We predict the bulk thermal conductivity of Lennard-Jones argon and Stillinger-Weber silicon using the Green-Kubo ͑GK͒ and direct methods in classical molecular dynamics simulations. While system-sizeindependent 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 ͑2002͔͒ must be applied to direct method results for multiple system sizes. We find 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 K͒. To understand this discrepancy, we perform lattice dynamics calculations to predict phonon properties and from these, length-dependent thermal conductivities. From these results, we find 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. To aid in future studies, we present a simple metric for determining if the system sizes used in direct method simulations are sufficiently large so that the linear extrapolation procedure can accurately predict the bulk thermal conductivity.

The accuracies of two theoretical expressions for thermal boundary resistance are assessed by comparing their predictions to independent predictions from molecular dynamics ͑MD͒ simulations. In one expression ͑R E ͒, the phonon distributions are assumed to follow the equilibrium, Bose-Einstein distribution, while in the other expression ͑R NE ͒, the phonons are assumed to have nonequilibrium, but bulk-like distributions. The phonon properties are obtained using lattice dynamics-based methods, which assume that the phonon interface scattering is specular and elastic. We consider ͑i͒ a symmetrically strained Si/Ge interface, and ͑ii͒ a series of interfaces between Si and "heavy-Si," which differs from Si only in mass. All of the interfaces are perfect, justifying the assumption of specular scattering. The MD-predicted Si/Ge thermal boundary resistance is temperature independent and equal to 3.1ϫ 10 −9 m 2-K/ W below a temperature of ϳ500 K, indicating that the phonon scattering is elastic, as required for the validity of the theoretical calculations. At higher-temperatures, the MD-predicted Si/Ge thermal boundary resistance decreases with increasing temperature, a trend we attribute to inelastic scattering. For the Si/Ge interface and the Si/heavy-Si interfaces with mass ratios greater than two, R E is in good agreement with the corresponding MD-predicted values at temperatures where the interface scattering is elastic. When applied to a system containing no interface, R E is erroneously nonzero due to the assumption of equilibrium phonon distributions on either side of the interface. While R NE is zero for a system containing no interface, it is 40%-60% less than the corresponding MD-predicted values for the Si/Ge interface and the Si/heavy-Si interfaces at temperatures where the interface scattering is elastic. This inaccuracy is attributed to the assumption of bulk-like phonon distributions on either side of the interface.

Two methods for predicting phonon frequencies and relaxation times are presented. The first is based on quasiharmonic and anharmonic lattice dynamics calculations, and the second is based on a combination of quasiharmonic lattice dynamics calculations and molecular dynamics simulations. These phonon properties are then used with the Boltzmann transport equation under the relaxation-time approximation to predict the lattice thermal conductivity. The validity of the low-temperature assumptions made in the lattice dynamics framework are assessed by comparing to thermal conductivities predicted by the Green-Kubo and direct molecular dynamics methods for a test system of Lennard-Jones argon. The predictions of all four methods are in agreement at low temperature ͑20 K͒. At temperatures of 40 K ͑half the Debye temperature of Lennard-Jones argon͒ and below, the thermal-conductivity predictions from the two methods that use lattice dynamics calculations are within about 30% of those made using the more accurate Green-Kubo and direct molecular dynamics methods. The thermal-conductivity predictions using the lattice dynamics techniques become inaccurate at high temperature ͑above 40 K͒ due to the approximations inherent in the lattice dynamics framework. We apply the results to assess the validity of ͑i͒ the isotropic approximation in modeling thermal transport and ͑ii͒ the common assertion that low-frequency phonons dominate thermal transport. Lastly, we suggest approximations that can be made within the lattice dynamics framework that allow the thermal conductivity of Lennard-Jones argon to be estimated using two orders of magnitude less computing effort than the Green-Kubo or direct molecular dynamics methods.

The suitability of the Green-Kubo method for predicting the thermal conductivity of nanocomposites is assessed by studying model Lennard-Jones superlattices. Good agreement is found when comparing the predicted cross-plane thermal conductivities to independent predictions from the direct method. The link between the superlattice unit cell design and the thermal conductivity tensor is then explored. We find that complex, multilayered unit cell designs can reduce the cross-plane thermal conductivity by 17% compared to the minimum value predicted for superlattices with only two layers in the unit cell. These results suggest new directions that can be explored for reducing thermal conductivity, which is desirable in applications such as designing materials for thermoelectric energy conversion.

Molecular dynamics simulations are used to examine the effect of interfacial species mixing on the thermal conductivity of Stillinger-Weber Si/ Si 0.7 Ge 0.3 and Si/Ge superlattices at a temperature of 500 K. The thermal conductivity of Si/ Si 0.7 Ge 0.3 superlattices is predicted to not depend on the interfacial species mixing and to increase with increasing period length. This period length dependence is indicative of incoherent phonon transport and related to decreasing interface density. The thermal conductivity of Si/Ge superlattices is predicted to depend strongly on the interface quality. For Si/Ge superlattices with perfect interfaces, the predicted thermal conductivity decreases with increasing period length before reaching a constant value, a trend indicative of coherent phonon transport. When interfacial species mixing is added to the model, however, the thermal conductivity is predicted to increase with increasing period length, indicating incoherent phonon transport. These results suggest that the assumption of coherent phonon transport made in lattice dynamics-based models may not be justified.

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. The thermal conductivities of films and wires with micron and nanometer dimensions have been measured and predicted to be less than that of the corresponding bulk material. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] The reduced thermal conductivity makes it difficult to remove excess heat (e.g., generated in electronics) but can benefit thermoelectric energy conversion. This reduction is due to changes in the phonon density of states 4,6,8,13,17 and phonon-boundary scattering. The density of states effect is only important in very small nanostructures [e.g., suspended Stillinger-Weber (SW) silicon films thinner than 20 nm (Ref. 17)] and is not discussed here. Our focus is on the boundary scattering effect in nanostructures with bulk-like density of states.Modeling work at different levels of sophistication has attempted to predict the thermal conductivity reduction in films and wires. Flik and Tien 1 and Majumdar 2 proposed film models based on a single phonon group velocity and lifetime (i.e., the gray approximation). More detailed calculations that include quantum statistics and the mode dependence of the phonon properties have proven successful at predicting experimental data for silicon nanostructures with minimal fitting parameters. 8,10,16 Lattice dynamics calculations 17,18 and Monte Carlo-based methods 11 have also been used to elucidate the underlying phonon physics.We recently proposed a closed-from high-temperature model for the cross-plane thermal conductivity of a film and used it to assess size effects in molecular dynamics thermal conductivity predictions. 21 Here, we extend this model, which contains no fitting parameters, to the in-plane direction and to wires. The predictions are then compared to experimental data for silicon nanostructures. Our model does not seek to supplant more detailed calculations but to provide a straightforward method for predicting thermal conductivity reduction in nanostructures.The film and wire geometries are shown in Figs The summation is over all phonon modes with wave vector j and dispersion branch m, c ph is the mode volumetric specific heat, and v g,i (j, m) is the i component of the group velocity vector. The phonon transport is described using a set of mode-and system-size-dependent lifetimes, s(j, m, L or D), defined as the average time between successive scattering events.Converting the summation over wave vector in Eq.(1) to an integral in ...

To elucidate the relationship between a crystal's structure, its thermal conductivity, and its phonon dispersion characteristics, 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 novel 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 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.

The thermal resistance of semiconductor thin films is predicted using lattice dynamics ͑LD͒ calculations and molecular dynamics ͑MD͒ simulations. We consider Si and Ge films with thicknesses, L F , 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 structures͒. 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 L F Ͻ 2 nm, the thin film thermal resistance increases rapidly with increasing film thickness, a trend we attribute to changes in the allowed vibrational states in the film. These changes are found to affect the dependence of the phonon transmission coefficient on incidence angle