A Raman spectroscopy signature for characterizing defective single-layer graphene: Defect-induced I(D)/I(D′) intensity ratio by theoretical analysis

To distinguish defects in defective single-layer graphene (DSLG), we developed a method combining first principles density functional theory and tight-binding that quantifies defect-induced Raman intensities. Analysis of defect potentials for defects with vacancies and/or bond rotation has shown that on-site variation dominates the scattering, and also quantified effects of oxygen adsorption. Defect potentials for DSLG were subsequently used in calculation of the electron–defect matrix elements and Raman intensities. I(D)/I(D′) intensity ratios, dependent on defect topology and oxygen impurity adsorption, were elucidated for mono-vacancy, double-vacancy, Stone–Wales, and so-called 555-777 and 5555-6-7777 point defects in single-layer graphene. The results demonstrated for the first time the ability to distinguish between these defect types, also as dependent of oxygen adsorption, and were found consistent with a measured value for vacancies. Importantly, our theoretical prediction of the I(D)/I(D′) Raman intensity signature metric can assist in experimental characterization of defective realistic graphene samples for any defect type. Finally, analytical analysis of the angular dependence of the electron–defect scattering matrix elements revealed a node effect in intra-valley backscattering but not in inter-valley backscattering, rationalizing the observation that the D′ band intensity is mostly weaker than that of the D band.