Critical angle for interfacial phonon scattering: Results from ab initio lattice dynamics calculations

Abstract

Thermal boundary resistance is a critical quantity that controls heat transfer at the nanoscale, and which is primarily related to interfacial phonon scattering. Here, we combine lattice dynamics calculations and inputs from first principles ab initio simulations to predict phonon transmission at Si/Ge interface as a function of both phonon frequency and phonon wavevector. This technique allows us to determine the overall thermal transmission coefficient as a function of the phonon scattering direction and frequency. Our results show that, the thermal energy transmission is highly anisotropic while thermal energy reflection is almost isotropic. In addition, we found the existence of a global critical angle of transmission beyond which almost no thermal energy is transmitted. This critical angle around 50• . is found to be almost independent on the interaction range between Si and Ge, the interfacial bonding strength, and the temperature above 30 K. We interpret these results by carrying out a spectral and angular analysis of phonon transmission coefficient and differential thermal boundary conductance.

Thermal conductivity of Bi2Se3 from bulk to thin films: Theory and experiment

“…The condition f a + f r + f t = 1 holds. In general these parameters may depend on phonon energy and its incidence angle; they can be computed using molecular dynamics techniques [26]. A special limit case is a very rough surface for which f a = 1.…”

Phonon transmission at Si/Ge and polytypic Ge interfaces using full-band mismatch based models

“…2 In order to model the Kapizta resistance [9] [10], advanced atomistic Ab Initio [14] and Molecular Dynamics methods [15] [16] [17] have been used. However, these advanced approaches require a large amount of computational time and resources.…”

Calculation of Kapitza Resistance with Kinetic Equation

“…We will call the system of Equation (2,3,5,6) with amplitudes (18) and the Debye model of the phonon spectrum and the constant relaxation times "kinetic DMM. "…”

“…Computer simulation of lattice dynamics at the interface is the most common approach to tackle the problems of Kapitza resistance theory described in the contemporary research manuscripts. [ 14 ] Such questions as an effect of anharmonic scattering [ 15 ] and lattice symmetry [ 16 ] on phonon‐transmission through an interface, accuracy of DMM assumptions, [ 17 ] a critical angle concept, [ 18 ] and influence of chemical bonds on phonon‐transmission coefficient [ 19 ] are investigated by computer modeling. These works significantly improve our understanding of the lattice dynamics at the interface; yet, questions about the form of the phonon distribution functions had not been previously considered.…”