Graphene (GR) remarkable mechanical and electrical properties - such as its Youngs modulus, low mass per unit area, natural atomic flatness and electrical conductance - would make it an ideal material for micro and nanoelectromechanical systems (MEMS and NEMS). However, the difficulty of attaching GR to supports coupled with naturally occurring internal defects in a few-layer GR can significantly adversely affect the performance of such devices. Here, we have used a combined contact resonance atomic force microscopy (CR-AFM) and ultrasonic force microscopy (UFM) approach to characterise and map with nanoscale spatial resolution GR membrane properties inaccessible to most conventional scanning probe characterisation techniques. Using a multi-layer GR plate (membrane) suspended over a round hole we show that this combined approach allows access to the mechanical properties, internal structure and attachment geometry of the membrane providing information about both the supported and suspended regions of the system. We show that UFM allows the precise geometrical position of the supported membrane-substrate contact to be located and provides indication of the local variation of its quality in the contact areas. At the same time, we show that by mapping the position sensitive frequency and phase response of CR-AFM response, one can reliably quantify the membrane stiffness, and image the defects in the suspended area of the membrane. The phase and amplitude of experimental CR-AFM measurements show excellent agreement with an analytical model accounting for the resonance of the combined CR-AFM probe-membrane system. The combination of UFM and CR-AFM provide a beneficial combination for investigation of few-layer NEMS systems based on two dimensional materials.
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