Low-force spectroscopy on graphene membranes by scanning tunneling microscopy

Intentionally Created Localized Bridges for Electron Transport Through Graphene Monolayer Between Two Metals

Monolayer graphene (1LG) is frequently unpredictably modified by supporting material so that it limits development of devices. Van der Waals interaction is dominant in the models describing the in-plane processes, including the electrical charge transport. However, the current flow perpendicular to the plane of the graphene is still less understood. This report analysed specific aspect of the perpendicular current and disclosed an original way to create transport bridges perpendicular to the plane across the 1LG. The most extraordinary finding is that the electron transport between two parallel metal surfaces can be shut down and opened if the metals are separated by the 1LG. The electron transmission can be intentionally varied in this metal - 1LG - metal (M-G-M) system by pressure. In the experimental study the AFM force curve and tunnelling current measurements were combined when the external load force (0 - 1200 nN) and electrical potential (-1.5 V - +1.5 V) were used. It is proved that for low voltages (< ±9 mV) a bridge is opened perpendicular to the graphene across the M-G-M systems by the external force, if the compression dependent Fermi level crosses electronic states in the interfaces and graphene. The localised bridges with diameter about 10 - 40 nm can be opened and kept continuously by the stabilised force in separated points of the system. However, the predictable changes can be produced in the system if the voltage and the force exceeded critical magnitudes. A combined model was proposed acceptable to explain the bridging and predictably modify the characteristics.

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.

Squeezed nanocrystals: equilibrium configuration of metal clusters embedded beneath the surface of a layered material

Shapes of functional metallic nanocrystals, typically synthesized either free in solution or supported on surfaces, are key for controlling properties. Here, we consider a novel new class of metallic nanocrystals, copper clusters embedded near the surface of graphite, which can be considered a model system for metals embedded beneath surfaces of layered materials, or beneath supported membranes. We develop a continuum elasticity (CE) model for the equilibrium shape of these islands, and compare its predictions with experimental data. The CE model incorporates appropriate surface energy, adhesion energies, and strain energy. The agreement between the CE model and the data is-with one exception-excellent, both qualitatively and quantitatively, and is achieved with a single adjustable parameter. The model predicts that the embedded island shape is invariant with size, manifest both by constant side slope and by constant aspect ratio. This prediction is rationalized by dimensional analysis of the relevant energetic contributions. The aspect ratio (width : height) of an embedded Cu cluster is much larger than that of a supported but non-embedded Cu cluster, due to resistance of the graphene membrane to deformation. Experimental data diverge from the model predictions only in the case of the aspect ratio of small islands, below a critical height of ∼10 nm. The divergence may be due to bending strain, which is treated only approximately in the model. Strong support for the CE model and its interpretation is provided by additional data for embedded Fe clusters. Most of these observations and insights should be generally applicable to systems where a metal cluster is embedded beneath a layered material or supported membrane, provided that shape equilibration is possible.