Spectroscopic SHG and spectroscopic ellipsometry study of silicon nanocrystals embedded in SiO$_{2}$

The light-emitting silicon nanocrystals (Si NCs) embedded in silica matrix open up the possibility for silicon photonics. Optical spectroscopy can help elucidate unique, but poorly understood, bonding structures at the nano-interfaces that are responsible for the efficient photoluminescence. Here we present SHG amplitude and phase spectra of a 1$\mu$m-thick layer of 3 nm $\pm$ 30{\%} diameter Si NCs prepared by implanting Si ions into SiO$_{2}$ then annealing in Ar or H$_{2}$/Ar mixture at 1100$^{\circ}$C using cross-polarized two-beam second-harmonic generation (XP2-SHG). We also measure the linear dielectric function of the NC layer using spectroscopic ellipsometry (SE). The linear spectra show a significant reduction in the dielectric functions in Si NCs compared to bulk silicon. The pronounced E$_{2}$ critical point transition peak is somewhat blueshifted to the bulk E$_{2}$ peak while E$_{1}$ transition is strongly suppressed. The SHG spectra are only slightly perturbed by annealing in hydrogen. A fit of the SHG amplitude and phase spectra using model resonance functions yields resonances different from the linear spectra. A model with an intermediate transition layer of variable composition between the Si NC core and the amorphous SiO$_{2}$ matrix is introduced to explain the linear and SHG spectra.