Formation of fluorine-containing defects and nanocrystals in SiO$_2$ upon implantation with fluorine, silicon, and germanium ions: Numerical simulation and photoluminescence spectroscopy

The incorporation of fluorine atoms into the silicon dioxide lattice upon F$^+$ ion implantation and the formation of silicon (germanium) nanocrystals in SiO$_2$ upon Si$^+$ (Ge$^+$) ion implantation have been numerically simulated. The calculations for F have been performed by the density functional theory (DFT) method; the calculations for Si and Ge have been carried out by combining the DFT (in the cluster approximation) and Monte Carlo methods. The energy gain of the fluorine atom attachment to one of silicon atoms with the formation of a nonbridging oxygen hole center (NBOHC) and an energy level appearing in the band gap has been demonstrated. In the case of ion implantation, the simulation at a dissolved Si (Ge) atom concentration of $\sim$ 2 at% has revealed the formation of nanocrystals (NCs) with an average size of $\sim$ 1 nm.