Phonon properties calculated with lattice dynamics using 2D models, rigid molecule models, and neural network potentials

In design of electronic devices, one of the key factors is their thermal management and thus it is important to know their thermal properties. Fortunately, it is becoming increasingly easier to obtain ab-initio thermal properties by obtaining atomic force interactions with density functional theory (DFT) and combining it with the solution to the Boltzmann transport equation (BTE) in anharmonic lattice dynamics (ALD). However, the usage of these methods can have limitations due to either their underlying assumptions or computational costs that can limit the number of materials studied or the ways in which they can be analyzed. In this work, methods of expanding the ALD technique are explored.

The thin film systems were studied using a slab method, in which the system was treated entirely as two-dimensional (2D), and then as a three-dimensional (3D) system with the cross-plane wave-vectors restricted to the possible values.A mapping algorithm was developed by examining the eigenvectors of the 2D modes and finding the periodicity within the unit cell. This was tested on films of Lennard-Jones (LJ) argon as well as graphene/graphite.

It was found that there is almost a one-to-one match between the 2D and 3D modes in the graphene/graphite system, but a mismatch between the modes in the LJ argon system. This was attributed to the fact that argon has to transition from an isotropic to an anisotropic system, while graphene/graphite remains anisotropic from the start. In addition, it was found that there are surface phonon modes present that cannot be mapped to any 3D modes. The thermal properties were then studied for the LJ argon system and a silicon system. It was found that while the conductivity usually decreases with decreasing thickness due to boundary scattering, there can be a sudden upturn at very low thicknesses. This was attributed to the change of density of states in these low thicknesses and an increasing contribution to conductivity from the low-frequency phonon modes.

A rigid body model was then applied to the ALD calculation in order to remove intra-molecular vibrations.This was tested on the LJ argon system with additional pair molecules designated, and then bench-marked against the preestablished method of Green-Kubo technique in molecular dynamics. The benchmark results were found to be reasonably close to one another, with differences found being explainable as differences between the two techniques. Then the stiff bond was represented using an additional harmonic interaction of varying stiffness to observe a convergence to the rigid system. An intermediate system was further studied and found to have a higher conductivity to due to a larger number of high group velocity modes.

A neural network potential was also developed for usage in lattice dynamics.The potential was trained on Tersoff silicon structures, with 28 different random seeds. It was found that the harmonic properties such as frequencies could be calculated without a problem. For anharmonic properties, however, it was found that while it is possible to obtain accurate average values, there can be significant variance between the different random seeds. This can be especially seen in the third-order force constants where force constants with negligible values will instead have a significant magnitude, and vice-versa. These challenges must be addressed before neural network potentials can be widely adopted as a method for ALD.