Atomic-scale observation of rotational misorientation in suspended few-layer graphene sheets

ISSN 2040-3364

2040-3364(2010)2:5;1-P

COVER ARTICLESingh et al.Atomic-scale observation of rotational misorientation in suspended few-layer graphene sheets

REVIEW ARTICLERiceNanoscale optical imaging by atomic force infrared microscopy

www.rsc.org/nanoscale Volume 2 | Number 5 | May 2010 | Pages 625–812

PAPER www.rsc.org/nanoscale | Nanoscale

Atomic-scale observation of rotational misorientation in suspendedfew-layer graphene sheets

Manoj K. Singh,*a Elby Titus,a Gil Goncalves,a Paula A. A. P. Marques,a Igor Bdikin,a Andrei L. Kholkinb

and Jos�e J. A. Gracioa

Received (in Z€urich, Switzerland) 11th September 2009, Accepted 12th November 2009

First published as an Advance Article on the web 7th January 2010

DOI: 10.1039/b9nr00256a

Single or few-layer graphene (FLG) sheets offer extraordinary electronic, thermal and mechanical

properties and are expected to find a variety of applications. Fully exploiting the properties of graphene

will require a method for the production of high-quality graphene sheets (almost pristine graphene) in

large quantities. In this regard, we report a two-step method for obtaining a homogenous colloidal

suspension of single or FLG sheets up to 0.15 mg ml�1 in N,N-dimethylformamide solution. The

graphene nanostructures are directly imaged using a high-resolution transmission electron microscope

(HRTEM) operated at 200 kV with a point resolution of 0.16 nm. We observed rotational

misorientation within the flake in the HRTEM images of 2, 4 and 6 layers of graphene sheets, giving rise

to Moir�e patterns. By filtering in the frequency domain using a Fourier transform, we reconstruct the

graphene lattice of each sheet and determine the relative rotation between consecutive graphene layers

up, to six separate sheets. Direct evidence is obtained for FLG sheets with packing that is different to

the standard AB Bernal packing of bulk graphite. Furthermore, we observed periodic ripples in

suspended graphene sheets in our TEM measurements. Electrostatic force microscopy was used to

characterize the electric potential distribution on the surface of FLG sheets on SiO2/Si substrates in

ambient conditions. The FLG sheets were found to exhibit a conducting nature with small potential

variations on the surface.

Introduction

Graphene, a two-dimensional carbon material, which takes the

form of a planar honeycomb lattice of sp2-bonded carbon atoms

has stimulated a vast amount of research interest in recent

years.1–7 Single or few-layer graphene (FLG) sheets have

attracted an enormous amount of interest in the last five years

because of their excellent mechanical, thermal and electronic

properties.8–12 However, the electrical properties of graphene

vary between single and FLG sheets.13–16 Therefore the method

of preparation of graphene is highly crucial to control the gra-

phene layers. In addition, the in-depth structural analysis of

graphene sheets is highly desirable in order to exploit this

material for future development of graphene-based nano-

electronic devices.17–19

Single-layer graphene was first isolated using the scotch-tape

method in 2004.20 This method also produces samples composed

of two or more atomic layers of graphene. However, this process

has significant disadvantages in terms of yield and throughput.

Fully exploiting the properties of graphene will require a method

for the production of high-quality graphene sheets (almost

pristine graphene) in large quantities. Two main routes are

possible: (i) large-scale growth, and (ii) large-scale exfoliation.

In the continuation of second approach, we are presenting

aCenter for Mechanical Technology & Automation, University of Aveiro,3810-193 Aveiro, Portugal. E-mail: [email protected]; Fax:+351234370953; Tel: +351234370830bDepartment of Ceramics and Glass Engineering & CICECO, University ofAveiro, 3810-193 Aveiro, Portugal

700 | Nanoscale, 2010, 2, 700–708

a two-step method for a homogenous colloidal suspension of

single or FLG sheets up to 0.15 mg ml�1 in N,N-dime-

thylformamide (DMF) solution.

The two-step approach includes; (i) high temperature

(�2000 �C) heat treatment of commercially available pyrolytic

graphite powders in a vacuum (<1 � 10�5 Torr) for 3 h (this heat

treatment may reduce contamination) followed by (ii) sonication

for 2 h by dissolving the heat-treated graphite in DMF using

a probe-tip sonicator. Furthermore, the pyrolytic graphite is

composed of a periodical stack of two-dimensional (2D) gra-

phene sheets (layers) along the c-axis. Each of these layers is

weakly bonded to its neighbouring layers by interlayer interac-

tion forces; the graphene layers can easily slide against each other

and peel off easily. As a result of the heat treatment of pyrolytic

graphite at high temperature under vacuum, the interactions

between graphene layers may soften, thus making their liquid-

phase exfoliation with DMF easier.21

Our approach provides single or FLG sheets (2–6 layers)

dispersed in DMF solution. The percentage of single-layer gra-

phene is low in comparison to FLG sheets (2–6 layers). More-

over, DMF is well documented for its high synthetic value, high

polarity and wide solubility range for both organic and inorganic

compounds, including single and multi-walled carbon nano-

tubes.22,23 Very recently, Liao et al.24 also proved that probe-tip

sonication is more powerful for the dispersion of carbon nano-

tubes in epoxy resin nanocomposites than bath sonication. This

might be the reason for achieving a relatively higher graphene

concentration in DMF solution compared to other reported

results.25–27 The homogenous colloidal suspension of graphene in

This journal is ª The Royal Society of Chemistry 2010

Scheme 1 Overview of the steps for the preparation of exfoliated single

or few-layer graphene sheets in N,N-dimethylformamide (DMF)

solution. The procedure started with pyrolytic graphite and was followed

by heat treatment at a very high temperature in vacuum, and probe-tip

sonication.

DMF could be a promising candidate for potential applications

such as energy-storage materials, polymer composites, liquid

crystal devices and photovoltaic applications.19,28–32

In our exfoliated samples, we observed a significant number of

rotational stacking faults with various rotation angles in two-

layer, four-layer and six-layer graphene sheets. The introduction

of rotational stacking faults in AB Bernal stacked graphene

bilayers changes the dispersion relationship close to the k-point

from parabolic (AB) to linear band behaviour (rotation disorder)

and leads to some monolayer graphene properties being observed

in two-layer and FLG films.13–16 Generally, atomic force

microscopy (AFM), optical imaging and Raman spectroscopy

are regularly used to determine the number of graphene layers

within graphene sheets.20,33,34 However, these techniques provide

only indirect proof of single or FLG sheets and also they cannot

determine the presence of rotational stacking faults within these

FLG structures. In addition, scanning tunnelling microscopy

(STM) is effective to produce atomically detailed images of

surfaces of graphite and graphene, along with rotational stacking

faults that give rise to superstructure in the STM images.35 The

superstructure attributed to Moir�e patterns35–37 is derived from

complex three-dimensional tunnelling.37 However, STM

measurements are experimentally challenging under ultrahigh

vacuum (UHV) conditions making the turnaround time for

characterization relatively long.38–41 On the other hand, trans-

mission electron microscopy (TEM) offers a faster approach for

direct imaging the atomic structure of rotational misorientation

in FLG sheets, which gives rise to Moir�e patterns.42 Here in our

experiment, we used a conventional high-resolution TEM (JEOL

2200F TEM/STEM) operated at 200 kV with a point resolution

of 0.16 nm, equipped with a GIF-2000 spectrometer. The elec-

tron beam was focused onto a monoatomic layer of graphene to

observe the ball-and-stick model of an atomic lattice structure. In

the structure, the bright contrast corresponds to atoms and dark

contrast to the gaps between them.43 In addition, we used elec-

trostatic force microscopy (EFM)44 to characterize the electrical

potential distribution on the surface of FLG sheets on SiO2/Si

substrates and proved that FLG sheets on SiO2/Si substrates

exhibit a conducting nature with small potential variations on the

surface.

Experimental section

Synthesis of high-quality single or few layer graphene sheets

Commercial available pyrolytic graphite powders (carbon

content >99 wt%, Sigma-Aldrich, 2 g) were heated to �2000 �C

for 3 h in a vacuum (<1 � 10�5 Torr) after being ground by

a pestle in a mortar. After heat treatment the graphite powders

were ground again and then dispersed in DMF (99.9 vol%,

500 ml) by using a probe-tip sonicator (Sonics Model VC 130,

20 kHz, probe tip (6 mm diameter), amplitude 80%, 2.2 kW) for

2 h. The resulting (4 mg ml�1, 100 ml) solution was treated in an

ultrasonic cleaner (KQ-100, frequency 40 kHz, output power

100 W) for 10 min, followed by high-speed centrifugation

(5000 rpm, 30 min) to remove big particles. The resultant

supernatant solution (gray colour) consisted of a homogenous

colloidal solution of graphene (0.15 mg ml�1) in DMF solution

(see Scheme 1).


Surface characterization

The surface morphology of exfoliated graphene samples was

examined by field-emission scanning electron microscopy

(Hitachi S-800, and SU-70, 30 keV) and optical microscopy

(Nikon Eclipse LV150 microscope), respectively. Moreover, the

sample topography and thickness measurement of exfoliated

graphene samples were performed by a commercial setup

Multimode, NanoScope IIIA, DI atomic force microscope

(AFM) in tapping mode. Micro-Raman spectra of the graphene

samples were obtained at room temperature using a Renishaw

spectrometer at 514 nm, with a notch filter cutting at �100 cm�1.

A 100� objective was used. Extreme care was taken to avoid

sample damage or laser-induced heating. The incident power

during the measurements was �0.04 mW.

Transmission electron microscopy and electron energy-loss

spectroscopy

A conventional high-resolution (HR) TEM (JEOL 2200F TEM/

STEM) was operated at 200 kV with a point resolution of

0.16 nm, equipped with a GIF-2000 spectrometer. Electron

energy-loss spectroscopy (EELS) experiments were carried out in

diffraction mode using a convergence semi-angle of 0.9 mrad,

a collection semi-angle of 1.8 mrad, a nominal spot size of

0.5 nm, an energy dispersion of 0.3 eV per pixel and an energy

resolution of approximately 1.2 eV.

Electrostatic force microscopy (EFM) measurements

A commercial setup Multimode, NanoScope IIIA, DI AFM with

a conductive tip was used to record the sample topography and

EFM phase. We used silicon cantilevers (NSG11) with a Pt

conductive coating. The tip was set to vibrate with a piezo having

a resonant frequency of 150.09 kHz and an amplitude of 30 nm.

Nanoscale, 2010, 2, 700–708 | 701

Fig. 2 (a) Optical microscopy images of single-layer, two-layer, four-

Results and discussion

The single or FLG sheets were synthesized by the procedure

outlined in Scheme 1. The procedure started with pyrolytic

graphite powder followed by heat treatment at very

high temperature in vacuum, and probe-tip sonication. The

as-synthesized products were initially observed with SEM,

optical microscopy, AFM and micro-Raman spectroscopy.

Fig. 1(a) shows an SEM image of an as-produced folded

graphene sheet (a paper-like structure) on a Si substrate.

Furthermore, we performed systematic optical microscopy

imaging of single or FLG samples on 300 nm SiO2/Si substrates

[see Fig. 1(b)–(d)]. These layers have a slightly different colour in

the optical microscope [Fig. 1(b)–(d), and Fig. 2(a)]. It appears

that the darker colour corresponds to thicker layers. A quick and

accurate method for determining the number of layers of gra-

phene sheets is required to accelerate research and exploitation of

graphene. In this direction, AFM measurement is the most direct

way to identify the number of layers of graphene sheets. Figs.

1(e)–(g) reveals AFM images of our exfoliated graphene sheets

Fig. 1 Microstructural analyses of graphene sheet. (a) SEM image of

exfoliated graphene sheet (with a paper-like morphology). (b)–(d) Optical

microscopy images of single or FLG sheet samples on 300 nm SiO2/Si

substrates which clearly show the single-layer, two-layer, and more than

four-layer graphene sheets, respectively. These layers have a slightly

different colour in the optical microscope. It appears that the darker

colour corresponds to thicker layers. (e)–(g) AFM images of graphene

sheets in tapping mode. (f) and (g) show 2–3 layer and four-layer gra-

phene sheets, respectively. The insets show the corresponding height

profiles. The overlapping of misoriented graphene sheets is clearly

indicated by a black dotted arrow in (g).

layer and six-layer graphene sheets on 300 nm SiO2/Si substrates. (b)–(e)

shows corresponding Raman spectra recorded from single-layer (black

dotted circle), two-layer (red dotted circle), four-layer (blue dotted circle),

and six-layer (green dotted circle), sheets respectively.

702 | Nanoscale, 2010, 2, 700–708

in tapping mode. Figs. 1(f) and (g) show 2–3 layer and 4-layer

graphene sheets, respectively. The insets shows the height

profiles. We also clearly observed the overlapping of graphene

sheets in the AFM images [indicated by a black dotted arrow in

Fig. 1(g)]. However, this technique has a very slow throughput,

and also an instrumental offset of �0.5 nm (caused by different

interaction forces) always exists, which is even larger than the

thickness of a graphene monolayer and data fitting is required to

extract the true thickness of the graphene sheets.45,46

Recently, Raman spectroscopy has been shown to be

a potential candidate for the non-destructive and quick charac-

terization of the number of layers of graphene. The shape of the

second-order band 2D is a characteristic that can be used to

distinguish the number of layers of AB-stacked graphene.47,48 We

performed Raman spectroscopy on single-layer (black dotted

circle), two-layer (red dotted circle), four-layer (blue dotted

circle), and six-layer (green dotted circle) graphene sample on

300 nm SiO2/Si substrates [see Fig. 2(a)]. Fig. 2(b)–(e), shows the

2D-band spectra of a single-layer (�2670 cm�1), and few-layer

(2, 4 and 6 layers) graphene samples, respectively. It can be seen

in Fig. 2(b)–(e), that the 2D-band becomes broader and blue-

shifted when the graphene thickness increases from single-layer

to FLG sheets. The Raman spectra of single or FLG sheets have

been well documented and discussed by many authors.49–52

Recently, Poncharal et al.53 compared Raman scattering spectra

from single-layer graphene with a bilayer in which the two layers

are arbitrarily misoriented. Ni et al.54 also discussed the elec-

tronic structures of 1 + 1 layer folded graphene sheets, which are

different from AB (Bernal) stacking. However, this technique

cannot determine the presence of rotational stacking faults or

rotation angles with in the FLG sheets or more complex struc-

tures. Therefore, we relied on atomically resolved high-resolution

TEM for in-depth study.55,56


Fig. 4 (a) Bright-field TEM image taken from a set of four graphene

layers [indicated by a red box in Fig. 3(b)]; the inset shows FFT taken

from the region indicated by a red box in (a). (b) HRTEM image of

(a) (indicated by red box region) showing a Moir�e pattern.

Detailed high-resolution TEM studies were performed on

individual or few-layer freely suspended graphene sheets. For

this experiment, the TEM samples were prepared by dipping

a carbon-coated TEM grid into the (graphene/DMF) solution

and allowing it to dry. Fig. 3(a) shows a bright-field TEM image

of graphene crystallites attached to a TEM grid. The suspended

graphene membranes consist of single-layer or FLG sheets. The

two-layered graphene is clearly visible and it is marked by red

square in Fig. 3(a). We also observed folded regions in the FLG

sheets, which give rise to Moir�e patterns from rotational stacking

faults [see the blue box in Fig. 3(b)]. Fig. 3(b) depicts a highly

magnified image of the green-square region of the Fig. 3(a).

Fig. 3(b) describes single-layer, two-layer and four-layer gra-

phene sheets, respectively. A 2D fast Fourier transform (FFT)

was performed in the region indicated by a white box in Fig. 3(b).

The FFT of a single hexagonal graphene network produces six

spots of 0.21 � 0.05 nm spacing which corresponds to a single

layer. Fig. 3(c) exhibits an HRTEM image of single-layer gra-

phene, which was acquired from the region indicated with red

dotted arrow. Fig. 3(d) shows the image reconstructed by

filtering in the frequency domain to remove unwanted noise. The

hexagonal graphene network is clearly resolved in the inset of

Fig. 3(d), showing the magnification of the small region indicated

with a green box. The C–C bond length is measured to be 1.4 �A�0.2 �A and the measured lattice constant is 2.5 �A � 0.2 �A, con-

firming that this is a single layer. However, in our graphene

sample we did not observed single or di-vacancy defects as

reported by previous methods.43,57 In addition, it is also quite

interesting to observe four graphene layers which are lying one

on top of another in the same TEM image, indicated by a red box

[Fig. 3(b)]. This is also further confirmed by FFT performed in

the region indicated with a red box in Fig. 4(a). This allows a set

Fig. 3 HRTEM images of a freely suspended graphene membrane.

(a) Bright-field TEM image of a suspended graphene membrane.

(b) Magnified view of the region denoted by a green box in (a); the inset

shows 2D FFT performed in the region indicated with a white box.

(c) HRTEM image of single-layer graphene acquired from the region

indicated with a red dotted arrow in (b). (d) Reconstructed image after

filtering in the frequency domain to remove unwanted noise, for clarity.

The inset shows the hexagonal graphene network.


of spots to be associated with each different orientation of the

graphene sheets within the layer. The FFT shows 24 spots which

resemble four different graphene layers. The HRTEM image of

the red box region shows Moir�e patterns [see Fig. 4(b)].

We found approximately 40–50% of the FLG sheets contain

regions with observable Moir�e patterns in the HRTEM images

arising from rotational stacking faults. These rotational faults

are most likely related to the back-folding of top graphene layers

during the exfoliation (as we observed in Fig. 3(b) indicated by

white dotted arrow). Intrinsic rotational stacking faults within

the graphite structure may also contribute to the number of

stacking disorders. In this work, we discuss in detail the simplest

Moir�e pattern (generated by only one rotational stacking fault)

and a complex Moir�e pattern (which consists of at least six

graphene layers), respectively.

A two-layer graphene sheet (two graphene layers separated by

0.40 � 0.02 nm) is clearly observed in Fig. 5(a) (indicated by

a blue box), which shows a TEM image of a FLG sheet con-

taining a top layer that has folded back and it is indicated by

a white dotted arrow in Fig. 3(b). Fig. 5(b) is a bright-field TEM

image of the region indicated with a red box in Fig. 5(a). A FFT

of Fig. 5(a) is included in the inset and shows two sets of hexa-

gons with a 7� rotation between them. Fig. 5(c) shows the image

reconstructed by filtering in the frequency domain to remove

unwanted noise. Fig. 5(d) clearly shows an HRTEM image of the

Moir�e pattern for the 7� rotational stacking fault presented in

Fig. 5(c). Figs. 5(e) and 5(f) show the reconstructed image of the

front and back graphene layers after filtering in the frequency

domain to remove unwanted noise.

We have also used electron energy-loss spectroscopy (EELS)

to analyse our FLG exfoliated sample. The single-layer or FLG

sheets exhibit unique behaviour in their EELS spectra.58 The low-

loss EELS spectrum of graphitic structures is dominated by

plasmon excitations consisting of p- and p + s-plasmons, both

exhibiting bulk and surface modes. The shape of the low-loss

EELS spectrum for graphitic structures is highly dependent on

the angle at which the incident beam hits the structure. Carbon

nanotubes are an excellent example of this, as demonstrated both

theoretically and experimentally.59,60 Interestingly, we have also

observed EELS spectra [taken in the region indicated with

a black box in Fig. 6(a)] from a freely suspended graphene sheet,

which is shown in the inset. Fig. 6(a) is more magnified view of

the region indicated by white box in Fig. 3(a). The plasmon

spectra shows that the p-mode, at 7 eV in graphite, has shifted to

Nanoscale, 2010, 2, 700–708 | 703

Fig. 5 HRTEM images of a two-layer graphene sheet. (a) Bright-field

TEM image of a two-layer graphene sheet. Two graphene layers sepa-

rated by 0.34 � 0.02 nm are clearly observed in the blue box. (b) TEM

image of the region indicated with a red box in (a). The inset shows the

FFT of the region indicated with a red box in (a), which shows two sets of

hexagons with a 7� rotation between them. (c) FFT image corresponds to

(b), for clarity. (d) HRTEM image of the Moir�e pattern for the

7� rotational stacking fault presented in (c). (e)–(f) are the reconstructed

images of the front and back graphene layers after filtering in the

frequency domain to remove unwanted noise.

Fig. 6 (a) HRTEM image of the edge of a FLG sheet with at least six

layers. The inset shows the EELS spectra acquired from the black-box

region. (b) High-magnification bright-field TEM image of the black-box

region (c) HRTEM image of the blue-box region, showing a clear Moir�e

pattern. (d) FFT of panel (b) (blue-box region) showing six sets of hexag-

onal spots corresponding to six different graphene layer orientations.
4.98 eV. Furthermore, the spectrum also exhibits a p + s-surface
mode at 23 eV, which is very near to the 26 eV seen in graphite.61

We expect that there are at least six layers of graphene in that

area. However, we further confirm this by HRTEM imaging

[the Moir�e pattern shown in Fig. 6(b) and (c)] taken from the

same area. Fig. 6(b) depicts a bright-field TEM image of the

black box region indicated in Fig. 6(a). Fig. 6(c) shows an

HRTEM image of the region [indicated by a blue box in

Fig. 6(b)] containing Moir�e patterns. The plateau between 15 and

30 eV starts to appear, which becomes more pronounced as the

number of sheets increases. The plasmon maximum keeps

moving to higher energies, accompanied by further broadening.

The plasmon structure for more than 10 sheets strongly resem-

bles that of graphite.62 However, we could not perform EELS

spectra on a single-layer graphene sheet using our HRTEM

system. The theoretical predictions for p and p + s-surface

plasmon modes in free-standing single graphene sheets give �4.5

eV and �14.5 eV, which are substantially different from the six-

layer graphene sheet.58

704 | Nanoscale, 2010, 2, 700–708

The Moir�e pattern was observed to be more complex in six-

layered graphene sheets [Fig. 6(a)]. A FFT was also taken from

this region, Fig. 6(d), and shows 36 spots. One set of six spots

corresponds to each graphene layer. So, this indicates that at

least six layers in this region have an average 10� rotation with

respect to each other. The rotation angle and d-spacing between

two consecutive spots is clearly indicated in a more detailed way

in Fig. 7. The formation of this type of complex Moir�e pattern is

relatively different from the result described by Warner et al.62

Fig. 8(a)–(f) shows the reconstructed images for each graphene

layer produced by filtering in the frequency domain.

These isolated graphene membranes could offer a unique

platform for understanding the formation of ripples in sus-

pended graphene.63 Here in our TEM observation we directly

observe corrugations and periodic ripples [indicated by the green

and white dotted arrows, respectively in Fig. 9(a)] in suspended


Fig. 7 The relative rotation angle and d-spacing between two consecu-

tive spots in more detail.

Fig. 8 (a)–(f) Reconstructed images showing the graphene layer asso-

ciated with the relative set of spots indicated in Fig. 7.

Fig. 9 (a) Bright-field TEM image of single or FLG membrane across

a TEM grid. The corrugations and ripples are directly imaged by TEM,

and are indicated by green and white dotted arrows, respectively. The

inset shows a schematic of a rippled graphene sheet. (b) TEM image of

magnified view of area denoted by the white dotted arrow in (a). (c)

Reconstructed image of (b) after filtering in the frequency domain to

remove unwanted noise for clarity. The ripples are clearly observed in the

red box of (c). (d) Ripples in more than one-layer graphene taken from

the area denoted by the green dotted arrow in (a). (d) and (e) show a

bright-field TEM image and the corresponding FFT image, respectively.

FLG sheets. The inset shows a schematic of a rippled graphene

sheet. In a recent experimental observation Meyer et al.64 also

found ripples in suspended graphene sheets. To better under-

stand the unusual behaviour of graphene, the researchers from

Radboud University [Fasolino et al.65] undertook atomistic

Monte Carlo simulations at room (300 K) and high (1000, 2000,

and 3500 K) temperatures. The researchers believe that the origin

of the ripples is to be found in the carbon–carbon bonding in

graphene. Fig. 9(b) shows a TEM image of a magnified view of

area denoted by a white dotted arrow in Fig. 9(a). Fig. 9(c) shows

a reconstructed image of Fig. 9(b) after filtering in the frequency

domain to remove unwanted noise for clarity. The ripples are

clearly observed in the red box of Fig. 9(c). We can also clearly

observe the ripples in more than one layer of graphene taken

from the area denoted by a green dotted arrow in Fig. 9(a).

Figs. 9(d) and (e) show a bright-field TEM image and the cor-

responding FFT image, respectively. The inset shows a high-

magnification image taken from the red dotted area. A recent


article by Guinea et al.,66 successfully discussed the effect of

ripples in graphene on the density of states (DOS). They show

that at strong ripple disorder, a divergence in the DOS can lead

to an ordered ground state. They also discussed the formation of

dislocations in corrugated systems, buckling effects in suspended

samples, and the changes in the Landau levels due to the inter-

play between a real magnetic field and the gauge potential

induced by ripples. Furthermore, Bao et al.67 reported the direct

observation and controlled creation of periodic ripples in sus-

pended graphene sheets and also investigated the effect of

rippling on the electrical properties of graphene-based nano-

electronic devices. A significant advantage of graphene is its two-

dimensionality, making it compatible with existing planar device

architectures. Moreover, recent theoretical work emphasizes the

influence of edge states,68 curved surfaces and rotational disorder

within FLG sheets and pentagonal or heptagonal defects69 on the

electronic states of graphene sheets. Also, electric screening is

expected to be poor in ideal graphene sheets70 even if these are

‘‘good conductors’’ at room temperature.

In this work, we used electrostatic force microscopy (EFM) to

characterize the electric potential distribution on the surface of

FLG sheets on SiO2 ((300 nm)/Si substrates. We transferred our

exfoliated samples by a drop-casting method onto SiO2/Si under

ambient conditions. A commercial setup Multimode, Nano-

Scope IIIA, DI AFM with a conductive tip was used to record

Nanoscale, 2010, 2, 700–708 | 705

Scheme 2 Overview of the experiment. FLG sheets are deposited on

a SiO2 substrate on a highly-doped Si ground plane. Sample topography

and EFM phase are imaged simultaneously.

the sample topography and EFM phase in a two-pass mode

(Scheme 2). In the first pass, the AFM tip traces the sample

topography [Fig. 1(e)–(g) and 10(a)]. In the second pass the tip

follows the track derived in the first pass with a fixed lift-up

distance and measures the frequency shift caused by the elec-

trostatic force while the tip is biased by a voltage of a few volts.

We used silicon cantilevers (NSG11) with a Pt conductive

coating. The tip is set to vibrate with a piezo having a resonant

frequency of 150.09 kHz and amplitude of 30 nm. The interac-

tion force between the scanning tip and a conducting material

due to the applied bias voltage on the tip (responsible for the

frequency shift) can be understood with a capacitor model.71,72

EFM is an established technique for mapping the surface

potential of planar samples, including semiconductor nano-

crystals, thin films of polymers, polymer blends, and self-

assembled monolayers.44,73 Before performing experiments on

our exfoliated graphene sample, first we measured the EFM

signal on a conducting sample, which in principal should be

constant. Fig. 10(b) shows an EFM image of a graphene flake on

SiO2/Si substrates with a tip voltage (Vtip) of +3 V. To be more

specific, the EFM measurement was repeated several times on the

same area with Vtip of +3 V and 100 nm lift-up distance.

Figs. 10(c) and (d) shows height profiles and the corresponding

Fig. 10 AFM and EFM images of a graphene flake. (a) AFM image of

a graphene flake on a SiO2/Si substrate. (b) Corresponding EFM phase

image with tip voltage (Vtip) of +3 V. (c) and (d) show the height profile

and corresponding surface potential, respectively.

706 | Nanoscale, 2010, 2, 700–708

surface potential, respectively. The bright area corresponds to

the thin SiO2 layer and the dark area corresponds to a thin layer

of the graphene sheets, respectively. The above measurement

shows small surface potential variations on the surface of the

graphene flake.

Conclusions

We report a facile two-step method for the preparation of

homogenous colloidal suspensions of single or FLG sheets up to

0.15 mg ml�1 in DMF solution. The two-step approach includes;

(i) High temperature (�2000 �C) heat treatment of pyrolytic

graphite powders in a vacuum (<1 � 10�5 Torr) for 3 h followed

by (ii) sonication for 2 h by dissolving the heat-treated graphite in

DMF using a probe-tip sonicator. Our approach provides single

or FLG (2–6 layers) graphene sheets. However, in our experi-

ment the percentage of single-layer graphene is low in compar-

ison to FLG sheets. Taking into account the experimental

evidence discussed above, a conventional HRTEM (JEOL 2200F

TEM/STEM) operated at 200 kV is an effective tool for the direct

imaging of the graphene sheets at the atomic level. The inter-

pretation of HRTEM images is relatively simple and allows

rotational misorientation to be easily characterized by analyzing

in the frequency domain. These results show that the stacking in

FLG sheets is not always the assumed AB Bernal stacking

associated with bulk graphite. Here, we resolve the rotational

misorientation for up to six individual layers within the graphene

flake, and we show that the rotation angle between two consec-

utive layer is �10�. The complete atomic structural character-

ization of graphene flakes using HRTEM is necessary for its

future applications in graphene-based nanoelectronic

devices.19,28–32,74,75 Furthermore, the direct observation of peri-

odic ripples in suspended graphene sheets is also presented. EFM

was used to characterize the electric potential distribution on the

surface of FLG sheets on SiO2/Si substrates in ambient condi-

tions which exhibit small potential variations on their surface.

Systematic investigations are underway to further clarify the

formation of the rippling in graphene sheets and also how it

effects the electrical properties of single- or few-layer graphene

sheets.


Acknowledgements

The authors M. K. Singh, E. Titus, P. A. A. P. Marques, and

G. Goncalves would like to thank the Ciencia 2007 Program,

Foundation of Science and Technology (FCT – Portugal), and

INL (International Iberian Nanotechnology Laboratory) for the

financial support of this work.

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Atomic-scale observation of rotational misorientation in suspended few-layer graphene sheets

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