Lattice dynamics of silicon nanostructures

The lattice dynamical results of silicon nanostructures with all three different degrees of confinement (nanoslabs, nanowires, nanodots) are systematically analysed and presented using an adiabatic bond charge model. In the direction of propagation of these structures, it is found that the phonon branches change from flat, for the smallest nanostructures, to dispersive as the nanostructure size increases. It is also noted that in the direction of confinement all but the acoustic branches are generally flat, with very little dispersion. The trends in the variations of the lowest and highest confined modes at the Brillouin zone centre with nanostructure size are investigated. In particular, analytic expressions for the size variation of the highest mode with the dimensionality of the nanostructures have been presented. Also, an analytic fit has been presented for the size variation of the lowest non-zero acoustic mode with structure size. Finally, numerical calculations based upon Fermi's Golden Rule formula of the dependence of the lifetime of the lowest confined mode on nanostructure size and temperature have also been obtained and discussed.