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SC I ENCE ADVANCES | R E S EARCH ART I C L E

APPL I ED PHYS I CS

1Department of Electrical Engineering and Computer Science, Case School of En-gineering, Case Western Reserve University, Cleveland, OH 44106, USA. 2Instituteof Fundamental and Frontier Sciences, University of Electronic Science and Tech-nology of China, Chengdu, Sichuan 610054, China. 3Department of Physics, Col-lege of Arts and Sciences, Case Western Reserve University, Cleveland, OH 44106,USA. 4School of Applied and Engineering Physics, Cornell University, Ithaca, NY14853, USA.*These authors contributed equally to this work.†Present address: Department of Electrical Engineering, Stanford University,Stanford, CA 94305, USA.‡Corresponding author. Email: [email protected]

Lee et al., Sci. Adv. 2018;4 : eaao6653 30 March 2018

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Electrically tunable single- and few-layer MoS2nanoelectromechanical systems with broaddynamic rangeJaesung Lee,1* Zenghui Wang,2,1* Keliang He,3 Rui Yang,1† Jie Shan,3,4 Philip X.-L. Feng1‡

Atomically thin semiconducting crystals [such asmolybdenumdisulfide (MoS2)] have outstanding electrical, optical,and mechanical properties, thus making them excellent constitutive materials for innovating new two-dimensional(2D) nanoelectromechanical systems (NEMS). Although prototype structures have recently been demonstratedtoward functional devices such as ultralow-power, high-frequency tunable oscillators and ultrasensitive resonanttransducers, both electrical tunability and large dynamic range (DR) are critical and desirable. We report the firstexperimental demonstration of clearly defined single-, bi-, and trilayerMoS2 2D resonantNEMSoperating in the veryhigh frequency band (up to ~120 MHz) with outstanding electrical tunability and DR. Through deterministic mea-surement and calibration, we discover that these 2D atomic layer devices have remarkably broad DR (up to ~70 to110dB), in contrast to their 1DNEMS counterparts that are expected to have limitedDR. These 2Ddevices, therefore,open avenues for efficiently tuning and strongly coupling the electronic, mechanical, and optical properties inatomic layer semiconducting devices and systems.

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INTRODUCTIONIn the ubiquitous devices and systems that detect, transduce, and com-municate signals, dynamic range (DR), a ratio (often in decibel) be-tween the highest nondistorted magnitude (linear “signal ceiling”) ofa physical quantity (for example, intensity, energy/power, amplitudeof current, voltage, displacement, andpressure) and its lowest detectable(“noise floor”), is a critically importantmeasure (as illustrated in Fig. 1).In everyday life, the importance of DR is widely recognized by sensorysystems of humans and other animals. In hearing, human eardrumsnormally have DRs of ~100 to 120 dB, from sensing minimum soundpressure fluctuations (at ~10−5 N/m2, threshold of audibility) to reach-ing pain thresholds (at ~10 N/m2), in the range of ~0.5 to 10 kHz,whereas the DRs quickly decrease outside this frequency range (1, 2).Other animals (for example, cats and dolphins in aquatic environ-ments) can have comparable or even wider DRs in higher frequencybands. In regards to olfaction (sense of smell), canines can have a verylow threshold, thus broad DR for many kinds of odors, enabling suchanimals to smell and discern information beyond human olfactory cap-abilities (3). In engineering, broad DRs are indispensable in a widespectrum of applications and have been actively pursued in devicesand systems in every signal domain, including the electrical (for exam-ple, amplifiers) (4, 5), optical (photo detectors and cameras) (6), thermal(temperature sensors and calorimeters) (7), mechanical (pressure sen-sors) (8), and other transduction domains.

The critical importance of DR in signal transduction has presentedimportant challenges to promising new sensing technologies. For ex-ample, nanoelectromechanical systems (NEMS) offer a variety of

functionalities, and their performance metrics have been enhancedby reducing devices’ size (9), innovating and tailoring structures (10),and using newly emerging materials with unique properties (11–15).However, DR in suchNEMS can often be reducedwhen the device sizesbecome smaller—it is predicted that DR of carbon nanotube resonatorscould be below 0dB, thus completely eliminating liner operation regime(16). Consequently, it is imperative and attractive to explore effectiveapproaches to attaining both small device size and broad DR.

Besides large DR, in resonant NEMS, achieving continuous, wide-range frequency tuning is often essential for developing functions suchas ultralow-power signal transduction, generation, communication,and sensing, especially for systems requiring tunability and reconfi-gurability. Frequency tuning can be attained by applying externalforces to vary and control the stiffness of the devices, such as via theelectrostatic force induced by gate voltage (Vg), as illustrated in Fig. 1Dbased on modeling (also see discussions in section S3). In state-of-the-art resonant NEMS enabled by mainstreammaterials such as sil-icon (Si), silicon nitride (SiN), and silicon carbide (SiC), nonetheless,electrostatic tuning range is often very limited (usually only up to~1 to5%) because of the small fractional variations in stiffness that areachievable by external forces (17–23).

Here, we demonstrate atomic layer semiconductor NEMS resona-tors with excellent electrical tunability under different driving me-chanisms (including photothermal and electrostatic excitation) andcharacterize their dynamic behavior, from the completely undriven,Brownian motion thermomechanical noise floor all the way to thenonlinear responses with increasing drive. Greatly benefiting fromthe materials’ outstanding mechanical properties (ultra-elastic, lowareal mass density, high elastic modulus, and high intrinsic strength)(24–28), atomic layers such as semimetallic graphene and semi-conducting transition metal dichalcogenides (TMDCs) have beenused to innovate new two-dimensional (2D) NEMS devices. Amongexisting TMDC building materials, molybdenum disulfide (MoS2) isa semiconducting 2D crystal with unconventional and excellentproperties (25, 27–35). Its band structure depends on the numberof atomic layers (29, 30) and can be continuously tuned by strain(33–35), promising distinct advantages for coupling nanomechanical

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manipulations to its electrical, optical, and plasmonic (36) properties.Although initial experiments have demonstrated the potential ofusing MoS2 as NEMS resonators (37–40), major challenges remaintoward creating devices with unconventional attributes, advancedfunctionalities, and high performance. Here, we specifically addresstwo challenges: (i) electrical tunability (41–43), which often dictatesthe degree of control over the device resonance, critical to applica-tions such as tunable radio frequency signal transduction, generation,and communication (44), and (ii) the operating DR that affects howthe device responds to stimuli, because a large DR is required for anytransducer relying on performance in its linear regime (45, 46), suchas many NEMSmass (47) and force sensors (48, 49). Unlike previousstudies on DRs in the voltage domain (where the noise floors areobscured by extrinsic noise of measurement systems, thus yieldingonly compromised DRs), here, we achieve measurement down tothe device intrinsic noise floors, thus capable of resolving the intrinsicDRs in the actual displacement domain of devicemotion. The approachof exploiting atomic layer crystals for 2D NEMS significantly facilitatesthe attainment of surprisingly broad DRs in these ultimately thin de-vices and systems.


RESULTSWe first demonstrate nanomechanical resonators made of circularmembranes (Figs. 1 and 2) of atomic layer MoS2 crystals in the thick-ness limit of only 1 to 4 layers (1L to 4L). Atomic layerMoS2 flakes aremechanically exfoliated onto prefabricated circular microtrencheswith diameters of D ≈ 0.5 to 1.5 mm [D = 2a (a is radius)] to yieldsuspended drumhead structures (section S1). 1L to 4L devices are firstidentified by optical microscopy (Fig. 2, insets) and then confirmed byphotoluminescence (PL) measurements of their corresponding dis-tinct PL signatures (Fig. 2, right panels). The measured spectra withpronounced and intense PL peaks verify the high quality of our samples.We measure the nanomechanical resonances of these MoS2 mem-branes by using sensitive laser interferometry for motion readout(Fig. 1, A and B; see section S2 for details and analysis) at room tem-perature and in vacuum (p~ 5mTorr) (37). A 633-nm red laser is usedto detect motions (both undriven and driven). For excitation, we useeither amodulated 405-nmblue laser (Fig. 1A) or patterned electrodeswith applied ac gate voltage (Fig. 3B).

We first measure the device resonance response without exter-nal drive and then with optical excitation via photothermal effect

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Fig. 1. Nanomechanical resonances in atomically thin MoS2 drumhead membranes: Excitation, detection, tuning, and DR. (A) Illustration of ultrasensitive opticalinterrogation of the motions of drumhead-structured MoS2 resonators. A 633-nm red laser is used to probe both the undriven thermomechanical motions and thedriven vibrations excited by an amplitude-modulated 405-nm blue laser. (B) Schematic of the measurement system and scanning electron microscopy images of arraysof single- and few-layer MoS2 resonators with different drumhead diameters. Scale bars, 1 mm. Two electrical configurations (① and ②) are available, respectively, fordriven resonance and undriven thermomechanical noise floor measurements. BS, beam splitter; LPF, long-pass filter; PD, photodetector. (C) Illustration of DR for ageneric transducer. (D) Two types of frequency tuning (fres versus Vg) curves expected in NEMS resonators with electrostatic gate tuning.

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(Fig. 1A). Figure 2 shows the measured undriven thermomechanicalresonances (Fig. 2, A and C) and photothermally driven responses(Fig. 2, B and D) from four 1L to 4L devices. Typical 1L to 4L de-vices with a diameter D ≈ 1.5 mm exhibit resonance frequencies offres ~30 to 120 MHz and quality (Q) factors of Q ~ 40 to 1000 (fig.S3 shows an example of device resonance with Q exceeding 1000).

The sensitivemotion detection enables us to reveal the discretenessin integer numbers of MoS2 layers that are manifested in the devices’Brownian motion, with on-resonance displacement-domain thermo-mechanical noise spectral density, S1=2x;thðw0Þ ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4kBTQ=ðw3

0Meff Þp

(where kB is the Boltzmann constant, w0 = 2pfres, Meff is the effective


mass that scales with the integer number of layers for a given diameter,and Q is the quality factor), which sets the lower boundary of the de-vices’ linear response (section S2). For 1L to 3L devices, the thermo-mechanical motion amplitudes are discretized: Their Sx

1/2 values fallon separate surfaces (fig. S4), with thinner devices exhibiting greaterthermal motions due to smaller masses. This discreteness is a signa-ture of devices based on 2Dmaterials, whose thicknesses can only varyin discrete steps (thus discretized masses for a given device geometry,for example, circular, rectangular, or other shapes of drumheads).

We now investigate electrical tuning of the optically driven reso-nances. We fabricate electrodes onto the already suspended MoS2membranes by evaporating metal through a stencil mask, avoidingconventional chemical processes that usually contaminate the atomiclayer flakes. The devices (Fig. 3) exhibit tunable resonances upon vary-ing the gate voltage Vg. For a 2L membrane (D ≈ 1.5 mm) with aninitial tension g0 = 0.2 N/m (corresponding to an initial strain e0 =0.071%; see section S3), varying Vg from 0 to ±20 V symmetricallytunes down the resonance from 87 to 78 MHz (Fig. 3C).

Direct electrostatic excitation (Fig. 3B) is also enabled when anac voltage dVg

ac = dVg cos(wt) is superposed to the dc voltage Vg.Figure 3D shows the electrically driven resonance from a 2L device(D≈ 1.5 mm) with the initial tension g0 = 0.15 N/m and initial straine0 = 0.054%. Sweeping the dc gate voltage again (in the range of Vg = 0to ± 20 V) demonstrates strong tuning of the resonance (Fig. 3E),with fres(Vg) taking a “W”-shaped curve (see Fig. 1D)—fres first tunesdown when |Vg| is from 0 to ~15 V because of capacitive softening,then tunes up at higher |Vg| when tensioning induced by gatingbecomes dominant, leading to stiffening. Here, the stiffening from gat-ing is easily visible because of a relatively lower initial strain built inthis device than that in the device of Fig. 3C, where even higher |Vg|values would be needed to access the stiffening regime and to attainthe full W-shaped curve (section S3 and eq. S14). Furthermore, wehave observed a “U”-shaped frequency tuning curve in a 4L device(D ≈ 1.5 mm) with g0 = 0.11 N/m and e0 = 0.020%, an even lowerinitial strain (fig. S5). Peak amplitudes of electrically driven reso-nances exhibit linear dependence on |Vg| (Fig. 3E) because the driv-ing force at the frequency w/2p is proportional to dVg|Vg|, whereasthose of optically driven resonances appear to depend on |Vg| qua-dratically (Fig. 3C). Furthermore, in both driving schemes, Q valuesdecrease with |Vg| (Fig. 3F), suggesting extra damping and a loadedQ effect associated with |Vg| (section S3).

Toward efficient resonance tuning, there is a key trade-off be-tween the tuning range and the initial tension (or strain). 2D NEMSare especially attractive for simultaneously achieving higher frequencyand tunability due to greater stretchability (compared to conventionalNEMS). Accordingly, we define a figure of merit (FOMtuning = freshe0/ℰ; h, tuning range in percentage; e0, initial strain; ℰ, applied electri-cal field) to evaluate the tuning efficiency. Although the observedtuning characteristics are qualitatively consistent with other NEMSresonators (12, 17, 50, 51), these MoS2 devices show highly efficientfrequency tuning [84 parts per million (ppm)/electron charge; seesection S3] at much higher frequencies (and tension levels). TheirFOMtuning values greatly surpass conventional NEMS, matching thebest of graphene NEMS (section S3, fig. S6, and table S1). We notethat FOMtuning has the unit of hertz per (voltage per micrometer), veryintuitively quantifying the actual “efficiency” of frequency tuning by ap-plying electrical field.

Wenow investigate the high amplitude–drivenoperations. Figure 4Ashows that the resonance froma1Ldevice (D≈ 1.5mm, fres≈ 28.5MHz)

Fig. 2. Resonance characteristics of 1L, 2L, 3L, and 4L MoS2 membranes vi-brating at very high frequencies. (A to D) Measured nanomechanical resonance(left panel) and PL (right panel) for 1L to 4L MoS2 resonators with diameter D = 1.5 mm.The vertical dashed lines in right panels of (A) to (D) indicate the indirect interbandtransition in 2L to 4L MoS2 crystals, which are at lower energies than the direct inter-band transition (which is the only visible peak in the PL data from 1L MoS2). Insets:Optical images. Scale bars, 2 mm. Both undriven thermomechanical resonances [as in (A)and (C)] and optically driven resonances [as in (B) and (D)] are shown. Red dashed linesin resonance plots are fittings to a finite Q harmonic resonator. a.u., arbitrary units.

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exhibits bifurcation and hysteresis (as frequency is swept up anddown) under increased driving, with a clear Duffing nonlinearity(52). We model this by solving displacement x for a driven Duffingresonator, Meff€x þ ðMeffw0=QÞ :x þ k1x þ k3x3 ¼ Fext , where k1 andk3 are the linear and Duffing stiffness, with k1 = Meffw0

2, and k3/k1representing the degree of (cubic) nonlinearity. The solutions (dashedlines in Fig. 4A) recover themeasured bifurcation and backbone curve,from which we determine the critical amplitude, ac≈ 4.9 nm (onsetof the bifurcation; red solid circle in Fig. 4A). Likewise, analyzingthe measured softening response in a 2L device (D ≈ 1.5 mm, fres ≈90 MHz) leads to accurately determining ac ≈ 17 nm (Fig. 4B andsection S6).

Directly detecting both the thermomechanical noise floor and thenonlinear driven responses enables us, for the first time, to preciselymeasure the DRs of 2D NEMS resonators. The achieved DR of linearoperations is defined as (16)DRlinear;achieved ≡ 20 logð0:745ac=

ffiffiffiffiffiffiffiffiffiffiffiffi2SxDf

p Þ.Here, Sx

1/2 is the measured noise level (Fig. 4, C and D, bottom bluecurves), and Df is the measurement bandwidth (we choose Df = 1 Hz,which is widely used). Figure 4 (C and D) demonstrates DRlinear,achieved≈ 70 dB for 1L and 3L devices. The DRlinear,achieved values are limitedby excess electronic noise in the measurement, which increases thenoise floor. The best available (intrinsic) value, DRlinear,in, is set byonly the thermomechanical noise and onset of Duffing: DRlinear;in ≡20 logð0:745ac=

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2Sx;thDf

p Þ ≈ 76 dB for both devices (section S6).


The linear DRs of theMoS2 devices measured here are surprisinglyand exceptionally broad, surpassing the values reported in other 2Dsystems (11, 12, 53, 54), and are even higher than those in nanobeamsand nanowires (17, 23, 55–58). These great DR values can potentiallytranslate into high device performance, such as ultrahigh mass andforce sensitivities at room temperature and low phase noise in self-sustained oscillators (section S4).

Beyond the onset of Duffing nonlinearity, operations deep in thenonlinear regime are especially intriguing because MoS2 atomic layersare greatly stretchable with ultrahigh strain limits (25, 28, 59). Accord-ingly, we define a new DR of nonlinear operations, from the onset ofDuffing to themaximumachievable deflection afracture (red dotted linesin Fig. 4, C and D) at the fracture limit, DRnonlinear ≡ 20 log(afracture/0.745ac) (red regions). Data show DRnonlinear ~ 30 to 50 dB in thesedevices (section S5). This can potentially provide a new approachtoward directly probing mesoscopic dynamical processes such as res-onant bandgapmodulation, elasticity-plasticity transition, andprefrac-ture defects evolution, all in the 2D crystal platform.

Figure 5A summarizes the DRs of 1L, 2L, 3L, and 4L devices. Wenote that, given ac, Q, fres, and D, DR increases with the number oflayers, because thinner devices have lowermasses and therefore exhib-it larger thermomechanical motions, which reduce DR (section S8).Figure 5B illustrates the frequency scaling of drumhead MoS2 resona-tors. In contrast to thicker devices that behave like plates or disks,

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Fig. 3. Very high frequency MoS2 nanoelectromechanical resonators with great electrical tunability. (A) Optical image of a 2L MoS2 resonator (D ≈ 1.5 mm)contacted by metal electrode. (B) Schematic of electrical tuning and driving of a MoS2 NEMS resonator. (C) Gate tuning of optically driven resonance of a 2L MoS2resonator (D ≈ 1.5 mm), showing measured frequency response at 41 different Vg values, with data from Vg = 0, ±10, and ±20 V highlighted as examples. Colored dotsrepresent measured peak amplitudes (and their projections onto different planes) under different Vg values. (D) Response of an electrically driven 2L MoS2 resonator(D ≈ 1.5 mm) under increasing driving amplitudes. (E) Gate tuning of electrically driven resonance of the same MoS2 resonator as in (D), with the same conventions asin (C). (F) Gate tuning of quality (Q) factors for measured resonances in (C) and (E).

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single- to few-layer devices operate in the membrane limit and exhibitgreat fres responsivity to tension.

DISCUSSIONIt is worth noting that, although large frequency tunability is desirable,it could potentially translate the voltage noise in the gate voltage tofrequency instability of the device. We find that, for a typical device,


to tune the resonance frequency by applying a dc gate voltage (for ex-ample, 20 V)whilemaintaining the frequency stability achieved at 0-Vgate, it requires a dc power supplywith output voltage stability of about5 ppm, which is available in some commercial models (see section S7for detailed calculation).

The >70-dB linear DR values achieved and directly calibrated inthis work are the highest among all NEMS resonators based on low-dimensional (1D and 2D) nanomaterials reported to date and are

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Fig. 4. Discovering nanomechanical nonlinearity and very large DR in 1L, 2L, and 3L MoS2 resonators. (A) Duffing response measured from a 1L MoS2 resonator(D ≈ 1.5 mm). Solid curve: Experimental data showing hysteresis. Dashed curves: Theoretical frequency response curve of a Duffing resonator. The backbone curve,response curve under critical driving, and the critical amplitude ac are highlighted. (B) Nonlinear response of a 2L MoS2 resonator (D ≈ 1.5 mm) with increasing drivingamplitude. The backbone curve and the level of ac are illustrated. (C) Measured DR of a 1L MoS2 resonator (D ≈ 1.5 mm). The DR for linear operation (green zone) isdetermined by the measurement noise floor and the onset of nonlinearity [0.745ac, the 1-dB compression point below ac (16)]. The DR for nonlinear operation (redzone) is limited by the fracture strength of the material. (D) Measured DR for a MoS2 resonator (3L, D ≈ 1.5 mm), with the same conventions in (C).

Fig. 5. Scaling of DR and resonance frequency in atomically thin MoS2 resonators. (A) Intrinsic DR of 1L (green), 2L (magenta), 3L (blue), and 4L (black) devices(D = 1.5 mm) as a function of measured critical amplitude ac and fres

3/Q. (B) Resonance frequency scaling with device diameter D and MoS2 thickness t. Theory is shownas lines, and measured data points are sphere symbols. Dark yellow lines: fres versus D for 1L (0.7 nm) MoS2 membrane with surface tension g = 0.5 and 0.1 N/m. Grayline: fres versus D for t = 100 nm MoS2 plate. Curves: fres versus t for tensioned MoS2 plate resonators. For D ≈ 0.5 mm (magenta curves) and 6 mm (red curves),calculations are shown for g = 0.5, 0.2, and 0.1 N/m. For devices with 1.5-mm diameter (blue curves), additional tension values of g = 0.05, 0.02, and 0.01 N/m are alsoshown. Spherical symbols show the measured fres values for 1L (green), 2L (magenta), 3L (blue), and 4L (black) devices (D ≈ 1.5 mm). Data for thicker devices with D ≈ 6 mm(red) are taken from the study of Lee et al. (37).

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comparable to those in top-down nanomachined structures (fromconventional 3D crystals) that have much larger device volumesand much narrower frequency tunability. Table S3 compares theachieved DRs in NEMS resonators (and provides references to earlierwork), and fig. S8 summarizes such comparison and shows that the 2DNEMS in this work achieve high DRs while having small volumes(note the logarithmic scale on both axes). Such unique combinationof ultrasmall device volume, very wide frequency tunability, and broadDR has important implications for enabling novel sensing and signalprocessing functions in these atomically thin nanostructures.

The broad DRs achieved in these 2DNEMS resonators show strongcontrast to the DRs predicted for 1D NEMS resonators. This can beunderstood by considering the upper and lower limits of the DR andthat 2Dnanostructures have lower thermomechanical fluctuations thantheir 1D counterparts, with details provided in section S8. A detailedtheoretical analysis of DR in 2DNEMS is available in the literature (46).

In conclusion, we have demonstrated atomic layerMoS2 crystallineNEMS resonators with excellent electrical tunability of resonances andremarkably broad DRs, all achieved at the limit of single- to few-layer(1L to 4L) semiconductor devices. With careful measurements anddisplacement-domain calibration from Brownian motion thermome-chanical noise towell beyond the onset of Duffing nonlinearity, we areable to observe and deterministically quantify the intrinsic DRs ofthese 2D NEMS resonators. The surprisingly broad linear DRs (~70to 110 dB) are important attributes for making 2DNEMS an interest-ing new platform for exploring multiphysics coupling effects in 2Dcrystals and for pursuing resonant sensing (60–62) and ultralow-power information processing applications (63) in ultimately thinsolid-state systems. In addition, our demonstration of broad DRs in2D NEMS platforms opens up new possibilities for engineering largeDRs in nanoscale devices that conventionally only have compromisedDRs because of their highly miniaturized dimensions (16). Further-more, extremely large nonlinear DRs (~40 to 50 dB) up to device frac-ture offer rich nanomechanical dynamics in 2D resonators and mayfacilitate exploring many exotic physical effects [for example, chaos(64), mode coupling (65–67), and internal resonance (39)] thatstemmed from strong nonlinear interactions in such uniquely widenonlinear regimes built in these 2D resonant systems.

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MATERIALS AND METHODSDevice fabricationThe single- to few-layer (1L to 4L)MoS2 resonators were fabricated bymechanically exfoliating MoS2 crystal onto 290-nm SiO2 on Si sub-strateswith prepatternedmicrotrenches and cavities of various shapes.The diameters of the circularmicrotrench cavities on the substrates areD≈ 0.5, 0.75, 1, 1.25, and 1.5 mm, and depths are 250 and 290 nm.Wecleaned the substrate thoroughly by using Piranha, a mixture of sulfu-ric acid and hydrogen peroxide, before exfoliation of MoS2.

PL measurementPL responses from the fabricated MoS2 resonators were measured toconfirm the number of device layers. A 532-nm laser was focused onthe center of the suspended MoS2 diaphragm by using a microscopeobjective [100×, numerical aperture (NA) = 0.9], and laser power islimited below ~50 mW, to avoid excessive laser heating. PL responsesfrom the devices were resolved using a spectrometer (PrincetonInstruments SpectraPro) with grating (600 g/mm) and recordedusing a liquid nitrogen–cooled charge-coupled device.


Laser interferometry setup and resonance measurementFigure 1B shows the configuration and components used in themea-surement system. The resonancemotion was photothermally excitedand interferometrically detected using an amplitude-modulated405-nm diode laser and a 633-nm He-Ne laser, respectively. Bothlasers were focused using microscope objective (50×, NA = 0.5).The 405-nm laser was focused onto the substrate next to the device(~5 mm away), with an estimated spot size of ~5 mm. Laser power ofthe 405-nm laser is limited to below 250 mW. The 633-nm laser wasfocused on the center of the suspended MoS2 drumhead. The cali-brated on-device spot size of the 633-nm laser is ~1 mm, and the laserpower was adjusted to below 350 mW. A long-pass filter was installedin front of the photodetector to remove the signal from the 405-nmlaser. Reflected intensity of 633-nm light from the device was detectedby a photodetector and recorded with a spectrum analyzer and/or anetwork analyzer.

Electrical excitation of device resonance motionIn addition to the photothermal excitation, device motions were actu-ated using electrostatic force. Electrodes are made by evaporatingnickel onto the suspended MoS2 devices through a stencil mask. Thismethod does not require any chemical processing, and the MoS2membrane remains in its pristine condition. The electrical actuationwas performed by applying through a bias-T an ac + dc signal gener-ated by a network analyzer and a dc power supply.

SUPPLEMENTARY MATERIALSSupplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/3/eaao6653/DC1section S1. Device fabricationsection S2. Optical interferometry measurement systemsection S3. Electrical tuning of device resonancesection S4. Power handling, mass sensitivity, and frequency stabilitysection S5. Nanomechanical tuning and sensing of device strain and bandgapsection S6. Measuring nonlinearity and estimating critical amplitudesection S7. Translation of voltage fluctuations into frequency instabilitysection S8. Comparison of DR in 1D and 2D NEMS resonatorsfig. S1. Calculated displacement versus reflectance values for 1L to 3L MoS2 resonators.fig. S2. Calculated displacement-to-reflectance responsivity (ℜRef) and measureddisplacement-to-voltage responsivity (ℜV) values for 1L to 3L MoS2 resonators.fig. S3. Thermomechanical resonance with qualify (Q) factor exceeding 1000.fig. S4. Thermomechanical vibrations with distinct signatures of digitized thicknesses (numberof layers) as a function of fres and Q.fig. S5. Electrical gate turning of higher-mode resonances.fig. S6. FOM for frequency tuning: Comparison across reported 2D NEMS devices.fig. S7. Schematic for calculating the total surface area on a deformed membrane.fig. S8. Measured DR in 1D and 2D resonators operated at room temperature.fig. S9. Resonance frequency scaling with device diameter D and MoS2 thickness t.table S1. FOM for frequency tuning.table S2. List of devices with measured nonlinear characteristics.table S3. DRs measured in 1D and 2D resonators.References (68–80)

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Acknowledgments: We are grateful to a T. Keith Glennan Fellowship, Case School ofEngineering, and the Swagelok Center for Surface Analysis of Materials at Case WesternReserve University. Part of the device fabrication was performed at the CornellNanofabrication Facility/National Nanofabrication Infrastructure Network. P.X.-L.F. thanksY. Wu for help on scientific illustrations. Funding:We thank the support from National Academyof Engineering Grainger Foundation Frontiers of Engineering Award (FOE 2013-005), NSFCAREER Award (grant ECCS-1454570), Communications, Circuits, and Sensing Systems (CCSS)Award (grant ECCS-1509721), and Division of Materials Research (DMR) Award (grantDMR-0907477). Z.W. thanks support from the National Natural Science Foundation of China(grant 61774029) for the latest phase of his effort on this project. Author contributions: J.L.,Z.W., R.Y., and K.H. fabricated devices. J.L. and K.H. carried out resonance and PL measurementswith important technical support on apparatus and instrumentation from J.S. and P.X.-L.F.J.L., Z.W., and P.X.-L.F. analyzed the data and wrote the manuscript with comments from all otherauthors. P.X.-L.F. conceived the experiments and supervised the project. All authors havediscussed the results and given approval to the final version of the manuscript. Competinginterests: The authors declare that they have no competing interest. Data and materialsavailability: All data needed to evaluate the conclusions in the paper are present in the paperand/or the Supplementary Materials. Additional data related to this paper may be requestedfrom the authors.

Submitted 14 August 2017Accepted 7 February 2018Published 30 March 201810.1126/sciadv.aao6653

Citation: J. Lee, Z. Wang, K. He, R. Yang, J. Shan, P. X.-L. Feng, Electrically tunable single- andfew-layer MoS2 nanoelectromechanical systems with broad dynamic range. Sci. Adv. 4,eaao6653 (2018).

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dynamic range nanoelectromechanical systems with broad2Electrically tunable single- and few-layer MoS

Jaesung Lee, Zenghui Wang, Keliang He, Rui Yang, Jie Shan and Philip X.-L. Feng

DOI: 10.1126/sciadv.aao6653 (3), eaao6653.4Sci Adv

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