  Spherical shaped Si quantum dots (QDs) embedded into the SiO2 substrate are
considered in the single sub-band effective mass approach. Nonparabolicity of
the Si conduction band is described by the energy dependence of electron
effective mass. Calculations of low-lying single electron and hole energy
levels are performed. For small sizes QD (diameter D<6nm) there is a strong
confinement regime when the number of energy levels is restricted to several
levels. The first order of the perturbation theory is used to calculate neutral
exciton recombination energy taking into account the Coulomb force between
electron and heavy hole. The PL exciton data are reproduced well by our model
calculations. For weak confinement regime (size D>10 nm), when the number of
confinement levels is limited by several hundred, we considered the statistical
properties of the electron confinement. Distribution function for the electron
energy levels is calculated and results are discussed.
