Tight-binding calculations of the optical properties of Si nanocrystals in a SiO₂ matrix

We develop an empirical tight binding approach for the modeling of the electronic states and optical properties of Si nanocrystals embedded in a SiO2 matrix. To simulate the wide band gap SiO2 matrix we use the virtual crystal approximation. The tight-binding parameters of the material with the diamond crystal lattice are fitted to the band structure of β-cristobalite. This model of the SiO2 matrix allows us to reproduce the band structure of real Si nanocrystals embedded in a SiO2 matrix. In this model, we compute the absorption spectra of the system. The calculations are in an excellent agreement with experimental data. We find that an important part of the high-energy absorption is defined by the spatially indirect, but direct in k-space transitions between holes inside the nanocrystal and electrons in the matrix.