Predicting Phonon Thermal Conductance at Atomic Junctions: Nonequilibrium Green’s Function Approach Compared to Semiclassical Methods

Abstract

Phonon thermal conductance, λ, in nanostructures is a thermophysical property that is becoming increasingly difficult to accurately predict, especially as thermal management at interfaces of different materials is becoming a major engineering concern. The most widely used models for λ prediction are based on the Boltzmann Transport Equation (BTE), and the when junctions between two different materials enter the picture, the most common BTE-based models to predict the interfacial conductance are the Acoustic Mismatch Model (AMM) and Diffuse Mismatch Model (DMM). The models are developed with equilibrium assumptions. However, thermal transport is clearly nonequilibrium phenomenon. Recently, the Nonequilibrium Green’s Function (NEGF) formalism has been extended to phonon transport. The NEGF formalism is rooted in nonequilibrium quantum transport theory, making it ideal to study energy transfer applications, especially in nanosystems where the concept of thermal equilibrium breaks down due to the small dimensions of the transport regions. The purpose of this paper is to derive, from first principles, the NEGF formalism of thermal conductivity, and compare the assumptions of this formalism to the semi-classical Boltzmann models. The NEGF formalism is applied to a 1D atomic chain with varying masses and compared to similar predictions from BTE-based models.