Efficient approach for modeling phonon transmission probability in nanoscale interfacial thermal transport

Zhun-Yong Ong and Gang Zhang

Phys. Rev. B 91, 174302 – Published 6 May 2015; Erratum Phys. Rev. B 93, 019901 (2016)

Abstract

The Kapitza or interfacial thermal resistance at the boundary of two different insulating solids depends on the transmission of phonons across the interface and the phonon dispersion of either material. We extend the existing atomistic Green's function (AGF) method to compute the probability for individual phonon modes to be transmitted across the interface. The extended method is based on the concept of the Bloch matrix and allows us to determine the wavelength and polarization dependence of the phonon transmission as well as to analyze efficiently the contribution of individual acoustic and optical phonon modes to interfacial thermal transport. The relationship between the phonon transmission probability and dispersion is explicitly established. A detailed description of the method is given and key formulas are provided. To illustrate the role of the phonon dispersion in interfacial thermal conduction, we apply the method to study phonon transmission and thermal transport at the armchair interface between monolayer graphene and hexagonal boron nitride. We find that the phonon transmission probability is high for longitudinal (LA) and flexural (ZA) acoustic phonons at normal and oblique incidence to the interface. At room temperature, the dominant contribution to interfacial thermal transport comes from the transverse-polarized phonons in graphene (45.5%) and longitudinal-polarized phonons in boron nitride (47.4%).