Improved model of optical phonon confinement in silicon nanocrystals

We develop a model for calculating the Raman scattering spectra from phonons confined in for silicon nanocrystals, which is based on the familiar approach taking into account the uncertainty in the quasi-momentum of phonons localized in the nanocrystals. The model is considerably improved by taking into account dispersion of phonons not only in the magnitude of the quasi-momentum, but also in its direction. A significant refinement of the model is also due to the fact that phonon dispersion is calculated using the widely approved Keating model instead of being approximated by empirical expressions as was done in earlier approaches. The calculations based on this model make it possible to determine the sizes of silicon nanocrystals more precisely from analysis of the experimental Raman spectra.