Optical second-harmonic interferometric spectroscopy of Si ( 111 ) − SiO 2 interface in the vicinity of E 2 critical points

The direct electron transitions at the Si( 111)-SiO 2 interface are studied by combined second-harmonic (SH) intensity and phase spectroscopy with the SH photon energy range from 3.5 eV to 5 eV. A strong resonant behaviorof the quadratic optical response is observed in the vicinity of the E 2 (X,Σ) critical points (CP's) of the silicon band structure. Good representation of the experimental SH intensity and phase spectra is provided by a line shape of the quadratic susceptibility calculated both with excitonic and two-dimensional (2D) types of E 2 (X,Σ) CP's. The line-shape dependence of resonance energies, namely, repulsion of nearby E 2 (X,Σ) resonances in the case of a 2D CP in comparison with the excitonic ones, is observed.