Mapping the mechanical properties of a graphene drum at the nanoscale

The operation of graphene-based nanoelectromechanical systems (NEMS) crucially depends on the local mechanical characteristics of the graphene drum resonator. In particular, inhomogeneity in the residual strain (pre-strain) of the graphene membrane may affect the vibration dynamics as well as the energy dissipation. Despite its importance, achieving a precise local mapping of the pre-strain of a graphene membrane remains challenging. Here, we correlate scanning-probe force microscopy and Raman spectroscopy to map the local mechanical properties of circular monolayer-graphene drums. At odds with other techniques, we obtain maps of the membrane pre-strain with nanometric resolution and measure the effective Young's modulus in a non-invasive way. Moreover, we show that the common topographic artefacts stemming from tip-induced deformations can be precisely corrected using the information derived from force-spectroscopy data. As a result, the local map of the pre-strain can be correlated with the true morphology of the graphene drum. Our analysis demonstrates that graphene resonators can be characterized by a non-flat morphology and a non-uniform pre-strain distribution, as a consequence of complex boundary conditions at the edge of the membrane and in correlation with local material defects. Since these non-ideal features are strictly related to the growth and the fabrication procedures, our method can provide a useful screening tool for the development of 2D materials-based NEMSs.