Optical index profile of nonuniform depth-distributed silicon nanocrystals within $SiO2$

Optical properties of silicon nanocrystals (Si-ncs) prepared by silicon implantation into silicon oxide have been investigated by photoluminescence measurements and spectroscopic ellipsometry. The dielectric function associated with Si-nc uniformly and nonuniformly depth distributed has been determined by means of the Tauc–Lorentz (TL) model, using the Bruggemann effective medium approximation. The evolution of the Si-nc sublayer dielectric response as a function of the ion fluence has been established for volume fractions of Si excess varying between 9.1% and 50.4%. Comparison between the depth profile of optical indices determined by ellipsometry and TRIM calculations shows that for implanted Si volume fraction lower than 30%, the center and the width of the optical index profile agree with the spatial distribution of the implanted Si when both the swelling and the ion sputtering effects are taken into account. This is also valid in systems having two separate Si-nc sublayers, where the geometric characterization of the optical index variations has been computed from a data extrapolation. For a volume fraction of 50.4%, where the ion implantation performed at high fluence can activate the oxygen depletion from the material surface, the spatial distribution of the optical refractive index is deeper and narrower than the Si excess profile.