Imaging Mechanical Vibrations in Suspended Graphene Sheets

Abstract

5 pages, 4 figures.-- Printed version published May 14, 2008.Supporting information available: A detailed description of fabrication technique, a description of the FEM model, a comparison of the FEM model to analytical predictions for a beam under tension as well as recent simulations on nanotubes with slack, and a detailed description of the SFM technique to detect mechanical vibrations. Available at: http://pubs.acs.org/doi/suppl/10.1021/nl080201h/suppl_file/nl080201h-file002.pdfWe carried out measurements on nanoelectromechanical systems based on multilayer graphene sheets suspended over trenches in silicon oxide. The motion of the suspended sheets was electrostatically driven at resonance using applied radio frequency voltages. The mechanical vibrations were detected using a novel form of scanning probe microscopy, which allowed identification and spatial imaging of the shape of the mechanical eigenmodes. In as many as half the resonators measured, we observed a new class of exotic nanoscale vibration eigenmodes not predicted by the elastic beam theory, where the amplitude of vibration is maximum at the free edges. By modeling the suspended sheets with the finite element method, these edge eigenmodes are shown to be the result of nonuniform stress with remarkably large magnitudes (up to 1.5 GPa). This nonuniform stress, which arises from the way graphene is prepared by pressing or rubbing bulk graphite against another surface, should be taken into account in future studies on electronic and mechanical properties of graphene.The research has been supported by a EURYI grant and FP6-IST-021285-2 and by the NSF through the Cornell Center for Materials Research. Sample fabrication was performed at the Cornell Nanoscale Science and Technology Facility, a National Nanotechnology Infrastructure Network node, funded by NSF.Peer reviewe