Corrugation in exfoliated graphene: an electron microscopy and diffraction study.

Abstract

Low-energy electron microscopy and microprobe diffraction are used to image and characterize corrugation in SiO(2)-supported and suspended exfoliated graphene at nanometer length scales. Diffraction line-shape analysis reveals quantitative differences in surface roughness on length scales below 20 nm which depend on film thickness and interaction with the substrate. Corrugation decreases with increasing film thickness, reflecting the increased stiffness of multilayer films. Specifically, single-layer graphene shows a markedly larger short-range roughness than multilayer graphene. Due to the absence of interactions with the substrate, suspended graphene displays a smoother morphology and texture than supported graphene. A specific feature of suspended single-layer films is the dependence of corrugation on both adsorbate load and temperature, which is manifested by variations in the diffraction line shape. The effects of both intrinsic and extrinsic corrugation factors are discussed.

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Corrugation in Exfoliated Graphene: An
Electron Microscopy and Diffraction
Study
Andrea Locatelli,†,o,* Kevin R. Knox,‡,§,oDean Cvetko,?,?Tevfik Onur Mentes ¸,†Miguel Angel Nin ˜o,†
Shancai Wang,¶Mehmet B. Yilmaz,§,°Philip Kim,‡Richard M. Osgood, Jr.§,* , and Alberto Morgante?,#,*
†Elettra,SincrotroneTriesteS.C.p.A.,34149Basovizza,Trieste,Italy,‡DepartmentofPhysicsand§DepartmentofAppliedPhysics,ColumbiaUniversity,NewYork,New
York10027,?IOM-CNRLaboratorioTASC,34149Basovizza,Trieste,Italy,?FacultyforMathematicsandPhysics,UniversityofLjubljana,Ljubljana,Slovenia,¶Department
ofPhysics,RenminUniversityofChina,Beijing,China,°DepartmentofPhysics,FatihUniversity,34500,Buyukcekmece,Istanbul,Turkey,and#DepartmentofPhysics,
TriesteUniversity,Trieste,Italy.oContributedequallytothiswork.
G
tional attention in view of potential
applications that exploit its unique elec-
tronic and transport properties.1?3This
zero-gap semiconductor is characterized
by the linear dispersion of its valence and
conduction bands, which meet at inequiva-
lent charge-neutral points in momentum
space. Graphene shows an ambipolar
electric-field effect and an extremely high
mobility of charge carriers, described as
relativistic massless fermions, which results
in unique transport properties. For instance,
single- and double-layer graphene shows
anomalous, distinct quantum Hall
effects.4?7More recently, graphene’s un-
usual chemical properties, which in many
cases arise from its reduced dimensionality,
have become of interest.8,9In particular, the
chemical functionalization of graphene
opens exciting possibilities for practical en-
gineering of the electronic properties of
graphene.10
The transport properties of graphene
depend strongly on the quality of its crystal-
line lattice, the presence of defects and
dopants,andchargetransferfromadsorbed
or bound species.1Changes in conduc-
tance due to molecular adsorption are large
enough to permit the detection of indi-
vidual gas molecules by a graphene sen-
sor.11Crystal deformations, due to either in-
trinsic thermal fluctuations or interactions
with the substrate, largely contribute to
electron scattering11and any attendant de-
crease in conductivity and carrier
mobility.12?14In addition, corrugations and
defects are expected to affect the chemical
raphene, a single monolayer of car-
bon atoms arranged in a honey-
comb lattice, is attracting excep-
properties of graphene. Theoretical studies
show that surface defects and bonding ir-
regularities can lower reaction barriers.15Ex-
trinsic ripples and curvature can, in fact,
produce structure distortions showing do-
mains of lower than hexagonal symmetry.16
Such domains can exhibit admixture of sp2
and sp3C orbital character and ? orbital
misalignment, which in carbon nanotubes
are known to lead to increased reactivity.17
Thus, techniques which lead to the control
of topographic or morphological defects
can play an important role in improving the
properties of graphene for applications.
For instance, ultrahigh electron mobility
was recently achieved in suspended
graphene18and attributed to the concur-
rent effects of reduced contamination, the
absence of interaction with the substrate,
and the decreased surface corrugation.
Considerable experimental and theoreti-
cal effort has recently been dedicated to is-
sues related to the morphology of
*Address correspondence to
andrea.locatelli@elettra.trieste.it,
osgood@columbia.edu,
morgante@tasc.infm.it.
Received for review May 20, 2010
and accepted July 20, 2010.
Published online August 3, 2010.
10.1021/nn101116n
© 2010 American Chemical Society
ABSTRACT Low-energyelectronmicroscopyandmicroprobediffractionareusedtoimageandcharacterize
corrugationinSiO2-supportedandsuspendedexfoliatedgrapheneatnanometerlengthscales.Diffractionline-
shapeanalysisrevealsquantitativedifferencesinsurfaceroughnessonlengthscalesbelow20nmwhichdepend
onfilmthicknessandinteractionwiththesubstrate.Corrugationdecreaseswithincreasingfilmthickness,
reflectingtheincreasedstiffnessofmultilayerfilms.Specifically,single-layergrapheneshowsamarkedlylarger
short-rangeroughnessthanmultilayergraphene.Duetotheabsenceofinteractionswiththesubstrate,
suspendedgraphenedisplaysasmoothermorphologyandtexturethansupportedgraphene.Aspecificfeature
ofsuspendedsingle-layerfilmsisthedependenceofcorrugationonbothadsorbateloadandtemperature,which
ismanifestedbyvariationsinthediffractionlineshape.Theeffectsofbothintrinsicandextrinsiccorrugation
factorsarediscussed.
KEYWORDS: graphene · exfoliated graphene · corrugation · roughness ·
morphology · ?-LEED · LEEM
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single-layer graphene, addressing in particular the ori-
gin of any intrinsic corrugation and its relationship to
crystal stability. In one of the earliest of such experi-
ments, transmission electron microscopy revealed that
both single- and double-layer suspended graphene dis-
play perfect crystalline structure in the short-range but
are intrinsically corrugated in the long-range, with de-
formations in the out-of-plane direction extending to a
distance of 1 nm and a surface normal variation of 5°.19
A recent experimental investigation has shown that
long-wavelength ripples in graphene can be controlled
by inducing mechanical or thermal strain.20However,
it is believed that at finite temperature, even in the ab-
sence of applied strain, ripples at small wavelengths are
present in graphene sheets. In fact, buckling in the di-
rection normal to the lattice plane has been invoked to
explain the stability of 2D crystals, as it serves to effi-
ciently suppress long-wavelength phonons,21?23which
would otherwise cause lattice melting at any finite tem-
perature, as demonstrated by the pioneering work of
Peierls,24Landau,25and later by Mermin.26Recent theo-
retical studies confirm that the intrinsic corrugation in
suspended graphene originates from thermal fluctua-
tions and has a well-defined dependence on
temperature.27,28At sufficiently small length scales,
such corrugation is well described by the theory of flex-
ible membranes in the harmonic approximation. At a
critical wavelength, estimated to be 20 nm, anharmonic
corrections, which couple the bending and stretching
modes, become dominant and prevent the membrane
from crumpling.27
By contrast, corrugations measured in supported
graphene are expected to be extrinsic in origin, arising
from the interaction of graphene with the substrate. In
particular, scanning probe experiments have shown
corrugation wavelengths for supported graphene that
are in the range of 10?30 nm.16,29?31Analyses of the
height?height correlation functions in such measure-
ments indicate that graphene has a lower roughness
than the SiO2support;16this arises because the ener-
getic cost of elastic lattice deformation prevents the
graphene film from conforming exactly to the substrate
topography. In one study of supported graphene us-
ing STM, corrugation was reported with a preferential
wavelength of 15 nm and attributed to an intrinsic ef-
fect31since it was not observed on the supporting
substrate.
Despite these important advances, further insight
into the corrugation of suspended graphene requires
measurements at both microscopic and mesoscopic
length scales, that is, at length scales from interatomic
distances to several hundred nanometers; this large
range of length scales has not been examined exten-
sively in previous suspended graphene experiments.
STM measurements have provided valuable insights on
supported graphene from the microscopic scale up to
?100 nm. However, since STM probing is accompanied
by atomic forces due to tip?sample interaction, this
technique cannot be easily extended to suspended
graphene. Thus, a noninvasive approach is required.
In this paper, we describe such an investigation of
the corrugation in both freely suspended and SiO2-
supported exfoliated graphene layers. Our approach
takes full advantage of the multiple techniques offered
by a low-energy electron microscope (LEEM)32,33to ob-
tain a full characterization of the corrugation features in
graphene. LEEM allows direct, real-space imaging of
the sample morphology over large surface areas (up to
several tens of micrometer), with lateral resolution of 10
nm and high structure sensitivity. In addition, this tech-
nique enables microprobe low-energy electron diffrac-
tion (?-LEED) measurements that are restricted to a sur-
face area of only a few square micrometers, thus
providing access to the reciprocal space. Most impor-
tantly ?-LEED is sensitive to crystal deformations on
length scales from ?20 nm down to interatomic dis-
tances, thus complementing the real-space images by
providing additional information about corrugation at
very short length scales. By combining these two elec-
tron microprobes, we are able to access both the micro-
scopic and mesoscopic regimes and thus the crossover
length scale of both intrinsic and extrinsic corrugation.
RESULTS AND DISCUSSION
ImagingofGrapheneFilmThickness.Animportantaspect
of our experiments is the ability to measure, in situ, the
thickness of each graphene sample. Specifically, LEEM
can be used to determine precisely the number of lay-
ers in thin films by analyzing the modulation in the elec-
tron reflectivity between consecutive Bragg peaks at
very low electron energy. Such intensity modulation,
generally referred to as quantum-size contrast,34,35
arises due to the quantized energy levels in the film
and the formation of quantum-well resonances (QWRs).
In the so-called phase accumulation model,36QWRs
are described by the Bohr?Sommerfeld quantization
rule, which sets the condition for a resonance by the ex-
istence of constructive interference between electron
waves scattered at the film interface and at the surface:
Here, the scalar k(E) is the perpendicular wave vector
of an electron in the film, E its energy (relative to the
Fermi level), t is the interlayer distance, m is the film
thickness (in monolayers), ?surf(E) and ?if(E) are the
energy-dependent phase shifts for reflection of elec-
trons at the surface and at the interface, respectively,
and n is an integer. In the case of suspended graphene,
?if(E) ? ?surf(E), the phase shift for reflection at the
vacuum interface. The same condition can be assumed
to hold in the case of SiO2-supported graphene, as the
graphene film is known to be (partially) suspended on
the substrate.31
2k(E)mt + Φsurf(E) + Φif(E) ) 2πn(1)
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The one-dimensional phase condition described by
eq 1 is analogous to that for a resonance in a
Fabry?Perot cavity and explains why the LEEM micro-
scope can be effectively used as an electron interferom-
eter for probing the thickness of ultrathin films.37Equa-
tion 1 can be inverted to determine the existence
condition for QWRs.35,38In this way, one obtains a for-
mula for the film thickness m, at which QWRs occur as
a function of the allowed wave vectors k(E), and the
quantum number, ?:
QWRs (and thus maxima in electron reflectivity) are
found for ? ? m ? n, with 1 ? ? ? m. Minima in reflec-
tivity are found for ? ? m ? n ? 1/2. It has been shown
that m ? 1 quantum interference peaks, and thus m ?
1 maxima and m minima in the electron reflectivity, are
produced by a film thickness of m layers.34,38
Figure 1 (top panel) shows a LEEM image of an area
composed of graphene layers of different thicknesses
on a SiO2substrate, each with a different gray scale in-
tensity. Characteristic LEEM IV spectra (obtained in
bright-field mode, i.e., using the specular beam) from
similar regions with graphene sheets ranging in thick-
ness from 1 to 6 ML are shown in the middle panel of
the figure. Solid and open circles in the bottom of Fig-
ure 1 indicate the electron energies at which maxima
(minima) in electron reflectivity are observed, respec-
tively. As can be seen, the predictions of the phase ac-
cumulation model obtained using eq 2, represented by
continuous (dashed) curves in the figure, match the ex-
perimental data closely. Details of the calculations are
given in the Methods section.
The intensity modulations in the IV spectra of exfoli-
ated multilayer graphene samples closely resemble the
previously reported spectra of epitaxial graphene on
SiC.39,40The single-layer LEEM IV spectrum of SiO2-
supported graphene (dashed curve in Figure 1, middle)
is instead completely featureless. The identification of
this featureless spectrum with single-layer graphene is
confirmed by LEED measurements, which show a clear
6-fold symmetry, in contrast to the 3-fold symmetry ob-
served for multilayer samples. As expected, no Bragg
peaks were observed in the LEED IV spectrum of single-
layer graphene. In fact, no such peaks can be seen for
suspended or SiO2-supported single-layer graphene, as
the Bragg condition originates from constructive inter-
ference between waves scattered at different crystal
planes.
LEEMImagingofGrapheneCorrugation.Duetoitshighlat-
eral resolution and thickness sensitivity, LEEM provides
access to the local morphology of suspended and sup-
ported graphene samples. Figure 2 shows LEEM images
of a large multi-thickness graphene flake on the SiO2
substrate, into which micrometer-sized cylindrical cavi-
ties have been etched, as described in the Methods sec-
tion. The disks correspond to the suspended portions
of the film. The variation in the local thickness of the
film (indicated by labels in Figure 2A) becomes evident
at an electron kinetic energy of 4.2 eV, due to the
quantum-size contrast. In all samples under study and
for all thicknesses examined, the suspended portions of
our samples appeared brighter in LEEM than those sup-
ported on SiO2. This is consistent with the reduced in-
tensity and broader width of the zero-order diffraction
IV curves recorded on all SiO2-supported samples (see
Figure 2). This type of contrast arises due to surface cor-
rugation because the finite angular acceptance of the
microscope rejects e-beam reflections from surface
planes tilted beyond the cutoff angle as determined
by a contrast aperture.41Thus, a surface that scatters
the e-beam over a wide range of off-normal angles will
appear darker than a flat one, aligned normal to the
beam. We note that this effect occurs even if the wave-
length of the corrugation is below the lateral resolu-
tion of the microscope.
Figure 1. (Top) LEEM image of a multi-thickness graphene
sheet supported on SiO2: the local thickness is indicated by
the labels; (middle) LEEM IV spectra of supported graphene
films of differing thicknesses. The spectra demonstrate large
variations in the electron reflectivity as a function of the
electron kinetic energy (start voltage). The intensity modula-
tions observed in multilayer samples (continuous lines) are
induced by electron confinement. The curves have been off-
set for clarity. (Bottom) Solid (open) circles identify the elec-
tron kinetic energies and film thicknesses at which maxima
(minima) in electron reflectivity are observed. The continu-
ous (dashed) lines represent the predictions for such
maxima (minima), obtained using eq 2 for different quan-
tum numbers ?, with the film thickness treated as a continu-
ous variable.
m(E,ν) )
[Φsurf(E) + Φif(E)]/2π + ν
1 - k(E)t/π
(2)
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LEEM images at higher magnification show clearly
the origin of the contrast difference observed between
suspended and supported regions. High lateral resolu-
tion images of single, double, and trilayer graphene are
shown in Figure 3A?C. The higher reflectivity of the
single-layer suspended disk (A) is due to the presence
of large flat regions normal to the e-beam (appearing
bright in the figure), which in some cases extend up to
lengths of about 50 nm. These bright areas are fewer
and smaller on the supported part of the film but be-
come larger on thicker samples. We observe that the
patterns in Figure 3 change when tilting the e-beam il-
lumination, which causes different surface planes to be-
come visible. This behavior confirms that the contrast
observed in LEEM arises from variations in the local sur-
face normal of a static smooth surface. It can be ar-
gued that the more pronounced corrugation observed
in supported regions might be induced by the interac-
tion with the substrate16,29?31and therefore is extrinsic
in origin. Adsorbates are another possible source of cor-
rugation. It is, in fact, known that even small quantities
of impurities can determine crystal deformation, as has
been pointed out in a recent STEM study.42
Although LEEM cannot provide absolute height in-
formation, the LEEM images in Figure 3 can be used to
estimate the horizontal correlation length. The bright
regions correspond to clean flat areas, where local
height variations are small and correlated (we note
that different bright regions may have different
heights). Thus, the horizontal correlation length ? (i.e.,
the distance beyond which height fluctuations are no
longer correlated) corresponds to the average size and
distribution of these bright regions. We have computed
? by measuring the full width at half-maximum of the
autocorrelation function central peak from intensity
profiles taken across the LEEM images (see the lower
part of Figure 3). In this way, we find values of 24 ? 0.3
and 30 ? 0.3 nm for single-layer supported and sus-
pended graphene, respectively, which increase to ?36
nm for both supported and suspended bilayer
graphene. Our value of 24 nm for supported single-
layer graphene compares favorably to previously re-
ported correlation lengths measured by STM on SiO2-
supported graphene, which vary in the range of 10 to
about 30 nm.16,29,31The weak oscillations observed in
the autocorrelation function of single-layer suspended
regions (see Figure 3) reveal a preferential ripple wave-
length of several tens of nanometers (?60 nm), which
points to the mounded nature of the suspended
graphene surface.
Finally, we note that the high lateral resolution LEEM
images in Figure 3A?C clearly show that the disk edges
appear rough. This roughness, which is due to the im-
perfectedgedefinitionoftheetchedwell,indicatesthat
graphene has the flexibility to conform to edge sur-
face features at the 10 nm scale. In addition, a close ex-
amination of the images also reveals the presence of
darker lines (resembling veins) extending across the
graphenethroughoutthesupportedandsuspendedre-
Figure 2. (A) LEEM image at 4.2 eV of suspended disks and SiO2-
supported graphene (disk diameter is 5 ?m). The local thickness, in units
of graphitic layers (indicated by labels), was determined by measuring
theelectronreflectivitycurvesintheenergyintervalof1to8eV;(B)LEEM
imageofthesameregionatelectronkineticenergyof38eV;(C)LEEMim-
age of the suspended portion of the single-layer region at electron ki-
netic energy of 10 eV. (Bottom) Zero-order diffraction LEED IV curves of
SiO2-supported and suspended trilayer graphene.
Figure 3. (A?C) LEEM images at 10 eV illustrating the morphology of
suspended and SiO2-supported graphene: (A) single layer, (B) bilayer,
and (C) trilayer suspended graphene disks and surrounding supported
areas. (Bottom) Intensity autocorrelation function curves of the SiO2-
supported (dashed line) and suspended regions shown in (A).
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gions. As can be seen by comparing Figure 2A,B, these
are not steps separating regions of different thickness.
The origin of these features could be short wavelength
wrinkles in the graphene membrane, in accord with
similar observations reported in a recent STEM study.42
LEED Measurements of Surface Corrugation. Due to the in-
trinsic sensitivity of the line shape of diffracted elec-
tron beams to local height variations, microprobe low-
energy electron diffraction (?-LEED) was used to probe
the roughness of SiO2-supported and suspended re-
gions of uniform thickness. In particular, ?-LEED meas-
urements allowed us to access lattice distortions at
length scales below the horizontal correlation length
(few tens of nanometers in single- and double-layer
graphene), thus complementing the LEEM data pre-
sented in the previous section.
The most prominent feature that was observed in
all graphene samples was the broadening of the diffrac-
tion profile with increasing perpendicular electron mo-
mentum transfer. Figure 4 shows profiles of the central
diffraction beam of single-layer suspended graphene
at multiple kinetic energies, together with best fits ob-
tained using a multidimensional Lorentzian. This line
shape provides an excellent approximation to the ex-
pected diffraction line shape for rough surfaces (see the
Supporting Information provided). The fit function was
convolved with a Gaussian in order to take into account
the response function of the instrument, which has a
transfer width of 10 nm. This width is constant within
the energy range of pertinence to this study.
Figure 5 shows the variation of the half width at half-
maximum (hwhm) of the (00) diffraction beam as a
function of increasing perpendicular momentum trans-
fer of the probe electrons, k?? (kin? kout)n ˆ ? 2|kin|,
for SiO2-supported and suspended graphene (left and
right panels in the figure, respectively). Each data point
in the figure was obtained by fitting the (00) diffrac-
tion beam with a multidimensional Lorentzian line pro-
file, as shown in Figure 4. As can be seen, film thick-
ness and the presence of a supporting substrate have
a significant influence on the evolution of peak broad-
ening. We observe that peak broadening is always less
pronounced in suspended than in supported samples.
For example, suspended bilayer graphene films show
such narrow diffraction peaks that their widths are com-
parable to those of thick supported graphite films.
The broadening of the central diffraction peak with
increasing k?is not observed on thick graphite films
on SiO2(which are expected to be atomically flat) that
have undergone the same preparation and cleaning
procedure as that used for graphene (see the curve la-
beled TG in Figure 5). For all graphite flakes, the hwhm
was less than 0.05 Å?1, and nearly independent of k?.
This value is considerably smaller than that measured
on SiO2-supported and suspended single-layer
graphene (?0.45 Å?1at k??8 Å?1).
Figure 4. Profile across the (00) diffraction beam of
single-layer suspended graphene at multiple electron en-
ergies. Multidimensional Lorentzian fits are shown as
solid lines. See text for details. The curves have been off-
set for clarity.
Figure 5. Variation of the (00) diffraction beam hwhm (circles) for different
graphene films as a function of the electron momentum transfer k?, meas-
ured at room temperature. The dashed vertical lines indicate resonances cor-
respondingtoout-of-phasediffractionconditionsinmultilayers.Thecontinu-
ous lines represent best fits using eq 3. The hwhm curves for SiO2-supported
and suspended graphene are shown in the left and right panels, respectively.
The film thickness is indicated by the numeric labels; TG refers to thick graph-
ite film on SiO2.
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