Suspended Graphene Membranes Research Articles

Controlled ripple texturing of suspended graphene membranes due to coupling with ultracold atoms

We discuss the possibility to create hybrid quantum systems that combine ultracold atoms with graphene membranes. We investigate a setup in which a cold atom cloud is placed close to a free-standing sheet of graphene at distances on the order of a few hundred nanometers. The atoms then couple to the graphene membrane via Casimir-Polder forces. Temporal changes in the atomic state of the atomic cloud changes the Casimir-Polder interaction, thereby leading to the creation of a backaction force in the graphene sheet. This setup provides a controllable way to engineer ripples in a graphene sheet.

Ultrafast quantitative nanomechanical mapping of suspended graphene

Understanding the mechanical properties of suspended graphene membranes is crucial to the development of graphene nano-electromechanical devices. PeakForce QNM (quantitative nanomechanical mapping) atomic force microscopy imaging was used to rapidly map the nanomechanical properties of a range of suspended graphene membranes. The force–displacement behavior of monolayer graphene extracted from the peak-force imaging map was found to be comparable to that taken using standard nanoindentation. By fitting to a simple elastic model, the two-dimensional elastic modulus was measured at around 350 N m−1, corresponding to a Young's modulus of around 1 TPa. Nanomechanical parameters which can be directly extracted from force curve data in real time. Inset shows a dissipation map of a suspended graphene membrane.

Electromechanical Piezoresistive Sensing in Suspended Graphene Membranes

Monolayer graphene exhibits exceptional electronic and mechanical properties, making it a very promising material for nanoelectromechanical devices. Here, we conclusively demonstrate the piezoresistive effect in graphene in a nanoelectromechanical membrane configuration that provides direct electrical readout of pressure to strain transduction. This makes it highly relevant for an important class of nanoelectromechanical system (NEMS) transducers. This demonstration is consistent with our simulations and previously reported gauge factors and simulation values. The membrane in our experiment acts as a strain gauge independent of crystallographic orientation and allows for aggressive size scalability. When compared with conventional pressure sensors, the sensors have orders of magnitude higher sensitivity per unit area.

Pressure sensors based on suspended graphene membranes

A novel pressure sensor based on a suspended graphene membrane is proposed. The sensing mechanism is explained based on tight binding calculations of strain-induced changes in the band structure. A CMOS compatible fabrication process is proposed and used to fabricate prototypes. Electrical measurement data demonstrates the feasibility of the approach, which has the advantage of not requiring a separate strain gauge, i.e. the strain gauge is integral part of the pressure sensor membrane. Hence, graphene membrane based pressure sensors can in principle be scaled quite aggressively in size.

Microscopic characterisation of suspended graphene grown by chemical vapour deposition

We present a multi-technique characterisation of graphene grown by chemical vapour deposition (CVD) and thereafter transferred to and suspended on a grid for transmission electron microscopy (TEM). The properties of the electronic band structure are investigated by angle-resolved photoelectron spectromicroscopy, while the structural and crystalline properties are studied by TEM and Raman spectroscopy. We demonstrate that the suspended graphene membrane locally shows electronic properties comparable with those of samples prepared by micromechanical cleaving of graphite. Measurements show that the area of high quality suspended graphene is limited by the folding of the graphene during the transfer.

Ultrahigh conductivity of large area suspended few layer graphene films

Room-temperature (atmospheric-pressure) electrical conductivity measurements of wafer-scale, large-area suspended (few layer) graphene membranes with areas up to 1000 μm2 (30 μm × 30 μm) are presented. Multiple devices on one wafer can be fabricated with high yield from the same chemical vapor deposition grown graphene sheet, transferred from a nickel growth substrate to large opening in a suspended silicon nitride support membrane. This represents areas two to orders of magnitude larger than prior transport studies on any suspended graphene device (single or few layer). We find a sheet conductivity of ∼2500 e2/h (or about 10 Ω/sq) of the suspended graphene, which is an order of magnitude higher than any previously reported sheet conductance of few layer graphene.

Electron transparent graphene windows for environmental scanning electron microscopy in liquids and dense gases

Due to its ultrahigh electron transmissivity in a wide electron energy range, molecular impermeability, high electrical conductivity and excellent mechanical stiffness, suspended graphene membranes appear to be a nearly ideal window material for in situ (in vivo) environmental electron microscopy of nano- and mesoscopic objects (including bio-medical samples) immersed in liquids and/or in dense gaseous media. In this paper, taking advantage of a small modification of the graphene transfer protocol onto metallic and SiN supporting orifices, reusable environmental cells with exchangeable graphene windows have been designed. Using colloidal gold nanoparticles (50 nm) dispersed in water as model objects for scanning electron microscopy in liquids as proof of concept, different conditions for imaging through the graphene membrane were tested. Limiting factors for electron microscopy in liquids, such as electron beam induced water radiolysis and damage of the graphene membrane at high electron doses, are discussed.

In Situ Observation of Electrostatic and Thermal Manipulation of Suspended Graphene Membranes

Graphene is nature's thinnest elastic membrane, and its morphology has important impacts on its electrical, mechanical, and electromechanical properties. Here we report manipulation of the morphology of suspended graphene via electrostatic and thermal control. By measuring the out-of-plane deflection as a function of applied gate voltage and number of layers, we show that graphene adopts a parabolic profile at large gate voltages with inhomogeneous distribution of charge density and strain. Unclamped graphene sheets slide into the trench under tension; for doubly clamped devices, the results are well-accounted for by membrane deflection with effective Young's modulus E = 1.1 TPa. Upon cooling to 100 K, we observe buckling-induced ripples in the central portion and large upward buckling of the free edges, which arises from graphene's large negative thermal expansion coefficient.

Theory of the suspended graphene varactor

We report the theory and design equations of the suspended graphene varactor, wherein device capacitance is tuned by the voltage controlled deflection of a suspended graphene membrane. A simple model based on large membrane deflection predicts a capacitor tuning range of 76%, with a membrane pull-in voltage tuneable from 1 V to 30 V. An intrinsic electric quality factor approaching 200 is predicted based on experimentally determined Young's modulus and sheet resistance.

Thermal conductivity measurements of suspended graphene with and without wrinkles by micro-Raman mapping

The thermal conductivity (κ) of suspended graphene membranes made by chemical vapor deposition (CVD) was measured by micro-Raman mapping. Cracks and wrinkles present in these suspended graphene membranes were identified by micro-Raman mapping, and κ values and their statistics were obtained on membranes free of such imperfections in a single mapping. Based on this new technique, an average κ value of 1875 ± 220 W m−1 K−1 at 420 K was measured on 26 suspended graphene membranes that were free of wrinkles, ∼27% higher than the average value measured from 12 graphene membranes with wrinkles. These results suggest that the variation in published thermal conductivity values for suspended graphene samples could, at least in part, be due to the presence or absence of wrinkles.

Thermal Casimir-Polder interaction of different atoms with graphene

The thermal correction to the energy of Casimir-Polder interaction of atoms with a suspended graphene membrane described by the Dirac model is investigated. We show that a major impact on the thermal correction is made by the size of the gap in the energy spectrum of graphene quasiparticles. Specifically, if the temperature is much smaller than the gap parameter (alternatively, larger or of the order of the gap parameter), the thermal correction is shown to be relatively small (alternatively, large). We have calculated the free energy of the thermal Casimir-Polder interaction of atoms of He, Na, Rb, and Cs with graphene described by both the hydrodynamic and Dirac models. It is shown that in exact computations using the Dirac model, one should use the polarization operator at nonzero temperature. The computational results for the Casimir-Polder free energy obtained in the framework of hydrodynamic model of graphene are several times larger than in the Dirac model within the separation region below 2$\mu$m. We conclude that the theoretical predictions following from the two models can be reliably discriminated in experiments on quantum reflection of different atoms on graphene.

Ultrathin Oxide Films by Atomic Layer Deposition on Graphene

In this paper, a method is presented to create and characterize mechanically robust, free-standing, ultrathin, oxide films with controlled, nanometer-scale thickness using atomic layer deposition (ALD) on graphene. Aluminum oxide films were deposited onto suspended graphene membranes using ALD. Subsequent etching of the graphene left pure aluminum oxide films only a few atoms in thickness. A pressurized blister test was used to determine that these ultrathin films have a Young's modulus of 154 ± 13 GPa. This Young's modulus is comparable to much thicker alumina ALD films. This behavior indicates that these ultrathin two-dimensional films have excellent mechanical integrity. The films are also impermeable to standard gases suggesting they are pinhole-free. These continuous ultrathin films are expected to enable new applications in fields such as thin film coatings, membranes, and flexible electronics.

Ripping Graphene: Preferred Directions

The understanding of crack formation due to applied stress is key to predicting the ultimate mechanical behavior of many solids. Here we present experimental and theoretical studies on cracks or tears in suspended monolayer graphene membranes. Using transmission electron microscopy, we investigate the crystallographic orientations of tears. Edges from mechanically induced ripping exhibit straight lines and are predominantly aligned in the armchair or zigzag directions of the graphene lattice. Electron-beam induced propagation of tears is also observed. Theoretical simulations account for the observed preferred tear directions, attributing the observed effect to an unusual nonmonotonic dependence of graphene edge energy on edge orientation with respect to the lattice. Furthermore, we study the behavior of tears in the vicinity of graphene grain boundaries, where tears surprisingly do not follow but cross grain boundaries. Our study provides significant insights into breakdown mechanisms of graphene in the presence of defective structures such as cracks and grain boundaries.

Quantum reflection of ultracold atoms from thin films, graphene and semiconductor heterostructures

We show that thin dielectric films can be used to enhance the performance of passive atomic mirrors by enabling quantum reflection probabilities of over 90% for atoms incident at velocities of ∼1 mm s−1, achieved in recent experiments. This enhancement is brought about by weakening the Casimir–Polder attraction between the atom and the surface, which induces the quantum reflection. We show that suspended graphene membranes also produce higher quantum reflection probabilities than bulk matter. Temporal changes in the electrical resistance of such membranes, produced as atoms stick to the surface, can be used to monitor the reflection process, non-invasively and in real time. The resistance change allows the reflection probability to be determined purely from electrical measurements without needing to image the reflected atom cloud optically. Finally, we show how perfect atom mirrors may be manufactured from semiconductor heterostructures, which employ an embedded two-dimensional electron gas to tailor the atom–surface interaction and so enhance the reflection by classical means.

Molecular dynamics study of the dewetting of copper on graphite and graphene: Implications for nanoscale self-assembly

Thin-film dewetting can be exploited to self-assemble and organize nanoparticles. Crucial to this effort is the understanding of the nanoscale liquid phase dynamics, and molecular dynamics simulations (MD) provide a powerful tool in this respect. In this paper we demonstrate that MD simulations utilizing a Lennard-Jones (LJ) interface potential can be effectively used to study various wetting regimes of nanoscale Cu disks on graphite. It was found that both the dewetting velocity and the equilibrium contact angle increase with a decrease in the Cu-C potential, and that the retraction velocities obtained are characteristic of dewetting phenomena governed by inertial and capillary forces. This phenomena leads to a change in morphology, from disks to nanodroplets, which, in turn, when using the most accurate LJ potential, jump off the graphitic substrate with a velocity on the order of 140 m/s. This ejection velocity is consistent with the previous experimental observation that nanoscale Au triangles deposited on graphite or glass jump when exposed to a pulsed laser above the melting threshold. Interestingly, the Cu ejection velocity decreases when the liquid Cu disks are deposited on a suspended graphene membrane. Finally, a Rayleigh-Plateau-like instability, which leads to the breakup of a pseudo-one-dimensional liquid Cu nanowire in nanodroplets, is revealed when the MD simulations are performed using different LJ interface potentials.

Graphene-based sample supports for in situ high-resolution TEM electrical investigations

Specially designed transmission electron microscopy (TEM) sample carriers have been developed to enable atomically resolved studies of the heat-induced evolution of adsorbates on graphene and their influence on electrical conductivity. Here, we present a strategy for graphene-based carrier realization, evaluating its design with respect to fabrication effort and applications potential. We demonstrate that electrical current can lead to very high temperatures in suspended graphene membranes, and we determine that current-induced cleaning of graphene results from Joule heating.

Transfer-Free Batch Fabrication of Large-Area Suspended Graphene Membranes

We demonstrate a process for batch production of large-area (100-3000 microm(2)) patterned free-standing graphene membranes on Cu scaffolds using chemical vapor deposition (CVD)-grown graphene. This technique avoids the use of silicon and transfers of graphene. As one application of this technique, we fabricate transmission electron microscopy (TEM) sample supports. TEM characterization of the graphene membranes reveals relatively clean, highly TEM-transparent, single-layer graphene regions ( approximately 50% by area) and, despite the polycrystalline nature of CVD graphene, membrane yields as high as 75-100%. This high yield verifies that the intrinsic strength and integrity of CVD-grown graphene films is sufficient for sub-100 microm width membrane applications. Elemental analysis (electron energy loss spectroscopy (EELS) and X-ray energy-dispersive spectroscopy (EDS)) of the graphene membranes reveals some nanoscaled contamination left over from the etching process, and we suggest several ways to reduce this contamination and improve the quality of the graphene for electronic device applications. This large-scale production of suspended graphene membranes facilitates access to the two-dimensional physics of graphene that are suppressed by substrate interactions and enables the widespread use of graphene-based sample supports for electron and optical microscopy.

Controlled ripple texturing of suspended graphene and ultrathin graphite membranes

Graphene is nature's thinnest elastic material and displays exceptional mechanical and electronic properties. Ripples are an intrinsic feature of graphene sheets and are expected to strongly influence electronic properties by inducing effective magnetic fields and changing local potentials. The ability to control ripple structure in graphene could allow device design based on local strain and selective bandgap engineering. Here, we report the first direct observation and controlled creation of one- and two-dimensional periodic ripples in suspended graphene sheets, using both spontaneously and thermally generated strains. We are able to control ripple orientation, wavelength and amplitude by controlling boundary conditions and making use of graphene's negative thermal expansion coefficient (TEC), which we measure to be much larger than that of graphite. These results elucidate the ripple formation process, which can be understood in terms of classical thin-film elasticity theory. This should lead to an improved understanding of suspended graphene devices, a controlled engineering of thermal stress in large-scale graphene electronics, and a systematic investigation of the effect of ripples on the electronic properties of graphene.

General Elasticity Theory for Graphene Membranes Based on Molecular Dynamics

ABSTRACTWe have studied the mechanical properties of suspended graphene membranes using molecular dynamics (MD) and generalized continuum elasticity theory (GE) in order to develop and assess a continuum description for graphene. The MD simulations are based on a valence force field model which is used to determine the deformation and the elastic energy of the membrane (EMD) as a function of external forces. For the continuum description, we use the expression Econt = Estretching + Ebending for the elastic energy functional. The elastic parameters (tensile rigidity and Poisson ratio) entering Econt are determined by requiring that Econt = EMD for a set of deformations.Comparisons with the MD results show excellent agreement. We find that the elastic energy of a supported graphene sheets is typically dominated by the nonlinear stretching terms whereas a linear description is valid only for very small deflections. This implies that in some applications, i.e. NEMS, a linear description is of limited applicability.