Non-metallic crystalline materials conduct heat by the transport of quantized atomic lattice vibrations called phonons. Thermal conductivity depends on how far phonons travel between scattering events-their mean free paths. Due to the breadth of the phonon mean free path spectrum, nanostructuring materials can reduce thermal conductivity from bulk by scattering long mean free path phonons, whereas short mean free path phonons are unaffected. Here we use a breakdown in diffusive phonon transport generated by high-frequency surface temperature modulation to identify the mean free path-dependent contributions of phonons to thermal conductivity in crystalline and amorphous silicon. Our measurements probe a broad range of mean free paths in crystalline silicon spanning 0.3-8.0 mm at a temperature of 311 K and show that 40±5% of its thermal conductivity comes from phonons with mean free path 41 mm. In a 500 nm thick amorphous silicon film, despite atomic disorder, we identify propagating phonon-like modes that contribute 435±7% to thermal conductivity at a temperature of 306 K.

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.

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.