Phonon confinement in Ge nanocrystals in silicon oxide matrix

Spherical Ge nanocrystals well-dispersed in amorphous silicon oxide matrix have been synthesized with different sizes, and significant size-dependent Raman shift and broadening have been observed. The lattice constant of Ge nanocrystals well-bonded to silicon oxide matrix has been characterized nearly size-independent. With our proposed stress generation and relaxation mechanisms, stress effects in our samples have been analyzed to be insignificant with respect to phonon confinement effects. The phenomenological model introduced by [Richter, Wang, and Ley, Solid State Commun. 39, 625 (1981] with Gaussian weighting function and TO2 phonon dispersion function has been found to give a quite good description of the measured size-dependence of Raman shift and broadening. A 3-peak fitting method has been proposed to determine Ge nanocrystal size and film crystallinity. After physically quantizing quantum-confined one-dimensional elastic waves, we have deduced that each quantum-confined phonon possesses an instantaneous momentum of a given magnitude hk with an equal chance of being either positive or negative and momentum conservation is retained in an electron-phonon scattering process. Therefore, on the basis of the first-principle microscopic model and our experimental results, we deduced that Raman scattering in spherical nanocrystals is a concurrent two-phonon process, one phonon generation and one phonon transition. (C) 2011 American Institute of Physics. [doi:10.1063/1.3503444]