Modeling of Polarization-Specific Phonon Transmission Functions Through Interfaces

The atomistic Green’s function (AGF) method has been used successfully in previous research to predict the transmission function for energy carriers at interfaces. In this work, the method is extended to capture the transmission function for each phonon polarization. The inputs for this extension are the same as for the original AGF method. Furthermore, this method does not require any complex manipulation of harmonic matrices and can be applied to different materials and geometries. The eigenvectors and eigenvalues of the overall density of states matrices are manipulated to yield the density of states matrix for each polarization. A decomposed self-energy is calculated from the density of states matrix for each polarization and used to calculate the transmission function for a particular phonon branch. In a pure bulk material such as silicon, each transmission function exhibits a frequency-independent value of unity, which matches the theoretical prediction. In heterogeneous bulk materials, the transmission function is reduced significantly due to the contact of dissimilar materials. The summation of the decomposed transmission functions is shown to reproduce the result from a direct AGF calculation in which all branches were treated together.