  The mechanism of DC-Electric-Field-Induced Second-Harmonic (EFISH) generation
at weakly nonlinear buried Si(001)-SiO$_2$ interfaces is studied experimentally
in planar Si(001)-SiO$_2$-Cr MOS structures by optical second-harmonic
generation (SHG) spectroscopy with a tunable Ti:sapphire femtosecond laser. The
spectral dependence of the EFISH contribution near the direct two-photon $E_1$
transition of silicon is extracted. A systematic phenomenological model of the
EFISH phenomenon, including a detailed description of the space charge region
(SCR) at the semiconductor-dielectric interface in accumulation, depletion, and
inversion regimes, has been developed. The influence of surface quantization
effects, interface states, charge traps in the oxide layer, doping
concentration and oxide thickness on nonlocal screening of the DC-electric
field and on breaking of inversion symmetry in the SCR is considered. The model
describes EFISH generation in the SCR using a Green function formalism which
takes into account all retardation and absorption effects of the fundamental
and second harmonic (SH) waves, optical interference between field-dependent
and field-independent contributions to the SH field and multiple reflection
interference in the SiO$_2$ layer. Good agreement between the phenomenological
model and our recent and new EFISH spectroscopic results is demonstrated.
Finally, low-frequency electromodulated EFISH is demonstrated as a useful
differential spectroscopic technique for studies of the Si-SiO$_2$ interface in
silicon-based MOS structures.
