E. S. Landry

Size-dependent model for thin film and nanowire thermal conductivity

We present an analytical model for the size-dependence of thin film and nanowire thermal conductivity and compare the predictions to experimental measurements on silicon nanostructures. The model contains no fitting parameters and only requires the bulk lattice constant, bulk thermal conductivity, and an acoustic phonon speed as inputs. By including the mode-dependence of the phonon lifetimes resulting from phonon-phonon and phonon-boundary scattering, the model captures the approach to the bulk thermal conductivity of the experimental data better than gray models based on a single lifetime.

Phonon band structure and thermal transport correlation in a layered diatomic crystal

To elucidate the three-way relationship among a crystal’s structure, its phonon dispersion characteristics, and its thermal conductivity, an analysis is conducted on layered diatomic Lennard-Jones crystals with various mass ratios. Lattice dynamics theory and molecular dynamics simulations are used to predict the phonon dispersion curves and the thermal conductivity. The layered structure generates directionally dependent thermal conductivities lower than those predicted by density trends alone. The dispersion characteristics are quantified using a set of band diagram metrics, which are used to assess the contributions of acoustic phonons and optical phonons to the thermal conductivity. The thermal conductivity increases as the extent of the acoustic modes increases, and it decreases as the extent of the stop bands increases. The sensitivity of the thermal conductivity to the band diagram metrics is highest at low temperatures, where there is less anharmonic scattering, indicating that dispersion plays a more prominent role in thermal transport in that regime. We propose that the dispersion metrics i provide an indirect measure of the relative contributions of dispersion and anharmonic scattering to the thermal transport, and ii uncouple the standard thermal conductivity structure-property relation to that of structure-dispersion and dispersion-property relations, providing opportunities for better understanding of the underlying physical mechanisms and a potential tool for material design.

Effect of film thickness on the thermal resistance of confined semiconductor thin films

The thermal resistance of semiconductor thin films is predicted using lattice dynamics (LD) calculations and molecular dynamics (MD) simulations. We consider Si and Ge films with thicknesses, LF, between 0.2 and 30 nm that are confined between larger extents of the other species (i.e., Ge/Si/Ge and Si/Ge/Si structures). The LD predictions are made in the classical limit for comparison to the classical MD simulations, which are performed at a temperature of 500 K. For structures with LF 2 nm, the MD-predicted thermal resistances are independent of the film thickness for the Ge/Si/Ge structures and increase with increasing film thickness for the Si/Ge/Si st...

Droplet evaporation: A molecular dynamics investigation

Molecular dynamics simulations are used to model the evaporation of a Lennard–Jones argon nanodroplet into its own vapor for a wide range of ambient temperatures and ambient pressures. The transitions from (i) high to low Knudsen number evaporation and (ii) subcritical to supercritical evaporation are observed. At a low ambient pressure of 0.4 MPa, the initial droplet Knudsen number is 1 and the droplet diameter decreases linearly with time, consistent with kinetic theory predictions. For a moderate ambient pressure of 3.0 MPa, the initial droplet Knudsen number is 0.1 and the square of the droplet diameter decreases linearly with time. For a high ambient pressure of 6.1 MPa, the evaporation is supercritical and the number of atoms in the droplet decreases linearly for the majority of the droplet lifetime. A technique is introduced to maintain a constant ambient pressure over the droplet lifetime, allowing for the observation of the influence of the ambient conditions on the droplet surface temperature. W...

MOLECULAR DYNAMICS PREDICTION OF THE THERMAL CONDUCTIVITY OF SI/GE SUPERLATTICES

Molecular dynamics simulations and the non-equilibrium direct method are used to predict the thermal conductivity of a Si/Ge superlattice modeled by the Stillinger-Weber potential at a temperature of 300 K. We focus on the methodology of making the thermal conductivity prediction (limited effort has been made to model Si/Ge nanocomposites in the literature) and find that proper selection of the size and composition of the thermal reservoirs is important.Copyright

SUBCRITICAL AND SUPERCRITICAL NANODROPLET EVAPORATION: A MOLECULAR DYNAMICS INVESTIGATION

Molecular dynamics simulations are used to investigate the subcritical and supercritical evaporation of a Lennard-Jones (LJ) argon nanodroplet in its own vapor. Using a new technique to control both the ambient temperature and pressure, a range of conditions are considered to define a transition line between subcritical and supercritical evaporation. The evaporation is considered to be supercritical if the surface temperature of the droplet reaches the LJ argon critical temperature during its lifetime. Between ambient temperatures of 300 K and 800 K, the transition from subcritical to supercritical evaporation is observed to occur at an ambient pressure 1.4 times greater than the LJ argon critical pressure. For subcritical conditions, the droplet lifetimes obtained from the simulations are compared to independently predicted lifetimes from the D2 law.Copyright

Superlattice Analysis for Tailored Thermal Transport Characteristics

Molecular dynamics simulations and the Green-Kubo method are used to predict the thermal conductivity of binary Lennard-Jones superlattices and alloys. The superlattice thermal conductivity trends are in agreement with those obtained through the direct method, verifying that the Green-Kubo method can be used to examine thermal transport in heterostructures. The simulation temperature and the constituent species are fixed while the superlattice period structure is varied with the goals of (i) minimizing the cross-plane thermal conductivity and (ii) maximizing the ratio of in-plane to cross-plane thermal conductivities. The superlattice thermal conductivity in both the cross-plane and in-plane directions is found to be greater than the corresponding alloy value and less than the value predicted from continuum theory. The anisotropy of the thermal conductivity tensor is found to be at a maximum for a superlattice with a uniform layer thickness. Lattice dynamics calculations are used to investigate the role of optical phonons in the thermal transport.Copyright

SIZE-DEPENDENT MODEL FOR THIN FILM THERMAL CONDUCTIVITY

We present a closed-form classical model for the size dependence of thin film thermal conductivity. The model predictions are compared to Stillinger-Weber silicon thin film thermal conductivities (in-plane and cross-plane directions) calculated using phonon properties obtained from lattice dynamics calculations. By including the frequency dependence of the phonon-phonon relaxation times, the model is able to capture the approach to the bulk thermal conductivity better than models based on a single relaxation time.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

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