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Graphene kirigami


For centuries, practitioners of origami (‘ori’, fold; ‘kami’, paper) and kirigami (‘kiru’, cut) have fashioned sheets of paper into beautiful and complex three-dimensional structures. Both techniques are scalable, and scientists and engineers are adapting them to different two-dimensional starting materials to create structures from the macro- to the microscale1,2. Here we show that graphene3,4,5,6 is well suited for kirigami, allowing us to build robust microscale structures with tunable mechanical properties. The material parameter crucial for kirigami is the Föppl–von Kármán number7,8 γ: an indication of the ratio between in-plane stiffness and out-of-plane bending stiffness, with high numbers corresponding to membranes that more easily bend and crumple than they stretch and shear. To determine γ, we measure the bending stiffness of graphene monolayers that are 10–100 micrometres in size and obtain a value that is thousands of times higher than the predicted atomic-scale bending stiffness. Interferometric imaging attributes this finding to ripples in the membrane9,10,11,12,13 that stiffen the graphene sheets considerably, to the extent that γ is comparable to that of a standard piece of paper. We may therefore apply ideas from kirigami to graphene sheets to build mechanical metamaterials such as stretchable electrodes, springs, and hinges. These results establish graphene kirigami as a simple yet powerful and customizable approach for fashioning one-atom-thick graphene sheets into resilient and movable parts with microscale dimensions.

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Figure 1: Patterning and manipulating graphene.
Figure 2: Measuring the bending stiffness of monolayer graphene.
Figure 3: Stretchable graphene transistors.
Figure 4: Remote actuation.

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We thank D. Nelson, M. Bowick, A. Kosmrlj, J. Alden, A. van der Zande, and R. Martin-Wells for discussions. We thank E. Minot for assistance with electrolyte gating. We thank R. Hovden for discussions on three-dimensional reconstruction theory and techniques, and R. Hovden, M. Hanwell, and U. Ayachit for developing and supporting the TomViz three-dimensional visualization software. We thank J. Wardini, P. Ong, A. Zaretski, and S. P. Wang for additional graphene samples, and F. Parish with Cornell’s College of Architecture, Art, and Planning for assistance with the paper models. We also acknowledge the Origami Resource Center ( for kirigami design ideas. This work was supported by the Cornell Center for Materials Research (National Science Foundation, NSF, grant DMR-1120296), the Office of Naval Research (N00014-13-1-0749), and the Kavli Institute at Cornell for Nanoscale Science. Devices were fabricated at the Cornell Nanoscale Science and Technology Facility, a member of the National Nanotechnology Infrastructure Network, which is supported by the NSF (ECCS-0335765). K.L.M. and P.Y.H. acknowledge support from the NSF Graduate Research Fellowship Program (DGE-1144153 and DGE-0707428). Tomography visualization software development was supported by a SBIR grant (DE-SC0011385).

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Device design and actuation techniques were developed by M.K.B., A.W.B., P.A.R., S.P.R., and K.L.M. under the supervision of P.L.M. Fabrication and characterization was performed by the above authors with additional support from A.R.R., J.W.K., and B.K. Bending stiffness measurements were designed by A.W.B. and P.L.M. and carried out by M.K.B., P.A.R., and K.L.M. with data analysis by S.P.R., A.W.B., M.K.B., K.L.M., and P.A.R. under the supervision of P.L.M. Electrical measurements were performed by K.L.M. and M.K.B. under the supervision of P.L.M. Three-dimensional reconstructions were performed by P.Y.H. under the supervision of D.A.M. The paper was written by M.K.B. and P.L.M., with assistance from P.A.R., A.W.B., K.L.M., and P.Y.H. and in consultation with all authors.

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Correspondence to Paul L. McEuen.

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The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 Characterization of representative graphene.

a, Scanning electron microscope image of chemical vapour deposition graphene on copper foil. All the graphene used in these experiments was predominantly single-layer, with some small bilayer patches. The larger-scale contrast variations show the copper grains. Scale bar is 10 µm. b, Raman spectrum of chemical vapour deposition graphene transferred to SiO2/Si (285-nm oxide layer) substrate. The spectrum shows graphene’s characteristic G peak at 1,580 cm−1 and two-dimensional peak at 2,700 cm−1; the ratio between the two indicates that the graphene is primarily monolayer. A small D peak at 1,350 cm−1 indicates low disorder. The small peak at 2,450 cm−1 is background. c, High-contrast bright-field TEM image of graphene transferred over 10-nm-thick Si3N4 windows shows continuous monolayer graphene. Scale bar is 1 µm. d, False-colour composite image of dark-field TEM images showing grain size and shape. The graphene is polycrystalline, with grain sizes of the order of micrometres. Scale bar is 1 µm. e, TEM diffraction pattern for region shown in c and d.

Extended Data Figure 2 Atomic force microscopy of graphene.

a, Exfoliated, unprocessed monolayer graphene. Step height along the red line shown on the height (z) map is 1.0 ± 0.3 nm. b, c, Representative data from aluminium-free chips that are run in parallel with the devices used in bending stiffness measurements. Step heights are 2.5 ± 0.4 nm and 2.4 ± 0.5 nm. Chips that look clean under the optical microscope typically have 2–4 nm total step heights. We occasionally see higher residue lines at the edges of the graphene, as in c. The PMMA residue is not sufficiently thick to explain the notably increased bending stiffness of the graphene (see Methods). Scale bars are 1 µm.

Extended Data Figure 3 Thermal motion of graphene cantilever gold pads.

a, Time trace of the x position of the gold pad centroid on a 40 µm × 10 µm graphene cantilever, showing the first 20 s of a 20-min trace. The x direction is perpendicular to the profile of the gold pad, as indicated in the inset. b, PSD (Sxx ) of the full 20-min time trace from a. The blue data points were included in the fit to the Brownian motion PSD function (dashed line); the red data points from about 10−3 Hz to about 10−1 Hz were excluded, because they show considerable 1/f noise as a result of the motion of the probe holding the cantilever. We integrate the fitted function Sxx to determine . For the device shown, = (130 nm)2, the spring constant k = 2.4 × 10−7 N m−1, and the bending stiffness κ = 3 keV.

Extended Data Figure 4 Bending stiffness measurements.

a, We also performed a rough measurement of the spring constant using the force of gravity on the gold pads. After lifting the cantilever off the surface, the vertical deflection xg is determined using the shallow depth of focus of the microscope, adjusted for the change in index of refraction. The gravitational force Fg (corrected for buoyancy) yields the spring constant: k = Fg/xg. For the 50-µm-long cantilever shown (scale bar is 10 μm) with a 2-pN gold pad and xg = 25 µm, we find that k = 8 × 10−8 N m−1. We repeated the measurement for a variety of devices of varying length L and width W = 10 µm. We have observed that the cantilevers sometimes curve downwards even in the absence of an applied force, presumably due to residual materials or strains in the graphene, so these gravitational measurements probably have a systematic offset. b, The measured spring constants of 10-µm-wide devices are shown on a plot of spring constant versus device length for the thermal fluctuation (black), gravitational deflection (blue), and laser force measurements (red). The data from all three techniques (plus additional laser data for devices with other widths, as in Fig. 2) are shown in the inset as a histogram. Data with stars are from the same device, using the three different measurement techniques.

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Manipulating a large sheet of graphene (1x speed)

Once the graphene has been released from the surface, it can crumple dramatically, similar to a large sheet of paper. Surfactants in the solution allow the graphene to return to its original shape. Lifting a graphene device (2x speed). Driving the micromanipulator into an attached gold pad lets us fully release the device and lift it up off of the surface (AVI 9538 kb)

Stiff graphene kirigami spring extends by ~70% (2x speed)

Using a micromanipulator driven into one gold pad, we can repeatedly stretch and relax a kirigami spring. Soft graphene kirigami spring extends by ~240% (2x speed). A different kirigami pattern results in a softer spring that stretches dramatically. Z-scan used in 3D reconstruction (background subtracted). The left side of this spring is being held up by the probe tip, while the right side is still stuck to the substrate. (AVI 10872 kb)

Infrared laser focused on a kirigami pyramid’s central pad and Kirigami pyramid actuation, laser filtered out of the video (1x speed).

The laser is fired from below the pyramid and pushes upwards on the pad, causing it to go out of focus. Twisting graphene with an iron pad and rotating magnetic field (2x speed). Surfactant in the solution allows the graphene to unfold again. A graphene hinge, actuated by a long graphene arm. Large field of view shows the mechanism. A graphene hinge after 1000 cycles (1x speed). This device survived through 10,000 cycles. (AVI 16523 kb)

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Blees, M., Barnard, A., Rose, P. et al. Graphene kirigami. Nature 524, 204–207 (2015).

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