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We study the effect of confinement on the phonon properties of ultra-narrowsilicon nanowires of side sizes of 1-10nm . We use the modified valence forcefield method to compute the phononic dispersion, and extract the density ofstates, the transmission function, the sound velocity, the ballistic thermalconductance and boundary scattering-limited diffusive thermal conductivity. Wefind that the phononic dispersion and the ballistic thermal conductance arefunctions of the geometrical features of the structures, i.e. the transportorientation and confinement dimension. The phonon group velocity and thermalconductance can vary by a factor of two depending on the geometrical featuresof the channel. The <110> nanowire has the highest group velocity and thermalconductance, whereas the <111> the lowest. The <111> channel is thus the mostsuitable orientation for thermoelectric devices based on Si nanowires since italso has a large power factor. Our findings could be useful in the thermaltransport design of silicon-based devices for thermoelectric and thermalmanagement applications.

Calculation of Confined Phonon Spectrum in Narrow Silicon Nanowires using the Valence Force Field Method