Lattice thermal conductivity in a silicon nanowire with square cross section

We present a theoretical model of lattice thermal conductivity in a silicon nanowire with square cross section. This model takes into account the modifications of the acoustic phonon dispersion and boundary scattering on the side walls. A good approximation of exact lattice thermal conductivity is obtained by the yielded precise phonon dispersion relations under the xyz algorithm of Nishiguchi et al. [J. Phys.: Condens. Matter 9, 5751 (1997)] and the inclusion of three scattering events on the side walls from the phonon Boltzmann transport equation. Comparison is also made with the thermal conductivity of a cylindrical nanowire.