Modification of the lattice thermal conductivity in semiconductor rectangular nanowires

A model for lattice thermal conductivity in a semiconductor nanowire with a rectangular cross section is investigated. It is based on solving the equations of phonon radiative transfer taking into account interface scattering and modification of the acoustic phonon dispersion. From the numerical calculations, we predict a decrease by an order of magnitude of the lattice thermal conductivity of a 10-nm-thick and 20-nm-wide rectangular nanowire. The interface scattering and phonon confinement play important roles in the reduction of lattice thermal conductivity. The nanowire lattice thermal conductivity is found to decrease with increasing temperature at moderate and high temperatures. It is shown that the phonon confinement becomes more important than interface scattering in the highly specular scattering case. The effect of interface roughness scattering and phonon confinement on the lattice thermal conductance in a rectangular wire at low temperature is also examined. We calculate the contribution to the lattice thermal conductance due to the longitudinal mode for the catenoid contact. It is found that phonon confinement leads to a significant decrease of the lattice thermal conductance at sufficiently low temperatures $\text{(T<0.1}\mathrm{K}\mathrm{).}$