Nanoelectromechanical Sensors based on Suspended 2D Materials

The unique properties and atomic thickness of two-dimensional (2D) materials enable smaller and better nanoelectromechanical sensors with novel functionalities. During the last decade, many studies have successfully shown the feasibility of using suspended membranes of 2D materials in pressure sensors, microphones, accelerometers, and mass and gas sensors. In this review, we explain the different sensing concepts and give an overview of the relevant material properties, fabrication routes, and device operation principles. Finally, we discuss sensor readout and integration methods and provide comparisons against the state of the art to show both the challenges and promises of 2D material-based nanoelectromechanical sensing.


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 depends 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 are 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) or and autonomous mobility, which are expected to drive the demand for integrated and highperformance 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 in 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 membranebased NEMS sensors 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.

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  [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]. 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, bi-layer 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 the Young's modulus, piezoresistive gauge factor and optical bandgap. It should be noted that only a few of the materials listed in Table 1

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 on the target substrate) as shown in red color in  and polymeric residues of a few nanometer 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 (Figure 1a,f) or wet (Figure 1b,g) transfer, it is important to minimize the impact of subsequent process steps to 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 ( Figure 1a [162]. In the following we now discuss the main electrical readout mechanisms of 2D sensors, piezoresistive, capacitive and transconductance readout.

Piezoresistive readout
The piezoresistive effect is defined as the change in electrical resistivity due to applied mechanical strain, which is related to the deflection of a membrane. The gauge factor (GF) is a measure for the piezoresistive effect [163]: It is defined as the ratio of the change in the electrical resistance ΔR to the change Δε= ΔL/L in mechanical strain (change in absolute length). The geometric deformation is described by the term 1+2ν, with ν as the Poisson's ratio.

Capacitive readout
Capacitive readout is an alternative method to determine the deflection of 2D membranes.
For a deflection δ, the capacitance of a drum with area A and gap g is given by Cdrum = Aε0/(gδ). The responsivity therefore scales as dC/dδ = Aε0/g 2 and increases by reducing the gap g.
With respect to other deflection readout mechanisms, the important advantage of capacitive readout is that the capacitance only depends on the geometry of the structure, regardless of the membrane resistance and temperature. In practice however, it is difficult to fabricate membranes with gaps smaller than 100 nm with sufficient yield [127] without causing stiction during fabrication. Also, a small gap limits the maximum membrane deflection and thus, the maximum dynamic pressure range of the device. An alternative approach to increase responsivity is therefore to increase the area of the membranes, for instance by placing many graphene sensors in parallel [87]. Another challenge is that there are usually parasitic parallel capacitances Cpar present between the top and bottom electrodes that need to be minimized to reduce power consumption and increase signal-to-noise ratio. This can be achieved by utilization of an insulating layer with a low dielectric constant and sufficient breakdown strength, a small overlap area between top and bottom electrodes (using local gates) and the utilization of an insulating, low dielectric constant substrate [87]. A unique feature of monolayer membranes, such as monolayer graphene with low carrier densities is that their capacitance is lowered by an effective series quantum capacitance [170], especially close to the Dirac point. When a readout voltage Vg is applied across the sensor to determine its capacitance, this will not only affect the quantum capacitance, but can also result in an electrostatic pressure Pel = ε0Vg 2 /(g-δ) 2 that adds to the gas pressure and deflects the membrane. These effects need to be considered to accurately operate capacitive graphene pressure sensors, either by proper modeling, or by proper calibration.

Transconductance readout
Transconductance readout is a sensitive electrical readout method for 2D material membranes (see e.g. [171], [172]). It requires a three-terminal geometry, in which the conductivity of the 2D membrane is measured between a source and drain electrode, while a voltage is placed on a nearby gate electrode. When the membrane is deflected, the capacitance between gate and membrane changes and results in a different charge Q on the membrane (Q = CVg), which results in a change in charge density and thus a different conductivity of the membrane, similar to that in the channel of a field-effect transistor.

Readout of resonant sensors
For resonant sensors, usually a vector network analyzer or spectrometer is used to determine the resonance frequency from a frequency spectrum or the transfer characteristic. In order to continuously monitor a resonance frequency, the resonant sensor can be configured in a direct feedback loop as a self-sustained oscillator that generates a signal with a sensor signal dependent frequency, that can for example simply be read-out by a digital frequency counter circuit that counts the number of zero-crossings per second. This method has been applied successfully to MEMS squeeze-film pressure sensors [173]. In more advanced implementations readout can be performed using phased locked loops [174]. Nevertheless, the feasibility of realizing an integrated portable resonant graphene sensor still needs to be proven.

Actuation methods
Actuation methods for 2D membranes include electrostatic actuation, opto-or electrothermal  [181]. In general, for realizing most types of sensors concepts, the challenge is more in the readout than in the actuation. Nevertheless, for sensors that utilize actuation voltages and currents, these need to be stable and noise-free, since any drift and noise at the actuation side will end up in the readout signal. The effects of noise can be mitigated by using a longer time-averaging, or by placing membranes in parallel to increase responsivity [87], [182].

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 doublyclamped 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 graphene, 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 1) 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 pn: 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 meff, 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.

Pressure sensors
Silicon-based pressure sensors were the first microelectromechanical systems (MEMS) product to reach volume production [184]. 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.

Piezoresistive pressure sensors
The basic geometries and their operation principles of 2D piezoresistive pressure sensors are shown in Figure 3a-c and Figure 3d-f, respectively. The first subfigures (Figure 3a,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 (Figure 3d-f)  Even though graphene enables very thin membranes, its piezoresistive gauge factor GF = (ΔR/R)/ε is relatively low (see Table 1Fehler! Verweisquelle konnte nicht gefunden werden.) [35], [188]. Other 2D materials have higher gauge factors (see Table 1) and are promising for improving piezoresistive pressure sensor sensitivity, as demonstrated for PtSe2  [191] or silicon nanowires [10], [192] can also be used for piezoresistive sensors, due to their high GFs [193]. 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]. Capacitive pressure sensors 2D capacitive pressure sensors (Figure 3h,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 (Figure 3j-l). As can be seen in Fig. 3m, 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 3m, the sensor is most sensitive when the pressure difference across it is zero. although these options come with significant engineering challenges.

Tension-induced resonant pressure sensors
Resonant tension-induced pressure sensors monitor, similar to piezoresistive pressure sensors, 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 . It is still unclear whether this is related to wrinkling effects [198], 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.
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. example device [21]. [21]. Squeeze-film pressure sensor: (g) fabrication of the suspended membrane, (h) example device [175].

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 (Figure 4g,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 ωres 2 = ω0 2 (ΔP=0)

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 (Figure 4l,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 [199] 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 (Figure 4n-p). With a transferless process flow (Figure 1d), 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.

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 [200]. For a pressure change ΔP, the SNR is The noise itself does not depend on the responsivity, but the capacitive signal dC = ΔP dC/dP does depends 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: 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 [200]. 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 × dωres/dP × Q. We assume Q = 3 for graphene at atmospheric pressure [201].
With these rough estimates of the SNR, based on an optimal performance of the readout system, different pressure sensors types can be directly compared to each other, which is shown in Figure 5. An SNR of 5.5×10 -6 Pa -1 was calculated for both the PtSe2 membrane-

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 keff. 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 = keff/meff 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 . 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 [207] , which is currently not the case with graphene.

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 (Figure 6g-j) [209]. In these works, a highly sensitive electronic read-out 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.  [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].

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. [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

Hall sensors
When a conductor, that is biased on one side, is exposed to an external magnetic field, charge  . Again, suspending these sensors will enhance the surface area and sensitivity, albeit at the cost of more challenging fabrication schemes, so that one has to choose an optimum cost/performance scenario.
Finally, repeatability and drift of gas sensors is a major general challenge, since the chemical binding energy of the gas molecules to the 2D material needs to be paid to remove the molecules and restore the sensor to its initial state. If the binding energy is close to kBT this might be performed by heating, otherwise light can be used to decrease recovery times. that small molecules such as H2 and CO2 permeate the membranes by a factor 1,000 faster than argon, nitrogen and methane gas. This methodology can also be used for permeation based gas sensing, as was shown in [261] where a change in gas composition caused an osmotic pressure across a graphene membrane. This pressure is a consequence of the permeability differences of the different gases, that effectively resulted in the graphene acting as a semi-permeable membrane. For even larger pore sizes, when going from molecularsieving to effusion dominated permeation, these sensing principles can be utilized for gas sensing [262], although with lower selectivity.

Graphene mass sensors
The low mass of graphene makes it an interesting candidate for accurate mass sensing. Such a sensor, shown in Figure 7l graphene nano-membranes 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 .  Figure 1), (b),(c) example device [146] and readout of an example device [146]. Gas sensor: (e) fabrication of the suspended membrane and ribbon, (f)example device [246]. (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 [250], (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, (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, (r) example device [268]. (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 [268].

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 (Figure 7q 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.

Discussion and conclusions
While the field of silicon-based MEMS sensors is getting mature, the advent and discovery of 2D materials has 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, 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 last 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 [276]. 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 non-suspended 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.