  The second-harmonic interferometric spectroscopy (SHIS) which combines both
amplitude (intensity) and phase spectra of the second-harmonic (SH) radiation
is proposed as a new spectroscopic technique being sensitive to the type of
critical points (CP's) of combined density of states at semiconductor surfaces.
The increased sensitivity of SHIS technique is demonstrated for the buried
Si(111)-SiO$_2$ interface for SH photon energies from 3.6 eV to 5 eV and allows
to separate the resonant contributions from $E^\prime_0/E_1$, $E_2$ and
$E^\prime_1$ CP's of silicon.
