Use of Atomistic Phonon Dispersion and Boltzmann Transport Formalism to Study the Thermal Conductivity of Narrow Si Nanowires

We study the thermal properties of ultra-narrow silicon nanowires (NW) with diameters from 3 nm to 12 nm. We use the modified valence-force-field method for computation of phononic dispersion and the Boltzmann transport equation for calculation of phonon transport. Phonon dispersion in ultra-narrow 1D structures differs from dispersion in the bulk and dispersion in thicker NWs, which leads to different thermal properties. We show that as the diameter of the NW is reduced the density of long-wavelength phonons per cross section area increases, which increases their relative importance in carrying heat compared with the rest of the phonon spectrum. This effect, together with the fact that low-frequency, low-wavevector phonons are affected less by scattering and have longer mean-free-paths than phonons in the rest of the spectrum, leads to a counter-intuitive increase in thermal conductivity as the diameter is reduced to the sub-ten-nanometers range. This behavior is retained in the presence of moderate boundary scattering.