Structural analysis of polycrystalline graphene systems by Raman spectroscopy

A theoretical model supported by experimental results explains the dependence of the Raman scattering signal on the evolution of structural parameters along the amorphization trajectory of polycrystalline graphene systems. Four parameters rule the scattering efficiencies, two structural and two related to the scattering dynamics. With the crystallite sizes previously defined from X-ray diffraction and microscopy experiments, the three other parameters (the average grain boundaries width, the phonon coherence length, and the electron coherence length) are extracted from the Raman data with the geometrical model proposed here. The broadly used intensity ratio between the C-C stretching (G band) and the defect-induced (D band) modes can be used to measure crystallite sizes only for samples with sizes larger than the phonon coherence length, which is found equal to 32 nm. The Raman linewidth of the G band is ideal to characterize the crystallite sizes below the phonon coherence length, down to the average grain boundaries width, which is found to be 2.8 nm. "Ready-to-use" equations to determine the crystallite dimensions based on Raman spectroscopy data are given.