Disorder and Defects in Two-Dimensional Materials Probed by Raman Spectroscopy

Abstract

This paper describes the fundamentals of using Raman spectroscopy to characterize disorder in two-dimensional (2D) systems caused by the presence of defects. From the dimensionality point of view, in 2D crystalline structures disorder can be described as addition of point-like (zero-dimensional, 0D) or line-like (one-dimensional, 1D) defects. To characterize the amount of 0D and 1D defects separately, two spectral parameters are needed. The two basic parameters are related to defect-induced activation of forbidden Raman modes and to defect-induced confinement of phonons. A two-dimensional Raman phase diagram can be built based on geometrical considerations, and the geometrical parameters are governed by fundamental aspects such as phonon and electron coherence lengths and Raman cross sections. We apply the general picture to the well-studied case of graphene amorphization, which has been studied since the 70’ies, with the two basic parameters being represented by the peak linewidths (Γ) and by the integrated intensity ratio (AD/AG) between the defect-induced (D) mode and the Raman allowed graphene (G) mode. The amorphization of graphene has been fully described in the terms presented here thanks to the development of standard materials with well-controlled amount of either point-like or line-like defects.