Lattice dynamics of ultrasmall silicon nanostructures

A systematic study of the lattice dynamics of ultrasmall silicon nanostructures (nanoslabs, nanowires, and nanodots) is presented from the application of an adiabatic bond charge model. Characteristic features and trends unique to these structures are examined thoroughly. The smallest nanostructures are found to be characterized by the novel feature of gaps in the density of phonon states. Such gaps rapidly vanish with decreasing level of confinement of states as the size of the nanostructures increases. The results obtained for the highest confined mode for the three types of nanostructures have been fitted to analytic expressions following an extended Jusserand-type formulation. An expression has also been obtained for the size variation of the lowest nonzero zone-center mode. These expressions help explain and lend support to recently reported Raman scattering measurements. The present theoretical predictions for the variation of these modes will prove useful in accurate experimental determination of the confining size of the nanostructures.