Quantum effects in the Raman spectrum of a quantum dot

The spectrum of electronic Raman scattering from two-dimensional (2D) and 3D n-type semiconductor quantum dots is calculated within the random-phase approximation. The electron gas is assumed to be homogeneous inside the dots. For a 2D circular quantum dot the plasmon Raman band was found to consist of single peaks distributed around the cneter of the band in a frequency interval of the order of Landau damping. This fine structure of the plasmon Raman band is due to the discreteness of electronic excitations in a dot. In order to find out the role of electronic elastic scattering from irregular boundaries of the dots we consider a 3D spheroidal (in average) dot and apply the statistical description of one-particle energy levels in the dot. By using Dyson statistical ensembles within the quasiclassical approximation we show that noticeable quantum oscillations of the plasmon Raman band show up for the symplectic Dyson ensemble.