SUPPLEMENTARY INFORMATION

SUPPLEMENTARY INFORMATION Controlled Ripple Texturing of Suspended Graphene and Ultrathin Graphite Membranes Wenzhong Bao, Feng Miao, Zhen Chen, Hang Zhang, Wanyoung Jang, Chris Dames, Chun Ning Lau * I. Materials and Methods A. Fabrication of suspended graphene Suspended graphene membranes are prepared by the standard mechanical cleavage technique on Si/SiO 2 wafers with pre-patterned trenches. Membranes that are 1, 2 and 3-layer thick are identified by color contrast in an optical microscope and/or Raman spectroscopy. The Si substrates are p-doped to act as back gates, and the thickness of silicon and SiO 2 are 500 μm and 300 nm, respectively. The trenches are defined by photolithography followed by plasma etching in a reactive ion etcher (RIE) system. The depths of trenches range from 100 to 250 nm, and width from 2 to 4 μm. Devices with electrodes are fabricated by direct deposition of Ti/Au metals through shadow masks that are carefully aligned to selected graphene sheets. B. Imaging Suspended Graphene Membranes in SEM The graphene sheets are located by color contrast in an optical microscope. The graphene wrinkles are imaged using both a Veeco Multimode atomic force microscope (AFM) operated in tapping mode and a scanning electron microscope (SEM). We have compared SEM and AFM images on several graphene sheets, and conclude that both images yields similar parameters, e.g. extent of sag into the trench, and wavelengths and direction of ripples. We also observe that the ripples in graphene are not visible in SEM unless the device is imaged at a high tilting angle, nature nanotechnology www.nature.com/naturenanotechnology 1

supplementary information typically 75-85º. As shown in Fig. S1, the graphene membrane appears to be flat and ripple-free when imaged at 0º (i.e. top view) or 45º; however, when imaged at large angles (>75º), the membrane displays prominent, periodic ripples. The majority of the images presented in the manuscript are taken at 80º. Most of the as-prepared graphene membranes display strain-induced ripples. Occasionally, however, flat graphene or sagging sheets are also observed (Fig. S2). C. Graphene Annealing The graphene membranes are annealed in a furnace in argon gas at a flow rate 0.6 slm for 20 minutes. The annealing temperature varies from 400K to 750K. Some of the membranes are annealed inside an SEM chamber in vacuum using a custom-built heater stage, as discussed below. II. In Situ SEM Thermal Expansion Studies A. SEM Heating Stage The in situ SEM thermal expansion studies were conducted in an FEI Quanta SEM with four electrical feedthroughs, using a custom heating stage designed for accurate temperature measurements. Standard graphene samples on silicon substrates (4 mm x 4 mm x 0.5 mm) were mounted to a heated aluminum base plate using a thin layer of high-temperature cement (thermal conductivity 1.6 W/m.K). Temperature was measured using a fine-gauge K-type thermocouple (diameter 2 mil 50 μm) cemented directly to the top of the silicon chip. To minimize errors in the temperature measurement, the thermocouple bead was embedded approximately 1 mm into the cement and located as close as practical to the top of the silicon (Fig. S3). This configuration exploits heat conduction through the cement to bring the temperature of the thermocouple junction as close as possible to the temperature of the silicon substrate. We assume conservative 2 nature nanotechnology www.nature.com/naturenanotechnology

supplementary information values for the thermal conductivity of the thermocouple wires (50 W/m K), and the worst-case emissivity (ε=1) of all materials. Using standard heat transfer theory, we calculate that the temperature of the thermocouple junction is within 2K of the silicon temperature even at 725K. We have also conservatively estimated the temperature difference between the silicon and the center of the graphene flake to be 0.05K or less, which considers temperature gradients within the silicon, heat transfer through the oxide layer, contact resistance between graphene and oxide, heat conduction through the graphene, and black-body radiation to the surroundings. Taken together, the overall uncertainty in our temperature measurement is estimated as 4K at 725K, with the largest contribution simply being the uncertainty in the thermocouple calibration. B. Graphene s Thermal Expansion Coefficient (TEC) Graphene s TEC α(t) is calculated from the slope of the curve l(t) =L g (T)/L trench (T). The slope is the effective TEC of the graphene-trench system, given by α eff (T) = dl(t) dt = 1 L g (T + ΔT) ΔT L t (T +ΔT) L g(t) L t (T) = 1 L g (T) (1 + αδt) ΔT L t (T) (1+ α t ΔT) L g (T) L g (T) L t (T) L t (T) α α t ( ) if we take first order expansions, assuming αδt<<1. Here α and α t are the thermal expansion coefficients of graphene and the trench gap, respectively. Since the prefactor L g (T)/L t (T) is within 0.1% of unity, α eff α-α t or α α eff +α t. (S1) Because the Si substrate is 1700 times thicker and twice as stiff as the SiO 2 layer, the TEC of the trench gap is dominated by the TEC of the substrate: α t α Si. For slightly better accuracy we use α t 1.20 α Si in Eq. (S1), where the prefactor of 1.20 captures the higher order nature nanotechnology www.nature.com/naturenanotechnology 3

supplementary information effects of substrate curvature and the deformation of the free edges of the trench banks, as discussed in the next section. C. Thermal Expansion of Trenches on a Si/SiO 2 Substrate To the first order, the thermal expansion of the trench on a Si/SiO 2 substrate is dominated by Si, which is 1700 times thicker and twice as stiff as the SiO 2 layer. Further consideration reveals two higher-order phenomena that may also influence the effective TEC of the trench gap. (a). Upon a temperature increase ΔT, the difference in TECs between the substrate and the thin oxide induces an interfacial thermal stress; consequently, the substrate is strained and acquires a finite curvature. This phenomenon is qualitatively similar (although far smaller in magnitude) to that observed during the thermal expansion of a bi-metallic strip. The strain ε and radius of curvature R can be estimated using the well-known Stoney formula 1 for a thin-film-on-substrate system, given by ε = σ d 2 f f ( 1 v s ) E and R = s d s E s d s 6σ f d f 1 v s ( ) ( )ΔT E f 1 v f where σ f = α s α f ( ) is the thermal stress in the oxide. Here α is the TEC, d the thickness, ΔT the temperature increase, ν the Poisson s ratio, E the elastic constant, and the subscripts f and s indicate thin film and substrate, respectively. Using d s =500 μm, d f =300 nm, and standard values α Si ~3x10-6 K -1, α SiO2 ~5x10-7 K -1, E Si 160 GPa, E SiO2 70 GPa, ν Si 0.22 and ν SiO2 0.16, we estimate σ f 62.5 MPa, R~450m, and ε -2x10-7. The corresponding change in the trench gap is of order δ~1x10-15 m. Thus, within an accuracy of 1 part per million, the TEC of the trench gap is unaffected by the curvature induced by differential thermal expansion. 4 nature nanotechnology www.nature.com/naturenanotechnology

supplementary information (b). A second, and more subtle, factor is the free edge effect while the bottom surface of the SiO 2 is bonded to and expands as much as the silicon substrate, the top SiO 2 surface is free and and the vertical walls of the trench disrupt the otherwise uniform in-plane tensile stress distribution within the film. Because α f <α sub, the upper surface of the SiO 2 expands less than its lower surface, causing the walls of the trench to acquire a very slight slant outwards upon heating 2. In fact, the upper bound of thermal expansion of the top of the trench is (2α sub -α f )ΔT, if the expansion of the top of the thin film is completely independent of that of the bottom, if the thin film is perfectly incompressible, and if we neglect any resultant curvature of the film. To quantify this free-edge effect, we use 3D finite element simulations (COMSOL software) to evaluate the deformations of the trench-substrate system. Our results show that the thermal expansion of the gap at the top of the trench is roughly 120% that of bare silicon, which is reasonable considering the constraint by the Si substrate, and the oxide s small thickness and Poisson s ratio. III. Effect of Annealing on Suspended Graphene Membranes After annealing, all graphene membranes display more prominent ripples in the y- direction, and/or buckling in the x-direction (Fig. S4-5). Apart from membranes that buckle or sag towards the substrate (Fig. 2 in main text), upward buckling is also observed (Fig. S5). For graphene membranes that have been thermally cycled to high temperatures (>~600 K), some completely collapsed, settling onto the bottom of the trenches without breaking (Fig. S4). Fig. S6 shows the morphological changes of graphene membranes through several thermal cycles via in situ SEM imaging in vacuum. Invariably, the graphene sheets become smoother (rippled) upon heating (cooling) with each cycle. nature nanotechnology www.nature.com/naturenanotechnology 5

supplementary information IV. Other Ripple Formation Mechanisms In addition to mechanical strains, thermal fluctuations may also induce ripples. However, numerical simulations 3-5 show that thermally induced ripples are random, dynamic, with amplitudes of ~ 1 Å at 300K. In contrast, the ripples in our devices are periodic, static, with amplitudes 1-3 orders of magnitude large than those predicted, thus are unlikely to arise from thermal fluctuations. Another ripple-inducing mechanism is molecular adsorption, which has been shown theoretically to yield ripples in as-prepared, suspended graphene 5,6. However, for devices thermally cycled under vacuum, any desorbed molecular species are unlikely to adsorb on the graphene surface again. Thus, if molecular adsorption is the main rippling mechanism, the graphene sheet is not expected to exhibit further morphological changes after the first thermal cycle. This is incompatible with experimental data: Fig. S6 establishes the repeatability of the morphological changes through several thermal cycles. We therefore exclude molecular adsorption/desorption as the ripple formation mechanism in our experiments. V. Electrical Measurement of Suspended Graphene Devices Our ability to controllably create ripples in graphene opens a door systematic investigation of ripples effects on graphene s electrical properties, which have hitherto remained theoretical conjectures. However, standard lithographical processes, which are detrimental to suspended graphene membranes, cannot be employed to fabricate electrodes. We overcome this technical challenge by evaporation through custom-made shadow masks that are carefully aligned to the trenches. As an initial demonstration, we fabricate suspended graphene devices 6 nature nanotechnology www.nature.com/naturenanotechnology

supplementary information with two electrodes on each side of the trench (Fig. S7a), allowing measurements of both suspended and substrate-supported portions of the same graphene sheet. Devices with both random and periodic ripples can be fabricated. Fig. S7b shows the 2-probe conductance G of a single layer graphene device, whose suspended portion displays small random ripples, as a function of the electrostatically induced charge density n ind. Comparing with the substratesupported part, the suspended part of graphene has much higher mobility, with a sharper Dirac point that is closer to n ind =0, indicating smaller density of charged impurities. Thus, despite small ripples, the device mobility is substantially enhanced by eliminating the substrate. This is consistent with prior results from high-mobility suspended graphene devices 7,8, which are also likely to contain ripples. VI. Online Movie This movie consists of images taken in an SEM, and shows the wrinkle formation in a suspended single-layer graphene sheet as it cools from 500K to 300K. nature nanotechnology www.nature.com/naturenanotechnology 7

supplementary information References S1 Freund, L. B. & Suresh, S. Thin Film Materials. (Cambridge University Press, 2003). S2 Shen, Y.-L., Suresh, S. & Blech, I.A., Stresses, curvatures, and shape changes arising from patterned lines on silicon wafers, J. Appl. Phys. 80, 1388 (1996). S3 Abedpour, N. et al. Roughness of undoped graphene and its short-range induced gauge field. Phys. Rev. B 76, 195407 (2007). S4 Fasolino, A., Los, J. H. & Katsnelson, M. I. Intrinsic ripples in graphene. Nature Mater. 6, 858-861 (2007). S5 Thompson-Flagg, R. C., Moura, M. J. B. & Marder, M. Rippling of graphene. Europhys. Lett. 85, 46002 (2009). S6 Elias, D. C. et al. Control of graphene s properties by reversible hydrogenation. Science 323, 610 (2009). S7 Bolotin, K. I., Sikes, K. J., Hone, J., Stormer, H. L. & Kim, P. Temperature-dependent transport in suspended graphene. Phys. Rev. Lett. 101, 096802 (2008). S8 Cerda, E. & Mahadevan, L. Geometry and physics of wrinkling. Phys. Rev. Lett. 90, 074302 (2003). 8 nature nanotechnology www.nature.com/naturenanotechnology

supplementary information Supplementary Figures 5μm 2μm 5μm 0 45 75 Fig. S1. SEM Images of a graphene sheet imaged at different tilting angles. Note that the ripples are observable only at a large tilting angle, >75º. 1μm 2μm 1 μm 1μm Fig. S2. SEM images of several different as-deposited few-layer graphene membranes. nature nanotechnology www.nature.com/naturenanotechnology 9

supplementary information L 1 mm SiO 2 graphene H 0.5 mm Cement Thermocouple wire h < 0.2 mm Si T Si T graphene T Si < 0.05 C T Si T Fig. S3. Schematic of the heater stage for in situ SEM imaging. junction < 2.0 C 10 nature nanotechnology www.nature.com/naturenanotechnology

supplementary information c 2 μm b 1μm a 2μm Fig. S4. SEM images of three graphene membranes before (left) and after annealing (right). nature nanotechnology www.nature.com/naturenanotechnology 11

supplementary information a b c d 1 μm 5μm Fig. S5. (a). AFM image of a graphene membrane device before annealing. Upper panel: AFM topography image. Lower panel: Line trace along the dotted line in the upper panel. (b). same as (a), after annealing to 550 K. (c). SEM image of a few-layer graphene membrane that buckles upwards after annealing. (d). Ripples in a few-layer graphene membrane over a triangular opening on the substrate. 12 nature nanotechnology www.nature.com/naturenanotechnology

supplementary information a b Fig. S6. In situ SEM imaging of graphene sheets through thermal cycles. Scale bars: 1 µm. (a). A bilayer graphene sheet with pre-existing ripples are thermally cycled between 300K and 425 K. (b). A single layer graphene sheet is relatively flat immediately after deposition. It is then thermal cycled to successively higher temperatures up to 675K. nature nanotechnology www.nature.com/naturenanotechnology 13

supplementary information Fig. S7. (a) SEM image of a bi-layer suspended graphene device with random ripples. (b) G(n ind ) for suspended (red) and substrate-supported (blue) part of a single layer graphene device, which has randomly oriented ripples with amplitudes of 5-15 nm and wavelengths of 0.6 2 μm. The measurements are performed at 1.5K. The gate coupling efficiencies are n ind /V g ~ 2.3x10 10 and 7.2 x10 10 cm -2 V -1 for suspended and supported graphene sheets, respectively. 14 nature nanotechnology www.nature.com/naturenanotechnology