Multiphonon resonant Raman scattering in nanocrystals

We have studied the multiphonon resonant Raman scattering from confined and interface polar optical phonons in spherical nanocrystallites. The intermediate virtual states in the scattering process are taken into account as Wannier-Mott confined excitons in a spherical dot. Fröhlich interaction between excitons and optical phonons has been considered and general selection rules for the exciton-phonon matrix elements and multiphonon scattering processes in the case of spherical quantum dots have been derived. It is shown that for a second-order process, two phonons are created with the same angular momentum ${(l}_{p_1}{=l}_{p_2})$ while, in a third-order process, the second emitted (or absorbed) phonon with angular momentum $l_{p_2}$ must fulfill the triangular property $|l_{p_1}-l_{p_3}|<~l_{p_2}<~l_{p_1}{+l}_{p_3}.$ In the general case, the sum of phonon momentum projections on the z axis $m_{p_1}{+m}_{p_2}+\cdots =0.\mathrm{}$ We have performed multiphonon Raman cross-section calculations of CdSe quantum dots of various sizes up to third order and present detailed comparison with available experimental data. The effect of size distribution is studied; we show that a broad dispersion of nanocrystal sizes has important consequences on the multiphonon Raman spectra. The experimental relative intensities between phonon overtones are correctly described in the framework of the present model. Also, an analysis of the applicability of the Huang-Rhys factor for quantum dot systems is presented and several contradictions found in the literature concerning this parameter have been explored.