Acoustic vibrations of semiconductor nanocrystals in doped glasses

Polarization-dependent low-frequency off-resonant Raman scattering has been studied from various commercially available filter glass samples, which contain ${\mathrm{CdS}}_x{\mathrm{Se}}_{1-x}$ nanoparticles embedded in a glass matrix. In order to distinguish the confined acoustic phonons from the glass background, the spectra have been compared with those obtained from the base material, which does not contain nanoparticles. Polarized and depolarized scattering from confined acoustic phonons was distinctly resolved near the laser line and overtones of the polarized modes were observed. A theoretical treatment, which establishes a relation between the particle size, the frequencies, and the widths of various phonons, taking into account the matrix influence on the vibrational spectrum and on its damping, is presented. The material-dependent generalized form of this model enables one to use it for any given combination of particle and matrix materials. A good agreement between the experimental and the theoretical results is found. The nanoparticle sizes obtained from Raman scattering agree well with those obtained from transmission electron microscope and anomalous small angle x-ray scattering experiments.