Modeling nanostructure lattice thermal conductivity The dispersion relation role

We present an analytical model for the lattice thermal conductivity of semiconductor nanostructures, based on solving the Boltzmann transport equation in the relaxation time approximation. The improved model is then used to predict the lattice thermal conductivity of three samples of silicon nanowire (Si NW) with diameters 50, 98, and 115 nm. Derived formulas of the lattice thermal conductivity and correction term are presented, which differs from that of Callaway in that it considers the acoustic phonon dispersion relation. Combining the scattering relaxation rate for phonon-phonon, mass difference and boundary was carried out in the analysis of the experimental data and also considering the separate contributions for transverse and longitudinal phonons. The present theoretical model of lattice thermal conductivity agrees well with the available experimental data of Si NW over a wide range of temperature.