  A new real space quantum mechanical approach with local field effects
included is applied to the calculation of the optical properties of silicon
nanocrystals. Silicon ellipsoids are studied and the role of surface
polarization is discussed in details. In particular, surface polarization is
shown to be responsible for a strong optical anisotropy in silicon ellipsoids,
much more pronounced with respect to the case in which only quantum confinement
effects are considered. The static dielectric constant and the absorption
spectra are calculated, showing that the perpendicular and parallel components
have a very different dependence on the ellipsoid aspect ratio. Then, a
comparison with the classical dielectric model is performed, showing that the
model only works for large and regular structures, but it fails for thin
elongated ellipsoids.
