Quantifying Modal Thermal Conductivity in Amorphous Silicon
While there are several methods, e.g., anharmonic lattice dynamics and normal mode decomposition, to compute the modal lattice vibrational information in perfect crystals, the modal information of vibrations, e.g., vibrational relaxation time, group velocity and mean free path, in amorphous solids are still challenge to be captured. By systematically analyzing the normal mode decomposition and structure factor methods, we conclude that the vibrational dispersion can be calculated by applying effective wave vectors in the structure factor method, while the vibrational relaxation time calculated by the normal mode decomposition method is questionable since the group velocity cannot be defined on the Gamma point. We also show that the anharmonicity caused by the system temperature has little effect on the relaxation times of the propagating modes in amorphous materials, and therefore, the corresponding modal and total thermal conductivity is temperature independent when all the vibrations are assumed to be excited. The non-propagating modes, i.e., diffusons, conduct heat via thermal coupling between different vibrational modes, and can be calculated by harmonic lattice dynamics using Allen-Feldman theory. As a result, the thermal conductivity contributed from diffusons is also temperature independent when all the vibrational modes are activated which is the situation in molecular dynamics simulations. The total thermal conductivity concerning both propagons (50%) and diffusons (50%) agree quite well with the results computed using Green-Kubo equilibrium molecular dynamics. By correcting the excitation state of the vibrations in amorphous solids, the thermal conductivity calculated by the structure factor method and Allen-Feldman theory can fully capture the experimentally measured temperature-dependent thermal conductivity.