VIBRATIONAL RESONANT RAMAN-SCATTERING IN SPHERICAL QUANTUM DOTS - EXCITON EFFECTS

We develope a theoretical model of first order resonant Raman scatteri ng in spherical nanocrystals which includes excitonic effects. Using a matrix diagonalization technique, the exciton wavefunctions and energ y states as a function of quantum dot radius are calculated. The Frohl ich interaction between excitons and optical vibrational modes has bee n 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 calcu lated for spherical CdS and GaAs nanocrystals. Contrary to the case of uncorrelated electron-hole pairs, strong scattering appears even in t he case of infinite barriers. The results obtained for this case are c ompared with calculations for finite barriers. The selection rules for optical transitions and exciton-lattice interaction are derived for s pherical dots in the dipole approximation. Only exciton states and vib rational modes with angular momentum equal to zero are allowed in this approximation.