Comparison of Scattering Rates and Thermal Conductivity in Diamond Using Dispersion Curve Data

Abstract

The understanding of the mechanism of thermal energy transfer in thin films ranging in thicknesses from micro-scale to nano-scale is becoming very important. Thin films must be modeled at the atomic level and this entails treating the heat transfer as vibrations in a crystal lattice. The concept of phonons can be used to model the vibrational energy of the crystal. Phonon scattering rates and thermal conductivity are investigated for Cubic C (diamond). Boundary scattering, Umklapp processes, and Normal processes are the mechanisms considered for heat flow resistance. The normal processes are included due to there indirect effect on resistance (through phonon redistribution). Three symmetry directions [001], [110], [111], and three polarizations for each direction in the first Brillouin zone are considered. The main purpose of the paper is to study the effect of the curvature of the phonon dispersion curves when computing the phonon scattering rates and thermal conductivity. A comparison of thermal conductivity for each polarization and symmetry direction is made between a continuum model, a linear curve fit and a polynomial curve fit of dispersion data. A comparison is also made between the scattering rates for each polarization, symmetry direction as well as the group velocity for each.