The lattice thermal conductivity of a semiconductor nanowire

Mei-Jiau Huang, Wen-Yen Chong, Tai-Ming Chang
2006 Journal of Applied Physics  
It has been found experimentally as well as theoretically that the lattice thermal conductivity can be largely reduced by the size confinement effect. The significant boundary scattering effect is one of the dominant factors. In most existing lattice thermal conductivity models, an empirical relation is used for this scattering rate. An unconfined or confined phonon distribution obtained based on the phonon Boltzmann equation and the relaxation time approximation is then employed to calculate
more » ... e lattice thermal conductivity. In this work, we first attempt to derive an analytical form of the boundary scattering rate for phonon conduction in a semiconductor nanowire and then claim two reasonable ways to take it into account correctly. Consistent mathematical models in the sense that the effects of the size confinement on ͑i͒ the phonon dispersion relation, ͑ii͒ the phonon distribution, ͑iii͒ the phonon group and phase velocities, and ͑iv͒ the Debye temperature are finally proposed.
doi:10.1063/1.2203721 fatcat:cwj3sfh4krcl3f2q6qq4jgzsty