Nanoelectromechanical Sensors Based on Suspended 2D Materials

Abstract

1. Introduction

Two-dimensional (2D) materials have excellent material properties for sensor applications due to their large surface-to-volume ratio and unique electrical, mechanical, and optical properties [1, 2]. More recently, the potential of 2D materials for sensing has been further extended by freely suspending 2D materials to form atomically thin membranes, ribbons, or beams [3–6]. These types of suspended 2D material structures enable a new class of 2D suspended NEMS sensors, which is the focus of the present review. Suspending 2D materials eliminates substrate interactions, increases their thermal isolation, and gives them freedom of motion, which opens a whole range of mechanical sensing modalities. In fact, many of the current micro- and nanoelectromechanical system (MEMS and NEMS) devices can be realized using suspended 2D materials, offering smaller dimensions, higher sensitivity, and novel functionalities compared to their silicon-based MEMS and NEMS counterparts. This is because the performance and sensitivity of NEMS sensors often depend critically on the thickness of the suspended membrane or beam, which can reach its ultimate thinness when using suspended 2D materials. Moreover, new types of sensors can be enabled by exploiting the unique properties of 2D materials. Sensors in which the nanomechanical and/or electrical response of suspended 2D materials is used to sense environmental parameters can be classified as 2D material NEMS sensors. Such 2D NEMS sensors therefore have the potential to provide novel and/or better solutions for applications such as the Internet of Things (IoT) and autonomous mobility, which are expected to drive the demand for integrated and high-performance sensors for years to come.

Early studies investigated the application of graphene in NEMS as resonant structures [7], which provide ultimate sensitivity for mass detection down to the hydrogen atom limit [8]. An overview of graphene-based nanoelectromechanical resonators was provided in a 2013 review paper [9], and the utilization of graphene and carbon nanotubes in NEMS was briefly summarized by Zang et al. [10]. However, it has recently become clear that graphene has potential for enabling a much wider range of NEMS sensors, with transition metal dichalcogenide (TMD) and 2D semiconductor materials also emerging in this application space [6, 11, 12].

In this work, we present a review of 2D material NEMS sensors based on suspended graphene and related 2D materials operating in vacuum or gaseous environments. We discuss the relevant material properties, describe key fabrication technologies, and evaluate the potential for Complementary Metal Oxide Semiconductor (CMOS) integration of 2D material NEMS sensors, specifically focusing on those topics relevant for these sensors that are not covered by previous reviews [13–15]. We present suitable transduction mechanisms that are of particular relevance to NEMS sensors and finally review the state of the art in 2D membrane-based NEMS sensor applications, discussing pressure sensors, accelerometers, oscillators, resonant mass sensors, gas sensors, Hall effect sensors, and bolometers. This latter part of the paper is organized by application, not by material.

2. Material Properties of Suspended 2D Materials

In designing sensors and deciding on how to fabricate them, it is important to select a suitable 2D material. For that purpose, we discuss here the material properties that are relevant for nanoelectromechanical sensing. In fact, not all 2D materials are suitable to form suspended structures. As for graphene, many of its material properties are beneficial for forming freely suspended membranes, beams, and ribbons, including chemical stability at atmospheric conditions, excellent mechanical robustness, stretchability of up to about 20% [16], a Young's modulus of 1 TPa [17], intrinsic strength of 130 GPa [17], room-temperature electron mobility of 2.5 × 10⁵ cm²/Vs [18], excellent transparency, uniform optical absorption of ≈2.3% in a wide wavelength range [19], impermeability to gases [20, 21] (except hydrogen [22]), and the ability to sustain extremely high current densities [23]. Because graphene shows very strong adhesion to SiO₂ surfaces [24], it can be suspended in one atom layer thick membranes that are mechanically stable [25] and can be readily chemically functionalized [26]. However, it is important to point out that some of the extreme properties have been measured only in mechanically exfoliated, high-quality graphene samples that do not contain grain boundaries [27] or for graphene on specific substrates such as hexagonal boron nitride [18, 28].

Beyond graphene, other 2D materials also show promising properties for the use as membrane sensors, such as their relatively high in-plane stiffness and strength [29]. For instance, Young's moduli of monolayer h-BN, MoS₂, WS₂, MoSe₂, and multilayer WSe₂ are reported to be 865 GPa, 270 GPa, 272 GPa, 177 GPa, and 167 GPa, respectively [29], in line with theoretical predictions [30]. Furthermore, the intrinsic strength of h-BN and MoS₂, two of the most studied 2D materials beyond graphene, is reported to be ~70.5 GPa and~22 GPa, with fracture strains of 6-11% and 17%, respectively [29], comparable to graphene. Hexagonal BN is an insulator that is used as a substrate and as encapsulation material for graphene and other 2D materials to improve their electronic transport properties [28] and mechanical stability. The piezoresistive gauge factors of monolayer MoS₂ and bilayer MoS₂ and PtSe₂ have been reported to be about −148 ± 19, −224 ± 19, and −84 ± 23, respectively [6, 31], which are up to two orders of magnitude higher than commonly reported values in graphene with gauge factors (GF) between 2 and 6 [25, 32–35]. Therefore, compared to graphene, transition metal dichalcogenides (TMDs) offer piezoresistive readout of NEMS with much higher responsivity. Other 2D TMDs such as WS₂, MoSe₂, and WSe₂ are also predicted to have much higher piezoresistive gauge factors than graphene [36, 37], emphasizing the potential of TMD-based piezoresistive membrane sensors. Table 1 compares the 2D material properties that are most relevant and interesting for applications based on suspended membranes, such as Young's modulus, piezoresistive gauge factor, and optical bandgap.

The values in Table 1 are extracted from measurements at room temperature under application relevant conditions. Some properties like charge carrier mobility values have only partly been investigated for the suspended 2D materials. The terms “suspended” and “supported” therefore indicate how the value was obtained. In general, due to differences in fabrication and characterization procedures, large variations in the different material properties are found in literature, which leaves many open questions for NEMS device functionality. In addition, built-in stress in suspended 2D materials is generally large and difficult to control, while having a tangible influence on the static and dynamic characteristics of 2D material NEMS [72]. Built-in stress in fully clamped graphene membranes can reach 10² to 10³ MPa [17, 20, 38, 73–78] while stress in doubly clamped graphene ribbons or beams can reach 10¹ MPa [7, 79–83] or about 200 MPa to 400 MPa in graphene ribbons with suspended silicon proof mass [72]. The built-in stress can substantially influence the resonance frequencies of resonators and accelerometers, as well as the force-induced deflection and strain in suspended 2D material membranes [72]. The fabrication process can further influence built-in stress, i.e., through design features, material growth, and the transfer material [73].

It should be noted that only a few of the materials listed in Table 1 have been shown to survive as self-suspended 2D material membrane, ribbon, or beam structure [3–5, 7]; however, many of these 2D materials may still be employed in NEMS sensors in form of multilayers or in combination with more stable suspended support layers such as graphene to form suspended heterostructures [63, 84, 85]. 2D materials may also be combined with polymer layers to form suspended membranes and beams [6, 86, 87]. The buckling metrology method has been recently revisited as an alternative method to determine Young's modulus of 2D materials and generally results in comparable experimental values as conventional metrology methods (where available) [88].

3. Fabrication Methods for Suspended 2D Material Devices

3.2. Fabrication of Devices with Suspended Membranes

There are several routes to fabricate devices with suspended membranes (often called “drums”), beams, or ribbons of 2D materials. These routes can be distinguished by (1) the method of 2D material application (2D material transfer from the growth substrate to a target substrate in contrast to 2D material growth directly on the target substrate as shown in red color in Figures 1(a)–1(e)) and (2) the method of creation of cavities below the membranes (etching underneath the 2D material in contrast to 2D material transfer onto a preetched cavity, as shown in green color in Figures 1(f)–1(j)).

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Figure 1

2D NEMS device fabrication methods. (a–e) Create a 2D material layer on the device substrate, where for (a) and (b) the device substrate is prepatterned and for (c–e) the substrate is patterned afterwards. (f)–(j) show post 2D material layer fabrication steps to create suspended membranes.

Figures 1(a) and 1(b) show the option where the device substrates are fabricated before 2D material transfer. This includes the etching of cavities over which the 2D material is to be suspended, as well as the fabrication of electrical contacts, gate electrodes, or sensing electrodes. Subsequently, 2D materials are transferred and suspended using wet transfer [121] or dry transfer using PDMS stamps [122], frame-based [99, 122–125], or other methods [126], each with its advantages and disadvantages [84]. It should be noted that compared to conventional transfer, transfer of 2D materials over cavities is challenging. Stamp transfer (Figure 1(f)) can fail by delamination due to low adhesion forces, rupture of the membranes at cavity edges, and stiction on the cavity bottom [127]. Alternatively, the transfer layer can be removed by etching (Figure 1(g)), which poses other challenges. The application of pressure on the stamp can affect the value and uniformity of the pretension in the suspended membrane and thus influence its mechanical resonance frequency and stiffness. Moreover, nonuniformity of the strain in the transfer layer can lead to wrinkled graphene membranes, and polymeric residues of a few nanometers from the stamp can be present [128]. In general, few-layer membranes are more stable, show a higher yield of intact membranes after fabrication [127], and can be suspended across larger areas.

After the 2D material is successfully suspended using dry (Figures 1(a) and 1(f)) or wet (Figures 1(b) and 1(g)) transfer, it is important to minimize the impact of subsequent process steps in order to reduce the risk of damaging the membrane and decreasing the yield of suspended 2D material membranes [84]. Process steps involving liquids suffer from capillary effects during drying and evaporation of the liquids, which typically decreases the yield of intact membranes [84]. Critical point drying (CPD) helps in this respect, but cannot be applied to membranes that seal holes because the high CPD pressures of more than 50 bar outside pressure can break the membranes. Here, a “transfer last” method (Figures 1(a) and 1(f)) is an option to create sealed membranes as required for absolute or sealed gauge pressure sensors [129]. Another option is to seal the membrane at a later stage in the process [21]. Ribbons can be either structured on the growth substrate and then transferred with alignment routines [130] or have to be structured after suspension, which is technologically extremely challenging.

Some of the issues can be avoided by either growing [131, 132] or transferring unsuspended 2D materials directly on the device substrate [72, 133] (Figures 1(c)–1(e)). It can then be patterned and subsequently the membrane can be released by isotropically underetching (Figures 1(h) and 1(i)), by using a sacrificial layer [134–137] or by releasing the membranes from the backside (Figure 1(j)). The remaining through-hole can be left open or resealed after release [133, 138]. Process steps that avoid capillary forces during drying, such as CPD or hydrofluoric acid (HF) vapor etch, can be used to avoid stiction and increase the yield of intact suspended membranes. Cleaning procedures for suspended 2D material devices are very delicate, because traditional methods used in MEMS manufacturing, such as ultrasonic-assisted dissolving or oxygen plasma ashing, are aggressive towards suspended 2D materials, and thus, these approaches are not suitable [137].

3.3. CMOS Integration

Eventually, it will become of interest to monolithically integrate suspended 2D materials with CMOS integrated circuits (ICs). Depending on the type of sensor and fabrication flow, the sensor can be integrated both in the front end (Figure 2(a)) and in the back end (Figure 2(b)) of the CMOS process. In both cases, devices with suspended 2D material membranes should be fabricated in a CMOS compatible way by growing the materials on wafer-sized substrates or by selective growth. The best process candidates are CVD and TAC, where the 2D material size is limited only by the reactor size. Wafer-scale transfer of graphene has been demonstrated and can in principle be integrated as a back-end-of-the-line process [139–143]. Direct growth of 2D materials in the back-end-of-the-line (Figure 2(b)) is only permitted if the growth temperature is below 450°C, which is for example possible for PtSe₂ with a growth temperature of 400°C or less [119, 144]. To realize CMOS integration, many challenges still need to be addressed. In particular, front-end-of-the-line integration (Figure 2(a)) of suspended 2D materials is still very challenging [13], because the material needs to survive all subsequent CMOS process steps. Besides realizing high-yield methods for the process steps discussed above, compatibility to CMOS temperature budgets, material interactions, delamination requirements, low contact resistances, packaging methods, and reliability requirements will need to be dealt with.

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Figure 2

CMOS integration of 2D NEMS sensors in backend. (a) NEMS sensor devices integrated in the backend with interconnect layers stacked on top and frontend. (b) Integration of the 2D material in the frontend on top of the interconnect layers. The silicon IC substrate (dark grey) with transistors (blue) and interconnect metals (gray/yellow) is shown. Red arrows indicate the location of the black suspended graphene.

Metrology is a general and ongoing challenge towards commercialization of 2D materials. This is augmented in membrane-based structures; scanning electron microscopy (SEM) is an option, but typically alters membrane properties due to the electron beam-assisted deposition of hydrocarbon molecules. Raman spectroscopy is a noninvasive method if applied with low laser power and can be extended to Raman tomography [145], which allows taking three-dimensional images of the entire device. Laser scanning microscopy is also feasible and noninvasive and can provide information about membrane deflection [146]. In addition, atomic force microscopy (AFM) [147], resonant interferometry [148], and colorimetry [149] can give useful information on the mechanical shape and stiffness of suspended 2D membranes.

4. Readout and Transduction Mechanisms

A number of electrical transduction mechanisms can be utilized for readout of 2D material NEMS sensors. Although optical readout and analysis techniques [7, 148] are very convenient and useful for fundamental studies, we focus here on electrical readout techniques since they are more easily and seamlessly integrated for practical NEMS sensor devices.

The main electromechanical transduction and readout techniques suitable for 2D material NEMS sensors are piezoresistive readout, capacitive readout, and transconductance readout. In addition, the electrical resistance of 2D material membranes can be used to sense changes in temperature, strain, carrier concentration, or mobility that are induced by surface interactions (e.g., gas adhesion causes doping of the 2D material). It is important to note that the electrical resistance of 2D materials, especially graphene, is extremely sensitive to various environmental parameters, which means that parameters such as small changes in the air humidity [150–153], light [154, 155], gases [119, 151, 152, 156], or temperature can strongly affect the electronic properties of a 2D material. Thus, for reliable use as sensors, these cross-sensitivity effects either have to be eliminated, by shielding or packaging, or they should be corrected for based on a calibration curve that eliminates environmental changes using input from a temperature or humidity sensor or reference device that is integrated in the same system [6, 25]. For resistance and Hall voltage measurements of 2D material NEMS sensors, it is important to realize low contact resistances and use high-mobility graphene, a general topic that receives considerable attention [157–162]. In the following, we now discuss the main electrical readout mechanisms of 2D sensors, piezoresistive, capacitive, and transconductance readout.

5. Mechanical Properties of Suspended 2D Material Membranes and Ribbons

2D material membranes and ribbons, specifically those made from graphene, can be made a factor 1000 thinner than those of current commercial MEMS sensor membranes or beams. As a consequence, these graphene membranes and ribbons have a much lower flexural rigidity. This allows either the reduction of the sensor size to only a few microns in diameter or side length while retaining the flexural softness of the membrane or beam or a significant increase in sensor responsivity. However, to enable these, several challenges need to be tackled. The membrane/ribbon deflection needs to be determined with nanometer precision using accurate transduction mechanisms and the pretension n₀ in the graphene needs to be low enough to ensure that the responsivity is not limited by it. For the deflection of a doubly clamped 2D material ribbon caused by a center point force, the deflection at the center of the ribbon is described by

where F is the load applied at the center of the ribbon, Z the resulting deflection of the ribbon at its center (for large deflection with respect to the thickness of the ribbon), E the Young's modulus of the 2D material, W the width of the ribbon, H the thickness of the ribbon, L the total length of the ribbon, and T the built-in tension force of the ribbon [72]. Another aspect of 2D material membranes and ribbons that is intrinsically different from conventional devices is that the force-deflection curve of indentation experiments tends to become nonlinear at much smaller deflections than for bulk materials, due to the small thickness and high Young's modulus in graphene in combination with geometric nonlinearities (from the second term on the right-hand side of equation (2)) related to membrane stretching. This effect increases the stiffness and reduces the sensor linearity, which in principle can be corrected by proper calibration. It will increase operation range but reduces responsivity and will therefore require tradeoffs between dynamic range and responsivity [182]. Since graphene membranes and ribbons have a much smaller area, they feature higher thermomechanical “Brownian motion” noise [177] that translates, for example, for a circular membrane to a pressure noise p_n:

where T is the temperature, Q the quality factor, and ω₀ the resonance frequency of the membrane. This equation shows that on the one hand 2D material pressure sensors have reduced noise due to their small effective mass m_eff, whereas on the other hand thermomechanical noise will increase as a consequence of their smaller area and higher resonance frequency. Nevertheless, it is often not the thermomechanical noise that limits NEMS sensor resolution in practice, but readout noise.

A further requirement on membrane properties in many NEMS sensors, such as in some pressure sensor, is that the membrane may need to be hermetically sealed, such that the pressure in the reference cavity is constant and gas leakage is negligible during its lifetime [21]. Despite the impermeability of graphene for gases [20, 22], it was found that gas can leak via the interface between the substrate and the graphene. This leakage path needs to be sealed for long-term pressure stability inside the reference cavity [21]. In pressure sensing applications, it is typically preferred to maintain a vacuum or a very low gas pressure environment in the cavity below the 2D material membrane, to avoid internal pressure variations with temperature according to the ideal gas law, or alternatively, methods to correct for these using an integrated temperature sensor are required.

6. 2D Material NEMS Sensors

6.1. Pressure Sensors

Silicon-based pressure sensors were the first microelectromechanical system (MEMS) product to reach volume production [183]. The number of pressure sensors produced per year currently exceeds a billion units per year. Whereas the field of pressure sensing also includes liquid, tactile, and touch sensing applications, we focus here on gas pressure sensors using suspended membranes, with main applications as altimeters, barometers, gas control, and indoor navigation. MEMS pressure sensors usually determine the pressure from the pressure difference Δp (see equation (1)) across a plate that induces a deflection δ = αΔpA²/t³, a geometry and material dependent factor α.

Commercial MEMS sensors can resolve pressure differences as small as 1 Pa, corresponding to altitude changes of only 5 cm. To reach this resolution, an extremely low stiffness of the mechanical plate is required, resulting in diaphragm sizes of several hundreds of microns at membrane thicknesses in the order of 0.5-10 μm. In addition, highly sensitive membrane deflection detection circuitry is used, conventionally based on piezoresistive readout, but recently also capacitive readout, such as the SBC10 pressure sensor of Murata with a responsivity of 55 fF/kPa [184]. Reducing the size and improving the sensitivity of pressure sensors are generally of interest. For example, size may be a decisive form factor for wearable electronics. Enhanced sensitivity of 2D sensors may also enable new applications that are currently not feasible, like altimeters with sub-cm resolution for indoor navigation or pressure sensors for presence detection. Moreover, higher sensor sensitivity can reduce size, acquisition time, power consumption, and cost of readout electronics.

In the following, we will first discuss two types of static graphene pressure sensors: piezoresistive and capacitive pressure sensors. Then, we will discuss two types of resonant pressure sensors and Pirani pressure sensors. Finally, we will compare the different types of pressure sensors.

6.1.1. Piezoresistive Pressure Sensors

The basic geometries and the operation principles of 2D piezoresistive pressure sensors are shown in Figures 3(a)–3(c) and Figures 3(d)–3(f), respectively. The first subfigures (Figures 3(a) and 3(h)) show the device fabrication according to methods described in Figure 1 (coloring shows 2D material transfer or growth and method to suspend the membranes). When the membrane is bent by a pressure difference, it introduces strain into the material (Figures 3(d)–3(f)) which is detected as a resistance change (Figure 3(g)). It is important to note that gasses or moisture that is in contact with the suspended 2D material membrane typically affects its resistance, which can interfere with the piezoresistive signal during pressure measurements [25, 35, 151]. In addition to self-suspended graphene membranes [25], graphene resistors have been used to piezoresistively detect the motion of membranes made from SiN [185] or polymers [186]. Even though graphene enables very thin membranes, its piezoresistive gauge factor GF = (ΔR/R)/ε is relatively low (see Table 1) [25, 35]. Other 2D materials have higher gauge factors (see Table 1) and are promising for improving piezoresistive pressure sensor sensitivity, as demonstrated for PtSe₂ [6]. The membrane area of graphene [25] and PtSe₂ [6] devices can be reduced to around 170 μm², which is significantly smaller than the area (90000 μm²) of conventional MEMS pressure sensors [172, 187]. Low-dimensional materials, such as carbon nanotubes [188, 189] or silicon nanowires [10, 190], can also be used for piezoresistive sensors, due to their high GFs [191]. However, these materials can only be used as sensing elements and usually need a separate membrane to support them, in contrast to 2D membranes that can have both a mechanical and electrical function. Such purely 2D material membranes combine a very thin membrane with the intrinsic readout mechanism and potentially enable up to four orders of magnitude smaller device footprints [6, 25].

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Figure 3

Piezoresistive NEMS pressure sensor. (a) Fabrication method of the suspended membrane (according to Figure 1). (b, c) Example device image [6]. (d–f) Working principle: pressure difference causes tension which alters the membrane resistance by the piezoresistive effect. (g) Graphene piezoresistive pressure sensor measurement [25]. Capacitive pressure sensor: (h) fabrication of the suspended membrane. (i) Device schematic [182]. (j–l) Working principle: a pressure difference causes the membrane to deflect and alter the capacitance between the graphene and the bottom electrode. (m) Device measurement [182].

6.1.2. Capacitive Pressure Sensors

2D capacitive pressure sensors (Figures 3(h) and 3(i)) consist of a capacitor, which is formed between the membrane and a bottom electrode, such that a pressure change results in a capacitance change (Figures 3(j)–3(l)). As can be seen in Figure 3(m), the capacitance is a nonlinear function of pressure. This is both due to the nonlinearity in the capacitance-deflection relation and due to the nonlinearity in the pressure-deflection curve (equation (3)). Main parameters that can influence the shape of this curve are the gap size, membrane thickness, Young's modulus, pretension, membrane radius, and quantum capacitance. As can be seen from the slope of the curve in Figure 3(m), the sensor is most sensitive when the pressure difference across it is zero.

When a capacitive pressure sensor is made out of a single graphene drum, its capacitance and change in capacitance is very small. For readout, it requires detecting a small capacitance change on a large parasitic background capacitance. Even when using insulating quartz substrates to reduce the parasitic capacitance [182], it is difficult to measure the capacitance changes, since responsivities of a drum with a 5 micron diameter are at most 0.1 aF/Pa, which at a voltage of 1.6 V corresponds to only 1 electron moving onto the graphene for a pressure change of 1 Pa. By utilizing a high-frequency AC signal to charge and discharge the capacitor many cycles, signal-to-noise ratios can be improved to achieve a resolution of 2-4 aF/√Hz, requiring at least 20-40 of these drums in parallel to reach a pressure resolution of 1 Pa with an acquisition time of 1 second [192]. Recently, capacitive pressure sensors have been reported with many graphene drums in parallel that outperform the best commercial capacitive pressure sensors (SBC10 of Murata, responsivity 55 aF/Pa [184]) and that could be read out using a commercial IC [193]. With a large 5-layer graphene membrane, a responsivity of 15 aF/Pa was reached [194] and an even higher responsivity of 123 aF/Pa was reached with graphene-polymer membranes [87]. Increasing drum diameter or further gap or tension reduction can also improve responsivity of graphene pressure sensors, although these options come with significant engineering challenges.

6.1.3. Tension-Induced Resonant Pressure Sensors

Resonant tension-induced pressure sensors, similar to piezoresistive pressure sensors, monitor the effect of gas pressure on the strain in a membrane. However, here, the change in strain is monitored via its effect on the resonance frequency of the graphene membrane (Figures 4(a) and 4(b)). Bunch et al. [20] first utilized this effect to characterize the pressure difference across sealed graphene membranes in 2008. This demonstration of the extreme sensitivity of the resonance frequency to pressure was later confirmed with sealed graphene [21] and MoS₂ [195] membranes, resulting in variations in the fundamental resonance frequency of more than a factor of 4 (Figures 4(c)–4(f)). A theoretical analysis of the dependence of the resonance frequency of a circular membrane on pressure found that the values of Young's modulus that were extracted from the experimental fits are anomalously low [21]. It is still unclear whether this is related to wrinkling effects [196], deviations from the theoretical shape and tension, or squeeze-film, slippage, or delamination effects. Also, the pressure dependence of the quality factor of tensioned membranes is not fully understood [136] and might not only depend on the pressure difference but also on the individual gas pressures below and above the membrane.

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Figure 4

Tension-induced pressure sensor: (a) fabrication method of the suspended membrane (according to Figure 1) and (b) example device [21]. (c–e) Working principle: the gas pressure difference across the membrane causes a membrane deflection and tension change that is measured via the resonance frequency. (f) Graphene tension-induced pressure sensor measurement [21]. Squeeze-film pressure sensor: (g) fabrication of the suspended membrane and (h) example device [175]. (i, j) Working principle: the stiffness and compressibility of the gas under the membrane increases the stiffness of the membrane that is measured via the mechanical resonance frequency. (k) Example measurement of a graphene-based squeeze-film pressure sensor [175]. Graphene Pirani pressure sensor: (l) fabrication of the suspended membrane; (m) example device of a Pirani pressure sensor [132]. (n, o) Working principle: the temperature, and temperature-dependent resistance, of the suspended, Joule-heated graphene beam depends on the pressure-dependent gas cooling rate. (p) Example measurement of a Pirani pressure sensor based on graphene [132].

Typical responsivities dω₀/dp are larger than 200 Hz/Pa. It typically takes 1/200 second to determine a frequency change of 200 Hz; therefore, this indicates that it might be possible to resolve pressure changes of 1 Pa in less than 5 ms. To actually achieve this, temperature [176], mass loading, and other effects that affect the resonance frequency of the membrane need to be prevented or corrected with proper calibration using additional sensors. The low Q (Q of approximately 3) of graphene at atmospheric pressure will increase the power and time required to accurately determine the resonance frequency.

It should be emphasized that the high responsivity of tension-induced pressure sensors can be attributed to the extreme thinness of graphene, which results in a low mass and thus in a very high initial resonance frequency ω₀, but also in a relatively large strain and related tension-induced resonance frequency changes when the graphene “balloon” is inflated.

6.1.4. Squeeze-Film Resonant Pressure Sensors

A second type of resonant pressure sensor is the squeeze-film pressure sensor. In contrast to the previously discussed sensors, squeeze-film pressure sensors do not require a hermetically sealed cavity (Figures 4(g) and 4(h)). The operation mechanism is based on the measurement of compressibility of gas inside the cavity under the graphene membrane. The compression occurs when the time it takes for pressure in the cavity to equilibrate is much longer than the period of the motion of the membrane, effectively trapping the gas in the cavity. It follows from the ideal gas law that the resonance frequency is ω_res² = ω₀²(P = 0) + A P/(m g), where m is the membrane mass, so the low areal mass density of graphene is an advantage that increases the responsivity Δω_res/ΔP of the sensor. The change in the resonance frequency with respect to the vacuum value ω₀ is dependent on the mass and geometry of the graphene cavity (Figures 4(i) and 4(j)). It has been shown [175] that the small graphene thickness and cavity depth result in a frequency change as large as 10-90 Hz/Pa, which is a factor of 5-45 higher than that in conventional MEMS squeeze-film sensors despite the smaller area of the device (Figure 4(k)). More recently, the feasibility of fabricating squeeze-film pressure sensors using transferless graphene (Figure 1(d)) has been demonstrated [132].

6.1.5. Pirani Pressure Sensors

Pirani pressure sensors operate by measuring the pressure-dependent thermal conductivity of the surrounding gas via its influence on the temperature-dependent resistance of a suspended membrane (Figures 4(l) and 4(m)). In contrast to all other pressure sensors discussed above, the Pirani sensor does not mechanically move during operation. Conventionally, Pirani sensors are only used in vacuum systems. However, in [197], it was shown that the sensitivity range of these sensors can be brought to atmospheric pressure by reducing the gap down to 400 nm. The advantage of using graphene for Pirani sensors is that it takes much less power to heat a thin beam than a thick beam, and the temperature of the graphene beam depends more strongly on the cooling by surrounding gases due to its large surface-to-volume ratio (Figures 4(n)–4(p)). With a transferless process flow (Figure 1(d)), the feasibility of graphene Pirani pressure sensors was recently demonstrated [132]. It should be noted that the response of Pirani pressure sensors is gas dependent, due to differences in thermal conductivity of different gases. This property might be employed to utilize the Pirani sensor as a gas sensor, when complemented by a pressure sensor that is independent of the type of gas.

6.1.6. Pressure Sensor Comparison

Important benchmark parameters for comparing different pressure sensors include size, power consumption, acquisition time, cross-sensitivity, reliability, and production cost. In terms of performance, the capability to detect small pressure changes ΔP is an important parameter to compare the different sensors. To detect the signal of such a small change, it needs to be larger than the pressure noise in the system, i.e., the signal-to-noise-ratio (SNR) needs to exceed 1. Usually, the electrical readout noise (Johnson-Nyquist) is the dominant noise source that limits the SNR in these systems [198]. For a pressure change ΔP, the SNR is determined to compare the different types of pressure sensors (piezoresistive, capacitive, and squeeze-film). The noise in a capacitive pressure sensor can be determined by using the charge noise of the capacitor σQ=4kBTC and the total energy costs for a measurement E_tot = Pt_readout = NCV², where k_B is the Boltzmann constant, T the temperature, C the capacitance, P the electrical power consumption, t_readout the readout time over which the measurement results are averaged, V the voltage, and N the number of measurements [198]:

Noise=σC=4kBTC/NV=C4kBTPt.

(4)

The noise itself does not depend on the responsivity, but the capacitive signal dC = ΔP dC/dP does depend on the pressure change ΔP as well as the responsivity. By taking the ratio, the SNR can be calculated for the capacitive pressure sensor defined as

SNRCAP=1C0dCdPPtreadout4kBT∆P.

(5)

Here, C₀ is the capacitance in the unloaded state. Note that the minimum detectable pressure change corresponds to solving this equation for ΔP for SNR = 1. For comparison, the SNR can be determined for a piezoresistive pressure sensor. An expression like (5) is found, with the term 1/C₀ × dC/dP being replaced by 1/R₀ × dR/dP for piezoresistive pressure sensors [198]. In case of the squeeze-film pressure sensor, a factor Q needs to be added resulting in 1/C₀ × dC/dP being replaced by 2/ω₀ × dω_res/dP × Q. We assume Q = 3 for graphene at atmospheric pressure [199].

With these rough estimates of the SNR, based on an optimal performance of the readout system, different pressure sensor types can be directly compared to each other, which are shown in Figure 5. An SNR of 5.5 × 10⁻⁶ Pa⁻¹ was calculated for both the PtSe₂ membrane-based piezoresistive by Wagner et al. [6] and the commercial capacitive pressure sensors Murata SCB10H [184], which shows one of the highest SNR values available. The graphene membrane-based squeeze-film by Dolleman et al. [175] and capacitive pressure sensor by Davidovikj et al. [182] show values of 4.7 × 10⁻⁶ Pa⁻¹ and 0.3 × 10⁻⁶ Pa⁻¹, respectively. A SNR of 0.3 × 10⁻⁶ Pa⁻¹ and 0.3 × 10⁻⁷ Pa⁻¹ could be calculated for the piezoresistive graphene-based sensor by Wang et al. [185] and by Smith et al. [25], respectively. These 2D material sensors were also compared to other low-dimensional material-based NEMS pressure sensors (carbon nanotubes, Stampfer et al. [188]; silicon nanowires, Zhang et al. [172]) as well as to another commercial sensor, Epcos C35 [200], which is summarized in Figure 5. The PtSe₂ sensors show a factor of 5 to 200 higher SNR and up to 5 orders of magnitude smaller sensor area in comparison to state-of-the-art pressure sensors.

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Figure 5

SNR comparison of piezoresistive (PR), capacitive (CAP), and squeeze-film (SQF) MEMS pressure sensors. Included are Wagner et al. [6], Murata SCB10H [184], Dolleman et al. [175], Stampfer et al. [188], Epcos C35 [200], Zhang et al. [172], Wang et al. [185], Davidovikj et al. [182], and Smith et al. [25].

7. Graphene Microphones

A microphone is essentially a pressure sensor that operates at audible or ultrasound frequencies. Similar to pressure sensors, the extreme thinness and the resulting flexibility of suspended 2D materials make them highly susceptible to sound pressure variations and thus suitable for application as microphones. In the last decades, MEMS microphones have replaced most conventional microphones in mobile devices and have become a billion-dollar market, where often multiple microphones are employed for realizing directionality and noise cancellation. The key advantage of using suspended graphene as a microphone membrane is its low stiffness k_eff. In conventional microphones, the stiffness cannot be lowered much further, because for a flatband frequency response it is required to have a resonance frequency ω₂ = k_eff/m_eff that exceeds the audible bandwidth (usually >20 kHz). Since graphene is extremely thin, it has a very small mass, allowing low stiffness to be combined with a high resonance frequency, offering interesting prospects for enabling wide bandwidth microphones that can detect small sound pressures. In addition, the low mass of graphene might be advantageous to reduce the pressure noise level based on equation (3). Besides improved performance, the advantages of graphene can also be utilized for area downscaling of microphones while maintaining current performance. This in turn can facilitate low-cost arrays of microphones that can enable directionality and might find applications in 3D ultrasound imaging and noise cancellation. Challenges in reaching sufficient signal-to-noise ratio are even much tougher in microphones than in pressure sensors since current typical MEMS microphones boast responsivities (sensitivities) of >10 mV/Pa and impressive pressure noise levels below p_n < 10 μPa/√Hz [201]. This low-noise, high-responsivity performance has not yet been demonstrated with graphene membranes, but theoretically, graphene is expected to outperform conventional MEMS membranes according to equation (3).

Condenser microphones with multilayer graphene membranes (20-100 nm thick) were reported with radii varying from 12 mm down to 40 μm [146, 202, 203]. These devices cover a frequency range from the audible domain [202, 203] up to the ultrasonic domain [146]. Devices with a small membrane diameter (Figures 6(a)–6(f)) [146] operate over a wide frequency range that includes ultrasonic frequencies, while requiring low voltages, below the pull-in voltage of 1.78 V, which is well suited for use in mobile phones that provide a standard supply voltage of 2 V. Devices with a large membrane diameter [202, 203] require higher operation voltages but were also shown to function as a speaker. Importantly, some of the reported devices outperform high-end commercial nickel-based microphones over a significant part of the audio spectrum, with a larger than 10 dB enhancement of sensitivity, demonstrating the potential of graphene in microphone applications. Compared to conventional MEMS microphones with sensitivities of approximately -36 dB (around 15.8 mV/Pa), a supply voltage of 1.62-3.6 V [204], and an active membrane of 5 mm² [205], graphene-supported microphone diaphragms have sensitivities of up to 10 mV/Pa, at a supply voltage of 1 V, and a diaphragm size of 38.22 mm³ [206]. Thus, current silicon-based microphone technologies are even more sensitive than those using graphene, but microphone designs with two vibrating membranes are usually used to amplify the signal [205], which is currently not the case with graphene.

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Figure 6

Microphone: (a) fabrication method of the suspended membrane (according to Figure 1); (b, f) images of an example device [146]. (c–e) Working principle: the sound pressure-dependent deflection of the membrane is detected via its capacitance with respect to the backplate. Ultrasound detector: (a) fabrication of the suspended membrane; (h) example device [181] and (i, j) working principle: the graphene membrane is moved by the ultrasound-induced motion of its supports, and its motion is detected using transconductance readout. Accelerometer: (k) fabrication of the suspended membrane; (l, m) example device [72], (n–p) working principle: the acceleration-induced forces on the suspended mass cause tension in the graphene that is detected using the piezoresistive effect. (q) The output signal of an accelerometer [72].

8. Ultrasound Detection

Recently, graphene-based high-frequency geophones have been introduced to detect ultrasonic waves in a silicon substrate [181] and to detect generalized Love waves in a polymer film (Figures 6(g)–6(j)) [207]. In these works, a highly sensitive electronic readout was employed reaching a resolution in ultrasonic vibration amplitude of 7 pm/√Hz. Interestingly, this resolution is independent of the mechanical resonance frequency of the suspended graphene membrane. The coupling mechanism between the substrate vibrations into the graphene membrane is currently still under debate, as the detected amplitudes are seemingly large. Recent work using an interferometric detection scheme suggests that graphene not just acts as a detector of the ultrasonic vibrations and resonant modes in the substrate but also as an amplifier [180]. However, the physical origin of the strong coupling remains elusive. The possibility of using graphene for detecting vibrations or sound in solids could enable a new regime of ultrasound imaging at higher frequencies and smaller wavelengths than currently possible.

9. Accelerometers

In current silicon-based MEMS accelerometers, the springs and interdigitated readout electrodes cause a significant increase in the device area. On the one hand, this is caused by the requirement of a sufficiently small spring constant, which requires long compliant springs. On the other hand, for capacitive readout MEMS accelerometers, a sufficient capacitor area is required, which results in many interdigitated readout electrodes. Graphene and 2D materials on their own are not well suited for accelerometers, because their intrinsic mass is too small to achieve sufficient responsivity. 2D materials thus require an additional proof mass in the suspended region, which is displaced by acceleration forces. Although graphene has a small piezoresistive gauge factor, it can exhibit a large resistance change per Newton force (1/F × ΔR/R), because of its ultimate thinness. Its high Young's modulus and fracture strain further suggest that it is suitable for suspended devices with attached proof masses. Figures 6(n)–6(p) show an example of such a graphene NEMS accelerometer design, where the graphene simultaneously forms the springs of the spring-mass system and the piezoresistive transducer elements. The strain in the suspended graphene ribbons or membranes resulting from acceleration causes resistance changes in the graphene, due to the piezoresistive readout technique used in the accelerometers.

Double-layer graphene ribbons with large suspended silicon proof masses were realized with a conventional MEMS and NEMS manufacturing approach [72]. The graphene was suspended by dry etching followed by vapor HF etching to remove a sacrificial buried oxide layer (similar to Figure 1(h)). The suspended silicon proof masses had dimensions of up to 50 μm × 50 μm × 16.4 μm (Figures 6(k)–6(m)), which is more than three orders of magnitude heavier than the masses deposited on previous devices [208–210]. The graphene ribbons with suspended proof mass occupy at least two orders of magnitude smaller die areas than conventional state-of-the-art silicon accelerometers while keeping competitive sensitivity (Figures 6(n)–6(q)) [72]. After normalization, the relative responsivity (resistance change per proof mass volume) in graphene ribbon accelerometers is at least one order of magnitude larger than the silicon state of the art. This demonstrates the potential to shrink the size of graphene-based NEMS accelerometers and gyroscopes despite graphene's low gauge factor.

The sensitivity of graphene accelerometers can be further improved by increasing the attached mass or by reducing the width of the suspended graphene [72]. From the perspective of material selection, the use of other two-dimensional materials like MoS₂ [29, 31, 36] or PtSe₂ [6, 144] with significantly higher piezoresistive gauge factors would also potentially improve the device sensitivity, although these materials need to be carefully evaluated with respect to their mechanical stability and adhesion force to the substrate. To this end, device designs based on fully clamped membranes improve the mechanical robustness by avoiding edges that are starting points for tearing under stress. However, this approach is a compromise as the signal response of fully clamped membranes is generally lower than that of ribbons with identical proof masses and trench width due to the lower strain levels and parasitic parallel resistances [133].

In addition to the above-mentioned demonstrations of graphene NEMS accelerometers, there are a limited number of experimental realizations of suspended graphene membranes or ribbons with attached proof masses. Micrometer-sized few-layer graphene cantilevers with diamond allotrope carbon weights fabricated by focused ion beam deposition have been used to study the mechanical properties of graphene [208]. A kirigami pyramid was combined with cantilevers made of suspended graphene and supported 50 nm thick gold masses, but these devices had to be kept in liquid to maintain their mechanical integrity [209]. Finally, suspended graphene membranes circularly clamped by SU-8 that are supporting a mass made of either SU-8 or gold located at the center of the graphene membranes and that were evaluated as shock detector for ultrahigh mechanical impacts [210]. These reports utilized very small masses and some employed fabrication methods that are not considered compatible with semiconductor manufacturing. In addition, graphene-based resonant accelerometers have been proposed on theoretical grounds but not yet experimentally demonstrated [211–213]. In these concepts, the acceleration would act on suspended graphene beams or membranes, thereby resulting in added strain in the suspended graphene beams or membranes, thus causing a related shift in their resonance frequencies.

10. Hall Sensors

When a conductor that is biased on one side is exposed to an external magnetic field, charge carriers experience a Lorentz force that drives them in a direction perpendicular to the electric field and the external magnetic field. The resulting Hall voltage is a measure of the magnetic field and is proportional to 1/n, where n is the charge carrier concentration. The electronic structure of single-layer graphene results in a very low carrier density at the minimum of its conductivity and thus high Hall voltage. In addition, the charge carrier concentration can be tuned to reach high responsivity. The ultimate signal-to-noise ratio of Hall sensors is proportional to the mobility μ. The very low effective mass of charge carriers in graphene translates into very high mobility at room temperature, which enables high-performance graphene-based magnetic field sensors. The mobility in graphene depends to a large extent on the (dielectric) environment, i.e., the interface with its surroundings. Relevant to this review, high mobilities of up to μ = 200000 cm²/Vs have been measured in suspended graphene [214–216], which are significantly higher compared to up to μ = 20000 cm²/Vs for supported graphene on a SiO₂ substrate [217]. Suspended graphene Hall sensors are of interest (Figures 7(a)–7(d)) because the voltage sensitivity (SV) of linear Hall sensors depends on the charge carrier mobility μ (SV ∝ μ∙(W/L)), where W and L are the width and length of the device [218]. The carrier mobility of electrons is about 1241 cm²/Vs in silicon at a dopant concentration of approximately 1017 cm⁻³ at room temperature [219]. The intrinsic SV is thus approximately 160 times greater for suspended graphene (at μ = 200000 cm²/Vs) than for silicon. Also, graphene shows a linear Hall response over several hundred mT [220] and surpasses commercial Hall sensors based on silicon technology [221]. Nevertheless, commercial monolithic silicon Hall sensors produced with BiCMOS technology, such as the Infineon linear Hall sensor series TLE499x [222], reach sensitivities up to 300 mV/mT at an operation voltage of 5.5 V and an operation range of ±200 mT. These high values are achieved through of the use of integrated amplifier circuits and enhance the intrinsic Hall effect in silicon. Such established integration technology is still missing for graphene, but improvements may be expected as the technology matures [13, 14]. Recent results indicate that graphene mobilities can be quite high when encapsulating graphene by Al₂O₃ [218], hBN [18, 46], and WSe₂ [223]. This may be a promising route to also improve the performance of Hall sensors based on nonsuspended graphene [224, 225], which may be preferred for most applications, as it removes some of the fabrication challenges of suspended graphene membranes [146]. As discussed, the Hall effect provides an accurate method to detect the carrier concentration n. Suspended graphene Hall sensors, where the membrane is exposed to the environment, are thus promising as gas sensors, where molecules adsorbed to the graphene change its doping (=carrier density). Such sensors could be sensitive down to the single-molecule level [1].

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Figure 7

Hall sensor: (a) fabrication method of the suspended membrane (according to Figure 1) and (b, c) example device [146] and readout of an example device [146]. Gas sensor: (e) fabrication of the suspended membrane and ribbon and (f) example device [244]. (g, h) Working principle: gas molecules adhere to the (functionalized) 2D material and alter its resistance via electronic or chemical interactions. (i, j) Readout of an example device [248] and (k) typical sensor response plot of MoSe₂ sensors depending on electron-donating/withdrawing gas [110]. Mass sensor: (l) fabrication of the suspended membrane, (m) example device, and (n, o) working principle: by measuring the resonance frequency, the mass change of the membrane is derived. (p) Extracted mass and tension of the membrane during multiple loading cycles [83]. Bolometer: (q) fabrication of the suspended membrane and ribbon and (r) example device [266]. (s, t) Working principle: when radiation heats the membrane, this alters its tension and causes a shift in mechanical resonance frequency. (u) Readout of an example device with a graphene membrane [266].

11. Gas Sensors

12. Graphene Mass Sensors

The low mass of graphene makes it an interesting candidate for accurate mass sensing. Such a sensor, shown in Figures 7(l)–7(o), determines a mass change of the membrane or ribbon by monitoring changes in its resonance frequency. The mass change can be introduced by adsorbed or attached atoms or molecules on the surface of the membrane. The responsivity of resonant mass sensors is given by Δω_res = −½ω_res Δm/m_eff [261, 262], which shows that for a small mass m of the graphene membrane or ribbon, a relatively large frequency shift will occur. The high sensitivity of this principle was shown by adding and removing layers of pentacene with an equivalent mass of 6 layers of monolayer graphene and monitoring its effect on the resonance frequency of a graphene membrane (Figure 7(p)) [128]. Such suspended graphene resonant mass sensors are expected to find applications in fields where it is required to determine mass changes much less than a monolayer of a 2D material. In comparison, conventional quartz crystal monitors have been shown to be able to measure the mass of a single monolayer of graphene [128]. The sensitivity of graphene-based mass sensors can reach a value of 10⁻²⁷ g/Hz [263], which greatly outperforms silicon membrane-based sensors, with typical sensitivity values of only 10⁻¹⁸ g/Hz [264]. Commercial mass sensors have even lower sensitivity values of around 60 × 10⁻⁹ g/Hz [265]. In the ultimate limit, graphene nanomembranes with diameters of below 10 nm, which often occur naturally in graphene on silicon oxide substrate, have been theoretically predicted to be able to detect one hydrogen atom of mass, which would lead to a relative resonance frequency shift of 10⁻⁴.

13. Graphene Bolometers

Bolometers are devices to detect absorption of electromagnetic radiation and light by monitoring the resulting temperature changes in a material via changes in its electrical resistivity. Especially for long wavelength infrared and THz radiation, bolometers are of interest, since there are few alternative detectors available in this frequency regime. At room temperature, where superconducting bolometers cannot be realized, suspended graphene is an interesting material for utilization of low-cost bolometers due to its ultra-wideband electromagnetic absorption and low heat capacitance due to its atomic thickness (Figures 7(q)–7(u)). The high thermal conductivity and low temperature coefficient of resistance of graphene are drawbacks that have recently been mitigated by instead utilizing a resonant readout mechanism in a focused ion-beam structured suspended graphene bolometer (Figure 7(q)) [266]. However, cross-sensitivity to other signals (e.g., thermoelectric and photoelectric) needs to be also dealt with. Graphene-based resonant radiation detectors for the infrared range show a noise equivalent power of about 2 pW/Hz at room temperature [266] and are thus in the upper range of conventional infrared bolometers based on vanadium oxide or nickel (1-10 pW/Hz) [267–271].

There are many other types of 2D material-based photosensors, but they are usually not suspended and fall therefore outside the scope of this review.

14. Discussion and Conclusions

While the field of silicon-based MEMS sensors is getting mature, the advent and discovery of 2D materials have brought us a set of nanomaterials for realizing novel NEMS sensors. Not only are these new materials thinner than any currently available CMOS or MEMS material, allowing drastic reductions of device size and enhanced sensitivity, there is also a larger range of materials emerging with exceptional properties. This large range of available material properties increases the freedom to engineer desired sensor properties for a particular application and to maximize sensitivity and reduce dimensions of the NEMS sensors. Moreover, by creating heterostructures of 2D materials, an even larger number of parameters will become available to optimize the sensor's electrical, mechanical, thermal, optical, chemical, and magnetic properties. The possibilities are expanding even further, since new types of ultrathin materials for NEMS applications continue to emerge, like those based on complex oxides [272] and 2D organic magnetic membranes [273].

In this review, we have given an overview of the NEMS sensors and proof-of-concept devices based on suspended 2D materials that have been demonstrated during the ast decade. These devices are almost always smaller than their conventional MEMS counterparts. Moreover, they show improved performance and sometimes even completely novel functionalities. Despite these successes, there are still enormous challenges ahead to demonstrate that 2D material-based NEMS sensors can outperform conventional devices on all important aspects. One of these tasks is the establishment of high-yield manufacturing capabilities [15]. We have given an overview and comparison of the different potential fabrication routes and their challenges, focusing on the challenges related to suspended sensors. In this respect, the recent EU experimental pilot line is expected to set a big step towards high quality, high-volume graphene devices [274]. Of course, a platform approach where multiple types of suspended sensors can be produced in a single production flow is desirable, but it remains to be seen to what extent this can be realized. Other remaining tasks are sensitive and customized electronic sensor readout circuits, packaging, and reliability testing for the 2D material NEMS sensors.

We believe that of all potential electronics applications for 2D materials, sensors made from nonsuspended 2D materials could be one of the first to become commercially available. Suspending the materials inherently adds process complexity and challenges and hence will likely take a longer time. Nevertheless, we are optimistic that, with joint efforts from both academia and industry, the first NEMS sensors based on 2D materials could hit the markets before the start of the next decade. In addition, 2D materials are now discussed for ultimate CMOS logic as stacked nanosheet transistors. This may trigger enormous, game-changing investments by industry that would upend any predictions made by us today.

Acknowledgments

References