  We report measurements of vibrational mode shapes of mechanical resonators
made from ultrathin carbon nanomembranes (CNMs) with a thickness of
approximately 1 nm. CNMs are prepared from electron irradiation induced
cross-linking of aromatic self-assembled monolayers (SAMs) and the variation of
membrane thickness and/or density can be achieved by varying the precursor
molecule. Single- and triple-layer freestanding CNMs were made by transferring
them onto Si substrates with square/rectangular orifices. The vibration of the
membrane was actuated by applying a sinusoidal voltage to a piezoelectric disk
on which the sample was glued. The vibrational mode shapes were visualized with
an imaging Mirau interferometer using a stroboscopic light source. Several mode
shapes of a square membrane can be readily identified and their dynamic
behavior can be well described by linear response theory of a membrane with
negligible bending rigidity. Applying Fourier transformations to the
time-dependent surface profiles, the dispersion relation of the transverse
membrane waves can be obtained and its linear behavior confirms the membrane
model. Comparing the dispersion relation to an analytical model, the static
stress of the membranes was determined and found to be caused by the
fabrication process.
