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

TL;DR

This paper introduces an eigenspectrum-based formulation of the atomistic Green's function method that decomposes phonon transmission into mode-specific contributions, aiding microscopic understanding of phonon transport at interfaces.

Contribution

The novel eigenspectrum-based AGF (EAGF) method directly links phonon modes to transmission, enabling detailed analysis of phonon scattering and mode conversion at interfaces.

Findings

Atomic intermixing increases phonon mode conversion.

Intermixing enhances thermal interface conductance.

EAGF helps identify dominant phonon modes in transport.

Abstract

While the atomistic Green's function (AGF) method has the potential to compute spectrally resolved phonon transport across interfaces, most prior formulations of the AGF method provide only the total phonon transmission function that includes contributions from all phonon branches or channels. In this work, we present a formulation of the conventional AGF technique in terms of phonon eigenspectra that provides a natural decomposition of the total transmission function into contributions from various phonon modes. The method involves the use of Dyson and Lippmann-Schwinger equations to determine surface Green's functions from the phonon eigenspectrum of the bulk, and establishes a direct connection between the transmission function and the bulk phonon spectra of the materials forming the interface. We elucidate our formulation of the AGF technique through its application to a microscopic picture of phonon mode conversion at Si-Ge interfaces with atomic intermixing. Intermixing of atoms near the interface is shown to increase the phase space available for phonon mode conversion and to enhance thermal interface conductance at moderate levels of atomic mixing. The eigenspectrum-based AGF (EAGF) method should be useful in determination of microscopic mechanisms of phonon scattering and identification of the specific modes that dominate thermal transport across an interface.