We present the science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems, targeting an evolution in technology, that might lead to impacts and benefits reaching into most areas of society. This roadmap was developed within the framework of the European Graphene Flagship and outlines the main targets and research areas as best understood at the start of this ambitious project. We provide an overview of the key aspects of graphene and related materials (GRMs), ranging from fundamental research challenges to a variety of applications in a large number of sectors, highlighting the steps necessary to take GRMs from a state of raw potential to a point where they might revolutionize multiple industries. We also define an extensive list of acronyms in an effort to standardize the nomenclature in this emerging field.

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Science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems

The stability of two-dimensional (2D) layers and membranes is subject of a long standing theoretical debate. According to the so called Mermin-Wagner theorem, long wavelength fluctuations destroy the long-range order for 2D crystals. Similarly, 2D membranes embedded in a 3D space have a tendency to be crumpled. These dangerous fluctuations can, however, be suppressed by anharmonic coupling between bending and stretching modes making that a two-dimensional membrane can exist but should present strong height fluctuations. The discovery of graphene, the first truly 2D crystal and the recent experimental observation of ripples in freely hanging graphene makes these issues especially important. Beside the academic interest, understanding the mechanisms of stability of graphene is crucial for understanding electronic transport in this material that is attracting so much interest for its unusual Dirac spectrum and electronic properties. Here we address the nature of these height fluctuations by means of straightforward atomistic Monte Carlo simulations based on a very accurate many-body interatomic potential for carbon. We find that ripples spontaneously appear due to thermal fluctuations with a size distribution peaked around 70 \AA which is compatible with experimental findings (50-100 \AA) but not with the current understanding of stability of flexible membranes. This unexpected result seems to be due to the multiplicity of chemical bonding in carbon.

Intrinsic ripples in graphene

Graphene, a single layer of carbon atoms in a honeycomb lattice, offers a number of fundamentally superior qualities that make it a promising material for a wide range of applications, particularly in electronic devices. Its unique form factor and exceptional physical properties have the potential to enable an entirely new generation of technologies beyond the limits of conventional materials. The extraordinarily high carrier mobility and saturation velocity can enable a fast switching speed for radio-frequency analog circuits. Unadulterated graphene is a semi-metal, incapable of a true off-state, which typically precludes its applications in digital logic electronics without bandgap engineering. The versatility of graphene-based devices goes beyond conventional transistor circuits and includes flexible and transparent electronics, optoelectronics, sensors, electromechanical systems, and energy technologies. Many challenges remain before this relatively new material becomes commercially viable, but laboratory prototypes have already shown the numerous advantages and novel functionality that graphene provides.

Graphene: An Emerging Electronic Material

Graphene, a monolayer of graphite sheet consisting of sp2 hybridized carbon atoms covalently bonded to three other atoms (discovered in 2004), has recently attracted the attention of chemical sensor researchers owing to its unprecedented structural, mechanical and electrical properties. Excellent mechanical strength (Young modulus ∼0.05 TPa), potentiality of ultrafast electron transport (highest mobility ∼200,000 cm 2 /V s) along with the best surface to volume ratio has opened up the opportunity to use the material for future gas and vapor sensors with ultra fast speed and long-term durability. Since it is a two dimensional material, every atom of graphene may be considered a surface atom and as a result every atom site may be involved in the gas interactions. This feature of graphene can eventually be responsible for its ultra sensitive sensor response with the lowest detection capability approaching even a single molecule. Further, the ease of functionalization of the material either by chemical means (absorption of many molecules like oxygen or hydrogen) or by application of voltage or pressure, facilitates bandgap-engineering which in turn may lead to a possible solution to the selectivity issues, the perennial problems of chemical sensors. In this review, the latest advancement and new perspectives of graphene based gas and vapor sensors have been discussed critically.

Recent developments on graphene and graphene oxide based solid state gas sensors

MEMS-based oscillators are an emerging class of highly miniaturized, batch manufacturable timing devices that can rival the electrical performance of well-established quartz-based oscillators. In this review, a description is given of the key properties of a MEMS resonator that determine the overall performance of a MEMS oscillator. Piezoelectric, capacitive and active resonator transduction methods are compared and their impact on oscillator noise and power dissipation is explained. An overview is given of the performance of MEMS resonators and MEMS-based oscillators that have been demonstrated to date. Mechanisms that affect the frequency stability of the resonator, such as temperature-induced frequency drift, are explained and an overview is given of methods that have been demonstrated to improve the frequency stability. The aforementioned performance indicators of MEMS-based oscillators are benchmarked against established quartz and CMOS technologies.

https://iopscience.iop.org/article/10.1088/0960-1317/22/1/013001/pdf

A review of MEMS oscillators for frequency reference and timing applications

In this paper, the performance of 6.35 MHz Lame-mode square resonators with different dimensions of straight-beam anchor supports is presented, with quality factor values exceeding one million in ambient pressures as high as 150 Pa. A maximum Q value of 1.70 million was experimentally measured for some of the square resonators at a vacuum pressure of 36 µTorr. The Q values of square resonators were relatively independent of pressure at levels below 100 Pa, which suggests that Q is pressure limited due to air damping only when pressures become higher than 100 Pa. Dimensions of straight-beam anchors placed at the four corners of the square resonator lead to tradeoffs among achievable Q, power handling capabilities and motional resistance. Longer anchor beams generally provide good signal-to-noise performance of a square resonator at lower dc bias; however, the resonator goes into the nonlinear regime at lower ac–dc drive amplitudes, which means reduced power handling capability. The benefit of shorter anchors is that the resonator is able to operate in a linear mode under high drive conditions. Depending on the type of application, anchor dimensions can be chosen such that the resonator's performance is optimal in terms of a quality factor, motional resistance and power handling. The resonators were fabricated using the silicon-on-insulator multi-user MEMS process from MEMSCAP.

http://iopscience.iop.org/article/10.1088/0960-1317/19/1/015017/pdf

High-Q bulk-mode SOI square resonators with straight-beam anchors

Characterization of nanomechanical graphene drum structures is presented in this paper. The structures were fabricated by mechanical exfoliation of graphite onto pre-etched circular trenches in silicon dioxide on a silicon substrate. Drum structures with diameters ranging from 3.8 to 5.7 µm and thicknesses down to 8 nm were achieved. Mechanical characterization of the devices was then carried out by using atomic force microscopy (AFM) to measure their electrostatic deflection. The structures were found to have linear spring constants ranging from 3.24 to 37.4 N m−1 and could be actuated to about 18–34% of their thickness before exhibiting nonlinear deflection. An analytical framework was formulated to model the deflection behaviour which was verified through finite element simulations (FEM). The experimental measurements agree well with analytical and finite element results using Young's modulus of 1 TPa. The resonance characteristics of the structures were derived by both plate theory and FEM simulations. It was found that our drum structures could potentially vibrate at frequencies in excess of 25 MHz. The small size and high operating frequencies of our nanomechanical graphene devices make them very promising for resonant mass sensing applications with 10−20 g Hz−1 sensitivity, a two order of magnitude improvement over other reported silicon structures.

https://iopscience.iop.org/article/10.1088/0960-1317/20/11/115029/pdf

Characterization of nanomechanical graphene drum structures

In this paper, we present comprehensive analysis of the nonlinearities in a micromechanical clamped-clamped beam resonator. A nonlinear model which incorporates both mechanical and electrostatic nonlinear effects is established for the resonator and verified by experimental results. Both the nonlinear model and experimental results show that the first-order cancellation between the mechanical and electrostatic nonlinear spring constants occurs at about 45 V dc polarization voltage for a 193 kHz resonator in vacuum pressure of 37.5 µTorr. Our study also reveals that the nonlinearity cancellation is helpful in optimizing the overall resonator performance. On top of improving the frequency stability of the resonator by reducing its amplitude-frequency coefficient to almost zero, the nonlinearity cancellation also boosts the critical vibration amplitude of the resonator (0.57 µm for the beam resonator with 2 µm nominal gap spacing), leading to better power handling capabilities. The results from the clamped-clamped beam resonator studied in this work can be easily generalized and applied to other types of resonators.

https://iopscience.iop.org/article/10.1088/0960-1317/18/6/065014/pdf

The nonlinearity cancellation phenomenon in micromechanical resonators

A fully differential CMOS readout circuit for SOI resonant accelerometer is reported. The readout circuit is essentially an oscillator, consisting of an oscillator and a low noise automatic amplitude control (AAC) loop. A differential sense resonator is proposed to facilitate fully differential circuit topology and improves the SNR under a 3.3-V supply. A second-order AAC loop filter and a novel chopper stabilized rectifier are employed in the AAC loop to remove the noises, in particular, the 1/f noise, and to minimize the phase noise caused by the amplitude stiffening effect. The strong driving feedthrough is avoided by separating the drive and sense operation in the time domain, while using the same electrodes. The complete resonant accelerometer operates under a 3.3-V supply and achieves 140-Hz/g scaling factor, 20 mug/radicHz resolution and 4 mug bias stability. The readout circuit draws 7 mA under 3.3-V supply.

A CMOS Readout Circuit for SOI Resonant Accelerometer With 4- $\mu \rm g$ Bias Stability and 20- $ \mu\rm g/\sqrt{{\hbox{Hz}}}$ Resolution

In this paper, a simple and effective experimental approach has been used to extract the mechanical properties of suspended nanomechanical graphene devices using atomic force microscopy (AFM). The main objective of this work is to study the deflection behaviour of graphene devices as a function of layer number (1–5 layers) and anchor geometry which has not been widely investigated so far. Elastic and nonlinear responses of the devices were obtained using AFM nanoindentation. The estimated linear (2.5 N m−1 to 7.3 N m−1), nonlinear spring constants (1 × 1014 N m−3 to 15 × 1014 N m−3) and pretension (0.79 N m−1 to 2.3 N m−1) for the monolayer (3.35 A) to five layer (16.75 A) graphene devices of diameter 3.8 µm show an obvious increasing trend with increase in graphene thickness. The effect of anchor geometry on the force versus deflection behaviour of these devices has also been investigated. The Raman spectroscopy results confirm the absence of defects in the pristine and indented devices. Using the continuum mechanics model, the Young's modulus and 2D elastic modulus of a monolayer graphene device have been found to be 1.12 TPa and 375 N m−1 respectively. The high stiffness and low mass of these devices make them well suited for sensing applications.

https://iopscience.iop.org/article/10.1088/0960-1317/22/10/105024/pdf

Moorthi Palaniapan

Papers

High-Q bulk-mode SOI square resonators with straight-beam anchors

Characterization of nanomechanical graphene drum structures

The nonlinearity cancellation phenomenon in micromechanical resonators

A CMOS Readout Circuit for SOI Resonant Accelerometer With 4- $\mu \rm g$ Bias Stability and 20- $ \mu\rm g/\sqrt{{\hbox{Hz}}}$ Resolution

Elastic and nonlinear response of nanomechanical graphene devices