  We develop a generic theory for the resonant inelastic light (Raman)
scattering by a conduction band quantum plasma taking into account the presence
of the filled valence band in doped semiconductor nanostructures within a
generalized resonant random phase approximation (RPA). Our generalized RPA
theory explicitly incorporates the two-step resonance process where an electron
from the filled valence band is first excited by the incident photon into the
conduction band before an electron from the conduction band falls back into the
valence band emitting the scattered photon. We show that when the incident
photon energy is close to a resonance energy, i.e. the valence-to-conduction
band gap of the semiconductor structure, the Raman scattering spectral weight
at single particle excitation energies may be substantially enhanced even for
long wavelength excitations, and may become comparable to the spectral weight
of collective charge density excitations (plasmon). Away from resonance, i.e.
when the incident photon energy is different from the band gap energy, plasmons
dominate the Raman scattering spectrum. We find no qualitative difference in
the resonance effects on the Raman scattering spectra among systems of
different dimensionalities (one, two and three) within RPA. This is explained
by the decoherence effect of the resonant interband transition on the
collective motion of conduction band electrons. Our theoretical calculations
agree well (qualitatively and semi-quantitatively) with the available
experimental results, in contrast to the standard nonresonant RPA theory which
predicts vanishing long wavelength Raman spectral weight for single particle
excitations.
