Quantitative characterization of defect size in graphene using Raman spectroscopy

The quantitative determination of the lattice disorder present in graphene layers will be crucial if this 2-D material is to be commercialized. Raman spectroscopy has been shown to be a powerful technique for characterizing the density of these defects in graphene layers. Here, we study the evolution of Raman spectra with defect size, for vacancy defects created via ion bombardment. Raman spectroscopy was used to analyze the variation in the D-peak and G-peak intensity ratio for single-layer graphene, whilst the equivalent defects in highly ordered pyrolytic graphite were characterized using scanning tunneling microscopy to determine their lateral dimensions. Vacancy defects of larger lateral sizes were shown to have an associated coalescence of defects at a larger inter-defect distance, through changes in the intensity ratio of the D-and G-peaks, as well as the D-peak width. This is in agreement with a phenomenological model previously determined for calculating the defect density in graphene layers, and experimentally reveals the effect of graphene defect size for Raman spectroscopy measurements. Importantly, these results show how the graphene defect size must be obtained separately to allow the quantification of the graphene defect density using Raman spectroscopy. The measurement of single-layer graphene with several different defect sizes has also enabled an accurate determination of the phase-breaking length of graphene of 2.4 +/- 0.6 nm.