Phonon confinement and size effect in Raman spectra of ZnO nanoparticles.

We study Raman spectra of ZnO nanoparticles of 5-12 nm size in the whole range of the first-order phonon bands. We apply the 3D phonon confinement model (PCM) for the interpretation of the observed Raman spectra. It is found that PCM is well applicable to the acoustic modes as well as to the optical ones, despite the fact that PCM has been thought not to be suitable for acoustic phonons. We show that the asymptotic behavior of PCM for the small-size limit is more consistent with the observation than that of the elastic sphere model (ESM). Furthermore, PCM gives detailed information on the complex size-dependent shapes of the phonon bands.