Effects of crystallite size distribution on the Raman-scattering profiles of silicon nanostructures

Raman scattering (RS) from semiconductor nanostructures provide excellent information on the size of the crystallites. Processing history of most nanocrystalline semiconductors suggests natural incorporation of a distribution of crystallite sizes. In this paper, we report on the influence of crystallite size distribution on the shifts in RS frequencies and line shapes. A phenomenological model is developed to obtain an analytical expression for the Raman spectral profile from semiconductor nanostructures having a Gaussian distribution in the crystallite sizes. Computer simulations of RS profiles on nanocrystalline silicon (nc-Si) demonstrate the effects of a size distribution on the Raman shifts. In particular, the effects on the asymmetry in Raman line shapes are emphasized. The model is applied to the published Raman data on nc-Si samples where size distributions are known from the direct measurements. The size distribution obtained from Raman analysis is in good agreement with that reported by direct measurement techniques. Further, Raman as well as photoluminescence measurements were made on the same spots on our stress-free porous silicon samples using a Raman microprobe. The present model leads to crystallite size distributions self-consistent with the photoluminescence data.