Monitoring Electrostatically-Induced Deflection, Strain and Doping in Suspended Graphene using Raman Spectroscopy

Abstract: Electrostatic gating offers elegant ways to simultaneously strain and dope atomically thin membranes. Here, we report on a detailed \textit{in situ} Raman scattering study on graphene, suspended over a Si/SiO$_2$ substrate. In such a layered structure, the intensity of the Raman G- and 2D-mode features of graphene are strongly modulated by optical interference effects and allow an accurate determination of the electrostatically-induced membrane deflection, up to irreversible collapse. The membrane deflection is successfully described by an electromechanical model, which we also use to provide useful guidelines for device engineering. In addition, electrostatically-induced tensile strain is determined by examining the softening of the Raman features. Due to a small residual charge inhomogeneity $\sim 5\times 10^{10}~\rm cm^{-2}$, we find that non-adiabatic anomalous phonon softening is negligible compared to strain-induced phonon softening. These results open perspectives for innovative Raman scattering-based readout schemes in two-dimensional nanoreso