One-phonon Raman scattering from arrays of semiconductor nano-crystals

We re-consider Raman scattering by LO-type phonons in a small semi-conductor crystal and derive a simple formula taking into account the higher order confined phonon modes, to describe the asymmetric Raman lineshapes observed experimentally. For a single crystalline sphere, we explicitly calculate the relative contributions of the confined modes with different values of the radial quantum number. For arrays of such spheres, we argue that, apart from a superposition of the above contributions from individual scatterers, there exists a collective scattering by a coherent mode which involves many spheres, unless their concentration is too small. This collective scattering is determined by an effective dielectric function of the composite medium and peaks near the Fröhlich frequency. We apply these principles to the analysis and modelling of Raman spectra taken from CdS doped SiO₂ films. © 1997 Published by Elsevier Science Ltd.