  We study the effect of confinement on the phonon properties of ultra-narrow
silicon nanowires of side sizes of 1-10nm . We use the modified valence force
field method to compute the phononic dispersion, and extract the density of
states, the transmission function, the sound velocity, the ballistic thermal
conductance and boundary scattering-limited diffusive thermal conductivity. We
find that the phononic dispersion and the ballistic thermal conductance are
functions of the geometrical features of the structures, i.e. the transport
orientation and confinement dimension. The phonon group velocity and thermal
conductance can vary by a factor of two depending on the geometrical features
of the channel. The <110> nanowire has the highest group velocity and thermal
conductance, whereas the <111> the lowest. The <111> channel is thus the most
suitable orientation for thermoelectric devices based on Si nanowires since it
also has a large power factor. Our findings could be useful in the thermal
transport design of silicon-based devices for thermoelectric and thermal
management applications.
