Characterization of Nanocrystal Size Distribution using Raman Spectroscopy with a Multi-particle Phonon Confinement Model.

Analysis of the size distribution of nanocrystals is a critical requirement for the processing and optimization of their size-dependent properties. The common techniques used for the size analysis are transmission electron microscopy (TEM), X-ray diffraction (XRD) and photoluminescence spectroscopy (PL). These techniques, however, are not suitable for analyzing the nanocrystal size distribution in a fast, non-destructive and a reliable manner at the same time. Our aim in this work is to demonstrate that size distribution of semiconductor nanocrystals that are subject to size-dependent phonon confinement effects, can be quantitatively estimated in a non-destructive, fast and reliable manner using Raman spectroscopy. Moreover, mixed size distributions can be separately probed, and their respective volumetric ratios can be estimated using this technique. In order to analyze the size distribution, we have formulized an analytical expression of one-particle PCM and projected it onto a generic distribution function that will represent the size distribution of analyzed nanocrystal. As a model experiment, we have analyzed the size distribution of free-standing silicon nanocrystals (Si-NCs) with multi-modal size distributions. The estimated size distributions are in excellent agreement with TEM and PL results, revealing the reliability of our model.