Electrothermally Tunable Graphene Resonators Operating at Very

make it an ideal candidate for nanoelectromechanical systems (NEMS) with ... We report on the first experimental demonstration of electrothermally tun...
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Letter Cite This: Nano Lett. 2018, 18, 1678−1685

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Electrothermally Tunable Graphene Resonators Operating at Very High Temperature up to 1200 K Fan Ye,† Jaesung Lee,† and Philip X.-L. Feng* Department of Electrical Engineering and Computer Science, Case School of Engineering, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, Ohio 44106, United States S Supporting Information *

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 trilayer (1L, 2L, and 3L) graphene resonators with carefully controlled Joule heating, we have demonstrated remarkably broad frequency tuning up to Δf/f 0 ≈ 310%. Simultaneously, device temperature variations imposed by Joule heating are monitored using Raman spectroscopy; we find that the device temperature increases from 300 K up to 1200 K, 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

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in induced failure at large gate voltage; and it also introduces considerable energy dissipation (i.e., loaded Q effects) and deteriorates quality (Q) factors (ΔQ/Q0 ≈ 58.5%)9,11 of devices. Besides electrostatic frequency tuning, another important scheme is direct electromechanical tuning in piezoelectric devices where a direct current (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

ano/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 regime1−3 and force detection down to the single-spin and zepto-Newton range4,5), and energy-efficient radio frequency (RF) signal processing and communication (e.g., resonators, mixers, filters, and oscillators6−8). 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 postfabrication 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© 2018 American Chemical Society

Received: November 4, 2017 Revised: January 25, 2018 Published: January 31, 2018 1678

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Figure 1. Illustration of graphene resonators with electrothermal excitation and tuning via Joule heating, along with the measurement system and signal transduction diagram. (a) A circular drumhead graphene resonator with Joule heating. The color of graphene bonds and atoms indicates the temperature gradient and profile (green and red colors represent low and 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 long-pass filter, photodetector, and beam splitter, respectively. All measurements are performed in moderate vacuum (∼20 mTorr). (c) Diagram for analysis of coupling effects in graphene resonators under electrothermal tuning.

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 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 SiC,15 devices built upon atomically thin 2D crystals have potential to exhibit frequency tunability16 thanks to their ultralow transverse flexural rigidity and ultrahigh breaking (strain) limit. As a hallmark of 2D materials, graphene17−19 is endowed with superior mechanical properties (e.g., Young’s modulus of EY ∼ 1 TPa and intrinsic strength of εlimit ∼ 25%20) and excellent thermal properties−in particular, thermal conductivity of κ ∼ 5000 W/(m·K),21 and unique negative thermal expansion coefficients22 (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 photothermal23 and electrostatic actuation schemes,16 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 chemical vapor deposition (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 trilayer (1L, 2L, and 3L) graphene resonators and investigate their electrothermally excited and tuned resonance characteristics at high temperature up to ∼1200 K, using Joule heating. We conveniently use dc voltage (Vdc) to electrothermally heat up graphene resonators, and apply alternating current (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 and 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 1679

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

Figure 3. Electrothermal tuning measured from the single-, bi-, and trilayer (1L, 2L, and 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(T). Green dashed lines indicate upper limit of frequency tuning, calculated using κ(T0) = 1700 W/(m·K), ϕ = 1.9 and α(T) varying from −3.7 × 10−6 to −1.8 × 10−6 as temperature increasing from 300 to 1000 K. Dark dashed lines indicate lower limit of frequency tuning, calculated using κ(T0) = 3000 W/(m·K), ϕ = 1.9 and α(T) varying from −3.7 × 10−7 to −1.8 × 10−7 as temperature increasing from 300 to 1000 K. 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: 5 μm).

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 Supporting Information S2). During electrothermal heating, several effects may come to play to

modulate resonance characteristics of graphene NEMS (Figure 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 1680

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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 voltage 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. On the basis of the measured results, we examine the electrothermal frequency tuning mechanism in these graphene resonators. As shown in Figure 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 (300 K),24 the temperature distribution in the graphene membrane during Joule heating is given by

further boosts up the frequency, and reduces energy loss in the graphene resonator, thus providing Q factor enhancement. We have fabricated 1L, 2L, and 3L circular drumhead graphene resonators with diameters of 3, 4, and 5 μm, respectively. The graphene flakes are exfoliated onto a PDMS stamp and then transferred onto prepatterned 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 low-yield 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 prefabricated microtrenches. For very thin graphene flakes drytransferred 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 Figure 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 Figure 1b. Figure 2a−f shows 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 ≈ 44.3 MHz with Q ≈ 59, f ≈ 14.4 MHz with Q ≈ 149, and f ≈ 10.7 MHz 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 f0 =

1/2 2.404 ⎛ γ300K + γT ⎞ ⎜ ⎟ πd ⎝ ρt ⎠

1 d ⎛⎜ dT ⎞⎟ P r + =0 r dr ⎝ dr ⎠ πR2tκ(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 = IsuspendedVsuspended (see Supporting Information Figure S10). The temperature-dependent thermal conductivity κ(T) is given by25 ⎛ T ⎞ϕ κ(T ) = κ(T0)⎜ 0 ⎟ ⎝T ⎠

(3)

where T0 refers to room temperature (300 K), κ(T0) is thermal conductivity at 300 K, 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 1/1 − ϕ ⎡ P(1 − ϕ) ⎛ r 2 ⎞⎤ 1−ϕ + T (r ) = ⎢T0 ⎜1 − 2 ⎟⎥ ⎢⎣ R ⎠⎥⎦ 4π tκT0 ϕ ⎝

(1)

where d is the diameter, γ300K is initial built-in tension at 300 K (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 (300 K), 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 (0.023 N/m) is higher than those in the 2L (0.009 N/m) and 3L (0.011 N/m) devices if β = 1. The Raman signatures (Figure 2g) clearly illustrate and verify the numbers of layers (thicknesses) of these graphene resonators. We then investigate the electrothermal tuning by gradually increasing the bias voltage and thus the power. Figure 3a,c,e shows power dependence of resonance frequency in the 1L, 2L, and 3L devices, respectively (the power calculations are shown in Supporting Information Figure S11). As power increases from 0.005 to 1.67 mW, the frequency upshifts from 44.3 to 109.0 MHz (Δf/f 0 ≈ 146.0%) in the 1L device. Similarly, the resonance frequencies increase from 14.4 to 34.4 MHz (Δf/f 0 ≈ 138.9%) in the 2L device and from 10.7 to 43.7 MHz (Δf/f 0 ≈ 308.4%) in the 3L device, as power is increased from 0.0013 to 2.99 mW, and from 0.026 to 6.14 mW, respectively. Correspondingly, the additional tension level γT is 0.117, 0.031, and 0.174 N/m in the

(4)

and the average temperature in the graphene membrane is given by 2π

Tavg =

R⎡

∫0 ∫0 ⎢⎣T01 − ϕ +

P(1 − ε) 4πtκT

ϕ

2π

R

(1 − )⎤⎦⎥ r2 R2

1/1 − ϕ

r dr dθ

∫0 ∫0 r dr dθ (5)

With temperature obtained by eq 5, the additional tension in the avg α(T)dT, suspended graphene membrane is γTavg = −EYt ∫ T300 where EY is Young’s modulus and α(T) is TEC of graphene. Therefore, the resonance frequency during Joule heating can be expressed as Tavg ⎛ ⎞1/2 γ − E t α ( T )d T ∫ Y 300K 2.404 ⎜ ⎟ 300 f0 = ⎟⎟ πd ⎜⎜ ρt ⎝ ⎠

(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. On the basis of above analysis, we theoretically calculate the limits of electrothermal frequency 1681

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Figure 4. 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) trilayer graphene resonators as the power increases. Measured temperature of the (c) single-, (e) bi-, and (g) trilayer 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 highest applied power (1.67 mW for 1L, 2.99 mW for 2L, and 6.14 mW for 3L).

contrast, evolution of the Q factor in the 3L resonator exhibits a different trend: Q factor gradually increases as power moves from 0 to 4 mW and it decreases when power is higher than 4 mW. 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 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 significantly,29 generating larger temperature gradient within suspended graphene area. This temperature gradient might lead to uneven and localized thermal expansion,24 which could yield wrinkles or ripples,30 resulting in higher damping thus lower Q factor. In a 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. 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 Figure 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 0 to 6.14 mW. We fit the measured G and 2D peaks to Lorentzian function to precisely determine the peak

tuning for our devices using previously reported values. The upper limit of frequency tuning is calculated by assuming κ(T0) = 1700 W/(m·K), ϕ = 1.9 and α(T) varying from 3.7 × 10−6 to 1.8 × 10−6 as temperature increasing from 300 to 1000 K, which are shown as green dashed lines in Figure 3a,c,e. Note that because 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 calculated by using κ(T0) = 3000 W/(m·K), ϕ = 1.9 and α(T) varying from 3.7 × 10−7 to 1.8 × 10−7 as temperature increasing from 300 to 1000 K, which are shown as dark dashed lines in Figure 3a,c,e. The shadowed regions in Figure 3a,c,e 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 (Figure 3b,f). 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 process,16 which may reduce energy dissipation such as surface loss.27 Further, the quality factor is determined by Q = f/ Γm, thus the Q factor could rise as frequency increases if the damping rate Γm is assumed to be relatively stable or constant. In 1682

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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, (b) 2L, and (c) 3L graphene resonators (red dashed lines are numerically fitting curves). Estimated thermal expansion coefficients (TECs) of (d) 1L, (e) 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.

graphene devices increase up to 1000 K, 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(T0) 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

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 2000 K from gray body emission.24,31 As power increases, both G and 2D peaks exhibit redshift and broadening due to anharmonic effects32 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 6 mW, due to apparent thermal emission, the background baseline level of Raman spectra increases significantly compared with intensity of Raman 2D peak.31 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 is smaller than Raman peaks) indicates that device temperature is less than 2000 K, enabling us to estimate temperature based on the firstorder temperature dependency equation ωT = ω300K + χ (T − 300 K)

2π

Tmeasured =

R⎡

∫0 ∫0 ⎢⎣T01 − ϕ +

P(1 − ϕ) 4πtκT ϕ 2π

R

(1 − )⎤⎦⎥

1/1 − ϕ

r2

R2

⎛

2

⎛ r2 ⎞ r exp⎜− 2 ⎟dr dθ ⎝ r0 ⎠

⎞

∫0 ∫0 r exp⎜⎝− rr 2 ⎟⎠dr dθ 0

(8)

where r0 refers to laser spot radius, which is 1 μm in our case. From the fitting (red dashed lines in Figure 4c,e,g), we find that κ(T0) ≈ 3000 W/(m·K) and ϕ ≈ 1.9 for the 1L, κ(T0) ≈ 1300 W/(m·K) and ϕ ≈ 1.9 for the 2L and κ(T0) ≈ 1700 W/(m·K) and ϕ ≈ 1.5 for the 3L device. By using the boundary conditions of T(R) ≈ 300 K and the extracted κ(T0) and ϕ, we calculate temperature profiles for the 1L to 3L devices. Under the highest applied power (1.67 mW for 1L, 2.99 mW for 2L, and 6.14 mW for 3L), the temperatures at the center of the 1L, 2L and 3L graphene membranes are 600, 1700, and 1050K as shown in insets of Figure 4c,e,g, respectively. The temperature-dependent thermal conductivities of the 1L to 3L devices are calculated using eq 3 and shown in Figure 5g,h,i, 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. 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

(7)

where ωT is frequency of G mode, ω300K is frequency of G mode at room temperature (300 K), T is temperature, and χ is first-order temperature coefficient in which χ = −0.016 cm−1/K for 1L graphene and χ = −0.015 cm−1/K for 2L and 3L graphene.21 The peak position and corresponding temperature of the 1L to 3L graphene during Joule heating are shown in Figure 4b−g, respectively. Because strain changes in these devices are much smaller than strain resolution of Raman measurement (resolution of our Raman system is ∼1 cm−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 1683

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where

df0 (Tavg) dTavg

df0 (Tavg) dTavg

×

⎛ πd ⎞ 2 ρ ⎟ ×⎜ E Y ⎝ 2.44 ⎠

to enhancing and engineering resonance characteristics of emerging graphene NEMS resonators. 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 Δf/f 0 ≈ 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 temperature of graphene increases up to 1200 K (∼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. The calculated frequency tuning agrees very well with experimental results. 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, self-annealing and refreshing adsorption based sensors, self-ovenized devices, and NEMS for high temperature and harsh environments.

(9)

is frequency gradient, which can be obtained by the

numerically fitting curve of frequency tuning over temperature (red dashed curves in Figure 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−3L graphene devices are shown in Figure 5b,d,f, 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 1 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 Figure 3a,c.e. The calculated results agree very well with experimental results. We further benchmark the key performance metrics of graphene electrothermal tuning achieved in this work by comparing with electrostatic gate tuning of graphene.16,34−39 As shown in Figure 6, we consider three important parameters:

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.7b04685. Fabrication method, experimental techniques, control experiments, calculations of temperature and thermal expansion coefficients, analysis of electrothermal heating power, and repeatability of frequency tuning (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

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

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.

Author Contributions †

F.Y. and J.L. contributed equally to this work. F.Y. fabricated the devices. F.Y. and J.L. carried out the measurements with important technical support on apparatus and instrumentation from P.X.- L.F. F.Y., J.L. and P.X.-L.F. analyzed the data and wrote the manuscript. P.X.-L.F. conceived the experiments and supervised the project.

highest voltage applied VDC,max across the suspended graphene, initial tension level γ300K and tuning range (defined as Δf/f 0). 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 tuning,16,34−39 demonstrating remarkable performance of electrothermal tuning. In addition, it offers such wide tuning range with very small Vdc of ∼0.6 V, showing excellent tuning efficiency. In the 1L and 2L devices with graphite electrodes, 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

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS 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 1684

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Nano Letters

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Infrastructure Network (NNIN), supported by the National Science Foundation (Grant ECCS-0335765).

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DOI: 10.1021/acs.nanolett.7b04685 Nano Lett. 2018, 18, 1678−1685