Abstract

A theoretical model of resonant hyper-Raman scattering by an ensemble of spherical semiconductor quantum dots has been developed. The electronic intermediate states are described as Wannier-Mott excitons in the framework of the envelope function approximation. The optical polar vibrational modes of the nanocrystallites (vibrons) and their interaction with the electronic system are analyzed with the help of a continuum model satisfying both the mechanical and electrostatic matching conditions at the interface. An explicit expression for the hyper-Raman scattering efficiency is derived, which is valid for incident two-photon energy close to the exciton resonances. The dipole selection rules for optical transitions and Frohlich-like exciton-lattice interaction are derived: It is shown that only exciton states with total angular momentum L=0,1 and vibrational modes with angular momentum l(p)=1 contribute to the hyper-Raman scattering process. The scattering spectrum and resonance profile are calculated for spherical CdSe zinc-blende-type nanocrystals. Their dependence on the dot radius and the influence of the size distribution on them are also discussed. [S0163-1829(99)00628-1].