Abstract

We develope a theoretical model of first order resonant Raman scattering in spherical nanocrystals which includes excitonic effects. Using a matrix diagonalization technique, the exciton wavefunctions and energy states as a function of quantum dot radius are calculated. The Frohlich interaction between excitons and optical vibrational modes has been considered in the framework of a continuum theory which includes the mechanical and the electrostatic matching boundary conditions at the interface. The Raman cross section and scattering efficiency are calculated for spherical CdS and GaAs nanocrystals. Contrary to the case of uncorrelated electron-hole pairs, strong scattering appears even in the case of infinite barriers. The results obtained for this case are compared with calculations for finite barriers. The selection rules for optical transitions and exciton-lattice interaction are derived for spherical dots in the dipole approximation. Only exciton states and vibrational modes with angular momentum equal to zero are allowed in this approximation.