Theory of one-phonon Raman scattering in semiconductor microcrystallites

We have developed a theory of one-phonon Raman scattering in semiconductor microcrystallites and quantum dots. In particular, we have given a complete description of the phonon modes of spherical structures embedded in another material, which includes a correct treatment of the mechanical and electrostatic matching conditions at the surface. We illustrate the theory for CdS microcrystallites in a glass matrix, which have interesting phonon properties since the TO phonon seems to have a positive dispersion in the bulk. We consider the Fröhlich interaction for resonance Raman scattering with laser energies between the first two confined electron-hole subband resonances. We also derive an electron-phonon interaction selection rule for spherical dots that only allows contributions from phonon states with angular momentum ${\mathit{l}}_{\mathit{p}}$=0 and ${\mathit{l}}_{\mathit{p}}$=1.