Probing thermal expansion of graphene and modal dispersion at low-temperature using graphene nanoelectromechanical systems resonators

Nanoelectromechanical systems were fabricated from single- and multilayer graphene sheets by mechanically exfoliating thin sheets from graphite over trenches in silicon oxide. Vibrations with fundamental resonant frequencies in the megahertz range are actuated either optically or electrically and detected optically by interferometry. We demonstrate room-temperature charge sensitivities down to 8 x 10(-4) electrons per root hertz. The thinnest resonator consists of a single suspended layer of atoms and represents the ultimate limit of two-dimensional nanoelectromechanical systems.

The discovery of graphene raises the prospect of a new class of nanoelectronic devices based on the extraordinary physical properties of this one-atom-thick layer of carbon. Unlike two-dimensional electron layers in semiconductors, where the charge carriers become immobile at low densities, the carrier mobility in graphene can remain high, even when their density vanishes at the Dirac point. However, when the graphene sample is supported on an insulating substrate, potential fluctuations induce charge puddles that obscure the Dirac point physics. Here we show that the fluctuations are significantly reduced in suspended graphene samples and we report low-temperature mobility approaching 200,000 cm2 V-1 s-1 for carrier densities below 5 x 109 cm-2. Such values cannot be attained in semiconductors or non-suspended graphene. Moreover, unlike graphene samples supported by a substrate, the conductivity of suspended graphene at the Dirac point is strongly dependent on temperature and approaches ballistic values at liquid helium temperatures. At higher temperatures, above 100 K, we observe the onset of thermally induced long-range scattering.

Static and dynamic mechanical deflections were electrically induced in cantilevered, multiwalled carbon nanotubes in a transmission electron microscope. The nanotubes were resonantly excited at the fundamental frequency and higher harmonics as revealed by their deflected contours, which correspond closely to those determined for cantilevered elastic beams. The elastic bending modulus as a function of diameter was found to decrease sharply (from about 1 to 0.1 terapascals) with increasing diameter (from 8 to 40 nanometers), which indicates a crossover from a uniform elastic mode to an elastic mode that involves wavelike distortions in the nanotube. The quality factors of the resonances are on the order of 500. The methods developed here have been applied to a nanobalance for nanoscopic particles and also to a Kelvin probe based on nanotubes.