1 School of Instrumentation Science and Opto-Electronics Engineering, Beihang University,Beijing 100191, China

2 Research Institute of Beihang University in Shenzhen, Shenzhen 518000, China

3 Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology,Shenzhen 518055, China

* Correspondence: licheng@buaa.edu.cn (C.L.); songxf@sustech.edu.cn (X.S.)

Abstract: Graphene resonant sensors have shown strong competitiveness with respect to sensitivityand size. To advance the applications of graphene resonant sensors, the damage behaviors ofgraphene harmonic oscillators after thermal annealing and laser irradiation were investigated bymorphology analysis and frequency domain vibration characteristics. The interface stress was provento be the key factor that directly affected the yield of resonators. The resulting phenomenon could beimproved by appropriately controlling the annealing temperature and size of resonators, therebyachieving membrane intactness of up to 96.4%. However, micro-cracks were found on the graphenesheets when continuous wave (CW) laser power was more than 4 mW. Moreover, the fluctuating lightenergy would also cause mechanical fatigue in addition to the photothermal effect, and the thresholddamage power for the sinusoidally modulated laser was merely 2 mW. In this way, based on theamplitude-frequency surface morphology of the graphene resonator, the thermal time constant of theorder of a few microseconds was confirmed to evaluate the damage of the graphene oscillator in situand in real time, which could be further extended for those resonators using other 2D materials.

Keywords: graphene resonator; interface stress; film thermal damage; thermal time constant

1. Introduction

Micro resonant sensors have been widely applied in aviation, aerospace engineeringand automation due to their high sensitivity, stable performance and direct frequency signaloutput. The resonator is the key element of resonant sensors, which dominantly affectsthe performance of the whole system. To develop a high-performance resonant sensor, thematerial of the micro resonators should be stiff, robust and stable.Graphene, an atom-thick two-dimensional material with a single-layer thickness of0.335 nm, has demonstrated excellent mechanical [1], optical [2], electrical [3] and thermalproperties [4]. These superior properties enable the new material with novel nanostructuresto be widely applied in the field of micro-electro-mechanical systems (MEMS) or photoelectric devices [5]. To be specific, graphene exhibits a high Young’s modulus of 1.0 TPa, a hightensile rate up to 20% [6] and extreme fatigue life of more than 109cycles [7], which makesit an appropriate material for harmonic oscillators. Particularly, the first graphene resonatorwas developed by transferring graphene onto the trenches of silicon oxide [8], actuatedby a modulated laser. Compared with the silicon counterpart, a graphene resonant sensorcould reach 45 times higher pressure sensitivity with a 25 times smaller membrane area [9].However, in terms of stability, the graphene resonators still cannot reach the same longterm stability as silicon resonators that can achieve a one-year frequency drift of merely0.01% [10]. This perfect stability of silicon resonators is not only due to the craftsmanshipof silicon resonators—for example, the complete sealing technology of the resonator—butalso the research of the damage resource, and the compensation methods [11–13]. Thus,research about the damage mechanism of graphene resonators is of vital importance, but ithas not been extensively discussed thus far. Moreover, it should be noted that, especiallyfor a merely ~0.335 nm thick membrane, it is much easier to lose integrity.

The damage of graphene resonators can be attributed to the manufacturing processand operating conditions. For the fabrication of resonators, suspended transfer of grapheneis a common step that might cause damage to the thin suspended membrane. Generally,graphene transfer in micro-mechanical systems is performed with the help of the widelyused polymethyl methacrylate (PMMA) [14], Polydimethylsiloxane (PDMS) [15] or otherpolymers, by spin-coating on the film onto the original substrate surface [16]. Here, wefocused on the commonly used transfer method with PMMA substrate. After transferring graphene to a target substrate, PMMA coating could be removed by annealing over300 ?C [17] or washed off in an acetone solution [18]. Considering the PMMA removalmethod, a previous study by Oshidari et al. [19] has shown that the thermal annealingprocedure could be employed to improve the resonator’s resonant frequency and qualityfactor. By using the Raman spectroscopy imaging technic, it was noticed that there is considerable strain induced in the suspended graphene flakes after annealing, including thefurnace annealing [20] or laser annealing [21]. Although this extra inner stress contributesto holding the graphene sheet tightly and causes a flatter membrane surface [22], the extrastrain in the annealing process would negatively induce the cracks on the graphene surface.According to Barton et al. [23], the diameter of suspended graphene would affect theperformance of the fabricated device. Hence, an appropriate annealing temperature for agraphene membrane with a specific diameter should be evaluated for better performanceof the graphene oscillator. Besides the transfer-induced damage in the fabrication process,the photothermal effect would also result in damage to the membrane. Generally, thelaser-induced damage can be characterized by the thermal effect and the non-thermal one.For the former, graphene absorbs photons and then releases them under the irradiation ofthe CW laser [24]. When the applied laser power is strong enough, the energy of phononscan break chemical bonds, thereby resulting in the thermal damage to graphene. The lattercould be divided into two aspects. One is due to the original defects, such as the vacancy,which would weaken the fatigue characteristics of the original material, which has beendiscussed in [7]. The other is due to the ultra-fast energy transfer mechanism unique tosolids. When the energy transmission speed of the laser pulse was obviously faster thanphonon relaxation time, electrons were excited, and thermions are created. These electronsin semiconductors could absorb energy and then cool down by giving it to other phononson a shorter time scale than thermal diffusion [25,26]. Melting, vaporization, or sublimationmight happen in this stage. Considering our experiment setup, the modulated frequencyof the laser was set in the range of 10 kHz to 5 MHz. However, since the phonon relaxationtime of graphene is generally in the picosecond order of magnitude [27], which is by farlower than the modulated period of (0.1 μs) the pulsed laser signal in our experiment, thiseffect mentioned above is not discussed in this paper.

The Raman spectroscopy technique has been used to evaluate the extent of damageby calculating the intensity of the D and G peaks [28]. However, in terms of the actualapplication, the Raman spectrometer lacks portability. Thus, considering that the surfacemorphology is suitable for early prediction regarding the resonant state before a resonanttest, herein a simple method was developed based on the principle of the Fabry–Pérot(F-P) interference to evaluate the extent of damage through the resonant behaviours of agraphene oscillator. Moreover, it can be seen from the measured resonant response that thethermal time constant acted as a real-time character for monitoring the resonant state of agraphene oscillator.

2. Experiment Methods

Figure 1a shows the process of making free-standing graphene with Cu patterns,wherein a multilayer graphene was grown on the copper (Cu) foil by the chemical vapordeposition. At first, a thin film of PMMA was spin-coated onto the surface of a chemicalvapor-deposited multilayer graphene (MLG). The formed MLG/PMMA film was transferred onto the surface of a copper mesh with multiple holes whose diameters were setas 20, 60 and 100 μm, respectively. Figure 1b shows the thickness of the used graphenemembrane, which was measured to be 3.57 nm by AFM (FSM Precision, FM-Nanoview6800, Suzhou, China). The sample with MLG/PMMA film was then placed in a furnaceand annealed at a temperature of 300, 375 or 450 ?C. Note that the annealing temperaturewas chosen according to the thermal decomposition characteristic of PMMA [29]. Then, anall-fibre experimental system was established to motivate and interrogate the motion ofgraphene sheets on the basis of Jin’s work [30], as shown in Figure 1c. In view of a smalldivergence angle when the laser was irradiated out of the optical fibre into the F-P cavity,the air cavity distance between the fibre and the sample would cause a weak energy loss.In this case, the distance between the membrane and the fibre end-face was controlledto be less than 50 μm via a broad-band laser and an optical spectrum analyser (OSA) onbasis of the F-P interference. In order to actuate the graphene membrane, the intensity oflaser S was modulated with a rate of 60% and then the membrane was optically heatedup and therefore shrank and expanded under the light-induced thermal stress. Then,the opto-mechanics principle in the F-P cavity was employed so as to detect this motionof the graphene, wherein the suspended graphene and the end-face of the optical fibreacted as a moving mirror and a fixed back-mirror, respectively. In this way, the deflectiondisplacement of the suspended graphene membrane could be obtained by a photodetector(PD). For the sake of minimizing the damage caused by excessive laser power, the laserpower was set to be as small as possible. To be specific, the light power for laser S andlaser R was set to 0.3 mW and 2 mW, respectively. In order to batch test the resonantcharacteristics of the graphene membrane, the graphene sample without PMMA coatingwas placed on a precise translation stage with a three-dimension displacement accuracy of1 μm (Figure 1d,e). In this way, along with the movement observation under a microscope,the light spot of the fibre laser could be adjusted properly in the centre of the membrane.Meanwhile, the photos were read out from computer in real-time, and Figure 1f showeda surface morphology comparison of graphene annealed at different temperatures. Themembranes annealed at a higher temperature showed more micro-cracks.

Figure 1. (a) The process of making free-standing graphene with Cu substrate, (b) the AFM topographic image of a graphene after transfer, (c) the experimental setup used to actuate and detect themotion of the resonators, (d) the schematic diagram and (e) experimental setup of the displacementcontrol, (f) the micrographs of 60-μm graphene membranes annealed at (i) 300, (ii) 375 and (iii) 450 ?C,scale bar: 20 μm.3. Results and Discussions3.1. Damage in the Annealing ProcessIn this section, the damage to the graphene harmonic oscillator after thermal annealingis presented. Graphene membranes annealed at a temperature of 300, 375 or 450 ?Cwere first observed under an optical microscope and scanning electron microscope (SEM)(FEI, Quanta 450 FEG, Reston, VA, USA) to analyse the breakage rate of the membrane,on micro- and nano-scales, respectively. Then, the resonant characteristics, includingquality factor and resonant frequency, were investigated by the aforementioned all-fibreexperimental system.

After the annealing process at each temperature, the intactness of the graphene wasobserved by an optical microscope. It has been found that graphene with a more than95% free-standing area has the potential to be fabricated as a well-behaved harmonicoscillator; thus, this kind of membrane was noted to be intact in this paper. To be specific,300 graphene membranes after each annealing process were randomly selected, and thenumber of intact membranes was counted. The statistical results are listed in Figure 2a.Figure 2a shows that the 20 μm-diameter membranes that annealed at 300 ?C exhibitedthe highest rate of intactness at up to 96.4%. Furthermore, graphene membranes weremore easily broken with a larger diameter or annealed at a higher temperature, such as375 ?C and 450 ?C. This phenomenon could be explained by the stress between PMMA andgraphene. In fact, with an increase in the temperature, the decomposition of PMMA coatinghappened in two stages. In the first stage (at about 220 ?C), the C=C bonds of PMMA werebroken, while the second stage primarily involved the random scission of C-C bonds at ahigher temperature (at about 300 ?C) [29]. In view of the mechanical properties of PMMA,the hardness and elastic modulus of PMMA film showed an increasing tendency on accountof the reduced chain length of the polymer and cross links of the polymer [31,32]. Therefore,it could be understood that, at a temperature of 300 ?C, there was generally a thin film ofPMMA left on the graphene surface [33], which kept the membrane rigid and protected thegraphene membrane from breaking apart, which is consistent with [23]. However, whenthe temperature rose above 300 ?C, the protection film of PMMA became thinner and left asingle membrane of suspended graphene, which was much more easily damaged.

Besides the stress between the graphene and PMMA, there was also a thermal interfacial interaction between the MLG and substrate in the heating process, which would alsocause damage to the graphene, especially at the edge of the entire membrane. A photo of atypical damaged graphene caused by thermal interaction between the MLG and substrateis shown in Figure 2b. To be specific, when the resonator was heated, the substrate with apositive thermal expansive efficient would impose tensile stress on the graphene with anegative thermal expansive efficient [34]. Graphene was adhered to the copper surface bythe Van der Waals force. So, for some weak points where graphene and the substrate werenot fitted closely, the intermolecular force was not strong enough to resist the relative slipbetween the membrane and the substrate. In this case, the graphene membrane tended tocrimp on the metal surface. If the range of the crimp was small, little cracks were foundon the graphene membrane, which is marked by point B in Figure 2b. Otherwise, if thecrimping range was large, a double-layer membrane was observed, as is shown by point Cin Figure 2b. In this case, the thickness of the membrane might double. The correspondingschematic diagram of graphene breakage is shown in Figure 2c.

Furthermore, in order to graphically depict the damage to the graphene membrane ona nano scale, the SEM photographs of the suspended graphene are given in Figure 3. It isworth mentioning that the small amount of PMMA on the graphene surface would lead to apoor image resolution. As a result, gold nanoparticles were sprayed on the PMMA surfaceto enhance its conductivity. Referring to Figure 3, the dark and bright areas of the imageare representative of the broken and the suspended graphene membrane, respectively. Forexample, in Figure 3f, area A represents the graphene membrane and ‘B’ represents thebroken area.

Figure 2. (a) The breakage rate of the annealed graphene membrane and (b) the microscope photograph of damaged graphene after annealing: points A, B and C represent flat graphene, graphenewith a hole and double-layer graphene, respectively. Scale bar: 10 μm, (c) the damage mechanism of thermal interfacial interaction, where A, B and C correspond to the regionss A, B and C inFigure 2b, respectively.

In this way, these SEM images were further binarized to calculate the proportion of thedamaged area. Thus, the microscopic broken rate of the membrane could be calculated asnumdark/numall, wherein numdark and numall represent the number of dark pixels and allpixels, respectively. It could be concluded that a higher annealing temperature T or a largersuspended radius R would result in a larger broken area. Taking the graphene (D = 20 μm, T = 300 ?C), for example, the graphene exhibited perfect intactness (100%). However, oncethe suspended diameter was increased to 100 μm, the breakage rate increased to 2.5%.When the annealing temperature was increased to 450 ?C, the breakage rate rose rapidlyto 30.9%. In the aforementioned experimental set up, the graphene breakage rate showedhigher sensitivity to the annealing temperature than the suspended diameter.Besides the breakage rate and the surface morphology of the membrane, which hasbeen mentioned above, the resonant characteristics were also investigated, including theresonant frequency and quality factor. Among these, the resonant frequency indicates thefundamental frequency of the oscillator, and the quality factor represents the energy lossper oscillation cycle, which is calculated by ω0/?ω, where ω0 is the natural frequencyand ?ω is the 3 dB bandwidth of the amplitude–frequency curve. Thus, the resonantcharacteristics of the graphene resonators were investigated at the aforementioned threeannealing temperatures, as illustrated in Figure 4.

Figure 4a shows that after annealing at 300 ?C, the resonant frequency showed aninverse proportion to the diameter of the graphene membrane. For various graphenefilms with different diameters, the average frequencies of each 30 samples were respectively calculated as f 20 = 1254.1 kHz (D = 20 μm), f 60 = 338.9 kHz (D = 60 μm) andf 100 = 153.5 kHz (D = 100 μm), and the standard deviation (STD) of frequencies were con-firmed as σ20 = 192.7 kHz (D = 20 μm), σ60 = 59.0 kHz (D = 60 μm) and σ100 = 46.2 kHz(D = 100 μm), respectively (Figure 4a). It can be also noticed that the distribution of theresonant frequencies is more concentrated for those resonators with small radii. This ispossibly because of the unpredictable breakage of the membrane, which induces moreunnecessary vibration modes of the membrane. As for the Q factor, the average valueswere calculated to be Q20 = 9.8, Q60 = 9.5 and Q100 = 7.8, and the STD values were σ20 = 2.26(D = 20 μm), σ60 = 2.50 (D = 60 μm) and σ100 = 3.34 (D = 100 μm), respectively (Figure 4c).The resonators with smaller diameters had higher Q factors and better consistency. Furthermore, these resonators all had a relatively low Q factor because the measurement wasexecuted at atmospheric pressure, and the air damping caused high energy loss for thevibrating micro-membrane. In application, the quality factor could be greatly enhanced bysealing the membrane in a vacuum, which could reach an order of thousands.

Figure 3. The binarized SEM photograph of graphene of different radius R and after annealing at different temperatures T, scale bar: 5 μm. The broken rate was noted in the brackets. (a) D = 20 μm, T = 300 °C (0%). (b) D = 20 μm, T = 375 °C (1.6%). (c) D = 20 μm, T = 450 °C (30.9%). (d) D = 60 μm, T = 300 °C (0%). (e) D = 60 μm, T = 375 °C (16.9%). (f) D = 60 μm, T = 450 °C (38.7%). (g) D = 100 μm, T = 300 °C (2.5%). (h) D = 100 μm, T = 375 °C (20.42%). (i) D = 100 μm, T = 450 °C (43.7%).

Besides the breakage rate and the surface morphology of the membrane, which has been mentioned above, the resonant characteristics were also investigated, including the resonant frequency and quality factor. Among these, the resonant frequency indicates the fundamental frequency of the oscillator, and the quality factor represents the energy loss per oscillation cycle, which is calculated by ω0/Δω, where ω0 is the natural frequency and Δω is the 3 dB bandwidth of the amplitude–frequency curve. Thus, the resonant characteristics of the graphene resonators were investigated at the aforementioned three annealing temperatures, as illustrated in Figure 4.

Figure 4a shows that after annealing at 300 °C, the resonant frequency showed an inverse proportion to the diameter of the graphene membrane. For various graphene films Figure 3. The binarized SEM photograph of graphene of different radius R and after annealing atdifferent temperatures T, scale bar: 5 μm. The broken rate was noted in the brackets. (a) D = 20 μm,T = 300 ?C (0%). (b) D = 20 μm, T = 375 ?C (1.6%). (c) D = 20 μm, T = 450 ?C (30.9%). (d) D = 60 μm,T = 300 ?C (0%). (e) D = 60 μm, T = 375 ?C (16.9%). (f) D = 60 μm, T = 450 ?C (38.7%). (g) D = 100 μm,T = 300 ?C (2.5%). (h) D = 100 μm, T = 375 ?C (20.42%). (i) D = 100 μm, T = 450 ?C (43.7%).When the annealing temperature was set as 375 ?C, 100 μm-diameter graphene wasunable to support itself after annealing. Hence, the resonant data for the 100 μm diametergraphene were not included in Figure 4b. The corresponding average frequencies of theresonators were measured to be f 20 = 3808.5 kHz (D = 20 μm) and f 60 = 661.3 kHz (D = 60μm), and the STD values were calculated to be 641.8 kHz and 348.4 kHz, accordingly. The Qfactors were measured to be 8.93 (D = 20 μm) and 6.85 (D = 60 μm) with the correspondingSTD values of 2.03 and 2.72, respectively (Figure 4d).For a circular membrane under tension, the fundamental frequency can be expressedas [23]

where D, Et and ρ are the diameter, the in-plain Young’s modulus and the in-plain densityof the graphene, respectively; S is the strain in the graphene membrane, and α is thedensity multiplier that describes the contaminating of the device. Moreover, the parameterρα is defined as the in-plain density of the suspended harmonic oscillator including thegraphene, PMMA residues and other additional mass. For the resonators at the sameannealing temperature, such as 300 ?C, graphene membranes were considered to havethe same in-plain mass density ρα. In terms of Equation (1), the ratio of the inner strainof 20 μm, 60 μm and 100 μm membranes were estimated to be S1:S2:S3 = 2.69:1.78:1.This strain possibly resulted from the Van der Waals force between the graphene andthe copper sidewall. At different temperatures, different mechanical energy might beintroduced via distortions of the graphene lattice [21]. For the resonators with the samediameter, taking the 20 μm-diameter membrane as an example, it could be inferred that themembrane after 375 ?C annealing had three times the resonant frequency compared to thecounterparts annealed at 300 ?C. Combining the surface appearance depicted in Figure 3, itcould be inferred that the inner strain was one of the main factors that caused damage tothe membrane.

Note that when the annealing temperature increased to 450 ?C, the fabricated resonators of all sizes were damaged with the damaged areas as shown in Figure 2b, and no relative data were recorded in Figure 4.

Figure 4. Statistics of resonance frequency and quality factor of graphene at different annealing temperatures and sizes: (a) Resonance frequency of graphene annealed at 300 °C; (b) the resonant frequency of graphene annealed at 375 °C; (c) Quality factor of graphene annealed at 300 °C; (d) Quality factor of graphene annealed at 375 °C.3.2.

Damage in the Laser Irradiation ProcessDamage not only occurs in the fabrication process, but also in the working process of the harmonic oscillator. In the previous study on the laser-induced damage, the graphene was often tested by a Raman spectrometer [35] or microscope [36] after laser irradiation, which is ex situ. For a micro-mechanical device, it would be more helpful to perform an in situ detection of the damage situation of the graphene. At this point, the observations in this letter would provide some insight. The 300 °C -annealed 60 μm-diameter graphene membrane was placed under an optical fibre end-face and irradiated by a sinusoidal modulated laser or constant laser. Each membrane was irradiated at a certain laser power for 600 seconds, and the diameter of the damage range was then recorded. Note that the shape of the damage range was sometimes not a strict circle, but an ellipse, in which case the diameter was recorded as half of the sum of the major axis and minor axis of the ellipse. The relationship between the damaged diameter and laser power is shown in Figure 5. Under a modulated laser, cracks were found on the membrane when the power went higher than 2 mW (Figure 5a,c). For the laser with constant power, the membrane centre started to break at a laser power of about 4–5 mW (Figure 5b,d). Note that the fibre optic laser power in our experiment was first measured by a handheld optical power meter (SAMZHE, SZ-GG01, Shenzhen, China) before the sample was irradiated. Thiscould be explained by the fact that a modulated laser would cause not only a heating effect but also alternating photothermal stress within the membrane. The photothermal stress would cause a thermal shock effect on the membrane and accelerate the damage of the membrane [37].

Figure 4. Statistics of resonance frequency and quality factor of graphene at different annealingtemperatures and sizes: (a) Resonance frequency of graphene annealed at 300 ?C; (b) the resonant frequency of graphene annealed at 375 ?C; (c) Quality factor of graphene annealed at 300 ?C; (d) Qualityfactor of graphene annealed at 375 ?C.

3.2. Damage in the Laser Irradiation ProcessDamage not only occurs in the fabrication process, but also in the working process ofthe harmonic oscillator. In the previous study on the laser-induced damage, the graphenewas often tested by a Raman spectrometer [35] or microscope [36] after laser irradiation,which is ex situ. For a micro-mechanical device, it would be more helpful to perform an insitu detection of the damage situation of the graphene. At this point, the observations inthis letter would provide some insight. The 300 ?C -annealed 60 μm-diameter graphenemembrane was placed under an optical fibre end-face and irradiated by a sinusoidalmodulated laser or constant laser. Each membrane was irradiated at a certain laser powerfor 600 seconds, and the diameter of the damage range was then recorded. Note that theshape of the damage range was sometimes not a strict circle, but an ellipse, in which casethe diameter was recorded as half of the sum of the major axis and minor axis of the ellipse.The relationship between the damaged diameter and laser power is shown in Figure 5.Under a modulated laser, cracks were found on the membrane when the power went higherthan 2 mW (Figure 5a,c). For the laser with constant power, the membrane centre startedto break at a laser power of about 4–5 mW (Figure 5b,d). Note that the fibre optic laserpower in our experiment was first measured by a handheld optical power meter (SAMZHE,SZ-GG01, Shenzhen, China) before the sample was irradiated. This could be explained bythe fact that a modulated laser would cause not only a heating effect but also alternatingphotothermal stress within the membrane. The photothermal stress would cause a thermalshock effect on the membrane and accelerate the damage of the membrane [37].

Figure 5. Surface morphology of graphene irradiated by (a) modulated laser, scale bar: 40 μm. and(b) constant laser (1–5 mW), scale bar: 40 μm. (c) damage radius statistics of graphene by modulatedpump laser and (d) CW laser.

As the modulated laser was verified with a higher possibility of damaging the membrane, the effect of the modulated laser on the graphene resonant characteristics was furtherexplored. Thus, the graphene membrane was excited with a modulated laser whose powerwas gradually increased from 1 mW to 5 mW. Meanwhile, the motion was recorded by aCW laser with an extremely small amount of power, so that this laser would barely damagethe structure of the graphene. The experiment results were recorded in Figure 6.

From the frequency domain, Figure 6a shows that the deflection of the oscillatorwould first increase when the exciting laser power went up. With a further increase ofthe excitation optical power, the burr of the amplitude–frequency curves increased. Thiswas because the frequency sweep needed to take about tens of seconds, during which theunstable state of the graphene exhibited a fluctuation of the reflected signal. When thelaser power finally exceeded 5 mW, a hole was found in the centre of the membrane and noresonance phenomenon could be recorded anymore.

According to Metzger et al. [38], a thermomechanical response of the suspendedgraphene could be gained from the frequency domain feature to characterize its thermalproperties. One important parameter is the thermal time constant, which describes theresponse time between the mechanical motion response of suspended graphene and thelaser irradiation that opto-thermally actuates the membrane. According to the heat transfertheory, the process of laser irradiation onto the graphene membrane can be considered asthe presence of an internal heat source. Combining the optical self-cooling of the deformableFabry–Perot cavity, the displacement of membrane z in the frequency domain could bewritten as [39]:

(2)where τ is the thermal time constant, R is the thermal resistance, C is the thermal capacitance(RC = τ), α is an effective thermal-expansion coefficient and P is the heating power. Aftertaking the derivative of Formula (2), the imaginary part of the response function reachedthe maximum amplitude when ωτ = 1. Thus, the thermal time constant τ of the graphenemembrane was calculated.

Figure 6. (a) The amplitude-frequency response changes when the excitation optical power increases from 0.5 mW to 5 mW. (b) The thermal time constant of the resonator changes when the excitation optical power increases from 1 mW to 5 mW; inset: the surface morphology of graphene. (c) The long-term static dwelling of graphene with different diameters. (d) The calculated Figure 6. (a) The amplitude-frequency response changes when the excitation optical power increasesfrom 0.5 mW to 5 mW. (b) The thermal time constant of the resonator changes when the excitationoptical power increases from 1 mW to 5 mW; inset: the surface morphology of graphene. (c) Thelong-term static dwelling of graphene with different diameters. (d) The calculated temperatureunder a gaussian laser spot for graphene with three different diameters (thermal conductivityκ = 500 W/(mK)); inset: the temperature distribution of the surface.

It was found that τ started to deviate at about 3 mW (Figure 6b) and then exhibitedlarge fluctuation. The same was the case when the real-time surface morphology started tocollapse (Figure 6c), which indicated that the thermal time constant could be a parameterto evaluate the vibration state of the graphene. After that, the thermal time constant wentup to about 6 μs from 4.7 μs, which meant a longer time between the actuation and themotion for a broken graphene membrane.

Then, long-term stability was considered. It was found that the graphene with asmaller diameter tended to have a longer working duration (Figure 6c, blue squares).Combining the surface appearance in Figure 6, there is a considerable possibility that theinitial rate of the damage area would have a directly negative effect on the long-termstatic dwelling of the graphene resonators. Thus, the fabrication method of the losslessgraphene membrane is a vital step for applications of graphene resonators and is worthy offurther investigation. Moreover, the temperature increase of the graphene sample undera Gaussian beam was simulated with Comsol software with multi-physics fields. Thesimulation result showed that the thermal effect would not lead to a serious break of theC-C bonds under this laser power [40,41]. That is, it was more likely that the mechanicalvibration accelerated this damage.

4. Conclusions

From the perspective of the application of graphene resonant sensors, the effect ofthe temperature-dependent annealing treatment on the intactness of suspended multilayergraphene was investigated through surface morphology observation to further evaluatethe resonant behaviours of graphene resonators after the thermal annealing process. Theexperimental results showed that an annealing temperature of 300 ?C leaves a certaindegree of PMMA residue, which can prevent the breakage of graphene while annealing.In contrast, when the annealing temperature rose to 375 ?C, more cracks, or even a totalcollapse, occur in the suspended membrane. In this way, although resonant frequenciesthat are twice as high could be achieved, the atmosphere pressure quality factor (Q20 = 8.9)of the resonator showed no synchronous improvement compared to the counterpartsannealed at 300 ?C (Q20 = 9.8).

Besides the annealing treatment, the effect of the laser irradiation on the intactness ofthe suspended multilayer graphene was also investigated. The damage was mainly causedby the modulated laser, which would induce both a thermal effect and mechanical fatigue.The damage threshold power for the modulated laser was found to be about 2–3 mW,which is about half the CW laser. Thus, the modulated laser power should be controlledcarefully in application. Moreover, it was found that the fluctuation of the thermal timeconstant could be applied to evaluate this damage in situ and in real time.Author Contributions: Y.L. performed the experiment and wrote the paper; C.L. conceived theidea and provided the support for the research; Z.W. and X.S. analyzed the experiment results; C.L.and S.F. proof-read the manuscript. All authors have read and agreed to the published version ofthe manuscript.Funding: This work was funded by the National Natural Science Foundation of China (62173021), Beijing Natural Science Foundation (4212039), Aviation Science Foundation of China (2020Z073051002), andScience Technology and Innovation Commission of Shenzhen Municipality (JCYJ20180504165721952).Data Availability Statement: The data presented in this study are available on request from thecorresponding author.Conflicts of Interest: The authors declare no conflict of interest.

References

1.

Lee, C.; Wei, X.; Kysar, J.W.; Hone, J. Measurement of the elastic properties and intrinsic strength of monolayer graphene. Science

2008, 321, 385–388. [CrossRef]

2.

Bonaccorso, F.; Sun, Z.; Hasan, T.A.; Ferrari, A.C. Graphene photonics and optoelectronics. Nat. Photonics 2010, 4, 611–622.

[CrossRef]

3. Pereira, V.M.; Castro, N.A.H. Strain engineering of graphene’s electronic structure. Phys. Rev. Lett. 2009, 103, 046801. [CrossRef] [PubMed]

4. Balandin, A.A.; Ghosh, S.; Bao, W. Superior thermal conductivity of single-layer graphene. Nano Lett. 2008, 8, 902–907. [CrossRef] [PubMed]

5. Xi, J.Y.; Jia, R.; Li, W.; Wang, J.; Bai, F.Q.; Eglitis, R.I.; Zhang, H.X. How does graphene enhance the photoelectric conversion

efficiency of dye sensitized solar cells? An insight from a theoretical perspective. J. Mater. Chem. A 2019, 7, 2730–2740. [CrossRef]

6. Jiang, J.; Wang, J.; Li, B. Young’s modulus of graphene: A molecular dynamics study. Phys. Rev. B 2009, 80, 113405. [CrossRef]

7. Cui, T.; Mukherjee, S.; Sudeep, P.M. Fatigue of graphene. Nat. Mater. 2020, 19, 405–411. [CrossRef] [PubMed]

8. Bunch, J.S.; van der Zande, A.M.; Verbridge, S.S. Electromechanical resonators from graphene sheets. Science 2007, 315, 490–493.

[CrossRef]

9. Dolleman, R.J.; Vidovikj, D.D.; Cartamil-Bueno, S.J. Graphene squeeze-film pressure sensors. Nano Lett. 2016, 16, 568–571.

[CrossRef]

10. Harada, K.; Ikeda, K.; Kuwayama, H. Various applications of resonant pressure sensor chip based on 3-D micromachining. Sens.

Actuator A Phys. 1999, 73, 261–266. [CrossRef]

11. Greenwood, J.C. Etched silicon vibrating sensor. J. Phys. E Sci. Instr. 1984, 17, 650–652. [CrossRef]

12. Mandle, J.; Lefort, O.; Migeon, A. A new micromachined silicon high-accuracy pressure sensor. Sens. Actuator A Phys. 1995, 46,

129–132. [CrossRef]

13. Vˇeí, J. Temperature compensation of silicon resonant pressure sensor. Sens. Actuator A Phys. 1996, 57, 179–182.

14. Kang, J.; Shin, D.; Bae, S. Graphene transfer: Key for applications. Nanoscale 2012, 4, 5527–5537. [CrossRef] [PubMed]

15. Kim, K.; Zhao, Y.; Jang, H. Large-scale pattern growth of graphene films for stretchable transparent electrodes. Nature 2009, 457,

706–710. [CrossRef]

16. Ali, U.; Karim, K.J.B.A.; Buang, N.A. A review of the properties and applications of Poly (Methyl Methacrylate) (PMMA). Polym.

Rev. 2015, 55, 678–705. [CrossRef]

17. Reina, A.; Jia, X.; Ho, J. Large area, few-layer graphene films on arbitrary substrates by chemical vapor deposition. Nano Lett.

2009, 9, 30–35. [CrossRef]

18. Schmid, S.; Bagci, T.; Zeuthen, E. Single-layer graphene on silicon nitride micromembrane resonators. J. Appl. Phys. 2014, 115, 054513. [CrossRef]

19. Oshidari, Y.; Hatakeyama, T.; Kometani, R. High quality factor graphene resonator fabrication using resist shrinkage-induced

strain. Appl. Phys. Lett. 2012, 5, 117201. [CrossRef]

20. Rouxinol, F.P.; Gelamo, R.V.; Amici, R.G. Low contact resistivity and strain in suspended multilayer graphene. Appl. Phys. Lett.

2010, 97, 253104. [CrossRef]

21. Robinson, J.T.; Zalalutdinov, M.K.; Cress, C.D. Graphene strained by defects. ACS Nano 2017, 11, 4745–4752. [CrossRef] [PubMed]

22. Cheng, Z.; Zhou, Q.; Wang, C. Toward intrinsic graphene surfaces: A systematic study on thermal annealing and wet-chemical

treatment of SiO2

-supported graphene devices. Nano Lett. 2011, 11, 767–771. [CrossRef] [PubMed]

23. Barton, R.A.; Ilic, B.; van der Zande, A.M. High, size-dependent quality factor in an array of graphene mechanical resonators.

Nano Lett. 2011, 11, 1232–1236. [CrossRef] [PubMed]

24. Currie, M.; Caldwell, J.D.; Bezares, F.J. Quantifying pulsed laser induced damage to graphene. Appl. Phys. Lett. 2011, 99, 211901.

[CrossRef]

25. Yoo, J.H.; In, J.B.; Park, J.B. Graphene folds by femtosecond laser ablation. Appl. Phys. Lett. 2012, 100, 233124. [CrossRef]

26. Lenner, M.; Kaplan, A.; Palmer, R.E. Nanoscopic Coulomb explosion in ultrafast graphite ablation. Appl. Phys. Lett. 2007,

90, 153119. [CrossRef]

27. Qiu, B.; Ruan, X. Reduction of spectral phonon relaxation times from suspended to supported graphene. Appl. Phys. Lett. 2012,

100, 193101. [CrossRef]

28. Lenner, M.; Kaplan, A.; Huehon, C. Ultrafast laser ablation of graphite. Phys. Rev. B 2009, 79, 184105. [CrossRef]

29. Ferriol, M.; Gentilhomme, A.; Cochez, M. Thermal degradation of Poly (methyl methacrylate) (PMMA): Modelling of DTG and

TG curves. Polym. Degrad. Stabil. 2003, 79, 271–281. [CrossRef]

30. Ma, J.; Jin, W. Fiber-optic ferrule-top nanomechanical resonator with multilayer graphene film. Opt. Lett. 2014, 39, 4769–4772.

[CrossRef]

31. Süske, E.; Scharf, T.; Schaaf, P. Variation of the mechanical properties of pulsed laser deposited PMMA films during annealing.

Appl. Phys. A. 2004, 79, 1295–1297. [CrossRef]

32. Nanzai, Y.; Miwa, A.; Cui, S.Z. Aging in fully annealed and subsequently strained Poly (methyl methacrylate). Polym. J. 2000, 32,

51–56. [CrossRef]

33. Xie, W.; Weng, L.; Ng, K.M. Clean graphene surface through high temperature annealing. Carbon 2015, 94, 740–748. [CrossRef]

34. Bao, W.; Miao, F.; Chen, Z. Controlled ripple texturing of suspended graphene and ultrathin graphite membranes. Nat. Nanotechnol.

2009, 4, 562–566. [CrossRef] [PubMed]

35. Roberts, A.; Cormode, D.; Reynolds, C.; Newhouse-Illige, T.; LeRoy, B.J.; Sandhu, A.S. Response of graphene to femtosecond

high-intensity laser irradiation. Appl. Phys. Lett. 2011, 99, 051912. [CrossRef]

36. Beltaos, A.; Kovaˇcevi′c, A.; Matkovi′c, A. Damage effects on multi-layer graphene from femtosecond laser interaction. Phys. Scr.

2014, 162, 014015. [CrossRef]

37. Takeuchi, Y. Thermal Stress; Science Press: Beijing, China, 1977; pp. 77–79.

38. Metzger, C.; Favero, I.; Ortlieb, A. Optical self-cooling of a deformable Fabry-Perot cavity in the classical limit. Phys. Rev. B 2008,

57, 1436–1446. [CrossRef]

39. Dolleman, R.J.; Houri, S.; Davidovikj, D. Optomechanics for thermal characterization of suspended graphene. Phys. Rev. B 2017,

96, 165421. [CrossRef]

40. Renteria, J.D.; Nika, D.L.; Balandin, A.A. Graphene thermal properties: Applications in thermal management and energy storage.

Appl. Sci. 2014, 4, 525–547. [CrossRef]

41. Lin, Y.; Lu, C.; Yeh, C. Graphene annealing: How clean can it be. Nano Lett. 2012, 12, 414–419. [CrossRef]