Joseph E. Turney

In-plane phonon transport in thin films

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 ex...

Cross-plane phonon transport in thin films

We predict the cross-plane phonon thermal conductivity of Stillinger-Weber silicon thin films as thin as 17.4 nm using the lattice Boltzmann method. The thin films are modeled using bulk phonon properties obtained from harmonic and anharmonic lattice dynamics calculations. We use this approach, which considers all of the phonons in the first Brillouin-zone, to assess the suitability of common assumptions. Specifically, we assess the validity of: (i) neglecting the contributions of optical modes, (ii) the isotropic approximation, (iii) assuming an averaged bulk mean-free path, and (iv) the Matthiessen rule. Because the frequency-dependent contributions to thermal conductivity change as the film thickness is reduced, assumptions that are valid for bulk are not necessarily valid for thin films.

Predicting Phonon Properties From Molecular Dynamics Simulations Using the Spectral Energy Density

Using lattice dynamics theory, we derive the spectral energy density and the relation between the spectral energy density and the phonon frequencies and relaxation times. We then calculate the spectral energy density and phonon frequencies and relaxation times for a test system of Lennard-Jones argon using velocities obtained from molecular dynamics simulations. The phonon properties, which can be used to calculate thermal conductivity, are compared to predictions made using (i) anharmonic lattice dynamics calculations and (ii) a technique that performs normal mode analysis on the positions and velocities obtained from molecular dynamics simulations.Copyright

Coupling Between Phonons and Fluid Particles in Water/Carbon Nanotube Systems

We investigate thermal transport in water/carbon nanotube (CNT) composite systems using molecular dynamics simulations. Carbon-carbon interactions are modeled using the second-generation REBO potential, water-water interactions are modeled using the TIP4P potential, and carbon-water interactions are modeled using a Lennard-Jones potential. The thermal conductivities of empty and water-filled CNTs with diameters between 0.83 nm and 1.66 nm are predicted using molecular dynamics simulation and a direct application of the Fourier law. For empty CNTs, the thermal conductivity decreases with increasing CNT diameter. As the CNT length approaches 1 micron, a length-independent thermal conductivity is obtained, indicative of diffusive phonon transport. When the CNTs are filled with water, the thermal conductivity decreases compared to the empty CNTs and transitions to diffusive phonon transport at shorter lengths. To understand this behavior, we calculate the spectral energy density of the empty and water-filled CNTs and calculate the mode-specific group velocities, relaxation times, and thermal conductivity. For the empty 1.10 nm diameter CNT, we show that the acoustic phonon modes account for 65 percent of the total thermal conductivity. This behavior is attributed to their long mean-free paths. When the CNT is filled with water, interactions with the water molecules shorten the acoustic mode mean-free path and lower the overall CNT thermal conductivity.Copyright

Comparison of Spectral Energy Density Methods for Predicting Phonon Properties

To predict the thermal conductivity of a dielectric or insulating material requires the phonon frequencies and lifetimes. Techniques for predicting these quantities have been proposed based in molecular dynamics simulation and lattice dynamics calculations. Here, two expressions for the phonon spectral energy density are described and applied to two test systems: Lennard-Jones argon and Stillinger-Weber silicon. One spectral energy density expression is derived from lattice dynamics theory, while the other uses only the atomic velocities from molecular dynamics simulation. We find that while the spectral energy density using only atomic velocities can predict the phonon frequencies, it is not generally able to predict the lifetimes due to terms omitted in the derivation.Copyright

Size Effects in Green-Kubo and Direct Method Molecular Dynamics Predictions of Thermal Conductivity

The bulk thermal conductivity of Lennard-Jones argon and Stillinger-Weber silicon is predicted using the Green-Kubo (GK) and direct methods in classical molecular dynamics simulations. While system-size independent thermal conductivities can be obtained with less than 1000 atoms for both materials using the GK method, the linear extrapolation procedure [Schelling et al. Phys. Rev. B 65, 144306 (2002)] must be applied to direct method results for multiple system sizes. It is found that applying the linear extrapolation procedure in a manner consistent with previous researchers can lead to an underprediction of the GK thermal conductivity (e.g., by a factor of 2.5 for Stillinger-Weber silicon at a temperature of 500 K). To understand this discrepancy, phonon properties are predicted from lattice dynamics calculations, and from these, length-dependent thermal conductivities. These results show that the linear extrapolation procedure is only accurate when the minimum system size used in the direct method simulations is comparable to the largest mean free paths of the phonons that dominate the thermal transport. This condition has not typically been satisfied in previous works.Copyright

Predicting the Phonon Properties of Carbon Nanotubes Using the Spectra Energy Density

Thermal transport by phonons in water/carbon nanotube (CNT) composite systems is investigated using molecular dynamics (MD) simulation. We calculate the spectral energy density of empty and water-filled CNTs and use it to extract the mode-specific phonon group velocities, relaxation times, and thermal conductivities. The total thermal conductivity predicted from the spectral energy density is consistent with what we predict using a direct application of the Fourier law in an MD simulation. The number of atoms and simulation runtime required to predict the spectral energy density, however, are both at least one order-of-magnitude smaller.Copyright

Phonon Transport in Thin Films: A Lattice Dynamics/Boltzmann Transport Equation Study

The cross-plane and in-plane phonon thermal conductivities of Stillinger-Weber (SW) silicon thin films are predicted using 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 cross-plane and in-plane thermal conductivities are reduced from the corresponding bulk value. This reduction is more severe for the cross-plane direction than for the in-plane direction. For the in-plane direction, we find that the predicted reduction in thermal conductivity gives a good lower bound to available experimental results. Including the effects of boundary scattering using the Matthiessen rule, which assumes that scattering mechanisms are independent, yields thermal conductivity predictions that are at most 12% lower than our more accurate results. Neglecting optical phonon modes, while valid for bulk systems, introduces 22.5% error when modeling thin films. Using phonon properties along the [001] direction (i.e., the isotropic approximation) yields bulk predictions that are 15% lower than that when all of the phonon modes are considered. For thin films, this deviation increases to 25%. Our results show that a single bulk phonon mean free path is an inadequate metric for predicting the thermal conductivity reduction in thin films.© 2010 ASME

Critically Assessing the Application of Quantum Corrections to Classical Thermal Conductivity Predictions

Quantum corrections can be used to map the thermal conductivity predicted in a classical framework [e.g., a molecular dynamics (MD) simulation] to a corresponding value in a quantum system. This procedure is accomplished by equating the total energies and energy fluxes of the classical and quantum systems. The validity of these corrections is questionable because they are introduced in an ad hoc manner and are not derived from first principles. In this work, the validity of these quantum corrections is examined by comparing the thermal conductivity of Stillinger-Weber silicon calculated using a full quantum mechanical treatment to a quantum-corrected value predicted from a classical framework between temperatures of 10 K and 1000 K. The quantum and classical predictions are obtained using anharmonic lattice dynamics calculations. We find discrepancies between the quantum-corrected predictions and the quantum predictions obtained directly. We investigate the causes of these discrepancies and from our findings, conclude that quantum thermal conductivities cannot be predicted by applying simple corrections to the values obtained from a purely classical framework.Copyright

THIN FILM THERMAL CONDUCTIVITY BY ANHARMONIC LATTICE DYNAMICS CALCULATIONS

Lattice dynamics calculations are used to investigate thermal transport in argon thin films with thicknesses ranging between one and ten nanometers. Quasi-harmonic lattice dynamics calculations are used to find the frequencies and mode shapes of non-interacting phonons. This information is then used as input for anharmonic lattice dynamics calculations, whereby we compute the frequency shift and lifetime of each phonon mode due to interactions with other phonons. The phonon frequencies, group velocities, and lifetimes determined with the lattice dynamics techniques are then used to compute the in-plane thermal conductivity of the thin films as a function of film thickness. The thermal conductivities predicted by the lattice dynamics methods are compared to predictions from molecular dynamics simulations. Differences in the phonon characteristics in thin films compared to bulk crystals are examined by comparing the contribution to the thermal conductivity as a function of frequency.Copyright