Electrothermally Tunable Graphene Resonators Operating at Very

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Electrothermally Tunable Graphene Resonators Operating at Very High Temperature up to 1200K Fan Ye, Jaesung Lee, and Philip X.-L. Feng Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.7b04685 • Publication Date (Web): 31 Jan 2018 Downloaded from http://pubs.acs.org on February 1, 2018

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Electrothermally Tunable Graphene Resonators Operating at Very High Temperature up to 1200K Fan Ye†, Jaesung Lee†, Philip X.-L. Feng Department of Electrical Engineering & Computer Science, Case School of Engineering, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, OH 44106, USA Corresponding Author. Email: [email protected]. Abstract The unique negative thermal expansion coefficient and remarkable thermal stability of graphene make it an ideal candidate for nanoelectromechanical systems (NEMS) with electrothermal tuning. We report on the first experimental demonstration of electrothermally tuned single- and few-layer graphene NEMS resonators operating in the high frequency (HF) and very high frequency (VHF) bands. In single-, bi-, and tri-layer (1L, 2L, and 3L) graphene resonators with carefully controlled Joule heating, we have demonstrated remarkably broad frequency tuning up to ∆f/f0 ≈ 310%. Simultaneously, device temperature variations imposed by Joule heating are monitored using Raman spectroscopy; and we find that the device temperature increases from 300K up to 1200K, which is the highest operating temperature known to date for electromechanical resonators. Using the measured frequency and temperature variations, we further extract both thermal expansion coefficients and thermal conductivities of these devices. Comparison with graphene electrostatic gate tuning indicates that electrothermal tuning is more efficient. The results clearly suggest that the unique negative thermal expansion coefficient of graphene and its excellent tolerance to very high temperature can be exploited for engineering highly tunable and robust graphene transducers for harsh and extreme environments. KEYWORDS: Graphene, Nanoelectromechanical Systems (NEMS), Frequency Tuning, Electrothermal, Thermal Expansion Coefficient (TEC), Thermal Conductivity -1-

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Nano/microelectromechanical systems (N/MEMS) vibrating at high frequencies have been employed in many important applications such as ultrasensitive detection of physical quantities toward their fundamental limits (e.g., mass sensing down to the single-atom regime1,2,3 and force detection down to the single-spin and zepto-Newton range 4 , 5 ), and energy-efficient radio frequency (RF) signal processing and communication (e.g., resonators, mixers, filters, and oscillators6,7,8). For these applications, continuous and wide-range tuning is highly desirable for the frequency-determining elements (i.e., resonators), which not only allows control of device operating regimes, but also permits great flexibility for post-fabrication reconfiguration and adjustment to adapt to various applications. Frequency tuning in N/MEMS resonators has been achieved predominantly by using gate voltage induced electrostatic forces that modify resonance frequency based on either capacitive softening9 or stiffening9,10 effects. Electrostatic frequency tuning, however, is limited by pull-in induced failure at large gate voltage; and it also introduces considerable energy dissipation (i.e., loaded Q effects) and deteriorates quality (Q) factors (∆Q/Q0 ≈ 58.5%)9, 11 of devices.

Besides electrostatic frequency tuning, another important

scheme is direct electromechanical tuning in piezoelectric devices where a DC polarization voltage applied across a doubly clamped piezoelectric layer directly alters the built-in tension thus the resonance frequency 12 , 13 , often in the range of ~0.5−1%.

Likewise, electro-

magnetomotive tuning is realized by applying a DC current through a doubly clamped device in the presence of a magnetic field, thus varying its static tension level and tuning its frequency, up to 6%

14

.

Furthermore, another interesting tuning mechanism is based on exploiting

electrothermal effects using Joule heating, which has been demonstrated in silicon carbide (SiC) nanobeam resonators, with tuning range up to 10%15. To achieve a wide frequency tuning range using electrothermal effect, device materials should possess superior electrical conductivity and

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thermal stability so as to efficiently heat up the device without performance degradation, as well as strong thermal-mechanical coupling effects (e.g., via high thermal expansion coefficient, TEC) for high-efficient frequency tuning. Compared with conventional N/MEMS devices with mainstream three-dimensional (3D) materials such as silicon (Si)12, aluminum nitride (AlN)13 and SiC15, devices built upon atomically thin 2D crystals have potential to exhibit frequency tunability 16 thanks to their ultralow transverse flexural rigidity and ultrahigh breaking (strain) limit. As a hallmark of 2D materials, graphene 17 , 18 , 19 is endowed with superior mechanical properties (e.g., Young’s modulus of EY~1TPa and intrinsic strength of εlimit~25%20) and excellent thermal properties – in particular, thermal conductivity of κ~5000W/(m·K)21, and unique negative thermal expansion coefficients 22 (which means graphene shrinks as its temperature increases).

These unusual

properties make graphene an outstanding candidate for NEMS. High performance graphene NEMS resonators have been demonstrated using photothermal 23 and electrostatic actuation schemes16, demonstrating great potential of graphene for future generations of NEMS resonators. While considerable efforts and progresses have been made on graphene resonators, very little work has been attempted on their high temperature operations. Given its exceptional thermal conductivity and stability (graphene CVD synthesis temperature is often >900°C), we envision graphene resonators may inherently exhibit better performance at higher temperature, making it intriguing to explore operations and frequency tuning via thermal effects, which may be more suitable for graphene NEMS than through conventional tuning schemes. In this work, we fabricate single-, bi-, and tri-layer (1L, 2L, and 3L) graphene resonators and investigate their electrothermally excited and tuned resonance characteristics at high temperature

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up to ~1200K, using Joule heating. We conveniently use DC voltage (VDC) to electrothermally heat up graphene resonators, and apply AC voltage (VAC) to excite resonance motions. Then, we simultaneously measure temperature and resonance characteristics of graphene resonators using a combined Raman spectroscopy and interferometric motion detection system.

Unlike

electrostatic tension manipulation (i.e., gate tuning) where performance of resonators may be compromised by capacitive softening and loaded Q effects, our electrothermal scheme exhibits both exceptional frequency tuning range and Q enhancement. Further, the TECs and thermal conductivities of the graphene devices during Joule heating are extracted, which exhibit similar temperature dependence as theoretically predicted.

Using the extracted TECs and thermal

conductivities, temperature profiles of graphene membrane are obtained (in the fashion that is consistent with the approach used in Refs. 24-25). We also compare our results with existing works on graphene electrostatic frequency tuning, and find that electrothermal tuning via Joule heating could achieve larger tuning ranges with smaller applied voltages. Figure 1a illustrates the scheme for electrothermal excitation and tuning of graphene NEMS resonators in this study. The suspended graphene is electrothermally heated up by a DC bias current, IDC, resulted from the DC bias voltage VDC from the drain (D) to the grounded source (S). Besides, a small AC voltage VAC superpoposed to the VDC, is applied to the graphene resonator. The small AC voltage changes the temperature periodically, though with a very small amplitude compared to that from the DC voltage, generating thermal forces on the graphene membrane.

This results in the graphene membrane expanding and shrinking periodically,

actuating the motion of graphene resonator. The back global gate should not be grounded, but instead is left floating, to efficiently avoid parasitic, unwanted electrostatic drive of the device motion (this has been carefully tested and verified in control experiments, described in

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Supporting Information S2). During electrothermal heating, several effects may come to play to modulate resonance characteristics of graphene NEMS (Fig. 1c).

First, as the device

temperature elevates, due to the unique negative thermal expansion coefficient, the thermal stress translates into additional built-in tension in suspended region, leading to frequency upshift in the graphene resonator. In addition, frequency upshift also increases stored mechanical energy in suspended graphene, resulting in boosted Q factor. Further, elevated temperature introduces thermal annealing effects on the graphene membrane, removing surface adsorbates and possible fabrication residues on the device surface, which further boosts up the frequency, and reduces energy loss in the graphene resonator, thus providing Q factor enhancement.

Figure 1: Illustration of graphene resonators with electrothermal excitation and tuning via Joule heating, and measurement system. (a) Circular drumhead graphene resonators with Joule heating. The color of graphene bonds and atoms indicates the temperature gradients (green and red colors represent low and

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high temperature of graphene respectively). Inset: zoom-in view of graphene-graphite metal contact region. (b) Combined Raman spectroscopy-optical interferometry measurement system. LPF, PD, and BS represent longpass filter, photodetector and beam splitter, respectively.

All measurements are

performed in moderate vacuum (~20mTorr). (c) Analysis of coupling effects of graphene resonators under electrothermal tuning.

We have fabricated 1L, 2L, and 3L circular drumhead graphene resonators with diameters of 3µm, 4µm, and 5µm, respectively. The graphene flakes are exfoliated onto a PDMS stamp and then transferred onto pre-patterned substrates.

This all-dry-transfer approach immediately

evades the necessity of conventional polymer coating, electron-beam lithographical patterning, solvents and metallization steps on top of graphene flakes, and also avoids highly risky and lowyield release processes requiring immersion in etching solutions for undercut and in solvents for critical point drying. This is ideally suited for fabricating suspended atomic layer devices and arrays of them on pre-fabricated microtrenches. For very thin graphene flakes dry-transferred onto microtrenches with surrounding electrodes, to minimize the contact resistance, we dry transfer thick graphite flakes, serving as ‘bridges’ between graphene atomic layers and metal electrodes (see graphite and metal contact in Fig. 1a), which could greatly facilitate achieving lower contact resistance and thus heat up the graphene membrane more efficiently. In the 3L device, 3L graphene flake can be in direct contact with Au electrodes. Raman spectroscopy and optical interferometry are employed to detect temperature and resonances as shown in Fig. 1b. Figure 2a to 2f show the optical microscope images of the 1L, 2L, and 3L graphene resonators and their fundamental-mode resonances measured at room temperature, respectively. We first investigate resonance characteristics of graphene resonators with small VDC and VAC and find f ≈ 44.3MHz with Q ≈ 59, f ≈ 14.4MHz with Q ≈ 149, and f ≈ -6-


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10.7MHz with Q ≈ 81, for the 1L, 2L, and 3L graphene resonators, respectively. Resonance frequency of the fundamental mode in circular drumhead graphene resonators during Joule heating can be determined by 1/ 2

2.404  γ 300K + γ T  f0 =   , ρt πd  

(1)

where d is diameter, γ300K is initial built-in tension at 300K (in unit of N/m), γT is additional tension induced by temperature change, and t is device thickness. ρ is mass density of device that can be determined by ρ=βρgraphene, where β is mass density ratio induced by possible adsorbates and ρgraphene is mass density of graphene. At room temperature (300K), with small VDC and VAC, γT approaches 0 and resonance frequency is mainly determined by γ300K. The 1L device shows a relatively higher fundamental frequency compared with the 2L and 3L devices at room temperature, showing γ300K in 1L device (0.023N/m) is higher than those in the 2L (0.009N/m) and 3L (0.011N/m) devices, if β =1.

The Raman signatures (Fig. 2g) clearly

illustrate and verify the numbers of layers (thicknesses) of these graphene resonators.

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Figure 2: Resonance characteristics of single-, bi-, and tri-layer (1L, 2L, & 3L) graphene resonators measured at room temperature. Optical microscopy images of the (a) single-, (c) bi-, and (e) tri-layer graphene resonators (the blue dash lines outline graphite electrodes). Scale bars in the upper row: (a) 50µm, (c) 100µm, and (e) 10µm. Scale bars in the lower row: 5µm. Fundamental-mode resonance of the (b) single-, (d) bi-, and (f) tri-layer graphene resonators. (g) Raman signatures measured from the single-, bi- and tri-layer graphene devices.

We then investigate the electrothermal tuning by gradually increasing the bias voltage power. Figure 3a, 3c, and 3e show power dependence of resonant frequency in the 1L, 2L, and 3L devices, respectively (the power calculations are shown in Supporting Information Figure S11). As power increases from 0.005mW to 1.67mW, the frequency upshifts from 44.7MHz to 109MHz (∆f/f0 ≈ 143.8%) in the 1L device. Similarly, the resonance frequencies increase from 14.8 MHz to 34.4MHz (∆f/f0 ≈ 132.4%) in the 2L device, and from 10.7MHz to 43.7MHz (∆f/f0 ≈ 308.4%) in the 3L device, as power is increased from 0.0013mW to 2.98mW, and from 0.026mW to 6.1mW, respectively. Correspondingly, the additional tension level γT is 0.117N/m, 0.031N/m, and 0.174N/m, in the 1L to 3L devices, respectively, under the highest power. We observe that the 1L and 2L devices require a higher bias voltage compared with the power -8-


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applied to the 3L device to achieve similar level of tuning. This observation results from the fact that two thick graphite flakes are transferred between graphene and metal, leading to a higher total resistance that requires higher power, due to voltage dividing effect. Based on the measured results, we examine the electrothermal frequency tuning mechanism in these graphene resonators. As shown in Fig. 1c, temperature rise introduced by Joule heating generates thermal stress in suspended graphene and induces additional tension γT, leading to frequency upshift. Assuming that Joule heating elevates temperature in the suspended graphene and temperature of supported regime remains near room temperature (300K)24, the temperature distribution in the graphene membrane during Joule heating is given by

1 d  dT  P =0, r + 2 r dr  dr  πR tκ (T )

(2)

where κ (T ) is the temperature-dependent thermal conductivity, R is the radius of graphene membrane, and P is the applied power on suspended graphene, which can be expressed as P = I suspendedVsuspended (see Supporting Information Figure S10). The temperature-dependent

thermal conductivity κ (T ) is given by25 φ

 T300K   ,  T 

κ (T ) = κ (T300K ) 

(3)

where T300K refers to room temperature (300K), κ (T300K ) is thermal conductivity at 300K and φ is a temperature-dependent power index, describing how the thermal conductivity is affected

by temperature. Substituting Eq. (3) into Eq. (2), the two-dimensional temperature profile of the graphene membrane is determined by -9-


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 P (1 − φ )  r   T ( r ) = T01−φ + 1 −   4πtκ T0φ  R 2    2

1 1−φ

,

(4)

and the average temperature in the graphene membrane is given by 1

Tavg =

2π

R

0

0

∫ ∫

 1−φ P (1 − ε )  r 2   1−φ T0 + 1 −   rdrdθ 4πtκ T φ  R 2    . 2π R θ rdrd ∫ ∫ 0

(5)

0

With temperature obtained by Eq. (5), the additional tension in the suspended graphene avg membrane is γ Tavg = − EY t ∫ 300 α (T ) dT , where EY is Young’s modulus and α(T) is TEC of

T

graphene. Therefore, the resonance frequency during Joule heating can be expressed as avg α (T ) dT 2.404  γ 300K − EY t ∫ 300 f0 =  πd  ρt

T

1/2

  .  

(6)

From Eq. (5) and Eq. (6), it can be seen that, under certain power, the frequency tuning range in graphene resonators mainly depends on two parameters: thermal conductivity and TEC. Generally, under certain power, wider frequency tuning could be achieved with a small thermal conductivity, which gives rise to higher temperature, and a large TEC. Based on above analysis, we theoretically calculate the limits of electrothermal frequency tuning for our devices using previously reported values. The upper limit of frequency tuning is calculated by assuming κ(T300K) = 1700W/(m·K), φ =1.9 and α(T) varying from 3.7×10-6 to 1.8×10-6 as temperature increasing from 300K to 1000K, which are shown as green dashed lines in Fig. 3a, 3c & 3e. Note, since experimental results of TECs at high temperature have not been reported, we extrapolate theoretical values from Ref. 26. Similarly, the lower limit of frequency tuning is -10-


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calculated by using κ(T300K) = 3000W/(m·K), φ =1.9 and α(T) varying from 3.7×10-7 to 1.8×10-7 as temperature increasing from 300K to 1000K, which are shown as dark dashed lines in Fig. 3a, 3c & 3e. The shadowed regions in Fig. 3a, 3c & 3e indicate available frequency tunability between these two limits described above.

Most of our experimental results are in these

shadowed regions. Some data points of 1L are beyond the high limit, suggesting the actual thermal conductivity could be smaller than the 1700W/(m·K) or the actual TEC might be larger than the used values. We also notice that the upper limit of the tuning range (230%) for the 1L device is much lower than those of the 2L (600%) and the 3L (900%) devices, which could be attributed to lower applied power on the 1L device. Besides wide frequency tuning, another pronounced merit of electrothermal tuning is Q factor enhancement (Fig. 3b & 3f). In the 1L device, we have achieved up to 10-fold Q enhancement during Joule heating. The observed Q enhancement could be attributed to several factors. First, high temperature induced by Joule heating anneals graphene devices, removing surface adsorbates such as air molecules and possible residues from fabrication process16, which may reduce energy dissipation such as surface loss27. Further, the quality factor is determined by Q = ƒ/Γm, thus the Q factor could rise as frequency increases, if the damping rate Γm is assumed to be relatively stable or constant. In contrast, evolution of the Q factor in the 3L resonator exhibits different trend: Q factor gradually increases as power moves from 0 to 4mW and it decreases when power is higher than 4mW. For the 2L device, Q factor continuously decreases when the device is heated up from room temperature. This Q factor deterioration at high temperature might be attributed to persistent surface contaminations and related dissipation. For example, some robust contaminants may not be easily desorbed or vaporized but can migrate on surface of resonator due to high kinetic energy from heating. This contamination related damping could be -11-


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more obvious when device surface is hot, leading to more damping at high temperature 28 . Beside, when temperature of graphene resonator increases, thermal conductively of graphene decreases significantly29, generating larger temperature gradient within suspended graphene area. This temperature gradient might lead to uneven and localized thermal expansion24, which could yield wrinkles or ripples30, resulting in higher damping thus lower Q factor. In practical case, temperature-dependent Q factor is determined by the interplay of the aforementioned several effects. Different initial conditions of devices (e.g., type and amount of adsorbates, and size of devices) may result in different Q evolution trend; and further investigations are required to understand the governing mechanisms of damping in these graphene resonators at elevated temperatures.

Figure 3: Electrothermal tuning measured from the single-, bi-, and tri-layer (1L, 2L, & 3L) graphene resonators. Frequency shifts of the (a) 1L, (c) 2L, and (e) 3L graphene resonators as power increases. Red dashed lines are calculated frequency with extracted κ(T), φ and α(T0). Green dashed lines indicate

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upper limit of frequency tuning, calculated using κ(T0) = 1700W/(m·K), φ = 1.9 and α(T) varying from 3.7×10-6 to -1.8×10-6 as temperature increasing from 300K to 1000K. Dark dashed lines indicate lower limit of frequency tuning, calculated using κ(T0) = 3000W/(m·K), φ = 1.9 and α(T0) varying from 3.7×10-7 to -1.8×10-7 as temperature increasing from 300K to 1000K.

Shadowed regions indicate

available frequency tunability between lower and upper limits. Quality (Q) factor changes of the (b) 1L, (d) 2L, and (f) 3L graphene resonators as power increases (scale bars: 5µm).

We now turn to discuss on the temperature variations in the 1L to 3L devices, as calibrated by measuring Raman peak shifts during Joule heating. As illustrated in Fig. 1b, we simultaneously monitor both resonance and Raman spectra during Joule heating using our optical-electrical combined system. Figure 4a shows the Raman spectra of the 3L graphene device with power increasing from 0V to 6.2mW. We fit the measured G and 2D peaks to Lorentzian function to precisely determine the peak positions, and the device temperature is extracted from the Raman peak shift. Raman thermometry has been well established in theory by considering anharmonic effects in lattice vibrations as temperature varies, and widely experimentally calibrated, such as by monitoring temperature of graphene up to 2000K from gray body emission24,31. As power increases, both G and 2D peaks exhibit redshift and broadening due to anharmonic effects 32 induced by electrothermal heating. It is worth noting that there is no obvious D peak even when we apply very high power, suggesting minimal defects generation during electrothermal tuning. At power higher than 6mW, due to apparent thermal emission, the background baseline level of Raman spectra increases significantly compared with intensity of Raman 2D peak31.

This

baseline increasing and Raman peak broadening make it difficult to identify peak position of 2D mode precisely. Accordingly, we use G peak shift to estimate temperature variations of the 1L to 3L graphene. Besides, the relatively low level of thermal emission (intensity of thermal emission

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is smaller than Raman peaks) indicates that device temperature is less than 2000K, enabling us to estimate temperature based on the first-order temperature dependency equation,

ωT = ω300K + χ (T − 300 K ) ,

(7)

where ωT is frequency of G mode, ω300K is frequency of G mode at room temperature (300K), T is temperature and χ is first-order temperature coefficient, in which χ = -0.016cm-1/K for 1L graphene and χ = -0.015cm-1/K for 2L and 3L graphene21. The peak position and corresponding temperature of the 1L to 3L graphene during Joule heating are shown in Fig. 4(b) to (g), respectively. Since strain changes in these devices are much smaller than strain resolution of Raman measurement (resolution of our Raman system is ~1cm-1, providing strain sensitivity of ~0.08%, which is much bigger than strain variation of our devices, only 0.05% even when it is at very high temperature)33, we neglect Raman shift contributed from strain level change caused by temperature variation. It should be noted that temperature estimated by Raman spectroscopy is weight averaged temperature under laser spot. Temperatures of both the 2L and 3L graphene devices increase up to 1000K, which can also be confirmed by the elevated baseline level in Raman spectra induced from thermal emission. Further insights in temperature variation can be gained by investigating temperature profile of the graphene membrane under Joule heating. By fitting measured temperature from Raman spectroscopy to our model, we obtain κ(T300K) and φ for the 1L to 3L devices. Considering the fact that the measured temperature from Raman spectroscopy is a weighted spatial average, because the intensity of the laser beam has Gaussian distribution, the measured temperature can be expressed by

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1

Tmeasured =

2π

R

0

0

∫ ∫

 1−φ P (1 − φ )   r2  r 2   1−φ T0 + 1 −   r exp  − 2  drdθ 4πtκ T φ  R 2    r0   , 2π R  r2  ∫0 ∫0 r exp  − r02  drdθ

(8)

where r0 refers to laser spot radius, which is 1µm in our case. From the fitting (red dashed lines in Fig. 4c, 4e and 4g), we find that κ(T0) ≈ 3000W/(m·K) and φ ≈ 1.9 for the 1L, κ(T0) ≈ 1300W/(m·K) and φ ≈ 1.9 for the 2L and κ(T0) ≈ 1700W/(m·K) and φ ≈ 1.5 for the 3L device. By using the boundary conditions of T(R) ≈ 300K and the extracted κ(T0) and φ, we calculate temperature profiles for the 1L to 3L devices. Under the highest applied power (1.67mW for 1L, 2.98mW for 2L and 6.17mW for 3L), the temperatures at the center of the 1L, 2L and 3L graphene membranes are 600K, 1700K and 1050K as shown in insets of Fig. 4c, 4e and 4g, respectively. The temperature-dependent thermal conductivities of the 1L to 3L devices are calculated using Eq. (3) and shown in Fig. 5g, 5h and 5i, respectively. The obtained thermal conductivities are much lower in the 2L and 3L devices compared to that of the 1L device, which could be attributed to possible contaminants in 2L and 3L devices, similar to Q deterioration in these two devices.

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Figure 4:

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Raman signatures, and temperature calibration from Raman spectroscopy during

electrothermal tuning of the graphene devices. (a) Evolution of Raman signatures from the 3L graphene device during Joule heating. G peak shift of the (b) single-, (d) bi-, and (f) tri-layer graphene resonators as the power increases. Measured temperature of the (c) single-, (e) bi-, and (g) tri-layer graphene devices via Raman G peak shift in (b), (d) and (f), respectively. Red dashed lines are fitting curves using Eq. (8). Insets: calculated temperature profiles with the applied power (1.67mW for 1L, 2.98mW for 2L and 6.17mW for 3L).

We estimate the TECs of the devices from measured frequency tuning and computed temperature from our model. The TECs of the device can be deduced by

α (Tavg ) = −2 f 0 (Tavg )

df 0 (Tavg ) dTavg

ρ

2

 πd  × ×  , EY  2.44 

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(9)

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where

df 0 (Tavg ) dTavg

is frequency gradient, which can be obtained by the numerically fitting curve of

frequency tuning over temperature (red dashed curves in Fig. 5a-e). The derivation of Eq. (9) is shown in Supporting Information S4. The average temperature Tavg is calculated using Eq. (5) and shown in Supporting Information Figure S8. The calculated TECs of the 1L to 3L graphene devices are shown in Fig. 5b, 5d & 5f, respectively. As temperature increases, TECs of all three devices increase initially and then decrease. Among three devices, TECs of the 2L and 3L graphene devices are one order of magnitude smaller than that of the 1L device, indicating the 2L and 3L devices have large mass density thus β. This larger mass density of the 2L and 3L devices might be attributed to persistent contaminations in suspended area, which also supports our aforementioned discussions of contamination induced Q degradation under high temperature in the 2L and 3L resonators. Using the extracted thermal conductivities and TECs, we return to the calculations of frequency tuning via Joule heating, which are shown as red dashed lines in Fig. 3a, 3c and 3e. The calculated results agree very well with experimental results.

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3000

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Figure 5: Frequency and thermal properties of graphene resonators during Joule heating. Temperature dependence of frequency during Joule heating in (a) 1L, (c) 2L, and (e) 3L graphene resonators (Red dashed lines are numerically fitting curves). Estimated thermal expansion coefficients (TECs) of (b) 1L, (d) 2L and (f) 3L graphene devices (Red dashed lines are numerically fitting curves). Estimated thermal conductivity of (g) 1L, (h) 2L and (i) 3L graphene devices.

We further benchmark the key performance metrics of graphene electrothermal tuning achieved in this work by comparing with electrostatic gate tuning of graphene16,34,35,36,37,38,39. As shown in Fig. 6, we consider three important parameters: highest voltage applied VDC,max across the suspended graphene, initial tension level γ300K and tuning range (defined as ∆f/f0). For our devices, we use γ300K when β=1, which might understate actual tension level of the devices. The 3L device with Au electrode exhibits tuning range almost twice as high as the largest frequency tuning achieved using electrostatic tuning16,34,35,36,37,38,39, demonstrating remarkable performance of electrothermal tuning. In addition, it offers such wide tuning range with very small VDC of ~0.6V, showing excellent tuning efficiency. In the 1L and 2L devices with graphite electrodes, -18-


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our devices, even with underestimated initial tension, still exhibit relatively wider tuning ranges compared with known electrostatic tuning ranges. All aforementioned results and comparisons clearly demonstrate electrothermal tuning is an excellent tool and important approach to enhancing and engineering resonance characteristics of emerging graphene NEMS resonators.

Figure 6:

Benchmarking of electrothermal tuning performance in graphene NEMS resonators.

Comparison of frequency tuning ranges between electrothermal tuning in this work and electrostatic tuning reported in literature.

In summary, we have demonstrated, for the first time, electrothermal frequency tuning of graphene resonators via Joule heating. We find that Joule heating could tune the resonance frequency in the 1L to 3L graphene devices very efficiently, with very broad tuning ranges up to ∆f/f0≈310%. Besides frequency tuning, we also observe Q factor enhancement with power ramping up. By monitoring Raman signatures during Joule heating, the temperature of graphene resonator is simultaneously calibrated while monitoring frequency tuning, indicating the

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temperature of graphene increases up to 1200K (~927°C), which proves that graphene resonators can operate at very high temperature with superior stability. Using the measured results and modeling, we have extracted TECs and thermal conductivities of the 1L to 3L graphene devices, which enable us to theoretically calculate temperature profile and frequency tuning. calculated frequency tuning agrees very well with experimental results.

The

The comparison

between electrothermal tuning and conventional electrostatic tuning reveals that electrothermal tuning is much more efficient with better performance.

This work demonstrates a unique

graphene NEMS platform which paves a way for engineering multifunctional NEMS and their emerging applications such as highly tunable voltage controlled NEMS oscillators, selfannealing and refreshing adsorption based sensors, self-ovenized devices, and NEMS for high temperature and harsh environments.

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ASSOCIATED CONTENT Supporting Information The supporting information includes fabrication method, experimental techniques, control experiments, calculations of temperature and thermal expansion coefficients, analysis of electrothermal heating power, and repeatability of frequency tuning. The supporting information is available free of charge via Internet at http://pubs.acs.org.

ACKNOWLEDGEMENT: We thank the support from National Science Foundation CAREER Award (Grant ECCS-1454570) and CCSS Award (Grant ECCS-1509721). Part of the device fabrication was performed at the Cornell NanoScale Science and Technology Facility (CNF), a member of the National Nanotechnology Infrastructure Network (NNIN), supported by the National Science Foundation (Grant ECCS-0335765).

AUTHOR INFORMATION: Corresponding Author Email: [email protected]

ORCID Fan Ye: 0000-0002-7621-6751 Jaesung Lee: 0000-0003-0492-2478 Philip X.-L. Feng: 0000-0002-1083-2391

Notes The authors declare no competing financial interest. †

Equal Contributions

F. Y. and J. L. contributed equally to this work.

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Table of Content (TOC) Graphic We electrothermally tune graphene nanoelectromechanical resonators with highest tuning range up to ∆ƒ/ƒ0 ≈ 310%. By calibrating temperature using Raman spectroscopy, we find that the device temperature increases from 300 K to 1200 K. Combining temperature and frequency tuning measurement, thermal expansion coefficients (TECs) and thermal conductivities are extracted. 45 ∆ƒ⁄ƒ0≈310%

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800 400

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