We report a rigorous analytical approach based on one-particle phonon confinement model to realize direct detection of nanocrystal size distribution and volume fraction by using Raman spectroscopy. For the analysis, we first project the analytical confinement model onto a generic distribution function, and then use this as a fitting function to extract the required parameters from the Raman spectra, i.e., mean size and skewness, to plot the nanocrystal size distribution. Size distributions for silicon nanocrystals are determined by using the analytical confinement model agree well with the one-particle phonon confinement model, and with the results obtained from electron microscopy and photoluminescence spectroscopy. The approach we propose is generally applicable to all nanocrystal systems, which exhibit size-dependent shifts in the Raman spectrum as a result of phonon confinement.
Dogan, I., & Sanden, van de, M. C. M. (2013). Direct characterization of nanocrystal size distribution using Raman spectroscopy. Journal of Applied Physics, 114(13), 134310-1/8. https://doi.org/10.1063/1.4824178