Evaluating arbitrary strain configurations and doping in graphene with Raman spectroscopy

Abstract

The properties of graphene depend sensitively on strain and doping affecting its behavior in devices and allowing an advanced tailoring of this material. A knowledge of the strain configuration, i.e. the relative magnitude of the components of the strain tensor, is particularly crucial, because it governs effects like band-gap opening, pseudo-magnetic fields, and induced superconductivity. It also enters critically in the analysis of the doping level. We propose a method for evaluating unknown strain configurations and simultaneous doping in graphene using Raman spectroscopy. In our analysis we first extract the bare peak shift of the G and 2D modes by eliminating their splitting due to shear strain. The shifts from hydrostatic strain and doping are separated by a correlation analysis of the 2D and G frequencies, where we find $\Delta \omega_{\rm 2D}/\Delta \omega_{\rm G} = 2.21 \pm 0.05$ for pure hydrostatic strain. We obtain the local hydrostatic strain, shear strain and doping without any assumption on the strain configuration prior to the analysis, as we demonstrate for two model cases: Graphene under uniaxial stress and graphene suspended on nanostructures that induce strain. Raman scattering with circular corotating polarization is ideal for analyzing frequency shifts, especially for weak strain when the peak splitting by shear strain cannot be resolved.