Motivated by recent experiments on suspended graphene showing carrier mobilities as high as 200,000 cm^2/Vs, we theoretically calculate transport properties assuming Coulomb impurities as the dominant scattering mechanism. We argue that the substrate-free experiments done in the diffusive regime are consistent with our theory and verify many of our earlier predictions including (i) removal of the substrate will increase mobility since most of the charged impurities are in the substrate, (ii) the minimum conductivity is not universal, but depends on impurity concentration with cleaner samples having a higher minimum conductivity. We further argue that experiments on suspended graphene put strong constraints on the two parameters involved in our theory, namely, the charged impurity concentration n_imp and d, the typical distance of a charged impurity from the graphene sheet. The recent experiments on suspended graphene indicate a residual impurity density of 1-2 \times 10^{10} cm^{-2} which are presumably stuck to the graphene interface, compared to impurity densities of ~10^{12} cm^{-2} for graphene on SiO_2 substrate. Transport experiments can therefore be used as a spectroscopic tool to identify the properties of the remaining impurities in suspended graphene.
Charged impurity (CI) scattering is one of the dominant factors that affect the carrier mobility in graphene. In this paper, we use Raman spectroscopy to probe the charged impurities in suspended graphene. We find that the 2D band intensity is very sensitive to the CI concentration in graphene, while the G band intensity is not affected. The intensity ratio between the 2D and G bands, I2D/IG, of suspended graphene is much stronger compared to that of non-suspended graphene, due to the extremely weak CI scattering in the former. This finding is consistent with the ultra-high carrier mobility in…
We study the mechanism of wrinkling of suspended graphene, by means of atomistic simulations. We argue that the structural instability under edge compression is the essential physical reason for the formation of periodic ripples in graphene. The ripple wavelength and out-of-plane amplitude are found to obey 1/4-power scaling laws with respect to edge compression. Our results also show that parallel displacement of the clamped boundaries can induce periodic ripples, with oscillation amplitude roughly proportional to the 1/4 power of edge displacement. The results are fundamental to graphene's a…
Declining the lattice thermal conductivity in graphene is essential for its thermoelectric applications. In high electron density systems, scatterings of phonons by electrons are no less than the phonon scatterings by other phonons. With the aid of first-principle calculations we examine the lattice thermal conductivity in graphene by inducing electron-phonon scattering externally. With experimentally tunable charge carrier density we find $\sim 50\%$ reduction of the lattice thermal conductivity at 200 K. The present study opens up new avenues for potential thermoelectric applications of grap…
We have studied electron scattering by out-of-plane (flexural) phonon modes in doped suspended graphene and its effect on charge transport. In the free-standing case (absence of strain) the flexural branch shows a quadratic dispersion relation, which becomes linear at long wavelength when the sample is under tension due to the rotation symmetry breaking. In the non-strained case, scattering by flexural phonons is the main limitation to electron mobility. This picture changes drastically when strains above $\bar{u}=10^{-4} n(10^{12}\,\text{cm}^{-2})$ are considered. Here we study in particular …
Free-standing exfoliated monolayer graphene is an ultra-thin flexible membrane, which exhibits out of plane deformation or corrugation. In this paper, a technique is described to measure the band structure of such free-standing graphene by angle-resolved photoemission. Our results show that photoelectron coherence is limited by the crystal corrugation. However, by combining surface morphology measurements of the graphene roughness with angle-resolved photoemission, energy dependent quasiparticle lifetime and bandstructure measurements can be extracted. Our measurements rely on our development …
Control of nucleation sites is an important goal in materials growth: nuclei in regular arrays may show emergent photonic or electronic behavior, and once the nuclei coalesce into thin films, the nucleation density influences parameters such as surface roughness, stress, and grain boundary structure. Tailoring substrate properties to control nucleation is therefore a powerful tool for designing functional thin films and nanomaterials. Here, we examine nucleation control for metals deposited on two-dimensional (2D) materials in a situation where substrate effects are absent and heterogeneous nu…
2D crystals, such as graphene, exhibit the higher strength and stiffness of any other known man-made or natural material. So far, this assertion has been primarily based on modelling predictions and on bending experiments in combination with pertinent modelling. True uniaxial loading of suspended graphene is not easy to accomplish; however such an experiment is of paramount importance in order to assess the intrinsic properties of graphene without the influence of an underlying substrate. In this work we report on uniaxial tension of graphene up to moderate strains of 0.8% ca.. This has been m…
We consider graphene sheet suspended above a conducting surface. Treating graphene as an elastic membrane subjected to Casimir force, we study its stability against attachment to the conductor. There exists a critical elevation at the edges below which the central part of suspended graphene nucleates a trunk that becomes attached to the conductor. The dependence of the critical elevation on temperature and dimensions of the graphene sheet is computed.
The mechanical response of single and multiple graphene sheets under uniaxial compressive loads was studied with molecular dynamics simulations, using different semi-empirical force fields at different boundary conditions or constrains. Compressive stress-strain curves were obtained and the critical stress/strain values were derived. For single layer graphenes, the critical stress/strain for buckling was found to scale to the inverse length square. For multilayer graphenes the critical buckling stress also decreased with increasing length, though at a slower rate than expected from elastic buc…
The sticking probability of cold atomic hydrogen on suspended graphene calculated by Lepetit and Jackson [Phys. Rev. Lett. {\bf 107}, 236102 (2011)] does not include the effect of fluctuations from low-frequency vibrations of graphene. These fluctuations suppress the sticking probability for low incident energies ($\lesssim 15$ meV).
We demonstrate high-resolution modification of suspended multi-layer graphene sheets by controlled exposure to the focused electron beam of a transmission electron microscope. We show that this technique can be used to realize, on timescales of a few seconds, a variety of features, including nanometer-scale pores, slits, and gaps that are stable and do not evolve over time. Despite the extreme thinness of the suspended graphene sheets, extensive removal of material to produce the desired feature geometries is found to not introduce long-range distortion of the suspended sheet structure.
In this work we demonstrate that a free-standing van der Waals heterostructure, usually regarded as a flat object, can exhibit an intrinsic buckled atomic structure resulting from the interaction between two layers with a small lattice mismatch. We studied a freely suspended membrane of well aligned graphene on a hexagonal boron nitride (hBN) monolayer by transmission electron microscopy (TEM) and scanning TEM (STEM). We developed a detection method in the STEM that is capable of recording the direction of the scattered electron beam and that is extremely sensitive to the local stacking of ato…
X-ray photoelectron spectroscopy of graphene is important both for its characterization and as a model for other carbon materials. Despite great recent interest, the intrinsic photoemission of its single layer has not been unambiguously measured, nor is the layer-dependence in free-standing multilayers accurately determined. We combine scanning transmission electron microscopy and Raman spectroscopy with synchrotron-based scanning photoelectron microscopy to characterize the same areas of suspended graphene samples down to the atomic level. This allows us to assign spectral signals to regions …
We report on suspended single-layer graphene deposition by a transfer-printing approach based on polydimethylsiloxane stamps. The transfer printing method allows the exfoliation of graphite flakes from a bulk graphite sample and their residue-free deposition on a silicon dioxide substrate. This deposition system creates a blistered graphene surface due to strain induced by the transfer process itself. Single-layer-graphene deposition and its "blistering" on the substrate are demonstrated by a combination of Raman spectroscopy, scanning electron microscopy and atomic-force microscopy measuremen…
Since the discovery of the Amonton's law and with support of modern tribological models, friction between surfaces of three-dimensional materials is known to generally increase when the surfaces are in closer contact. Here, using molecular dynamics simulations of friction force microscopy on suspended graphene, we demonstrate an increase of friction when the scanning tip is retracted away from the sample. We explain the observed behavior and address why this phenomenon has not been observed for isotropic 3-D materials.
The temperature dependence of the mobility in suspended graphene samples is investigated. In clean samples, flexural phonons become the leading scattering mechanism at temperature $T \gtrsim 10\,\,$K, and the resistivity increases quadratically with $T$. Flexural phonons limit the intrinsic mobility down to a few $\text{m}^2/\text{Vs}$ at room $T$. Their effect can be eliminated by applying strain or placing graphene on a substrate.
We study a suspended graphene sheet subject to the electric field of a gate underneath. We compute the elastic deformation of the sheet and the corresponding effective gauge field, which modifies the electronic transport. In a clean system the two-terminal conductance of the sample is reduced below the ballistic limit and is almost totally suppressed at low carrier concentrations in samples under tension. Residual disorder restores a small finite conductivity.
We investigate the electromechanical response of doubly clamped graphene nanoribbons to a transverse gate voltage. An analytical model is developed to predict the field-induced deformation of graphene nanoribbons as a function of field intensity and graphene geometry. This model is validated thought atomistic simulations using the combination of a constitutive charge-dipole model and a pseudo-chemical many-body potential. As a newly observed effect of electric polarization, this field-induced deflection allows the graphene to oscillate at its natural frequency, which is found to decrease drama…
Narrow gaps are formed in suspended single to few layer graphene devices using a pulsed electrical breakdown technique. The conductance of the resulting devices can be programmed by the application of voltage pulses, with a voltage of 2.5V~4.5V corresponding to an ON pulse and voltages ~8V corresponding to OFF pulses. Electron microscope imaging of the devices shows that the graphene sheets typically remain suspended and that the device conductance tends to zero when the observed gap is large. The switching rate is strongly temperature dependent, which rules out a purely electromechanical swit…
We theoretically consider, comparing with the existing experimental literature, the electrical conductivity of gated monolayer graphene as a function of carrier density, temperature, and disorder in order to assess the prospects of accessing the Dirac point using transport studies in high-quality suspended graphene. We show that the temperature dependence of graphene conductivity around the charge neutrality point provides information about how close the system can approach the Dirac point although competition between long-range and short-range disorder as well as between diffusive and ballist…
We have fabricated suspended few layer (1-3 layers) graphene nanoribbon field effect transistors from unzipped multiwall carbon nanotubes. Electrical transport measurements show that current-annealing effectively removes the impurities on the suspended graphene nanoribbons, uncovering the intrinsic ambipolar transfer characteristic of graphene. Further increasing the annealing current creates a narrow constriction in the ribbon, leading to the formation of a large band-gap and subsequent high on/off ratio (which can exceed 104). Such fabricated devices are thermally and mechanically stable: re…
The possibility to make 10 nm scale, and low-disorder, suspended graphene devices would open up many possibilities to study and make use of strongly coupled quantum electronics, quantum mechanics, and optics. We present a versatile method, based on the electromigration of gold-on-graphene bow-tie bridges, to fabricate low-disorder suspended graphene junctions and quantum dots with lengths ranging from 6 nm up to 55 nm. We control the length of the junctions, and shape of their gold contacts by adjusting the power at which the electromigration process is allowed to avalanche. Using carefully en…
We fabricate freely suspended nanosheets of MoS2 which are characterized by quantitative optical microscopy and high resolution friction force microscopy. We study the elastic deformation of freely suspended nanosheets of MoS2 using an atomic force microscope. The Young's modulus and the initial pre-tension of the nanosheets are determined by performing a nanoscopic version of a bending test experiment. MoS2 sheets show high elasticity and an extremely high Young's modulus (0.30 TPa, 50% larger than steel). These results make them a potential alternative to graphene in applications requiring f…
We report electrical transport measurements on a suspended ultra-low-disorder graphene nanoribbon(GNR) with nearly atomically smooth edges that reveal a high mobility exceeding 3000 cm2 V-1 s-1 and an intrinsic band gap. The experimentally derived bandgap is in quantitative agreement with the results of our electronic-structure calculations on chiral GNRs with comparable width taking into account the electron-electron interactions, indicating that the origin of the bandgap in non-armchair GNRs is partially due to the magnetic zigzag edges.
We have achieved mobilities in excess of 200,000 cm^2/Vs at electron densities of ~2*10^11 cm^-2 by suspending single layer graphene. Suspension ~150 nm above a Si/SiO_2 gate electrode and electrical contacts to the graphene was achieved by a combination of electron beam lithography and etching. The specimens were cleaned in situ by employing current-induced heating, directly resulting in a significant improvement of electrical transport. Concomitant with large mobility enhancement, the widths of the characteristic Dirac peaks are reduced by a factor of 10 compared to traditional, non-suspende…
Graphene nanoribbons present diverse electronic properties ranging from semiconducting to half-metallic, depending on their geometry, dimensions and chemical composition. Here we present a route to control these properties via externally applied mechanical deformations. Using state-of-the-art density functional theory calculations combined with classical elasticity theory considerations, we find a remarkable Young's modulus value of ~7 TPa for ultra-narrow graphene strips and a pronounced electromechanical response towards bending and torsional deformations. Given the current advances in the s…
Using molecular dynamics simulations, we probe a suspended graphene layer by a diamond-like-carbon tip at various temperatures. The force acting on the tip in the sliding direction is measured to be negative at liquid-helium temperature. This negative force is found to be associated with a spontaneous lateral oscillation of the suspended graphene in favor of a low interface potential corrugation. Our hypothesis is that, at low temperature, this oscillation induces an important hidden contribution to the friction force in the lateral direction. This functions as a particular energy dissipation …
The resistivity of ultra-clean suspended graphene is strongly temperature dependent for 5K<T<240K. At T~5K transport is near-ballistic in a device of ~2um dimension and a mobility ~170,000 cm^2/Vs. At large carrier density, n>0.5*10^11 cm^-2, the resistivity increases with increasing T and is linear above 50K, suggesting carrier scattering from acoustic phonons. At T=240K the mobility is ~120,000 cm^2/Vs, higher than in any known semiconductor. At the charge neutral point we observe a non-universal conductivity that decreases with decreasing T, consistent with a density inhomogeneity <10^8 cm^…
We extract experimentally the electronic thermal conductivity, $K_{e}$, in suspended graphene which we dope using a back-gate electrode. We make use of two-point dc electron transport at low bias voltages and intermediate temperatures (50 - 160 K), where the electron and lattice temperatures are decoupled. The thermal conductivity is proportional to the charge conductivity times the temperature, confirming that the Wiedemann-Franz relation is obeyed in suspended graphene. We extract an estimate of the Lorenz coefficient as 1.1 to 1.7 $\times 10^{-8}$ W $Ω$K$^{-2}$. $K_e$ shows a transistor eff…
We develop two types of graphene devices based on nanoelectromechanical systems (NEMS), that allows transport measurement in the presence of in situ strain modulation. Different mobility and conductance responses to strain were observed for single layer and bilayer samples. These types of devices can be extended to other 2D membranes such as MoS2, providing transport, optical or other measurements with in situ strain.
The measured frequencies and intensities of different first- and second- order Raman peaks of suspended graphene are used to show that optical phonons and different acoustic phonon polarizations are driven out of local equilibrium inside a sub-micron laser spot. The experimental results are correlated with a first principles-based multiple temperature model to suggest a considerably lower equivalent local temperature of the flexural phonons than those of other phonon polarizations. The finding reveals weak coupling between the flexural modes with hot electrons and optical phonons. Since the ul…
Graphene with high carrier mobility μ is required both for graphene-based electronic devices and for the investigation of the fundamental properties of graphene's Dirac fermions. It is largely accepted that the mobility-limiting factor in graphene is the Coulomb scattering off of charged impurities that reside either on graphene or in the underlying substrate. This is true both for traditional graphene devices on SiO2 substrates and possibly for the recently reported high-mobility suspended and supported devices. An attractive approach to reduce such scattering is to place graphene in an envir…
Two different points of view are available to understand the behavior of graphene at low energies. One is considering a large $N_F$ that makes graphene a semimetal, and another for small $N_F < 2.5$ that would make graphene a narrow gap semiconductor (D. T. Son, Phys. rev. B 75, 235423 (2007)), a prediction supported independently by Monte Carlo simulations (J. E. Drut and T. A. Lähde, Phys. Rev. Lett. 102, 026802 (2009), see also Phys. Rev. B 79, 241405(R) (2009)). Taking into account recently obtained experimental evidence for weakly coupled graphene layers, i.e. graphite (N. García et al., …
We investigate the thermal conductivity of suspended graphene as a function of the density of defects, ND, introduced in a controllable way. Graphene layers are synthesized using chemical vapor deposition, transferred onto a transmission electron microscopy grid, and suspended over ~7.5-micrometer size square holes. Defects are induced by irradiation of graphene with the low-energy electron beam (20 keV) and quantified by the Raman D-to-G peak intensity ratio. As the defect density changes from 2.0x10^10 cm-2 to 1.8x10^11 cm-2 the thermal conductivity decreases from ~(1.8+/-0.2)x10^3 W/mK to ~…
We demonstrate high-frequency mechanical resonators in ballistic graphene p-n junctions. Fully suspended graphene devices with two bottom gates exhibit ballistic bipolar behavior after current annealing. We determine the graphene mass density and built-in tension for different current annealing steps by comparing the measured mechanical resonant response to a simplified membrane model. We consistently find that after the last annealing step the mass density compares well with the expected density of pure graphene. In a graphene membrane with high built-in tension, but still of macroscopic size…
We demonstrate a fabrication scheme for clean suspended structures using chemical-vapor-deposition-grown graphene and a dry transfer method on lift-off-resist-coated substrates to facilitate suspended graphene nanoelectronic devices for technology applications. It encompasses the demands for scalable fabrication as well as for ultra-fast response due to weak coupling to environment. The fabricated devices exhibited initially a weak field-effect response with substantial positive ($p$) doping which transformed into weak negative ($n$) doping upon current annealing at the temperature of 4 Kelvin…
We study the intrinsic transport properties of suspended graphene devices at high fields (>1 V/um) and high temperatures (>1000 K). Across 15 samples, we find peak (average) saturation velocity of 3.6x10^7 cm/s (1.7x10^7 cm/s), and peak (average) thermal conductivity of 530 W/m/K (310 W/m/K), at 1000 K. The saturation velocity is 2-4 times and the thermal conductivity 10-17 times greater than in silicon at such elevated temperatures. However, the thermal conductivity shows a steeper decrease at high temperature than in graphite, consistent with stronger effects of second-order three-phonon sca…
Inspired by recent experimental realizations of two-dimensional (2D) metals and alloys, we theoretically investigate the stability and electronic properties of monolayer (ML) Fe-C compounds and pure Fe. According to our and others theoretical results, the experiment [Science 343, 1228 (2014)] proposed ML pure Fe square-lattices embedded in graphene (Gr) pores are energetically unstable compared to that of the Fe triangular-lattices in Gr. To solve the above contradiction, we search for the stable structures of ML Fe-C with various Fe to C ratios (as a generalization of ML Fe in Gr) using ab in…
Electrostatic gating offers elegant ways to simultaneously strain and dope atomically thin membranes. Here, we report on a detailed \textit{in situ} Raman scattering study on graphene, suspended over a Si/SiO$_2$ substrate. In such a layered structure, the intensity of the Raman G- and 2D-mode features of graphene are strongly modulated by optical interference effects and allow an accurate determination of the electrostatically-induced membrane deflection, up to irreversible collapse. The membrane deflection is successfully described by an electromechanical model, which we also use to provide …
The implementation of aberration-corrected electron beam lithography (AC-EBL) in a 200 keV scanning transmission electron microscope (STEM) is a novel technique that could be used for the fabrication of quantum devices based on 2D atomic crystals with single nanometer critical dimensions, allowing to observe more robust quantum effects. In this work we study electron beam sculpturing of nanostructures on suspended graphene field effect transistors using AC-EBL, focusing on the in situ characterization of the impact of electron beam exposure on device electronic transport quality. When AC-EBL i…
Near infrared pump-probe spectroscopy has been used to measure the ultrafast dynamics of photoexcited charge carriers in monolayer and multilayer graphene. We observe two decay processes occurring on 100 fs and 2 ps timescales. The first is attributed to the rapid electron-phonon thermalisation in the system. The second timescale is found to be due to the slow decay of hot phonons. Using a simple theoretical model we calculate the hot phonon decay rate and show that it is significantly faster in monolayer flakes than in multilayer ones. In contrast to recent claims, we show that this enhanced …
We report measurements of the cyclotron mass in graphene for carrier concentrations n varying over three orders of magnitude. In contrast to the single-particle picture, the real spectrum of graphene is profoundly nonlinear so that the Fermi velocity describing the spectral slope reaches ~3x10^6 m/s at n <10^10 cm^-2, three times the value commonly used for graphene. The observed changes are attributed to electron-electron interaction that renormalizes the Dirac spectrum because of weak screening. Our experiments also put an upper limit of ~0.1 meV on the possible gap in graphene.
The formation of atomic nanoclusters on suspended graphene sheets have been investigated by employing a Molecular dynamics simulation at finite temperature. Our systematic study is based on temperature dependent Molecular dynamics simulations of some transition and alkali atoms on suspended graphene sheets. We find that the transition atoms aggregate and make various size nanoclusters distributed randomly on graphene surface. We also report that most alkali atoms make one atomic layer on graphene sheets. Interestingly, the potassium atoms almost deposit regularly on the surface at low temperat…
The recent discovery of graphene has sparked significant interest, which has so far been focused on the peculiar electronic structure of this material, in which charge carriers mimic massless relativistic particle. However, the structure of graphene - a single layer of carbon atoms densely packed in a honeycomb crystal lattice - is also puzzling. On the one hand, graphene appears to be a strictly two-dimensional (2D) material and exhibits such a high crystal quality that electrons can travel submicron distances without scattering. On the other hand, perfect 2D crystals cannot exist in the free…
The production of new sensors, transducers and electronic components can benefit from the possibility to alter the electronic transport of metal-semicondutor-metal (MSM) devices. 2D materials are extremely appealing for those new technologies. This can determined by several phenomena as piezoelectric effect, piezoresistive effect and modulation of Schottky barrier. In particular, MoS$_2$, among other Transition Metal Dichalcogenides (TMDs), is predicted to show a transition from semiconductor to metal under strain. In this article we present measurements on the modulation of electronic transpo…
Atomic resolution high angle annular dark field imaging of suspended, single-layer graphene, onto which the metals Cr, Ti, Pd, Ni, Al and Au atoms had been deposited was carried out in an aberration corrected scanning transmission electron microscope. In combination with electron energy loss spectroscopy, employed to identify individual impurity atoms, it was shown that nano-scale holes were etched into graphene, initiated at sites where single atoms of all the metal species except for gold come into close contact with the graphene. The e-beam scanning process is instrumental in promoting meta…
We show that thin sheets under boundary confinement spontaneously generate a universal self-similar hierarchy of wrinkles. From simple geometry arguments and energy scalings, we develop a formalism based on wrinklons, the transition zone in the merging of two wrinkles, as building-blocks of the global pattern. Contrary to the case of crumple paper where elastic energy is focused, this transition is described as smooth in agreement with a recent numerical work. This formalism is validated from hundreds of nm for graphene sheets to meters for ordinary curtains, which shows the universality of ou…
Thermal conductivity $κ$ of both suspended and supported graphene has been studied by using molecular dynamics simulations. Obvious length dependence is observed in $κ$ of suspended single-layer graphene (SLG), while $κ$ of supported SLG is insensitive to the length. The simulation result of room temperature $κ$ of supported SLG is in good agreement with experimental value. In contrast to the decrease in $κ$ induced by inter-layer interaction in suspended few-layer graphene (FLG), $κ$ of supported FLG is found to increase rapidly with the layer thickness, reaching about 90% of that of bulk gra…
We report a deterministic 2D material (2DM) transfer method to assemble any-stacking-order heterostructures incorporating suspended ultra-thin 2D materials, such as single-layer graphene (SLG) and bilayer graphene (BLG). The transfer procedure relies on a single-step preparation nitrocellulose micro-stamp, which combines both outstanding adhesion and softness. It permits the dry pick-up of naked 2D crystals (graphene, MoS$_2$, and hBN) directly from a SiO$_2$ substrate, and to precisely transfer them on substrates or trenches. Optical and Raman data show that no significant defect is introduce…
The amount of rippling in graphene sheets is related to the interactions with the substrate or with the suspending structure. Here, we report on an irreversibility in the response to forces that act on suspended graphene sheets. This may explain why one always observes a ripple structure on suspended graphene. We show that a compression-relaxation mechanism produces static ripples on graphene sheets and determine a peculiar temperature $T_c$, such that for $T<T_c$ the free-energy of the rippled graphene is smaller than that of roughened graphene. We also show that $T_c$ depends on the structur…
The nature of its intrinsic ripples is the key factor for understanding the stability of suspended graphene, and for unraveling the long-standing theoretical debate of the existence of low-dimensional crystalline state. The rippling morphology of graphene, discovered also in other 2D materials, has a profound impact on its electronic, mechanical and chemical properties. Actually, before the discovery of graphene, rippling phenomena are widely observed: for example, the roughing transition of crystalline interface, the rippled phase in biomembrane, and crumpling of flexible sheet polymers model…
Graphene (GR) remarkable mechanical and electrical properties - such as its Young's modulus, low mass per unit area, natural atomic flatness and electrical conductance - would make it an ideal material for micro and nanoelectromechanical systems (MEMS and NEMS). However, the difficulty of attaching GR to supports coupled with naturally occurring internal defects in a few-layer GR can significantly adversely affect the performance of such devices. Here, we have used a combined contact resonance atomic force microscopy (CR-AFM) and ultrasonic force microscopy (UFM) approach to characterise and m…
