Imaging mechanical vibrations in suspended graphene sheets

TL;DR

This study uses advanced microscopy to image and analyze novel edge-localized vibrational modes in suspended graphene sheets, revealing significant non-uniform stress effects impacting their mechanical behavior.

Contribution

It introduces a new imaging method for nanoscale vibrations and uncovers previously unpredicted edge eigenmodes caused by non-uniform stress in graphene sheets.

Findings

Discovery of exotic edge eigenmodes with maximum amplitude at free edges

Identification of large non-uniform stress (up to 1.5 GPa) in graphene sheets

Implication of stress effects on electronic and mechanical properties of graphene

Abstract

We 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 non-uniform stress with remarkably large magnitudes (up to 1.5 GPa). This non-uniform 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.