The Atomistic Green's Function Method: An Efficient Simulation Approach for Nanoscale Phonon Transport

W. Zhang, Birck Nanotechnology Center and School of Mechnical Engineering, Purdue University
Timothy Fisher, Birck Nanotechnology Center and School of Mechanical Engineering, Purdue University
N. Mingo, NASA-Ames Center for Nanotechnology

Abstract

This article presents a general formulation of an atomistic Green’s function (AGF) method. The atomistic Green’s function approach combines atomic-scale fidelity with asymptotic treatment of large-scale (bulk) features, such that the method is particularly well suited to address an emerging class of multiscale transport problems. A detailed mathematical derivation of the phonon transmission functionis provided in terms of Green’s functions and, using the transmission function, the heat flux integral is written in Landauer form. Within this theoretical framework, the required inputs t ocalculate heat flux are equilibrium atomic locations and an appropriate interatomic potential. Relevant algorithmic and implementation details are discussed. Several examples including a homogeneous atomic chain and two heterogeneous atomic chains are included to illustrate thea pplications of this methodology.