonon data well. Molecular dynamics simulations are then performed to predict the thermal conductivity of bulk ${\text{Bi}}_{2}{\text{Te}}_{3}$ at different temperatures, and the results agree with experimental data well.