Strain Superlattices and Macroscale Suspension of Graphene

Letter pubs.acs.org/NanoLett

Strain Superlattices and Macroscale Suspension of Graphene Induced by Corrugated Substrates Antoine Reserbat-Plantey,*,†,⊥ Dipankar Kalita,† Zheng Han,† Laurence Ferlazzo,‡ Sandrine Autier-Laurent,§ Katsuyoshi Komatsu,§ Chuan Li,§ Raphael̈ Weil,§ Arnaud Ralko,† Laetitia Marty,† Sophie Guéron,§ Nedjma Bendiab,† Hélène Bouchiat,§ and Vincent Bouchiat† †

Université Grenoble Alpes, CNRS, I. Neel, F-38000 Grenoble, France Laboratoire de Photonique et de Nanostructures, CNRS, 91460 Marcoussis, France § Laboratoire de Physique des Solides, Université Paris-Sud-CNRS, 91400 Orsay, France ‡

S Supporting Information *

ABSTRACT: We investigate the organized formation of strain, ripples, and suspended features in macroscopic graphene sheets transferred onto corrugated substrates made of an ordered array of silica pillars with variable geometries. Depending on the pitch and sharpness of the corrugated array, graphene can conformally coat the surface, partially collapse, or lie fully suspended between pillars in a fakir-like fashion over tens of micrometers. With increasing pillar density, ripples in collapsed films display a transition from random oriented pleats emerging from pillars to organized domains of parallel ripples linking pillars, eventually leading to suspended tent-like features. Spatially resolved Raman spectroscopy, atomic force microscopy, and electronic microscopy reveal uniaxial strain domains in the transferred graphene, which are induced and controlled by the geometry. We propose a simple theoretical model to explain the structural transition between fully suspended and collapsed graphene. For the arrays of high density pillars, graphene membranes stays suspended over macroscopic distances with minimal interaction with the pillars’ apexes. It offers a platform to tailor stress in graphene layers and opens perspectives for electron transport and nanomechanical applications. KEYWORDS: Graphene, Membranes, Raman Spectroscopy, Strain, Ripples, Suspended Graphene

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electromechanical systems,11 whereas ripples in graphene-based transistors are known to alter the electrical conductivity.14 Nevertheless, these mechanically induced defects can be sometimes desirable as a means to engineer a controlled level of stress, either to generate an electrical gap,18−21 tuning optical conductivity,22 or to induce strong pseudomagnetic fields.23,24 Before reaching such a degree of control, it appears necessary to understand the interaction process between a polycrystalline graphene membrane and the destination substrate onto which it is wet-transferred. In this paper, we investigate the formation process of strain ripples and suspended features in graphene layers obtained by chemical vapor deposition on copper and subsequently transferred onto a substrate corrugated by an array of SiO2 nanopillars. We show how to engineer the formation of graphene ripples using an ordered substrate corrugation that defines self-organized strain domains forming sets of parallel ripples linking the pillars. By tuning the pillar array geometry (pitch and apex sharpness), we show that different membrane shape regimes can be reproducibly found. We explore both limits of low density arrays where graphene exhibits ripples domains and of very dense arrays for in which graphene does not ripple

raphene, the two-dimensional honeycomb carbon lattice, has unique mechanical properties such as strong in-plane rigidity combined with a huge elasticity, enabling it to withstand up to 25% elastic deformation.1 To date, it is the only atomically thin material that routinely provides stable and self-supported membranes, allowing a wide span of applications ranging from nanoelectonic and optomechanical devices to biology; notable recent results involving graphene membrane as the critical component include high electronic mobility devices showing fractional quantum hall effect,2 nanoelectromechanical systems,3 leak-proof membranes4 offering promising materials for water filtration5 and DNA sequencing.6 The development of graphene growth over centimeter scale areas and the improvement of transfer techniques make it all the more important to control the shape and geometry of graphene once transferred onto the destination substrate. Indeed, the possibility of growing continuous monolayer graphene7−10 onto sacrificial catalytic layers has enabled the manipulation of large areas of graphene and make it possible to transfer onto surfaces of arbitrary shape and composition. Once transferred to a flat surface or suspended,11−13 graphene membranes always display unwanted ripples that affect its electrical,14 thermal,15 and mechanical16 properties. Wrinkles (reminiscent as the one occurring in curtains) that develop in doubly clamped graphene membranes under uniaxial stress17 induce additional damping in © XXXX American Chemical Society

Received: May 3, 2014 Revised: July 28, 2014

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Figure 1. Transferred graphene on nanopillars. (a) Schematic view of graphene membrane deposited onto SiO2 nanopillar array. (b) Atomic force micrograph of graphene deposited on SiO2 nanopillars. (c) Schematics of graphene (in black) transferred onto nanopillars array (in blue). For dense array (a < a*), we observe fully suspended graphene over large areas. At low array density (a > a*), graphene conforms with the substrate and forms highly symmetric ripples

Figure 2. Graphene sheets deposited on corrugated substrates with increasing pillar density. Series of SEM micrographs showing the behavior of transferred graphene membrane for increasing density of 270 nm height silicon pillars. From a to d, the pillar pitch a is respectively equal to 2.3, 1.5, 1.4, and 0.25 μm. Note that despite the pillar sharpness, graphene is not pierced and still coats the apex. For sharp and low-density-packed pillar arrays (a), ripples do not join neighboring pillar but rather show a preferential direction presumably reminiscent of the copper surface step edges on which the graphene has grown.Author: Because there is no graph 8, this reference has been removed. Orientational order of ripples along the symmetry axes of the pillar network starts to appear for 1.5 μm pitch (b). At about the same density, partial suspension along symmetry lines could be observed (c), whereas for 250 nm pillar pitch (which is approximately equal to the pillar height), (d) the membrane becomes fully suspended in between pillars. Scale bars lengths are 2 μm

produces homogeneous monolayer graphene, up to several centimeter wide, with no second layer. They consist of a polycrystalline film with perfectly stitched crystal grains with a typical crystal size of 20 μm. The detailed fabrication process of nanopillar array is presented in the Supporting Information. A

but, on the contrary, stays fully suspended, fakir-like, over a dense array of nanopillars (cf. Figure1). Sample Preparation. The graphene sheets are obtained by chemical vapor deposition (CVD) growth on a sacrificial copper foil, as described in our previous work.9 This growth method B

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PMMA coating film is used as a flexible and supporting layer to increase rigidity of the graphene and deposit it onto the structured destination substrate, after acid etching of the copper foil growth substrate (cf. Supporting Information). The transfer is then performed by slowly scooping PMMA/graphene layer with the clean nanopillar substrate, followed by a unaided drying in air for 1 h. As residual liquid may be trapped under graphene, and to increase its chance of adhering onto the substrate, the whole sample was soft-baked before removing PMMA using acetone. The final structure consists of a monolayer graphene sheet on a SiO2 nanopillar array with variable pillar pitch a. Each nanopillar is about 260 nm high (height h) with an apex radius r of 20−50 nm, except for one sample that exhibits a flat mesa instead of sharp pillar (cf. Supporting Information Figure S9). The pillars are following a square lattice with a pitch a between two pillars varying from 250 nm to 3 μm (cf. Figure 1). Such a pillar array can be well described with the three parameters a, h, and r. In our study, we have kept r and h constant and investigate influence of a on the geometry of the transferred graphene membrane. Our method differs significantly from the one reported by another study25 that involved suspension of graphene over pillar arrays etched after graphene transfer. Those were obtained by in situ releasing the polymer membrane using etching through the graphene layer. Similar systems of graphene on pillars have been studied previously,25−27 mostly using pillar arrays with flat, mesalike ends. In the work of Tomori et al.,25 a crossed network of ripples merging each other at pillar centers is observed. This different ripple pattern (i.e., a second set of ripples following another symmetric diagonal direction) is most probably attributed to the fabrication process which involve the in situ formation of a pillar array and suspension after transfer by selectively dissolving the underlying substrate. In contrast, our fabrication process relies on the interaction of PMMA/graphene and free graphene layer in a fluidic environments with the prefabricated pillar array. It avoids contamination or alteration of the graphene because it is transferred at the last step and not exposed to electron beam (see Supporting Information). In our studies, we mainly focused on sharp pillars with variable pillar pitch a. Study of Ripple Domains Formation and Transition toward Suspended Graphene. Figure 2 shows the graphene layer deposited onto a square lattice of SiO2 nanopillars with a large pillar pitch a (typically a ∼ 1 μm). In this case, the graphene sheet always fully collapses over its entire surface, forming a conformal capping layer on the corrugated sample with many frowns called ripples that will be further analyzed using SEM and Raman spectroscopy. The graphene ripples linking pillars are always visible, reminiscent to what can be observed on a cloth covering a nonflat surface, with an orthoradial order emerging from pillars. Such ordering becomes more apparent as the pillar array density increases. It is worth noting that, depending on the array parameters (h and a, Figure 2a), the graphene tightly conforms to the pillars or hangs more loosely around the pillars in other cases (Figure 2b−d), leading to partially suspended features. In Figure 2a−b, cracks in the graphene membrane are visible, appearing as straight dark stripes and are attributed to gaps opened along grain boundaries. Different morphologies are observed experimentally: (i) for loose arrays, the graphene closely coats the pillars in a conformal fashion (cf. red arrow Figure 2a) or (ii) sometimes it is locally suspended around the pillars, leading to a tent-like feature (cf. Figure 2b−d). For slightly tighter arraystypically a = 1 μm(cf. blue arrow in

Figure 2b), the graphene ripples tend to be oriented along the symmetry axes of the underlying pillar array (in such case, linking first nearest neighbors). Experimentally, this collective behavior occurs if r is sufficiently small compared to the curvature radius of the typical ripples observed (i.e., ∼ 42 nm, cf. Figure 2b) and only in the same graphene grain boundary. Figure 3 presents the occurrence of ripples linking first, second, third, and fourth neighbors. The closer neighbor

Figure 3. Statistical analysis of the distribution of ripples in graphene membrane. (a) Graphene ripples distribution as a function of the for different geometrical configurations graphene ripples density e−1 j (first, second, third neighbor, etc.). The notation ej is introduced in the Supporting Information. The experimental data were extracted from a single square lattice (parameter a = 1.5 μm). (b) Graphene ripples diameter distribution. Data recorded from SEM micrographs. The central value is 42 nm (Gaussian fit), and the distribution width is about 21 nm. Inset: sketch of a ripple cut. Graphene ripple viewed as two half cylinders of opposite curvature.

configuration (i.e., lower ripple density) is clearly dominant. These observations raise questions about the formation of graphene ripples and their resulting geometrical configuration. When graphene is deposited onto the patterned substrate, its area is smaller than the area of the patterned specific surface of SiO2 because of the 3D character of the nanopillars. In other words, there is a topological mismatch between two surfaces, as an unstrained graphene membrane cannot fit the substrate exactly. The fact that the graphene/PMMA bilayer film has a planar geometry different and is incompatible with the nondevelopable28pillar arrays surface generates conical singularities around pillars.19 Stress extends spatially from the pillar apex and induces strain in graphene, which in turn generates orthoradial ripples during the drying. This effect was already well-described in macroscopic systems,29,30 which are known to persist down to the nanoscale, giving rise to ripples with nanoscale periodicity.17 To further describe the local shape of the membrane around a pillar, one has to describe the forces at work that drive the membrane toward its equilibrium shape. There are competing interactions at work: (i) the sum of all attractive interactions (van der Waals, electrostatic, capillary forces during transfer), which tend to force graphene to collapse onto the substrate, and (ii) internal rigidity within the films (PMMA/graphene and graphene) caused by the repulsion of π orbitals of graphene.12,13,19 Please note that this out-of plane rigidity differs from the even much stiffer one that originates from σ-bonds and makes graphene mechanically stable.31 In order to describe the competition between all these counteracting interactions, we note ,c , the energy density for the attractive interactions, and Er, the energy needed to create a graphene ripple. Following the notation introduced by Tersoff,32 we consider a graphene ripple C

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Figure 4. Raman map of TO-silicon peak intensity. Raman map of the intensity of the Si-TO mode at 521 cm−1 before (a) and after (b) the graphene transfer. The configuration of the transferred graphene is likely to be similar to the case presented in Figure 2b−c. Scale bars lengths are 3 mm.

Figure 5. Strain domains in graphene deposited on SiO2 nanopillars (a = 1 μm). (a)−(b) Raman maps of the G band intensity (a) and frequency (b). The blue and green arrows show strain domains with first and second nearest neighbors configuration, respectively (cf. insets where black dots symbolize the position of the nanopillars and dashed lines represent the 1D graphene ripples. Note: sketch scale is different from data scale). The distance ei between two consecutive ripples is represented in red. (c)−(d): Raman maps of the 2D band intensity (c) and frequency (d). The configuration of the transferred graphene is likely to be the same or similar to the case presented in (b)−(c). Laser wavelength is 532 nm. Scale bars lengths are 3 μm.

as a half cylinder, Er = (c0/R2)S0, where c0 is an elastic constant for curvature out of the plane33 (c0 = 1.4 eV), R is the ripple radius (see Figure 3b), and S0 = 2πLR is the surface of a cylinder (a ripple is viewed as two half cylinders of opposite curvature). In a first approximation, we simplify the integral ∫ ,c (r)⃗ d2r as Sc,c . A simple equilibrium condition can be written as ΔE = Sc ,c − Er Nr = 0

the transferred graphene membrane remains globally suspended on top of the nanopillars. To connect eq 1 to our experimental parameter a, we introduce the ripple density (a/ej), where ej is the characteristic distance between two parallel 1D graphene ripples (see Supporting Information). Therefore, the number of ripples of size L in a given surface L2 is Nr = L/ej. On the other hand, the surface of graphene in contact with the substrate is Sc = ejL − Ssusp, where Ssusp is the fraction of suspended graphene at the pillar edge and at the ripple. Introducing these notations in eq 1, we obtain a critical value of a* satisfying ΔE = 0 (cf. Supporting Information). This value of a* separates the two regimes of fully suspended graphene from collapsed and rippled graphene. Interestingly, expression of a* derived in Supporting Information) qualitatively explains the two main observations of our work: (i) the reduction of a leads to a full suspension of graphene when a < a* and (ii) ripple orientation is statistically in favor of

(1)

where Nr is the number of graphene ripple contained in a surface L2, and Sc is the surface of graphene that is in contact with the substrate. Regarding eq 1, if ΔE > 0, the energy cost to bend graphene remains smaller compared to the total attraction energy. In that case, the transferred graphene membrane collapses and fits the substrate except at some particular positions, forming 1D ripples. If ΔE < 0, the energy cost to bend graphene is now higher than the total attraction energy and D

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between the ripples axis on these two domains is equal to 45°, in agreement with this assignment. Graphene ripple lines are observed not only in the intensity signal of the Raman G and 2D bands, but also in the frequency mappingνG and ν2Dof these Raman bands (see Figure5b,d). It is worth noting that G and 2D intensities have opposite contrast (cf. Figure5a,c), which can be interpreted as a Raman interference effect that can induce opposite intensity modulation depending on the interference index λ/h for the given Raman wavelength, as detailed in a previous work.38 The complex morphology at a subresolution scale encountered here makes the interpretation of stress more difficult compared to graphene transferred on flat and flexible substrates (such as elastomer films41−43) for which the stress is supposed to be rather uniformly distributed. In our samples, stress is, by essence, extremely nonuniformly distributed and shows spatial variations at the microscopic scale (cf. Figure5b,d). However, the presence of organized periodic ripples domains is a peculiar situation, which simplifies strain distribution as it can be considered as a set of infinite 1D ripples. This allows a quantitative strain estimation using calibrated former studies on uniaxial and biaxial strain correspondence with Raman band frequencies. Along an unidimensional ripple, we neglect doping effects since graphene should feel similar electrostatic screening with respect to a flat region. Thus, this G-band softening is dominated by the presence of uniaxial stress considering that a graphene ripple can be seen as a linear defect that can only relax stress in one direction.31 The G-band frequency map (cf. Figure5b) presents isofrequency periodic lines corresponding to organized periodic ripples as observed on SEM images. A downshift of ΔνG = −2.8 cm−1 from a ripple region to a flat one would then corresponds to a stretching of the graphene membrane of about 0.1%, using the calibration given in ref 42. Here, we have considered so far in first approximation uniaxial strain, whereas a more realistic description should take into account the biaxial components.47,48,52 Grüneisen coefficient for biaxial strain is typically twice larger than uniaxial case, which leads to a lower value of the estimated biaxial strain about 0.05%, which defines the lower boundary of the estimated strain. In addition, this value may be underestimated as the laser spot is about six times larger than the ripple diameter (cf. Figure3b); therefore, the Raman signals of both flat unstrained graphene and highly strained graphene ripple are sampled and averaged. Interestingly, around a pillar, but still within our probe spatial resolution, graphene can be locally suspended and, thus, the electrostatic influence from the charges trapped in the substrate53 is lowered, which is expected to soften Raman G band.49,54,55 The 2D band frequencyν2Dshows a peculiar spatial correlation: as well as a downshift at the ripple position (as clearly see in Figure 5b for the G band), additional downshift is seen at the pillar position (cf. Figure5d). This suggests the presence of two concomitant phenomena leading to a decrease in the 2D band frequency: (i) around the pillar, but still within our probe spatial resolution, the graphene is locally suspended and, therefore, feels less electrostatic doping from substrate53 and (ii) the graphene is pinned at the top of the pillar, creating an extra tensile stress and downshifting the 2D band frequency.47,48,52 Both effects, electrostatic doping and stress, can reasonably be considered at the pillar position. Further high spatial resolution Raman studies, such as those given by TERS,56 together with electron transport through the graphene layer57 should give insights to discriminate between these two effects.

the nearest neighbor configuration found in the low ripple density regime. In addition, the critical pitch a* also show dependence in ,c , which is related to the physisorption properties of the substrate. Thus, this result is of crucial importance to engineer the corrugated substrate to influence the transferred graphene properties. These properties are governed by the generated stress and doping in the two different regimes (a < a* or a > a*). Raman Analysis of Collapsed and Suspended Membranes: Stress Superlattices. Both stress and doping are now probed by Raman spectroscopy. First of all, positions of the nanopillars are located before analyzing the Raman response of deposited graphene. The Raman spatial map in Figure 4a shows that the intensity of Si-TO peak at 520.7 cm−134 indeed follows the nanopillarsʼ periodicity. We find that the top of a nanopillar exhibits higher Raman intensity ISi than the bottom plane. This phenomenon is explained by optical interference enhancement35−39 due to variation of the silica film thickness over the silicon sample which acts as a back mirror (see Supporting Information). Therefore, interference conditions are different from the top to the basis of one nanopillar, which explains the modulation of the collected Raman scattered light along the substrate (cf. Figure 4a) and remains true once graphene is deposited on top (cf. Figure 4b). It is worth noting that the optical depth of focus is approximately 700 nm and, thus, greater than the pillar height, excluding any defocusing effect in that ISi modulation. However, at a given pillar position, optical conditions differ as the upper part of the optical cavity is now the graphene layer, absorbing 2.3% of light and defining new optical interference conditions.40 Note that Figure 4b yields information on the polycrystallinity of the graphene layers, made up of grains of different sizes. These grain boundaries are easily identified on the ISi Raman map because the silicon Raman signal is higher where there is no graphene. In both cases, before and after graphene deposition, the frequency of the Si-TO peak (see Supporting Information) does not vary along the nanopillar array. The analysis of Raman signal of the Si-TO peak, therefore, allows for the determination of the nanopillar position, which is also helpful for the interpretation of the graphene Raman response. The Raman response of monolayer graphene always shows G and 2D peaks that, in the presence of strain, experience frequency shift.41−48 For large strains (ε > 2%), it was shown that modesplitting of the G peak occur, giving rise to G+ and G− peaks. However, the Raman signature of graphene is also very sensitive to doping49 and thermal effects50 as well, leading to superimposed contributions. For the present work, the laser power is kept at 500 μW·μm−2 in order to avoid heating effects that are observed at higher laser power. Due to the bimodal dependence of both G and 2D band to strain and doping, it is rather complex to disentangle those two effects. Nevertheless, correlations between the frequency of G and 2D bands give a clear signature of the importance of doping and strain.51 Figure 5 shows confocal Raman maps in the plane of the nanopillar array substrate (a = 1 μm). Here, we carefully correlate the position of the nanopillars with the position of the observed shift on the graphene Raman signature. The two arrows in Figure 5a point out domains where Raman signatures of the G and 2D peaks are nonuniform and oriented along a given direction, forming a set of parallel lines. Knowing the exact position of the nanopillars from the Si-TO peak, we assign the domain pointed to by the blue (green) arrow to be constituted of graphene ripples linking the first (second) nearest neighbors. The angle E

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Figure 6. Full suspension of graphene on top of high-aspect ratio pillar arrays. (a)−(b) SEM micrographs of suspended graphene membrane on top of nanopillars square lattice (a = 250 nm). Scale bars represent 1μm. Note the presence of tears at graphene grain boundaries (a), which are consistent with previous Raman maps (cf. Figure5). (c) Raman spectra (G band) of monolayer graphene suspended on top of nanopillars square lattice (red line), collapsed on the substrate (blue line), and at suspended ramp region (dark line) for comparison. The frequency (width) of the G band is indicated on the graph.

region (cf. Supporting Information), as it is expected in case of strong uniaxial stress, which confirms that the stress contribution to the change on the Raman response is not major in that particular case. Note that doping alone cannot explain all the Raman features (G and 2D) observed in the supported region. It is, therefore, likely that the suspended graphene is less strained than the supported one. To summarize, when macroscopic graphene sheet is suspended on top of the nanopillars, both stress and doping are decreased in comparison with supported graphene. The resulting graphene is expected to exhibit properties that are closer to the intrinsic ones. In particular, we expect lower scattering of the conduction electrons and lower shift of the Fermi level, both of which should promote ballistic transport and high mobility for charge carriers. The use of macroscopic graphene sheet suspended on pillar arrays as demonstrated in this study provides two independent key points of great interest for nanoelectronics devices. First, such macroscale devices offer the possibility to observe high electronic mobility, which has been only shown on submicron scale.2,58 Second, periodic stress in graphene rises the question of the presence of stress induced superpotential in a 2D electron gas, leading to fundamental signature in mesophysics about charge carrier anisotropic behavior.57 So far, we have examined a square lattice of nanopillars. Considering now another type of pillars lattice, for example, a random lattice, the ripple propagation should then be impossible because of absence of high symmetry axis to maintain the ripple propagation. In such cases, the average distance between N pillars distributed over an area S would be ar = (S/N)1/2 and the critical value to get fully suspended graphene would be lower than the square lattice case ar* < a*. A recent study59 highlights the effect of pillars density (made from randomly deposited nanoparticles) on graphene ripples formation. These authors show AFM measurements leading to a critical pillars density, for which graphene ripples form a percolating network. In addition to the present work, this is therefore a first step toward large areas of fully suspended graphene. Devices made of macroscale suspended graphene are of interest both for fundamentals investigations (role of periodic potential created by the pillars,

Up to this point, we have examined the case of low pillar density (i.e., a > 1 μm), in which graphene is lying on the substrate and forms aligned ripples. However, if the pillars’ lattice pitch is a ≤ a*, the system should not be considered in the intermediate regime where the attractive and repulsive interactions are almost in equilibrium, as the bending of graphene is no longer more favorable at that scale (cf. Supporting Information). We observe that below a critical value a ≤ a*, the deposition leads to fully suspended graphene over large areas (cf. Figure6-ab). We have determined an upper and lower boundary for the value of the critical pillar pitch a*: 250 nm < a* < 1 μm. Raman spectra of the G band for suspended and supported graphene on a flat region (outside the nanopillar lattice) are shown in Figure6c. In the suspended case, the G-band frequency shows a downshift of about ΔνG = −11.9 cm−1 with respect to the supported case as well as a reduction in width (ΔΓG = −3 cm−1). Considering the fact that the electrostatic influence of the substrate (i.e., charge impurities) strongly weakens when graphene is suspended, this softening observed on the G band can be interpreted as a consequence of the decrease of charge transfer between the graphene and the substrate.53 Analysis of the 2D band (cf. Supporting Information) also confirms that graphene is less doped in the suspended case than in the supported one. According to ref 51, the increase in carrier density between the suspended case and the supported one is about 8 × 1012 cm−2. This confirms the reduction of doping for such macroscopic suspended graphene sheets. Nevertheless, the contribution of residual strain due to pinning of graphene at the top of nanopillar array would also downshift the G-band frequency. There exists on the side of the array a region where graphene is suspended and form some air wedge (ramp). By comparison between the strained graphene on the ramp with the low-doped suspended graphene, previous calibrations42 lead to an estimation of this strain, yielding approximately 0.1%, which is quite similar to the strain value extracted at a pillar position in the case where a > a*. This estimation is an average value because our spatial resolution is bigger than the interpillar distance. Moreover, no G-band splitting was observed in the suspended F

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collective low energy vibration mode, etc.) and for applied science (high mobility transparent electrodes, batch fabrication of mechanical resonators, etc.) Conclusion. In conclusion, using a set of prefabricated substrates with pillar arrays of variable aspect ratio, we have provided a platform to study the formation of suspended graphene membranes over tens of micrometers and the transition from this suspended state to a collapsed one that exhibits organized domains of parallel ripples joining the pillars. Depending of the array geometry and pitch, graphene films can tightly conform with the surface, partially collapse, or lie in a fakir-like fashion, suspended for an array parameter below 1 μm (pillar height of 260 nm). Different cases illustrate the competition between adhesive and rigid graphene behavior. Collapsed films display sets of parallel ripples organized in domains, thus forming strain domains of different configurations. These ripples are oriented along high symmetry axes of the pillar lattice. Such collective behavior is qualitatively described taking into account the ripples density and the corresponding bending energy. Stress domains corresponding to parallel ripple regions are then observed and studied by Raman spectroscopy mapping. Typical stress at the graphene ripple is about 1 GPa. Raman spectroscopy appears as a reliable and noninvasive investigation tool to quantitatively map stress variations in a 2D membrane, discriminate strained domains and identify order in the strain organization. In addition to controlling the stress of a graphene once transferred onto a substrate (control of ripple formation, and local strain), we have shown that, by decreasing pillar pitch, a transition toward a macroscale suspended graphene membrane takes place. In that latter case, the interaction with the substrate becomes minimal and offers a promising way to test the influence of suspended graphene with periodic substrate interaction.

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ASSOCIATED CONTENT

* Supporting Information S

Fabrication techniques, Raman spectrometer setup, neighbors indexing, derivation of critical pitch, statistical modeling of ripples domain formation, and illustrating graphics. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Present Address ⊥

ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Agence Nationale de la Recherche (ANR projects: MolNanoSpin, Cleangraph, Allucinan and Trico), European Research Council (ERC advanced grant no. 226558), the Nanosciences Foundation of Grenoble and Region Rhône-Alpes and the Graphene Flagship. We thank Edgar Bonet, Louis Gaudreau, Frank Koppens, Joël Moser, and Kevin Schädler for stimulating discussions.

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