A method for fabricating multiple free-standing structures on the same sheet of graphene is demonstrated. Mechanically exfoliated mono- and bilayer graphene sheets were sandwiched between two layers of polymethyl-methacrylate. Suspended areas were defined by e-beam exposure allowing precise control over their shape and position. Mechanical characterization of suspended graphene sheets was performed by nanoindentation with an atomic force microscopy tip. The obtained built-in tensions of 12 nN are significantly lower than those in suspended graphene exfoliated on an SiO2 substrate, and therefore permit access to the intrinsic properties of this material system

Casari, CARLO SPARTACO

Gomez Navarro, C.

Guzman Vazquez, F. J.

Rizzi, LAURA GIORGIA

Russo, Valeria

Sordan, Roman

Traversi, Floriano

New Journal of Physics

A method for fabricating multiple free-standing structures on the same sheet of graphene is demonstrated. Mechanically exfoliated mono- and bilayer graphene sheets were sandwiched between two layers of polymethyl-methacrylate. Suspended areas were defined by e-beam exposure allowing precise control over their shape and position. Mechanical characterization of suspended graphene sheets was performed by nanoindentation with an atomic force microscopy tip. The obtained built-in tensions of 12 nN are significantly lower than those in suspended graphene exfoliated on an SiO2 substrate, and therefore permit access to the intrinsic properties of this material system

TRAVERSI, FLORIANO

F. J. Guzman Vazquez

RIZZI, LAURA GIORGIA

RUSSO, VALERIA

CASARI, CARLO SPARTACO

C. Gomez Navarro

SORDAN, ROMAN

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T h e  o p e n – a c c e s s  j o u r n a l  f o r  p h y s i c sNew Journal of PhysicsElastic properties of graphene suspended on apolymer substrate by e-beam exposureFloriano Traversi1, Francisco Javier Gúzman-Vázquez2,Laura Giorgia Rizzi1, Valeria Russo3, Carlo Spartaco Casari3,Cristina Gómez-Navarro2,4 and Roman Sordan1,41 L-NESS, Department of Physics, Politecnico di Milano, Polo di Como,Via Anzani 42, 22100 Como, Italy2 Departamento de Física de la Materia Condensada, Universidad Autónomade Madrid, 28049 Madrid, Spain3 Department of Energy, Politecnico di Milano, Via Ponzio 34/3,20133 Milano, ItalyandCenter for Nano Science and Technology of IIT@PoliMI, Via Pascoli 70/3,20133 Milano, ItalyE-mail: cristina.gomez@uam.es and roman.sordan@como.polimi.itNew Journal of Physics 12 (2010) 023034 (8pp)Received 9 October 2009Published 24 February 2010Online at http://www.njp.org/doi:10.1088/1367-2630/12/2/023034Abstract. A method for fabricating multiple free-standing structures on thesame sheet of graphene is demonstrated. Mechanically exfoliated mono- andbilayer graphene sheets were sandwiched between two layers of polymethyl-methacrylate. Suspended areas were defined by e-beam exposure allowingprecise control over their shape and position. Mechanical characterization ofsuspended graphene sheets was performed by nanoindentation with an atomicforce microscopy tip. The obtained built-in tensions of 12 nN are significantlylower than those in suspended graphene exfoliated on an SiO2 substrate, andtherefore permit access to the intrinsic properties of this material system.4 Author to whom any correspondence should be addressed.New Journal of Physics 12 (2010) 0230341367-2630/10/023034+08$30.00 © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft2Contents1. Introduction 22. Experimental details 23. Results and discussion 54. Conclusion 8References 81. IntroductionGraphene, a recently isolated [1] one-atom-thick crystal of carbon atoms arranged in ahoneycomb lattice, has attracted a great deal of interest during the past few years owing toits remarkable electronic [2] and mechanical [3] properties. The unique combination of veryhigh carrier mobility [4], high intrinsic strength [3], and very low mass of suspended graphenesheets makes graphene ideal as a main building block of advanced nanoelectromechanicalsystems (NEMS) [5]. Graphene NEMS operate as highly sensitive resonators [6], with resonantfrequencies in the gigahertz range [7], and exhibit a new class of nanoscale vibrations [8].Most of the investigated NEMS have so far been fabricated by mechanical exfoliation ofgraphite. Owing to the very small probability of obtaining monolayer graphene in this process(∼1 monolayer graphene per 3 mm2), large arrays of pits or trenches were pre-patterned onthe substrates. Such a large etched area covers most of the chip and therefore prevents theintegration of suspended graphene with other devices. This problem can be mitigated byselective suspension of graphene sheets in which the underlying oxide is etched by bufferedhydrofluoric acid (BHF) only below selected graphene sheets [9]. However, wet etching is anisotropic process and the shape of the underetched area cannot be controlled. In addition, thesurface tension associated with this process leads to the collapse of suspended sheets if thesamples have not been critical-point dried [4, 9, 10]. Here we demonstrate a simple methodfor the fabrication of multiple suspended devices on the same sheet of graphene. The methoddoes not require critical-point drying and provides full control over the shape and position ofthe suspended areas. This was achieved by suspending mono- and bilayer graphene sheets on apolymer substrate in which suspended areas were defined by e-beam exposure. The sheets arefound to have much lower built-in tension than sheets exfoliated on an SiO2 substrate, whichallows access to the intrinsic properties of suspended graphene and provides predictable andreproducible resonant frequencies.2. Experimental detailsThe fabrication procedure is schematically depicted in figure 1. In the first step, e-beam-resist polymethyl-methacrylate (PMMA) dissolved in chlorobenzene was spin coated on ahighly doped Si substrate with 300 nm of thermally grown dry SiO2 on top. Different types ofPMMA were used, resulting in layer thicknesses between 90 and 250 nm after baking. Graphenesheets were deposited on PMMA by mechanical exfoliation [1] of highly oriented pyroliticgraphite (figure 1(a)). Possible mono- and bilayer graphene sheets were scanned by atomic forcemicroscopy (AFM) after they were identified by optical microscopy. While monolayer graphenedeposited on an SiO2 substrate usually exhibits a thickness of ∼1.2 nm under AFM, monolayerNew Journal of Physics 12 (2010) 023034 (http://www.njp.org/)3(a)(b)(c)2. PMMA1. PMMASiO2SiFigure 1. Schematic of the fabrication steps for suspending graphene on apolymer substrate. (a) Graphene is deposited on a polymer (e-beam-resistPMMA) previously spin coated on a highly doped Si substrate with an SiO2top layer. (b) A second polymer layer is deposited on top of the graphene. Areaswithin the blue rectangles are subsequently exposed to the e-beam. (c) Suspendedgraphene is obtained after exposed areas are developed.graphene deposited on PMMA exhibited a thickness of ∼1.6 nm. In the second step, the secondPMMA layer was spin coated on the top (figure 1(b)). After baking, rectangular areas across thesheets were exposed to the e-beam. In the third step, PMMA was developed by a standard methylisobutyl ketone/isopropyl alcohol developer, resulting in windows in the PMMA layer that crosseach graphene sheet, leaving parts of the graphene sheet suspended between the PMMA layersNew Journal of Physics 12 (2010) 023034 (http://www.njp.org/)4Figure 2. Raman spectra collected at 514.5 nm of monolayer (black) and bilayer(red) graphene deposited on a PMMA substrate. The spectrum of a bare PMMAsubstrate is shown in green.(figure 1(c)). The windows were made wider than the graphene sheet in order to develop thebottom PMMA layer from the sides. A much longer (∼10×) development time was requiredthan in the case of a double PMMA layer without embedded graphene, as the developer had topenetrate the bottom layer along the windows.The exact number of graphene layers deposited on the first PMMA layer was determinedby Raman spectroscopy. Figure 2 shows Raman spectra of mono- and bilayer grapheneexfoliated on a PMMA substrate. No significant contribution from the substrate, the spectrumof which is also shown in the same figure, is observed in the graphene spectra. The singleLorentzian and very intense second-order band (marked by 2D) allow a monolayer sheet to beidentified. The 2D peak exhibits the same evolution with the number of layers as in Ramanspectra of graphene deposited on a conventional SiO2 substrate [11]. The influence of theunderlying PMMA substrate was observed only when the first PMMA layer was very thick(>300 nm), but even in this case the typical shape of the graphene Raman bands was still clearlyvisible.A fabricated suspended graphene device is shown in figure 3. The graphene sheet wassuspended over five 1.2-µm-wide rectangular windows. The sheet consists of monolayer (thefirst two windows on the right-hand side) and bilayer parts (the other three windows). The shapeand position of the windows were defined by e-beam exposure after the sheet was initiallycharacterized by AFM. The windows have well-defined vertical sidewalls as the developerdissolves only the exposed parts of the PMMA layers. The windows are 450 nm deep and thesheet is freely suspended 200 nm above the surface of the SiO2 layer. Critical-point drying wasnot needed in fabrication because the surface tension of the developer is ∼4 times less than thatof BHF/H2O. Each of the suspended parts of the sheet forms a double-clamped beam whoselength is equal to the width of the corresponding window. Once the structure was fabricated, theexact length l and width w of each beam was determined by AFM. Non-contact mode was usedin order to avoid any damage to the sheet.Mechanical characterization of the fabricated suspended graphene sheets was performedunder ambient conditions. Deflection of the AFM tip ztip was measured while the tip waslowered by zpiezo, indenting the center of the suspended area. The force constant of the tipNew Journal of Physics 12 (2010) 023034 (http://www.njp.org/)52 µm(a)0 1 2 3 4 5 6 7 8 9 100100200300400Height (nm)Distance (µm)(b)Figure 3. A graphene sheet suspended over five PMMA windows. (a) AFMimage of the device. (b) Height profiles of the device along green and red sectionsin (a). The thicknesses of the bottom and top layers are 200 and 250 nm.ktip was calibrated by Sader’s method [12], allowing calculation of the force exerted on the tipin the linear regime (small deflections) as F = ktipztip. Several force–distance curves F versuszpiezo were acquired in each suspended structure (one is shown in red in figure 4(a)). Similarcurves on a hard SiO2 substrate (for which zpiezo = ztip) were used to calibrate the applied forceF and deflection of the sheets z = zpiezo− ztip (figure 4(a)). The elastic constant of the deviceswas then calculated as k = dF/dz in the low deformation regime, where F(z) is linear and thesheet is in the pure bending regime (figure 4(b)). In addition, no dynamic effects were found forindentation speeds of 10–500 nm s−1.3. Results and discussionThe elastic constant k of the suspended graphene sheet in the linear regime can be related to theelastic modulus E of graphene by the expression valid for a double-clamped beam under pointload as [13]k = 32Ew(t/ l)3 + 17T/ l, (1)New Journal of Physics 12 (2010) 023034 (http://www.njp.org/)6Figure 4. Force–distance curves measured by a tip with an elastic constantktip = 1.21 N m−1. (a) A curve measured on a hard substrate (black) andsuspended graphene sheet (red). The difference in zpiezo of the curves at a fixedforce F is equal to the displacement z of the sheet. (b) Force exerted on the sheetas a function of the displacement of the sheet. The elastic constant k of the sheetis calculated as the slope of the force–displacement curve in the linear regime.where t is the thickness of the sheet (t = 0.34 nm for monolayer graphene and t = 0.68 nm forbilayer graphene) and T is the built-in tension of the sheet. In the limit of vanishing tensionT → 0 a linear scaling of elastic constant k with w(t/ l)3 is expected. Experimental data for kversus w(t/ l)3 are plotted in figure 5(a) for 13 different suspended mono- and bilayer graphenesheets. The pronounced scatter exhibited in this plot indicates a non-negligible built-in tension,T > 0. These tensions are regularly present in most NEMS and result from the fabricationprocedures [5]. Particularly, for graphene, they have been attributed to forces applied on thesheet during the mechanical exfoliation process, which stretches the sheet on the substrate.The tension can be determined by rewriting equation (1) as Ek = E + (17/32)T l2/(wt3)where Ek = kl3/(32wt3). Experimental data for Ek versus l2/(wt3) are plotted for theinvestigated sheets in figure 5(b). A slope of the linear fit of the plotted data reveals a built-intension of T = 12 nN. However, the scatter that is also visible in this plot has a strong influenceon the intercept in the linear fit, which indicates a variation in E from sheet to sheet. Theelastic modulus can be estimated from equation (1) as the value at which the average tension〈T 〉 = 12 nN, i.e. E = (〈kl〉− 17〈T 〉)/〈32wt3/ l2〉 = 0.43 TPa.New Journal of Physics 12 (2010) 023034 (http://www.njp.org/)7Figure 5. Experimental values for elastic constants of suspended graphenesheets. (a) Elastic constant k as a function of sheet dimensions represented bya quantity w(t/ l)3. The experimental data do not follow the linear fit (plottedfor three different values of elastic modulus) expected in the limit of vanishingtension. (b) Scaled elastic modulus Ek = kl3/(32wt3) as a function of sheetdimensions can be fitted to a linear function.Variations in tension and elastic modulus and differences in E from recently reportedvalues E = 0.5–1 TPa [3, 14] are a consequence of the fabrication of the devices rather thanexperimental errors. Firstly, anisotropy of graphene leads to different values of elastic constantsdepending on the crystallographic orientation of graphene with respect to the PMMA windows.Secondly, numerical constants in equation (1) are very sensitive to slight changes in clampingconditions and point load configuration and can result in differences in the calculated elasticmodulus of up to a factor of two [13]–[15]. Thirdly, calculated values of elastic constantsdepend on the exact thickness of monolayer graphene; here, the interlayer spacing in graphitewas used. Fourthly, small resist residue stuck at certain points on the sheets can slightly altertheir thickness locally, giving rise to some scattering.The obtained tension T = 12 nN is at least one order of magnitude less than the tensionin graphene sheets exfoliated on an SiO2 substrate [7, 14] and comparable to that of reducedgraphene oxide sheets deposited from aqueous solution [10]. Such a low tension can beNew Journal of Physics 12 (2010) 023034 (http://www.njp.org/)8attributed to the relaxation of sheets during processing of the top PMMA layer. Consequentbaking and cooling of the sample lead to the expansion and retraction of the PMMA layers andsheet (which have opposite thermal expansion coefficients) reducing the built-in tension [16].Since built-in tension can significantly alter the resonant frequency of a beam it is of the utmostimportance in the fabrication of NEMS to use a structure with low built-in tension, so that itsproperties are not modified.4. ConclusionFree-standing graphene sheets were fabricated by patterning windows in a double-layeredPMMA stack in which graphene was sandwiched between the layers. The reported procedureresults in partially relaxed suspended graphene sheets with built-in tensions more than oneorder of magnitude smaller than in mechanically exfoliated suspended sheets deposited on aconventional SiO2 substrate. Low tension and high stiffness of fabricated free-standing graphenestructures will enable the realization of reliable graphene NEMS resonators operating in thegigahertz range.References[1] Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V and Firsov A A2004 Science 306 666–9[2] Castro Neto A H, Guinea F, Peres N M R, Novoselov K S and Geim A K 2009 Rev. Mod. Phys. 81 109–62[3] Lee C, Wei X, Kysar J W and Hone J 2008 Science 321 385–8[4] Bolotin K I, Sikes K J, Jiang Z, Klima M, Fudenberg G, Hone J, Kim P and Stormer H L 2008 Solid StateCommun. 146 351–5[5] Ekinci K L and Roukes M L 2005 Rev. Sci. Instrum. 76 061101[6] Bunch J S, van der Zande A M, Verbridge S S, Frank I W, Tanenbaum D M, Parpia J M, Craighead H G andMcEuen P L 2007 Science 315 490–3[7] Poot M and van der Zant H S J 2008 Appl. Phys. Lett. 92 063111[8] Garcia-Sanchez D, van der Zande A M, Paulo A S, Lassagne B, McEuen P L and Bachtold A 2008 NanoLett. 8 1399–403[9] Du X, Skachko I, Barker A and Andrei E Y 2008 Nat. Nanotechnol. 3 491–5[10] Gómez-Navarro C, Burghard M and Kern K 2008 Nano Lett. 8 2045–9[11] Ferrari A C et al 2006 Phys. Rev. Lett. 97 187401[12] Sader J E, Chon J W M and Mulvaney P 1999 Rev. Sci. Instrum. 70 3967–9[13] Gere J M and Timoshenko S P 1990 Mechanics of Materials (Boston: PWS-Kent)[14] Frank I W, Tanenbaum D M, van der Zande A M and McEuen P L 2007 J. Vac. Sci. Technol. B 25 2558–61[15] Landau L D and Lifshitz E M 1986 Theory of Elasticity (Oxford: Butterworth-Heinemann)[16] Bao W, Miao F, Chen Z, Zhang H, Jang W, Dames C and Lau C N 2009 Nat. Nanotechnol. 4 562–6New Journal of Physics 12 (2010) 023034 (http://www.njp.org/)

Elastic properties of graphene suspended on a polymer substrate by e-beam exposure

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Elastic properties of graphene suspended on a polymer substrate by e-beam exposure

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