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Graphene (GR) remarkable mechanical and electrical properties - such as itsYoung's modulus, low mass per unit area, natural atomic flatness and electricalconductance - would make it an ideal material for micro andnanoelectromechanical systems (MEMS and NEMS). However, the difficulty ofattaching GR to supports coupled with naturally occurring internal defects in afew-layer GR can significantly adversely affect the performance of suchdevices. Here, we have used a combined contact resonance atomic forcemicroscopy (CR-AFM) and ultrasonic force microscopy (UFM) approach tocharacterise and map with nanoscale spatial resolution GR membrane propertiesinaccessible to most conventional scanning probe characterisation techniques.Using a multi-layer GR plate (membrane) suspended over a round hole we showthat this combined approach allows access to the mechanical properties,internal structure and attachment geometry of the membrane providinginformation about both the supported and suspended regions of the system. Weshow that UFM allows the precise geometrical position of the supportedmembrane-substrate contact to be located and provides indication of the localvariation of its quality in the contact areas. At the same time, we show thatby mapping the position sensitive frequency and phase response of CR-AFMresponse, one can reliably quantify the membrane stiffness, and image thedefects in the suspended area of the membrane. The phase and amplitude ofexperimental CR-AFM measurements show excellent agreement with an analyticalmodel accounting for the resonance of the combined CR-AFM probe-membranesystem. The combination of UFM and CR-AFM provide a beneficial combination forinvestigation of few-layer NEMS systems based on two dimensional materials.

Mapping nanoscale dynamic properties of suspended and supported  multi-layer graphene membranes via contact resonance and ultrasonic scanning  probe microscopies