Exact scattering cross section for lattice-defect scattering of phonons using the atomistic Green's function method

TL;DR

This paper presents a numerically exact atomistic Green's function method to compute phonon scattering cross sections caused by lattice defects, enhancing the understanding and control of phonon scattering in thermoelectric materials.

Contribution

The paper introduces an atomistic Green's function approach for exact calculation of mode-resolved phonon scattering cross sections by lattice defects, applicable to complex nanostructures.

Findings

Accurately computes phonon scattering cross sections for isotopic defects.

Demonstrates the method on carbon nanotubes with encapsulated molecules.

Provides a tool for precise phonon scattering analysis in thermoelectric design.

Abstract

The use of structurally complex lattice defects, such as functional groups, embedded nanoparticles, and nanopillars, to generate phonon scattering is a popular approach in phonon engineering for thermoelectric applications. However, the theoretical treatment of this scattering phenomenon remains a formidable challenge, especially with regard to the determination of the scattering cross sections and rates associated with such lattice defects. Using the extended atomistic Green's function (AGF) method, we describe how the numerically exact mode-resolved scattering cross section $\sigma $ can be computed for a phonon scattered by a single lattice defect. We illustrate the generality and utility of the AGF-based treatment with two examples. In the first example, we treat the isotopic scattering of phonons in a harmonic chain of atoms . In the second example, we treat the more complex problem of phonon scattering in a carbon nanotube (CNT) containing an encapsulated C60 molecule which acts as a scatterer of the CNT phonons. The application of this method can enable a more precise characterization of lattice-defect scattering and result in a more controlled use of nanostructuring and lattice defects in phonon engineering for thermoelectric applications.