atomic patchwork quilts
Pinshane Y. Huang1*, Carlos S. Ruiz-Vargas1*, Arend M. van der Zande2*, William S. Whitney2, Mark P. Levendorf3,
Joshua W. Kevek4, Shivank Garg3, Jonathan S. Alden1, Caleb J. Hustedt5, Ye Zhu1, Jiwoong Park3,6, Paul L. McEuen2,6
& David A. Muller1,6
The properties of polycrystalline materials are often dominated by
the size of their grains and by the atomic structure of their grain
boundaries. These effects should be especially pronounced in two-
dimensional materials, where even a line defect can divide and
disrupt a crystal. These issues take on practical significance in
graphene, which is a hexagonal, two-dimensional crystal of carbon
atoms. Single-atom-thick graphene sheets cannow beproduced by
chemical vapour deposition1–3on scales of up to metres4, making
grain boundaries are predicted to have distinct electronic5–8,
magnetic9, chemical10and mechanical11–13properties that strongly
boundaries, few experiments have fully explored the graphene
grain structure. Here we use a combination of old and new trans-
mission electron microscopy techniques to bridge these length
scales. Using atomic-resolution imaging, we determine the loca-
tion and identity of every atom at a grain boundary and find that
different grains stitch together predominantly through pentagon–
heptagon pairs. Rather than individually imaging the several
billion atoms in each grain, we use diffraction-filtered imaging14
to rapidly map the location, orientation and shape of several
hundred grains and boundaries, where only a handful have been
By correlating grain imaging with scanning probe and transport
measurements, we show that these grain boundaries severely
weaken the mechanical strength of graphene membranes but do
not as drastically alter their electrical properties. These techniques
open a new window for studies on the structure, properties and
control of grains and grain boundaries in graphene and other
membranes used in this study. We grew predominately single-layer
graphene films on copper foils by chemical vapour deposition1
methods A, B and C. Unless otherwise stated, all data were taken on
graphene grown with method A, which was similar to the recipe
ultrapure copper foils18(99.999% pure rather than 99.8%) and method
C uses a rapid thermal processor furnace (Methods). These films were
transferred onto holey silicon nitride or Quantifoil transmission elec-
and Supplementary Information). One key innovation over previous
graphene TEM sample fabrication20was the gentle transfer of the gra-
phene onto a TEM grid using a minimum of polymer support and
to 90% of the TEM grid holes.
To characterize these membranes at the atomic scale, we used
aberration-corrected annular dark-field scanning transmission elec-
tron microscopy (ADF-STEM), where a 60-keV, a ˚ngstro ¨m-scale elec-
scattered electrons are collected. Keeping the electron beam voltage
below the ,100-keV graphene damage threshold was necessary to
limit beam-induced damage. Properly calibrated, this technique
images the location and atomic number21of each atom and, along
with TEM, has been used to study the lattice and atomic defects of
graphene and boron nitrene19,21–23. Figure 1b shows an ADF-STEM
image of the crystal lattice within a single graphene grain. Away from
the grain boundaries, such regions are defect free.
27u, forminga tilt boundary. Additional images of grain boundaries are
crystals are stitched together by a series of pentagons, heptagons and
distorted hexagons. The grain boundary is not straight, and the defects
*These authors contributed equally to this work.
1School of Applied and Engineering Physics, Cornell University, Ithaca, New York 14853, USA.2Department of Physics, Cornell University, Ithaca, New York 14853, USA.3Department of Chemistry and
University, Provo, Utah 84602, USA.6Kavli Institute at Cornell for Nanoscale Science, Ithaca, New York 14853, USA.
Figure 1 | Atomic-resolution ADF-STEM images of graphene crystals.
a, Scanning electron microscope image of graphene transferred onto a TEM
grid with over 90% coverage using novel, high-yield methods. Scale bar, 5mm.
b, ADF-STEM image showing the defect-free hexagonal lattice inside a
graphene grain. c, Two grains (bottom left, top right) intersect with a 27u
relative rotation. An aperiodic line of defects stitches the two grains together.
d, The image from c with the pentagons (blue), heptagons (red) and distorted
remove noise; scale bars, 5A˚.
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resembles structures proposed theoretically11,13, its aperiodicity con-
trasts with many of these models and will strongly affect the predicted
properties of grain boundaries. By analysing atomic scattering intens-
ities21, we confirm that the boundary is composed entirelyof carbon. In
addition, although high electron beam doses could induce isolated
bond rotations (Supplementary Fig. 3), the boundary was largely stable
grain boundaries are decorated by lines of surface particles and adsor-
more chemically reactive than the pristine graphene lattice.
atomic nuclei, and complementary scanning tunnelling microscopy,
ing thelocal properties of grain boundaries. Using these atomic-resolu-
tion approaches, however, tens of billions to hundreds of billions of
pixels would be needed to image even a single micrometre-scale grain
fully, with estimated acquisition times of a day or more. Other candi-
dates forcharacterizing grainsonlarger scales, such as low-energyelec-
tron microscopy18and Raman microscopy3, typically cannot resolve
small grains and may be difficult to interpret. Fortunately, electron
length scales: dark-field TEM (DF-TEM), which is a high-throughput,
diffraction-sensitive imaging technique14that can be implemented on
to foils about 100–300-nm thick14, but we demonstrate below that,
too dirty for atomic-resolution imaging. In this manner, DF-TEM pro-
vides a nanometre- to micrometre-scale grain analysis that comple-
ments ADF-STEM to give a complete understanding of graphene
grains on every relevant length scale.
Figure 2a, b shows a bright-field TEM image of a graphene sheet
along with the selected-area electron diffraction pattern created from
this region of the membrane. Owing to graphene’s six-fold symmetry,
electron diffraction from a single graphene crystal results in one set of
six-fold-symmetric spots. Figure 2b contains many such families of
spots, indicating that the field of view contains several grains of dif-
nanometre resolution using an objective aperture filter in the back
focal plane to collect electrons diffracted through a small range of
(Fig. 2c) shows only the grains corresponding to these selected in-
plane lattice orientations and requires only a few seconds to acquire.
By repeating this process using several different aperture filters, then
orientation, as shown in Fig. 2e–g.
The images obtained are striking. The grains have complex shapes
locations fromwhich manygrainsemanate.Small particlesand multi-
layer graphene also are often found near these sites; see, for example,
radiant sites when we use growth method A are comparable with
Raman and scanning electron microscope observations of graphene
nucleation1,3, suggesting that these locations are probably nucleation
in colloids and are consistent with crystallization around impurities24.
Similar multigrain nucleation on copper has recently been observed
using low-energy electron microscopy18. Significantly, each apparent
ing in a mean grain size much smaller than the nucleation density.
The distributions of grain size and relative angular orientation are
readily determined from DF-TEM images. As discussed below, grain
sizes are dependent on growth conditions, here ranging from hundreds
of nanometres to tens of micrometres for slight changes in growth con-
ditions. In Fig. 3a, we plot a histogram of grain sizes across several
samples grown using method A. The mean grain size, defined as the
square root of the grain area, is 250611nm (s.e.m.). This size is much
(6–30mm). The inset in Fig. 3a shows the cumulative probability of
finding multiple grains in a given area. This plot demonstrates that
the relative crystallographic angles between adjacent grains. Because of
graphene’s six-fold crystal symmetry, the diffractive imaging technique
only determines grain rotations modulo 60u. Consequently, the mea-
surable difference between grain orientations is from 0 to 30u (with, for
example, 31u measured as 29u). We observe a surprising and robust
preference for low-angle (,7u) grain boundaries and high-angle
(,30u) boundaries similar to that seen in Fig. 1.
Additional information about these orientations comes from the
diffraction data sampled across 1,200-mm2regions of graphene. The
broadened diffraction peaks in Fig. 3c (left) show a distinct six-fold
pattern, indicating that a significant fraction of the grains are approxi-
mately aligned across large areas This alignment can also be seen in
Fig. 3d, which is a low-magnification DF-TEM image showing grains
the membrane appears bright, indicating that these grains are all
approximately aligned. In contrast, a dark-field image of randomly
oriented grains would only show roughly one-sixth (10u/60u) of the
graphene membrane. In the diffraction pattern of a separately grown
sample (Fig. 3c, right), we instead find a clear 12-fold periodicity,
Figure 2 | Large-scale grain imaging using DF-
TEM. a–e, Grain imaging process. a, Samples
appear uniform in bright-field TEM images.
b, Diffraction pattern taken from a region in
a revealsthatthisarea ispolycrystalline.Placing an
electrons forming c, a corresponding dark-field
d, Using several different aperture locations and
colour-coding them produces e, a false-colour,
dark-field image overlay depicting the shapes and
lattice orientations of several grains. f, g, Images of
regions where many grains emanate from a few
points. Scale bars, 500nm.
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indicating that there are two main families of grains rotated from one
another by 30u. These distributions, which often contain smaller sub-
peaks (Supplementary Fig. 6), are consistent with the frequent obser-
vation of low-angle and high-angle (,30u) grain boundaries. We
attribute these alignments to registry to the copper substrate used for
graphene growth. Such registry has recently been observed in low-
of graphene growth on copper (100) and (111) surfaces15,16,18.
By directly correlating grain structure with growth methods, these
DF-TEM methods can be used to build on recent studies3that have
demonstrated links between island nucleation density and growth
conditions. Fig. 4a–c shows three composite DF-TEM images of
graphene grown using methods A, B and C. The slight differences
shape and crystallographic orientation of the CVD graphene. For
example, with growth method C we observed grains averaging
grown using method A. Our DF-TEM methods provide a powerful
characterization tool for understanding and controlling grain growth,
opens the door to the systematic exploration of the effects of grain
structure on the physical, chemical, optical and electronic properties of
graphene membranes. We find that such studies are further facilitated
because grain boundaries are visible in scanning electron microscopy
and atomic force microscopy (AFM) phase imaging owing to preferen-
tial decoration of the grain boundaries with surface contamination
probing the electrical and mechanical properties of grain boundaries.
We first examine the failure strength of the polycrystalline CVD gra-
imaging to image grains (Fig. 5a) and then pressed downwards with the
AFM tip to test the mechanical strength of the membranes. As seen in
Fig. 5b, the graphene tears along the grain boundaries. From repeated
measurements,wefind thatfailure occursatloadsof ,100nN,whichis
an order of magnitude lower than typical fracture loads of 1.7mN
reported for single-crystal exfoliated graphene26. Thus, the strength of
polycrystalline graphene is dominated by its grain boundaries.
We probed the electrical properties of polycrystalline graphene by
growth methods. Figure 4d shows a histogram of mobilities extracted
from four-point transport measurements. Devices grown using
methods A, BandChaveroom-temperaturemobilitiesof1,0006750,
7,30061,100 and 5,30062,300cm2V21s21(s.d.), respectively. The
mobilities for growth method A are comparable to previous results on
CVD graphene1, whereas the mobilities of growth methods B and C
are closer to those reported for exfoliated graphene27(1,000–
20,000cm2V21s21). By comparing these measurements with the cor-
responding DF-TEM images in Fig. 4a–c, we are surprised to find that,
To complement these bulk electrical measurements, we used scan-
ning probe a.c. electrostatic force microscopy28(AC-EFM) to test the
phene membrane devices29. One of these is shown schematically in
brane between two biased electrodes, measured using AC-EFM. In this
grainsize of 250nm, so a line scan across these3-mm-long membranes
should cross an average of 12 grains. However, no noticeable potential
drops were detected, indicating that most grain boundaries in these
devices are not strongly resistive interfaces. By assuming that the grain
boundary runs perpendicular to the line scan, we estimate an upper
the length of the grain boundary, to be compared with the sheet resist-
ance of Rgraphene5700V/% for the entire device. In other words, the
a 250-nm grain. Further measurements on six additional graphene
membranes, both suspended and unsuspended, and from different
growth methods, produced similar results. This small impact of grain
boundaries stands in starkcontrastto other materials, suchascomplex
in resistance over single crystals30.
0 5,000 10,000
μ (cm2 V–1 s–1)
Growth method A
Growth method B
Growth method C
Figure 4 | Grain structure and mobilities for three growth conditions.
condition. The mean grain sizes are 250611nm (s.e.m.; growth method A,
99.8% pure copper), 470636nm (s.e.m.; growth method B, 99.999% pure
anneal)). The graphene is visible through the 20-nm, perforated amorphous-
carbon Quantifoil support film. The graphene is broken over three of the
perforations in a. Scale bars, 2mm. d, Vertically stacked histogram of room-
temperature mobilities, m, measured from 39 devices using graphene growth
methods A, B, and C. N, number of devices. See Methods for further details.
Grain size (nm)
0 10 2030
Relative rotation (°)
0 400 800 1,200
Figure 3 | Statistical analysis of grain size and orientation. a, Histogram of
grainsizes,takenfromthreerepresentative samplesusingDF-TEM.The mean
grain size is 250611nm (s.e.m., n5535). Inset, plot of the cumulative
probability of having more than one grain given the area of a device.
b, Histogram of relative grain rotation angles measured from 238 grain
boundaries. c, d, Large-area diffraction patterns (c) and a low-magnification
DF-TEM image (d) show that grains are globally aligned near particular
directions. Scale bar, 2mm.
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The imaging techniques reported here provide the tools to char-
acterize graphene grains and grain boundaries on all relevant length
scales. These methods will be crucial both for exploring synthesis
strategies to optimize grain properties and for studies, such as those
described above, on the microscopic and macroscopic impact of grain
structure on graphene membranes. Thus, these results represent a
significant step forward in realizing the ultimate promise of atomic
membranes in electronic, mechanical and energy-harvesting devices.
TEM/STEM. We did ADF-STEM imaging using a NION UltraSTEM100 with
imaging conditions similar to those used in ref. 21. At 60kV, using a 33–35-mrad
imaging, we used a FEI Technai T12 operated at 80kV. Acquisition times for dark-
between real-space resolution and angular resolution in reciprocal space.
Scanning probe measurements. For AFM deflection measurements, we used a
MFP3D scope from Asylum Research. We used silicon AFM probes (Multi75Al,
and a tip radius of ,10nm. All imaging was done in tapping mode. For AC-EFM
on the tip. An a.c. voltage of V051V was applied through the electrodes at the
resonance frequency of the EFM cantilever, fcant<77kHz. An electrostatic force
drives the EFM cantilever to resonate, and the amplitude of motion is measured.
Full Methods and any associated references are available in the online version of
the paper at www.nature.com/nature.
Received 23 September; accepted 29 November 2010.
Published online 5 January 2011.
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Supplementary Information is linked to the online version of the paper at
Acknowledgements The authors acknowledge discussions with M. Blees, J. Cha,
S. Gerbode, J. Grazul, E. Kirkland, L. Fitting-Kourkoutis, O. Krivanek, S. Shi, S. Wang and
the Cornell Center for Materials Research and the Nanoscale Science and Engineering
Force Office of Scientific Research, DARPA-MTO and the MARCO Focused Research
Center on Materials, Structures, and Devices. Sample fabrication was performed at the
Additional facilities support was provided by the Cornell Center for Materials Research
(NSF DMR-0520404 and IMR-0417392) and NYSTAR.
Author Contributions P.Y.H., C.S.R.-V.and A.M.v.d.Z. contributed equally tothis work.
Electronmicroscopyand dataanalysis were carried out by P.Y.H. andD.A.M., withY.Z.
contributing to initial DF-TEM. Graphene growthand sample fabrication weredone by
A.M.v.d.Z. and C.S.R.-V. under thesupervision ofP.L.M. and J.P., aided by M.P.L., S.G.,
were done by C.S.R.-V. andJ.P., aided by S.G.All authors discussed the resultsand
Author Information Reprints and permissions information is available at
www.nature.com/reprints. The authors declare no competing financial interests.
Readers are welcome to comment on the online version of this article at
www.nature.com/nature. Correspondence and requests for materials should be
addressed to D.A.M. (firstname.lastname@example.org).
Figure 5 | AFM indentation and AC-EFM studies of graphene grain
boundaries. a, b, AFM phase images of a graphene grain before and after an
indentation measurement. a, Indentation takes place at the centre of this grain
as shown by the arrow. b, The region is torn along grain boundaries after
indentation. Scale bars, 200nm. c, Electrostatic potential, averaged over three
adjacent line scans along a suspended graphene sheet between two electrodes
(schematic at top) and measured using AC-EFM. Although on average each
line scan should cross 12 grains, no measureable features are present. Dashed
lines indicate the locations of the electrodes.
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METHODS Download full-text
ADF-STEM. ADF-STEM imaging was conducted using a NION UltraSTEM100
voltage electron beam was below the damage threshold energy31, the pristine
graphene lattice remains stable and defect free. High electron beam doses could
induceisolatedbond rotationsatgrainboundaries (SupplementaryFig. 4) similar
to those seen in ref. 32. Images presented in Figs 1–4 were acquired with the
medium-angle annular dark-field detector with acquisition times of between 16
and 32ms per pixel.
DF-TEM. TEM imaging was conducted using a FEI Technai T12 operated at
80 kV, which did not cause any apparent damage to the graphene membranes.
Acquisition time for dark-field images were 5–10s per frame. The spatial resolu-
tion in dark-field images ranges from 1 to 10nm and is set by the size of the
resolution in reciprocal space.
AC-EFM. A DI 4100 AFM with a signal access module was operated in lift mode
voltage V051V was applied through the electrodes at the resonance frequency of
the EFM cantilever, fcant<77kHz. An electrostatic force drives the EFM cantilever
to resonate, and the amplitude of motion is measured.
AFM imaging and deflection measurements. For AFM deflection measure-
ments, we used a MFP3D scope from Asylum Research. We used silicon AFM
mode. Images were taken with resolutions of 5123512 or 1,02431,024, with
acquisition times of at most 10min.
Graphene growth. We grew single-layer graphene using CVD on copper foils in
flow of 7 standard cubic centimetres per minute (s.c.c.m.) for 10min. We then
grew the graphene at 1,000uC by flowing CH4:H2at 150:7s.c.c.m. for 10–15min
(varying growth time within this range did not yield noticeably different results).
Samples are cooled for ,50min while the CH4:H2flow is maintained. Growth
method B: this is identical to method A, except we used higher purity (99.999%)
copper foil (Alfa Aesar #10950). Growth method C: we used a rapid thermal
processor tube furnace with a ,499 inner diameter (MTI Corporation). We
annealed copper foil (99.8% purity) at 1,000uC (H2, 300s.c.c.m.) for 30min,
and then grew the graphene at 1,000uC (CH4:H2, 875:300s.c.c.m.) for 60min.
Samples for DF-TEM. We transferred the graphene either to commercial holey
DF-TEM imaging through the carbon support.
thin PMMA support, which produced roughly 90% coverage of TEM grid holes
(that is, 90%of gridholeswereuniformlycoveredwithsuspendedgraphene). After
(2% in anisole, 4,000r.p.m. for 30s), without a post-baking step. Copper was then
etched away by floating the foil, PMMA side up, in a HCl/FeCl3copper etchant
contact with liquids, to avoid depositing unwanted residues on the PMMA side of
this layer. Finally, the PMMA–graphene layer is scooped out in pieces onto TEM
the PMMA layer, leaving the graphene freely suspended in a liquid-free release
process. These high-yield samples were used in DF-TEM because they provided
enough clean graphene to image large numbers of grains.
Samplesfor ADF-STEM.Our secondarytechniqueproducedcleaner,butlower-
yield,grapheneusingapolymer-free transfermethod. This techniqueis similarto
the methods of ref. 20, in which TEM grids are placed on top of the foil before
technique was to bake the final samples in a series of annealingprocesses increas-
ing in temperature. The grids were then baked in air at 350uC for 2h. In this
method, the samples are annealed in ultrahigh vacuum by ramping the temper-
ature to 950uC, holding this temperature steady for 15min and then cooling to
room temperature without active cooling. This annealing is done below the gra-
phene growth temperature, and the micrometre-scale grain structure did not
change afterwards. Thus, any change that may result from annealing should be
small in comparison with changes occurring during the formation of the grain
boundaries. A final step was to anneal the grids at 130uC for .8h before trans-
ferring theminairto the TEM. Because this transfermethoduses nosupport film
for the graphene as it is transferred, this method was a comparatively low-yield
transferprocess with coverage ofjust a fewpercent over the holes.The advantage
less surface carbon contamination—regions hundreds of nanometres wide
appeared atomically clean in ADF-STEM images.
Electrically contacted samples. We fabricated top-gated graphene devices in
four-point probe geometry (shown in Supplementary Fig. 11a, b, with electrodes
labelled). A transferred graphene film was patterned by photolithography and a
by fabricating 1.5-nm Ti/4.5-nm Au electrodes. We patterned a top gate, to mea-
sure the charge mobility in graphene,byelectronbeam evaporation first of 90nm
of silicon oxide as a dielectric layer and then of a Cr/Au layer (1.5nm/50nm),
without breaking vacuum between each evaporation.
For the EFM measurements, we fabricated electrically contacted, suspended
graphene by growing single-layer graphene on copper using CVD; patterning
the graphene into 3-mm-wide strips while still on the copper foil, using contact
gold electrodes and trenches.
31. Meyer, J. C., Chuvilin, A. & Kaiser, U. in MC2009, Vol. 3: Materials Science
(eds Grogger, W., Hofer, F. & Polt, P.) 347–348 (Graz Univ. Technology, 2009).
32. Suenaga, K. et al. Imaging active topological defects in carbon nanotubes. Nature
Nanotechnol. 2, 358–360 (2007).
33. Jiao,L.et al.Creation ofnanostructures withpoly(methylmethacrylate)-mediated
nanotransfer printing. J. Am. Chem. Soc. 130, 12612–12613 (2008).
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