Graphene Nanoelectromechanical Systems Research Articles

Graphene nanoelectromechanical systems as valleytronic devices

We investigate electronic transport in graphene nanoelectromechanical systems, known also as graphene nanodrums or nanomembranes. We demonstrate that these devices, despite their small values of strain between $0.1%$ and $1%$, can be used as efficient and robust valley polarizers and filters. Their working principle is based on the pseudomagnetic field generated by the strain of the graphene membrane. They work for ballistic electron beams as well as for strongly dispersed ones and can be also used as electron beam collimators due to the focusing effect of the pseudomagnetic field. We show additionally that the current flow can be estimated by semiclassical trajectories which represent a computationally efficient tool for predicting the functionality of the devices.

Design of strongly nonlinear graphene nanoelectromechanical systems in quantum regime

We report on the analysis and design of atomically thin graphene resonant nanoelectromechanical systems (NEMS) that can be engineered to exhibit anharmonicity in the quantum regime. Analysis of graphene two-dimensional (2D) NEMS resonators suggests that with device lateral size scaled down to ∼10–30 nm, restoring force due to the third-order (Duffing) stiffness in graphene NEMS can rise to equal or even exceed the force of linear stiffness, enabling strongly nonlinear NEMS resonators with anharmonic potential energy that produces sufficient deviation from a quantum harmonic spectrum, which is necessary toward realizing NEMS qubits. Furthermore, the calculations provide device design guidelines and scaling of anharmonicity in graphene NEMS to facilitate future fabrication of graphene NEMS qubits with the desired nonlinear dynamical characteristics and performance. The results in this work shall help open possibilities for engineering a new type of qubits based on 2D resonant NEMS, which may offer a much more miniaturized, densely packed, and scalable qubit platform, supplementing today's mainstream technologies such as superconducting and trapped ion qubits.

Flexural modes of graphene resonators derived from the reactive empirical bond-order potential

Flexural modes play an important role in mechanical, thermal, and electronic properties of two-dimensional materials. Graphene nanoelectromechanical systems have been found in wide applications and have attracted huge attention recently, where the molecular dynamics (MD) simulation has been an essential route for the investigation of the mechanical responses of the system. In this paper, based on the expressions and parameters of the reactive empirical bond-order potential for the carbon-carbon atomic interactions implemented in Large-scale Atomic/Molecular Massively Parallel Simulator, the linearized part of the force for each atom along the $z$ direction has been obtained, yielding the stiffness matrix of the graphene lattice. By diagonalizing the stiffness matrix, the flexural modes and their corresponding frequencies can be obtained. The results have been validated with MD simulations in circular and square graphene resonators with different sizes. Since the stiffness matrix for graphene resonators with arbitrary shapes can be obtained readily from our results, we expect broad applications where eigenfrequencies and flexural modes are needed in the analysis for the nanoscale resonators.

Spatially resolved optical excitation of mechanical modes in graphene NEMS

Emerging applications in nanoelectromechanical systems (NEMS) made from two-dimensional (2D) materials demand simultaneous imaging and selective actuation of the mechanical modes. Focused optical probes to measure and actuate motion offer a possible solution, but their lateral spatial resolution must be better than the size of the resonator. While optical interferometry is known to have excellent spatial resolution, the spatial resolution of the focused, laser-based optical driving is not currently known. Here, we combine separately scanned interferometry and optical drive probes to map the motion and forces on a suspended graphene nanomechanical resonator. By analyzing these maps with a force density model, we determine that the optical drive force has a spatial resolution on the order of the size of the focused laser spot. Using the optical force probe, we demonstrate the selective actuation and suppression of a pair of orthogonal antisymmetric mechanical modes of the graphene resonator. Our results offer a powerful approach to image and actuate any arbitrary high-order mode of a 2D NEMS.

Suspended Graphene Membranes with Attached Silicon Proof Masses as Piezoresistive Nanoelectromechanical Systems Accelerometers.

Graphene is an atomically thin material that features unique electrical and mechanical properties, which makes it an extremely promising material for future nanoelectromechanical systems (NEMS). Recently, basic NEMS accelerometer functionality has been demonstrated by utilizing piezoresistive graphene ribbons with suspended silicon proof masses. However, the proposed graphene ribbons have limitations regarding mechanical robustness, manufacturing yield, and the maximum measurement current that can be applied across the ribbons. Here, we report on suspended graphene membranes that are fully clamped at their circumference and have attached silicon proof masses. We demonstrate their utility as piezoresistive NEMS accelerometers, and they are found to be more robust, have longer life span and higher manufacturing yield, can withstand higher measurement currents, and are able to suspend larger silicon proof masses, as compared to the previous graphene ribbon devices. These findings are an important step toward bringing ultraminiaturized piezoresistive graphene NEMS closer toward deployment in emerging applications such as in wearable electronics, biomedical implants, and internet of things (IoT) devices.

Fiber-optic Lorentz force magnetometer based on a gold-graphene composite membrane

Because of its outstanding mechanical and electronic properties and unique transfer flexibility, graphene is ideal for miniature all-in-fiber nanoelectromechanical systems (NEMS) in ultrasensitive sensing applications; however, its application in magnetic detection is limited because of the lack of magnetic-optic response. Here, we demonstrate a high spatial resolution fiber-optic magnetic field sensor based on Lorentz force in a pseudo–magnetic-response quasi-static graphene NEMS. The ultra-compact design of this all-fiber-based sensor is achieved by integrating a hybrid gold-graphene membrane and two gold electrodes onto the hollow endface of a single-mode fiber. An electrical current flowing through the suspended membrane in a perpendicular magnetic field can generate Lorentz force to cause a nanoscale deformation of the membrane. The sensor has a much higher spatial resolution, which is nanometer-scale longitudinally, compared with conventional optical fiber magnetic sensors.

Electrothermally Tunable Graphene Resonators Operating at Very High Temperature up to 1200 K.

The unique negative thermal expansion coefficient and remarkable thermal stability of graphene make it an ideal candidate for nanoelectromechanical systems (NEMS) with electrothermal tuning. We report on the first experimental demonstration of electrothermally tuned single- and few-layer graphene NEMS resonators operating in the high frequency (HF) and very high frequency (VHF) bands. In single-, bi-, and trilayer (1L, 2L, and 3L) graphene resonators with carefully controlled Joule heating, we have demonstrated remarkably broad frequency tuning up to Δ f/ f0 ≈ 310%. Simultaneously, device temperature variations imposed by Joule heating are monitored using Raman spectroscopy; we find that the device temperature increases from 300 K up to 1200 K, which is the highest operating temperature known to date for electromechanical resonators. Using the measured frequency and temperature variations, we further extract both thermal expansion coefficients and thermal conductivities of these devices. Comparison with graphene electrostatic gate tuning indicates that electrothermal tuning is more efficient. The results clearly suggest that the unique negative thermal expansion coefficient of graphene and its excellent tolerance to very high temperature can be exploited for engineering highly tunable and robust graphene transducers for harsh and extreme environments.

Noninvasive Scanning Raman Spectroscopy and Tomography for Graphene Membrane Characterization.

Graphene has extraordinary mechanical and electronic properties, making it a promising material for membrane-based nanoelectromechanical systems (NEMS). Here, chemical-vapor-deposited graphene is transferred onto target substrates to suspend it over cavities and trenches for pressure-sensor applications. The development of such devices requires suitable metrology methods, i.e., large-scale characterization techniques, to confirm and analyze successful graphene transfer with intact suspended graphene membranes. We propose fast and noninvasive Raman spectroscopy mapping to distinguish between free-standing and substrate-supported graphene, utilizing the different strain and doping levels. The technique is expanded to combine two-dimensional area scans with cross-sectional Raman spectroscopy, resulting in three-dimensional Raman tomography of membrane-based graphene NEMS. The potential of Raman tomography for in-line monitoring is further demonstrated with a methodology for automated data analysis to spatially resolve the material composition in micrometer-scale integrated devices, including free-standing and substrate-supported graphene. Raman tomography may be applied to devices composed of other two-dimensional materials as well as silicon micro- and nanoelectromechanical systems.

Graphene transfer methods for the fabrication of membrane-based NEMS devices

Graphene has extraordinary mechanical and electronic properties, making it a promising material for membrane based nanoelectromechanical systems (NEMS). Here, three methods for direct transfer of chemical vapor deposited graphene onto pre-fabricated micro cavity substrates were investigated and analyzed with respect to yield and quality of the free-standing membranes on a large-scale. An effective transfer method for layer-by-layer stacking of graphene was developed to improve the membrane stability and thereby increase the yield of completely covered and sealed cavities. The transfer method with the highest yield was used to fabricate graphene NEMS devices. Electrical measurements were carried out to successfully demonstrate pressure sensing as a possible application for these graphene membranes.

Graphene nanoelectromechanical systems as stochastic-frequency oscillators.

We measure the quality factor Q of electrically driven few-layer graphene drumhead resonators, providing an experimental demonstration that Q ∼ 1/T, where T is the temperature. We develop a model that includes intermodal coupling and tensioned graphene resonators. Because the resonators are atomically thin, out-of-plane fluctuations are large. As a result, Q is mainly determined by stochastic frequency broadening rather than frictional damping, in analogy to nuclear magnetic resonance. This model is in good agreement with experiment. Additionally, at larger drives the resonance line width is enhanced by nonlinear damping, in qualitative agreement with recent theory of damping by radiation of in-plane phonons. Parametric amplification produced by periodic thermal expansion from the ac drive voltage yields an anomalously large line width at the largest drives. Our results contribute toward a general framework for understanding the mechanisms of dissipation and spectral line broadening in atomically thin membrane resonators.

Invited Presentation: Graphene Nanoelectromechanical Systems As Stochastic-Frequency Oscillators

We measure the quality factor Q of electrically-driven few-layer graphene drumhead resonators, providing an experimental demonstration that Q ~ 1/T , where T is the temperature. We develop a model that includes intermodal coupling and tensioned graphene resonators, yielding good quantitative agreement to experiment. Because the resonators are atomically thin, out-of-plane fluctuations are large. As a result Q is mainly determined by stochastic frequency broadening rather than frictional damping, in analogy to nuclear magnetic resonance. Additionally, at larger drives the resonator linewidth is enhanced by nonlinear damping, in qualitative agreement with a recent theory of damping by radiation of in-plane phonons[1]. Parametric amplification produced by periodic thermal expansion from the ac drive voltage yields an anomalously large linewidth at the largest drives. Our results contribute towards a general framework for understanding the mechanisms of dissipation and spectral line broadening in atomically thin membrane resonators.1. Croy, A.; Midtvedt, D.; Isacsson, A.; Kinaret, J. M. Phys. Rev. B 2012, 86, 235435.

Graphene nanoelectromechanical systems

Graphene possesses a combination of properties that make it extremely well suited for use in nanoelectromechanical systems (NEMS). Its exceptional mechanical properties include high stiffness and low mass, which lead to high resonant frequencies; and ultrahigh strength, which allows for strain tuning of frequency over a wide range. Its optical properties and high electronic mobility enable robust optical and electrical transduction, while its chemical inertness enables atomically thin devices. This paper reviews the basic properties of graphene NEMS, and recent work toward exploring device properties, readout techniques, and applications.

Electrically integrated SU-8 clamped graphene drum resonators for strain engineering

Graphene mechanical resonators are the ultimate two-dimensional nanoelectromechanical systems (NEMS) with applications in sensing and signal processing. While initial devices have shown promising results, an ideal graphene NEMS resonator should be strain engineered, clamped at the edge without trapping gas underneath, and electrically integratable. In this letter, we demonstrate fabrication and direct electrical measurement of circular SU-8 polymer-clamped chemical vapor deposition (CVD) graphene drum resonators. The clamping increases device yield and responsivity, while providing a cleaner resonance spectrum from eliminated edge modes. Furthermore, this resonator is highly strained, indicating its potential in strain engineering for performance enhancement.

Fabrication and performance of graphene nanoelectromechanical systems

As a result of the recent progress in fabricating large-area graphene sheets, graphene-based mechanical devices have become vastly easier to manufacture and now show even greater promise for a range of applications. This article reviews the progress of resonant graphene nanoelectromechanical systems and the possible applications of this technology to signal processing, sensing, and other areas. After discussing recent advances in fabrication and measurement techniques that make graphene resonators a viable technology, the article presents what is known about the performance of graphene mechanical systems. The authors also highlight unresolved questions, such as the source of the dissipation in graphene resonators, and discuss the progress made on these issues to date. The authors conclude with a discussion of important future directions for graphene research and the applications for which graphene nanomechanical devices may be well suited.

Electrostatic interactions between graphene layers and their environment

We analyze the electrostatic interactions between a single graphene layer and a ${\text{SiO}}_{2}$ substrate, and other materials which may exist in its environment. We obtain that the leading effects arise from the polar modes at the ${\text{SiO}}_{2}$ surface, and water molecules, which may form layers between the graphene sheet and the substrate. The strength of the interactions implies that graphene is pinned to the substrate at distances greater than a few lattice spacings. The implications for graphene nanoelectromechanical systems, and for the interaction between graphene and a scanning tunneling microscopy tip, are also considered.