Size Effects on Nanowire Phonon Thermal Conductivity: a Numerical Investigation Using the Boltzmann Equation

Analytical solution of the Boltzmann transport equation for phonon transport in Bi$\text{}_{0.95}$Sb$\text{}_{0.05}$ nanowire is obtained. Thermal conductivity was calculated from the analytical solution of the Boltzmann transport equation. We calculate the lattice thermal conductivity of Bi$\text{}_{0.95}$Sb$\text{}_{0.05}$ nanowire as a function of temperature for different wire thicknesses. The results show that thermal conductivity of nanowire can be significantly smaller than the bulk thermal conductivity. We show that low thermal conductivity Bi$\text{}_{0.95}$Sb$\text{}_{0.05}$ nanowire for thermoelectric applications would have a small diameter.