Electronic structure and optical properties of silicon crystallites: Application to porous silicon

We have calculated the electronic structure of spherical silicon crystallites containing up to 2058 Si atoms. We predict a variation of the optical band gap with respect to the size of the crystallites in very good agreement with available experimental results. We also calculate the electron-hole recombination time which is of the order of 10−4–10−6 s for crystallites with diameters of 2.0–3.0 nm. We conclude that small silicon crystallites can have interesting optical properties in the visible range. These results are applied to porous silicon for which we confirm that a possible origin of the luminescence is the quantum confinement.