Mode-resolved phonon transmittance using lattice dynamics: Robust algorithm and statistical characteristics

Abstract

Lattice dynamics (LD) enables the calculation of mode-resolved transmittance of phonons passing through an interface, which is essential for understanding and controlling the thermal boundary conductance (TBC). However, the original LD method may yield unphysical transmittance over 100% due to the absence of the constraint of energy conservation. Here, we present a robust LD algorithm that utilizes linear algebra transformations and projection gradient descent iterations to ensure energy conservation. Our approach demonstrates consistency with the original LD method on the atomically smooth Si/Ge interface and exhibits robustness on rough Si/Ge interfaces. The evanescent modes and localized effects at the interface are revealed. In addition, bottom-up analysis of the phonon transmittance shows that the anisotropy in the azimuth angle can be ignored, while the dependency on the frequency and polar angle can be decoupled. The decoupled expression reproduces the TBC precisely. This work provides comprehensive insights into the mode-resolved phonon transmittance across interfaces and paves the way for further research into the mechanism of TBC and its relation to atomic structures.