Atomistic S-matrix method for numerical simulation of phonon reflection, transmission, and boundary scattering

The control of phonon scattering by interfaces is critical to the manipulation of heat conduction in composite materials and semiconducting nanostructures. However, one of the factors limiting our understanding of elastic phonon scattering is the lack of a computationally efficient approach for describing the phenomenon in a manner that accounts for the atomistic configuration of the interface and the exact bulk phonon dispersion. Building on the atomistic Green's function (AGF) technique for ballistic phonon transport, we formulate an atomistic S-matrix method that treats bulk phonon modes as the scattering channels and can determine the numerically exact scattering amplitudes for individual two-phonon processes, enabling a highly detailed analysis of the phonon transmission and reflection spectrum as well as the directional dependence of the phonon scattering specularity. Explicit formulas for the individual phonon reflection, absorption, and transmission coefficients are given in our formulation. This AGF-based S-matrix approach is illustrated through the investigation of (1) phonon scattering at the junction between two isotopically different but structurally identical carbon nanotubes, and (2) phonon boundary scattering at the zigzag and armchair edges in graphene. In particular, we uncover the role of edge chirality on phonon scattering specularity and explain why specularity is reduced for the ideal armchair edge. The application of the method can shed new light on the relationship between phonon scattering and the atomistic structure of interfaces.