A convenient method for large-scale STM mapping of freestanding atomically thin conductive membranes

Fluctuation-induced current from freestanding graphene

At room temperature, micron-sized sheets of freestanding graphene are in constant motion, even in the presence of an applied bias voltage. We quantify the out-of-plane movement by collecting the displacement current using a nearby small-area metal electrode and present an Ito-Langevin model for the motion coupled to a circuit containing diodes. Numerical simulations show that the system reaches thermal equilibrium and the average rates of heat and work provided by stochastic thermodynamics tend quickly to zero. However, there is power dissipated by the load resistor, and its time average is exactly equal to the power supplied by the thermal bath. The exact power formula is similar to Nyquist's noise power formula, except that the rate of change of diode resistance significantly boosts the output power, and the movement of the graphene shifts the power spectrum to lower frequencies. We have calculated the equilibrium average of the power by asymptotic and numerical methods. Excellent agreement is found between experiment and theory.

New imaging modes for analyzing suspended ultra-thin membranes by double-tip scanning probe microscopy

Scanning probe microscopy (SPM) techniques are amongst the most important and versatile experimental methods in surface- and nanoscience. Although their measurement principles on rigid surfaces are well understood and steady progress on the instrumentation has been made, SPM imaging on suspended, flexible membranes remains difficult to interpret. Due to the interaction between the SPM tip and the flexible membrane, morphological changes caused by the tip can lead to deformations of the membrane during scanning and hence significantly influence measurement results. On the other hand, gaining control over such modifications can allow to explore unknown physical properties and functionalities of such membranes. Here, we demonstrate new types of measurements that become possible with two SPM instruments (atomic force microscopy, AFM, and scanning tunneling microscopy, STM) that are situated on opposite sides of a suspended two-dimensional (2D) material membrane and thus allow to bring both SPM tips arbitrarily close to each other. One of the probes is held stationary on one point of the membrane, within the scan area of the other probe, while the other probe is scanned. This way new imaging modes can be obtained by recording a signal on the stationary probe as a function of the position of the other tip. The first example, which we term electrical cross-talk imaging (ECT), shows the possibility of performing electrical measurements across the membrane, potentially in combination with control over the forces applied to the membrane. Using ECT, we measure the deformation of the 2D membrane around the indentation from the AFM tip. In the second example, which we term mechanical cross-talk imaging (MCT), we disentangle the mechanical influence of a scanning probe tip (e.g. AFM) on a freestanding membrane by means of independently recording the response of the opposing tip. In this way we are able to separate the tip-induced membrane deformation topography from the (material-dependent) force between the tip and the membrane. Overall, the results indicate that probing simultaneously both surfaces of ultra-thin membranes, such as suspended 2D materials, could provide novel insights into the electronic properties of the materials.

Low-force spectroscopy on graphene membranes by scanning tunneling microscopy

Two-dimensional atomically flat sheets with a high mechanical flexibility are very attractive as ultrathin membranes but are also inherently challenging for microscopic investigations. We report on a method using Scanning Tunneling Microscopy (STM) under ultra-high vacuum conditions for non-indenting low-force spectroscopy on micrometer-sized freestanding graphene membranes. The method is based on applying quasi-static voltage ramps with active feedback at low tunneling currents and ultimately relies on the attractive electrostatic force between the tip and the membrane. As a result a bulge-test scenario can be established. The convenience and simplicity of the method relies on the fact that the loading force and the membrane deflection detection are both provided simultaneously by the STM. This permits the continuous measurement of the stress-strain relation. Electrostatic forces applied are typically below 1 nN and the membrane deflection is detected at sub-nanometer resolution. Experiments on single-layer graphene membranes with a strain of 0.1% reveal a two-dimensional elastic modulus E_2D = 220 N m^-1.