Microscopic theory of the low frequency Raman modes in germanium nanocrystals

Abstract

We have studied the Raman intensities of low-frequency phonon modes in germanium $(\mathrm{Ge})$ nanocrystals (NC) with varying sizes by using a microscopic valence force field model. The results are compared with the predictions of the continuum model of Lamb using a projection method. We found that the $l=0$ spheroidal Lamb modes are Raman active in the parallel polarization scattering geometry, while the $l=2$ spheroidal Lamb modes are active in the crossed polarization geometry. This result agrees with the group theory prediction that the torsional Lamb modes are not Raman active, but is in disagreement with the identification of torsional Lamb modes in the crossed polarization Raman spectra of NC suggested by many authors.