  Graphene (GR) remarkable mechanical and electrical properties - such as its
Young's 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.
