  Engineering of the cross-section shape and size of ultra-scaled Si nanowires
(SiNWs) provides an attractive way for tuning their structural properties. The
acoustic and optical phonon shifts of the free-standing circular, hexagonal,
square and triangular SiNWs are calculated using a Modified Valence Force Field
(MVFF) model. The acoustic phonon blue shift (acoustic hardening) and the
optical phonon red shift (optical softening) show a strong dependence on the
cross-section shape and size of the SiNWs. The triangular SiNWs have the least
structural symmetry as revealed by the splitting of the degenerate flexural
phonon modes and The show the minimum acoustic hardening and the maximum
optical hardening. The acoustic hardening, in all SiNWs, is attributed to the
decreasing difference in the vibrational energy distribution between the inner
and the surface atoms with decreasing cross-section size. The optical softening
is attributed to the reduced phonon group velocity and the localization of the
vibrational energy density on the inner atoms. While the acoustic phonon shift
shows a strong wire orientation dependence, the optical phonon softening is
independent of wire orientation.
