Thermal conductivity of semiconductor nanowires from micro to nano length scales

We study the influence of phonon boundary scattering on the transport of thermal energy in semiconductor nanowires from micro to nano length scales. We use a kinetic theory model based on the Boltzmann transport equation that accurately calculates the reduction of the phonon mean free paths by considering their directional dependence and the fundamental statistical definition of the mean free path. As a result, our model does not use phenomenological formulas to account for the reduction of the phonon mean free paths due to boundary scattering. The transport of thermal energy is also fully divided into that carried by different polarizations by separating phonon group velocities and relaxation times for transverse and longitudinal phonons. We study the correctness of using frequency independent versus frequency dependent models for describing the specularity of the nanowire boundary. We also examine the validity of the assumption that phonons in the semiconductor nanowire maintain their bulk phonon dispersion relations and that modifications to the dispersion relations due to phonon confinement effects can be neglected. The thermal conductivities of silicon nanowires are calculated for different length scales and temperatures and good agreement is obtained with experiments. The theoretical results in this paper can be used to understand and quantitatively predict heat transport in nanowires, which is critical for increasing the efficiency of thermoelectric and electronic devices.