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While the atomistic Green's function (AGF) method has the potential tocompute spectrally resolved phonon transport across interfaces, most priorformulations of the AGF method provide only the total phonon transmissionfunction that includes contributions from all phonon branches or channels. Inthis work, we present a formulation of the conventional AGF technique in termsof phonon eigenspectra that provides a natural decomposition of the totaltransmission function into contributions from various phonon modes. The methodinvolves the use of Dyson and Lippmann-Schwinger equations to determine surfaceGreen's functions from the phonon eigenspectrum of the bulk, and establishes adirect connection between the transmission function and the bulk phonon spectraof the materials forming the interface. We elucidate our formulation of the AGFtechnique through its application to a microscopic picture of phonon modeconversion at Si-Ge interfaces with atomic intermixing. Intermixing of atomsnear the interface is shown to increase the phase space available for phononmode conversion and to enhance thermal interface conductance at moderate levelsof atomic mixing. The eigenspectrum-based AGF (EAGF) method should be useful indetermination of microscopic mechanisms of phonon scattering and identificationof the specific modes that dominate thermal transport across an interface.

Phonon Eigenspectrum-Based Formulation of the Atomistic Green's Function Method