Energy Transmission across Acoustically Mismatched Solid Junctions

TL;DR

This paper develops a lattice dynamic approach to analyze energy transmission across solid junctions, revealing mode-dependent effects and calculating thermal conductance for nanotube and Si-Ge interfaces.

Contribution

It introduces a scattering boundary method for calculating phonon transmission and provides detailed analysis of energy flux and conductance in mismatched solid junctions.

Findings

Mode-dependent phonon transmission in nanotube junctions.

Critical incident angle of 42 degrees for Si-Ge interface waves.

Kapitza conductance scales as T^{2.87} at low temperatures.

Abstract

We derive expression for energy flux in terms of lattice normal mode coordinates. Energy transmission across solid junctions from lattice dynamic point of view is given and its relation with atomic masses, lattice constants, and group velocities is clarified. A scattering boundary method (SBM) is proposed for calculating the amplitude transmission across solid junctions. The phonon transmission coefficients and thermal conductance are calculated for two kinds of acoustically mismatched junctions: different chirality nanotubes (11,0) to (8,0), and Si-Ge interface structure. Our calculation shows a mode-dependent transmission in nanotube junction due to the high symmetry vibrating motions for nanotube atoms, indicating its possible important role in nanotube mixture thermal conductance. Energy transmission and Kapitza conductance across the Si-Ge interface [001] are calculated for the Si-Ge diamond-type structure. It is shown that the energy transmission across the Si-Ge interface depends on the incident angle and on the interface mode conversion. A critical incident angle about 42 degrees numerically found for waves incident from Ge to Si. Our numerical result of the Kapitza conductance at temperature T=200K is G_K=4.6x10^8 W/(Km^2) We find numerically scaling law G_K proportional to T^{2.87} for [001] interface at low temperature.