Shear Modulus of Monolayer Graphene Prepared by Chemical Vapor

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Shear Modulus of Monolayer Graphene Prepared by Chemical Vapor Deposition Xiao Liu,*,† Thomas H. Metcalf,† Jeremy T. Robinson,† Brian H. Houston,† and Fabrizio Scarpa‡,§ †

Naval Research Laboratory, Washington, D.C. 20375, United States Bristol Centre for Nanoscience and Quantum Information, University of Bristol, BS8 1FD, United Kingdom § Advanced Composites Centre for Innovation and Science (ACCIS), University of Bristol, BS8 1TR, United Kingdom ‡

S Supporting Information *

ABSTRACT: We report shear modulus (G) and internal friction (Q−1) measurements of large-area monolayer graphene films grown by chemical vapor deposition on copper foil and transferred onto high-Q silicon mechanical oscillators. The shear modulus, extracted from a resonance frequency shift at 0.4 K where the apparatus is most sensitive, averages 280 GPa. This is five times larger than those of the multilayered graphene-based films measured previously. The internal friction is unmeasurable within the sensitivity of our experiment and thus bounded above by Q−1 ≤ 3 × 10−5, which is orders-of-magnitude smaller than that of multilayered graphene-based films. Neither annealing nor interface modification has a measurable effect on G or Q−1. Our results on G are consistent with recent theoretical evaluations and simulations carried out in this work, showing that the shear restoring force transitions from interlayer to intralayer interactions as the film thickness approaches one monolayer. KEYWORDS: graphene, shear modulus, internal friction, chemical vapor deposition, carbon, nanomechanics

G

modes involving torsional strains. Torsional modes have the advantage over the flexural modes for not having the thermoelastic loss15 and hence can improve Q and device sensitivity. Shear deformation also plays an important role in the wrinkling and rippling behavior of graphene, which, in turn, controls charge carrier scattering and electron mobility.16 Recently, we determined the shear modulus (G) of both rGO films (4−90 nm thick) and CVD-grown multilayered graphene on Ni (6 and 8 nm thick).17 In both cases, G was independent of the fabrication techniques and thicknesses, averaging 53 GPa, which is five times larger than that of graphite (Gin‑plane = 10 GPa, see below). The low-temperature internal friction (Q−1, the inverse of quality factor) below 10 K for both films was as high as the universal amorphous limit, which is dominated by the tunneling states originating from structural disorder in the atomic scale. Such high Q−1 values were not surprising given the small crystallite sizes and high density of defects as determined by atomic force microscope and Raman spectroscopy. Despite the growing interest for high-quality, CVD-grown graphene on Cu,14,18 the elastic moduli of such films have not yet been determined. Following our previous work on multilayered graphene-based films, here we report our experimental results of G and Q−1 of large-area single-layer

raphene, a two-dimensional allotrope of carbon covalently bonded in a hexagonal lattice, has attracted much attention due to its unique structure and promise in applications.1,2 Mechanically exfoliated graphene produces the best crystalline quality, from which most of its extraordinary electronic, optical, thermal, and elastic properties have been determined. Such pristine graphene has a Young’s modulus (E) of 1 TPa3 and mechanical quality factors (Q) of 104 at 5 K4 and 105 at 90 mK.5 These mechanical properties rival those of bulk diamond/graphite, making it an ideal material for highfrequency and high-sensitivity nanoelectromechanical applications,5−7 where high-elastic moduli, high-quality factor, and low mass are desired. However, it is rather impractical to harvest such flakes in meaningful quantities for large-scale production and integration into devices. Technologically more relevant is the synthesis of graphene films via growth on silicon carbide,8 chemical vapor deposition (CVD) on transition metals,9,10 or chemical reduction of graphene oxide in colloidal suspension.11 Each approach has generated graphene suitable for specific applications. Multilayered reduced graphene oxide (rGO) films were found to have E = 185 GPa, with Q = 4000,7 while E = 20812 and 250 GPa13 were found for single layers. CVD-grown graphene on Cu was found to have Q up to 9000 at 10 K.14 For graphene to be utilized as nanoelectromechanical resonators or nanosensors, it is important to determine both its Young’s and shear moduli as a whole in order to understand its structural integrity and limitations as a mechanical material. Shear modulus determines the resonance frequency of vibration © 2012 American Chemical Society

Received: November 29, 2011 Published: January 3, 2012 1013

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Figure 1. (a) Outline of the DPO. The left side shows the front view, where the hatched area is neck. The right side shows a microscopic picture of the front and back sides of the neck carrying a single-layer CVD graphene film with PMMA. (b) A Raman spectrum of our film. (c) A higher resolution SEM picture where grain boundaries and double-layered sites (darker dots) are visible.

Measurements of G and Q−1 were performed using the DPO technique.24 The DPOs were fabricated out of high-purity, Pdoped, ⟨100⟩-oriented silicon wafers, which had resistivities >5 kΩcm. The overall dimensions of a DPO are 28 mm high, 20 mm wide, and 0.3 mm thick; see the left side of Figure 1a. The main axes are along the ⟨110⟩ orientation. On the back of the DPO, a metal film (30 Å Cr and 500 Å Au) was deposited, covering the foot, leg, and wings (but not the neck or head) for electrostatic actuation and detection. The DPO was installed in the experimental apparatus by clamping it to an invar block using invar screws and a precision torque wrench. This minimized the effect of thermal contraction during cool down and ensured reproducibility after repeated remounting of the same DPO. We used the so-called second antisymmetric vibrational mode, oscillating at ∼5500 Hz (see movie in Supporting Information). It has an exceptionally small background internal friction Q−1 ≈ 2 × 10−8 at low temperatures (T < 10 K). During oscillation, the head and the wings vibrate out-of-phase with one another, giving rise to a torsional oscillation of the neck. This balanced oscillation produces very little motion in the foot, which minimizes external loss. Addition of a film on the neck area leads to a measurable shift of a DPO’s resonance frequency, fsub → fosc, and internal −1 −1 friction, Qsub → Qosc , even for a film as thin as graphene. From −1 the difference, Gfilm and Qfilm of the film can be calculated through

graphene grown on Cu by CVD. We find that G increases by another factor of 5 from that of multilayered graphene-based films and that Q−1 is virtually immeasurable within the instrument resolution. The averaged shear modulus value is consistent with recent theoretical evaluations19−23 and finite element method (FEM) simulations carried out specifically in this work to account for any extrinsic substrate effects. Together, these findings indicate that unlike the Young’s modulus, the shear modulus of graphene differs significantly from that of bulk graphite and the shear restoring force transitions from van der Waals interlayer to covalent intralayer interactions as the number of layers approaches unity. Graphene films were grown by low-pressure CVD on Cu foil in a quartz tube furnace at 1030 °C using a mixture of methane and hydrogen.10 Graphene-on-Cu substrates were coated with a polymethyl methacrylate (PMMA) film and then cut to the dimensions of the “neck” area of a high-Q, single-crystal silicon mechanical double-paddle oscillator (DPO; left side of Figure 1a) before etching the Cu foil in a transene copper etch and rinsing in water. Graphene films were then transferred onto the DPO neck using the established transfer techniques.10 To test for possible interface effects between graphene and the oscillator, the surface of the Si oscillators was either hydrogen terminated (hydrophobic) or treated in a mild oxygen plasma to produce a thin (∼1−3 nm) hydrophilic surface oxide. In either case, after transferring from water, the PMMA-graphene films were left to dry in air and annealed on a hot plate up to 130 °C for 10 min to improve adhesion. The protective PMMA coating was removed by soaking in acetone, followed by a rinse in methanol and isopropanol. The transferred films were inspected first using an optical microscope (OM) and second, after all elastic measurements were completed, by scanning electron microscope (SEM) and Raman spectroscopy. The second characterizations were done postmeasurement in order to avoid any possible detrimental effects from electrons or photons to the graphene films or the DPOs. A typical OM image of the front and backside of a DPO neck covered by a PMMA-graphene film is shown on the right side of Figure 1a. A Raman spectrum of a monolayer graphene film on the neck is shown in Figure 1b. A higher resolution SEM image in Figure 1c indicates the graphene films were ∼90−95% single layer with domain sizes up to ∼50 μm, as determined by submonolayer growth under identical conditions. To counter any possible effect of carbonaceous residues on these measurements and to improve film adhesion, the graphene covered DPOs were further annealed at 300 °C at 1 Torr of H2 flow for 3.5 h.

fosc − fsub 3Gfilmt film α = fsub 2Gsubtsub −1 Q film =

Gsubtsub −1 −1 −1 − Q sub (Q osc ) + Q osc 3Gfilmt film α

(1)

(2)

where t and G are the thicknesses and shear moduli, and “sub” denotes substrate, i.e., the bare oscillator. To determine the area of film coverage on the neck accurately, the coverage factor α is obtained from the stitched SEM images of graphene on both front and back sides. (It is possible for α to be larger than 1.) The shear modulus of Si along the neck of the DPO (⟨110⟩) is Gsub = 62 GPa,25 and tsub = 300 μm. The torsional moduli of a hexagonal system along an arbitrary in-plane axis can be written in terms of elastic tensor coefficients as:26 1/(Gin‑plane) = 1/(2C44) + 1/(2C66), where C66 = (C11 − C12)/2, and along the out-of-plane axis, Gout‑of‑plane = C44. Substituting C11, C12, and C44 with the experimental values found in bulk graphite,27 we have Gin‑plane = 10 GPa, and 1014

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Letter −1 is smaller than Qsub in Figure 2d. What is important here is that after analyzing the results of all the samples studied in this work, it is safe to conclude that the addition of graphene adds little to the overall mechanical loss of our DPOs within the uncertainty of our experiments. Presuming a detection limit of −1 −1 ΔQmin = 5 × 10−10, we calculate an upper bound of Qfilm ≤3× −5 10 . This is consistent with the observed high Q in 104 and in 105 found in suspended graphene sheets.4,5,14 From the frequency difference in Figure 2a,c, the shear modulus of a single-layer graphene film can be determined by applying eq 1, assuming tfilm = 0.34 nm. FEM simulation indicates that the second antisymmetric mode is not pure torsion and contains a 0.86% flexural component in the neck (see Supporting Information), hence the need for a minor correction to take out the Young’s modulus component. To the best of our knowledge, E for large-area, single-layer CVD graphene has not been published to date. As an upper bound, we use Efilm = 1.0 TPa (for a thickness of 0.34 nm) from measurements of exfoliated graphene.3 The corrected shear moduli Gfilm before and after annealing together with the coverage factor α are listed in Table 1 for all six samples measured in this work. We

Gout‑of‑plane = 5 GPa. As the torsional axis lies parallel to the film, our G results should correspond to the in-plane torsional modulus of a graphene film. Because Gin‑plane does not have further crystallographic orientation dependence, it should be the same no matter its structure is single or poly/microcrystal. So Gin‑plane = 10 GPa should serve as a reference point of the corresponding bulk value of our experiments. Note that as graphene films approach the 2D limit, there will be no C44 and C55. We can determine fosc and fsub with extremely high accuracy at low temperatures, ≲ 1 K, because Q is extremely high and fsub is nearly constant with temperature. Since elastic constants of diamond and graphite change less than 6% from low to room temperature,28,29 we treat the resonance frequency and shear modulus of the graphene-based films as constant in the temperature range of our experiment. Figure 2 shows examples of the temperature dependence of f and Q−1 of two DPOs before and after graphene transfer and

Table 1. Parameters and Shear Modulus Results of the Single-Layer Graphene Films Studied in This Worka graphene sample no.

substrate surface condition

coverage factor, α

Gfilm before anneal (GPa)

Gfilm after anneal (GPa)

1 2 3 4 5 6

hydrophobic oxygen plasma oxygen plasma oxygen plasma hydrophobic hydrophobic

1.6 1.6 1.0 1.3 1.0 1.2

251 455 311 269 282 261

346 434 317 269 258 225

a Sample run number, substrate surface condition, coverage factor α, shear moduli Gfilm at 1 K, before and after annealing as explained in the text.

Figure 2. Temperature-dependent resonance frequency f (a,c) and internal friction Q−1 (b,d) of two graphene samples before and after annealing at 300 °C. One of the DPOs has been treated with oxygen plasma, (a,b), and its effect on f and Q−1 are shown as double arrow bars. The legends are the same for all and are shown in (d).

can conclude that G is not affected by the interface modification between graphene and Si (i.e., H-terminated or oxidized) and that G is also not changed by 300 °C annealing. We note that since the films were deposited only on the torsional axis area, the mass loading induced frequency shift by any carbonaceous residues on the surface of the graphene films not reduced by the 300 °C anneal would be negligible within the uncertainty of our frequency measurements (see Supporting Information). Among these six measured shear moduli in Table 1, only one appears to be abnormally large, which we assign as an outlier. Averaging the remaining five samples yields G = 280 GPa, with standard deviation of ±36 GPa. The scatter of experimental results is within the reproducibility range of frequency measurements of the same DPO after reinstallation, most probably from the mass loading effect of incidental dust particles. The averaged shear modulus is approximately 5 times larger than that of multilayered rGO films measuring 4−90 nm thick or CVD-grown multilayered graphene on Ni measuring 6 and 8 nm thick, all measured in an identical fashion.17 It is interesting to note that the shear modulus of these multilayered graphene-based films is another factor of 5 larger than that of graphite in the same in-plane orientation.17 This empirical thickness dependence is shown in Figure 3. Such a strong thickness dependence of shear moduli contrasts the relatively weak dependence found in the Young’s moduli of exfoliated

after annealing at 300 °C. One DPO (Figure 2a,b) was treated with oxygen plasma for 30 s before transfer, while the other remained hydrophobic. The effect of the oxygen plasma on DPOs has been determined from separate measurements: It −1 of causes an upward shift in both fosc of 0.012 Hz and Qosc about 1−2 × 10−8, as indicated in Figure 2a,b. The frequency shift is much smaller than that caused by the addition of a graphene film (Figure 2a). It is, nevertheless, taken into account in the shear modulus calculations (eq 1) for all the three DPOs −1 treated with oxygen plasma. However, the increase of Qosc caused by the oxygen plasma is larger than any possible increase by an addition of a graphene film (Figure 2b). Notably, for the DPO not treated with oxygen plasma in Figure 2d, there is −1 . virtually no increase of Qosc While the effect of annealing on fosc is relatively small, its −1 is clearly visible. Annealing partially removes the effect on Qosc increased internal friction caused by the oxygen plasma, as can be seen in Figure 2b. In a separate set of measurements, we find that annealing in a H2 flow reduces the internal friction of a −1 −1 . This helps to explain why Qosc after annealing bare DPO, Qsub 1015

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Although our experimental technique has an incredibly high sensitivity, these experiments were performed using a film-onsubstrate structure. As such, it is important to recognize that extrinsic substrate factors could influence the properties of atomically thin materials. The fact that our results are insensitive to interface modifications, where graphene is deposited on either H-terminated or SiOx-terminated Si and subsequently annealed to improve film adhesion, suggests that interface effects are minimal for this system. Further evidence that the substrate is not influencing the measurement comes from our previous results for multilayered graphene-based films,17 in which both G and Q−1 are independent of film thicknesses varying from 4−90 nm. While our results represent the first shear modulus measurements of single-layer graphene, there have been quite a few theoretical works describing the shear modulus. In most of these theories, the shear modulus is considered in specific crystallographic orientations, like the armchair and the zigzag. We only list their averages in Table 2 if they differ by 20% at

Figure 3. Thickness dependence of shear modulus from single-layer graphene, to multilayered graphene, to bulk graphite. The closed and open circles labeled multilayer represents rGO and CVD grown graphene on Ni, respectively. The dashed line is a guide to the eye only.

graphene3,30 and of rGO,7,12,13 where E increases from multilayer to monolayer by a factor of 2 at most. Such disparity between G and E has been predicted theoretically with a FEM technique which creates an equivalence between the mechanical behavior of the multilayer graphene and the one of a sandwich structure.31 Our results constitute the first experimental evidence that the shear restoring force in graphene transitions from covalently bonded force in a single-core layer to interconnected van der Waals force that sandwiches them. Similar to our findings for graphene’s shear modulus, the internal friction difference between single- and multilayer films −1 for DPOs carrying three is just as striking. Figure 4 shows Qosc

Table 2. Comparison of Our Experimental Results with Theoretical Calculations Presented in This Worka graphene type CVD on Cu with substrate with substrate with substrate with substrate no substrate no substrate no substrate

G (GPa)

Y (GPa nm)

t (nm)

This Work DPO experiment 280 ± 36

95.2 ± 12.2

0.34

123.1

0.45

113

0.45

147.3

0.45

145

0.45

122.3

0.083

146

0.079

121.5

0.34

76.5

0.34

445

151

0.34

280

95.2

0.34

366−460

124.4−156.4

0.34

technique/method

FEM, biaxial shear, 276 AMBER model FEM, pure shear, 247 AMBER model FEM, biaxial shear, 326 Morse model FEM, pure shear, 320 Morse model FEM, biaxial shear, 1473 AMBER model FEM, biaxial shear, 1848 Morse model Previous Theoretical Work molecular 1464 mechanics, 19 AMBER model 225 FEM20

no substrate no atomistic Monte substrate Carlo simulation21 no FEM22 substrate no molecular dynamics, substrate AIREBO model23

Figure 4. Internal frictions of DPOs carrying three different graphene films: a 90 nm reduced graphene oxide, a 6 nm CVD graphene on Ni, and a monolayer graphene on Cu. The internal friction of a bare DPO is shown as a solid line.

a

−1 , of different types of graphene films. The internal friction, Qfilm multilayered rGO and CVD-grown graphene on Ni, calculated with eq 2, is as high as that of amorphous limit,17 while CVD−1 that is grown single-layer graphene on Cu has a Qfilm undetectable within the experimental uncertainty of the measurement. This suggests that the CVD single-layer graphene has a very low defect density that could possibly rival that of its exfoliated counterpart and be used in large-scale mechanical-based applications. It is, however, not clear whether the high internal friction of multilayered graphene-based films is based on a mechanism that is intrinsic to its structure, such as interlayer friction,32 or if it is caused by a high defect density in the material as it was fabricated.17

most. These results are largely consistent with our measurements. To consider the possible substrate effect, we carried out specific hybrid atomistic FEM simulations which are also listed in Table 2. Here the thickness of a pure graphene sheet is taken as 0.083 nm for the AMBER and 0.079 nm for the Morse potential, identified through the minimization of the total potential energy.19 The equivalent thickness of graphene on Si substrate in the presence of van der Waals interactions is the sum of the equilibrium Si−C planar distance (0.373 nm) and the pure graphene thickness defined above. The details of our

The first six calculations and in the literature, in terms of the averaged shear modulus G and the averaged shear rigidity Y = Gt of single-layer graphene; t is the thickness of single-layer graphene used to compute G.

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simulations and modeling are described in the Supporting Information. The comparison in Table 2 suggests that the value of an in-plane shear modulus of 280 GPa is compatible with our simulations assuming the presence of van der Waals interactions between the graphene and the Si substrate. Obviously, the reason that the theoretical G depends strongly on whether the graphene is on a Si substrate or not comes mainly from the assigned thicknesses for each case. Thus, the shear rigidity Y, which is defined as the product of G and t and is often used as a comparative metric to avoid the “Yakobson’s paradox” problem of the dispersion of engineering constants in nanostructures,33 is a better quantity to compare the overall shear elastic effects in Table 2. Our experimental Y is among the scatter of theoretical evaluations. It is important to note that most of the experimental and theoretical elastic moduli of graphene assumed a thickness of 0.34 nm. In reality, the elastic properties are determined by the product of the elastic moduli and the thickness. In addition, our experimental results indicate that the measured in-plane shear modulus is not affected by out-of-plane C44 contributions, as the graphene film is a pure 2D material. This conclusion is strengthened by the fact that the pure shear modulus values for a 2D planar material in Table 2 are close to C66.19,27 Our measurements have experimentally determined some of the elastic properties of CVD-grown, single-layer graphene films on Cu. Our results reveal a striking difference between single- and multilayered graphene films in both shear modulus and internal friction. This difference may have its origin in the transition of the shear restoring force from intralayer covalent to interlayer van der Waals interactions. The average shear modulus (280 GPa) of the films studied in this work compares favorably with most of the theoretical calculations based on single-layer pristine graphene structures. The high shear modulus and low internal friction point to a low defect density structure approaching that of the pristine graphene. Our findings give strong indication that this CVD material can be a vital alternative to be used in nanomechanical sensor applications.

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ASSOCIATED CONTENT

S Supporting Information *

A movie to demonstrate the mode shape, a finite element identification of flexural stiffness, an error analysis in frequency difference, and a detailed hybrid atomistic finite element analysis of shear modulus of single-layer graphene sheet. This material is available free of charge via the Internet at http://pubs.acs.org/.

■ ■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected].

ACKNOWLEDGMENTS This work was supported by the Office of Naval Research. We thank Dr. Keith Perkins for his support in the material fabrication and annealing.

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REFERENCES

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