Resonant Raman Scattering by Charge Density and Single Particle Excitations in Semiconductor Nanostructures: A Generalized Interband-Resonant Random-Phase-Approximation Theory

摘要

We develop a generic theory for the resonant inelastic light (Raman)scattering by a conduction band quantum plasma taking into account the presenceof the filled valence band in doped semiconductor nanostructures within ageneralized resonant random phase approximation (RPA). Our generalized RPAtheory explicitly incorporates the two-step resonance process where an electronfrom the filled valence band is first excited by the incident photon into theconduction band before an electron from the conduction band falls back into thevalence band emitting the scattered photon. We show that when the incidentphoton energy is close to a resonance energy, i.e. the valence-to-conductionband gap of the semiconductor structure, the Raman scattering spectral weightat single particle excitation energies may be substantially enhanced even forlong wavelength excitations, and may become comparable to the spectral weightof collective charge density excitations (plasmon). Away from resonance, i.e.when the incident photon energy is different from the band gap energy, plasmonsdominate the Raman scattering spectrum. We find no qualitative difference inthe resonance effects on the Raman scattering spectra among systems ofdifferent dimensionalities (one, two and three) within RPA. This is explainedby the decoherence effect of the resonant interband transition on thecollective motion of conduction band electrons. Our theoretical calculationsagree well (qualitatively and semi-quantitatively) with the availableexperimental results, in contrast to the standard nonresonant RPA theory whichpredicts vanishing long wavelength Raman spectral weight for single particleexcitations.