Applied Surface Science 282 (2013) 297–301

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Applied Surface Sciencejournal homepage: www.elsevier.com/locate/apsusc

Determination of non-uniform graphene thickness on SiC (0 0 0 1) by
X-ray diffraction
A. Ruammaitree ∗ , H. Nakahara, K. Akimoto, K. Soda, Y. Saito
Department of Quantum Engineering, Faculty of Engineering, Nagoya University, Nagoya 464-8603, Japana r t i c l e

i n f oArticle history:
Received 21 March 2013
Received in revised form 17 May 2013
Accepted 24 May 2013
Available online 2 June 2013
Keywords:
SiC
Epitaxial graphene
X-ray diffraction
Angle-resolved photoemission
spectroscopya b s t r a c t
Epitaxial graphene thickness distribution grown on Si-terminated SiC (0 0 0 1) surface was analyzed byusing an X-ray diffraction (XRD) pattern and a simple equation. These results were conﬁrmed by low accelerating voltage scanning electron microscopy and angle resolved photoemission spectroscopy. Despite
its simplicity, proposed XRD analysis provides fairly accurate information on layer spacing and thickness
distribution of graphene layers. It is expected that this method is useful for quick evaluation of graphene
layer numbers on large scale substrate.
© 2013 Elsevier B.V. All rights reserved.

1. Introduction
Graphene is an allotrope of carbon created by arrangement ofcarbon atoms in a two-dimensional honeycomb lattice. The unit cellof graphene, in which two carbon atoms are contained, is formedby two lattice vectors, |aG | = |bG | = 2.4589 Å [1,2]. In the electronic
band structure, graphene has two important bonding types whichare ␲ bond (perpendicular to the planar sheet) and ␴ bond (inplane sheet). Graphene also has many exotic properties such as
high mobility and linear dispersion (Dirac cone) at the K-point in
the Brillouin zone where the valence and conduction band toucheach other [3–5]. These unique properties of graphene make it apromising candidate for the future electronic [6,7] and photonic
devices [8].
Graphene can be formed by many ways such as mechanicalexfoliation of graphite, chemical vapor deposition (CVD) of carbonbearing gases on the surface of copper ﬁlms [9], and cutting open
nanotubes [10]. The growth of graphene by annealing SiC substrateis also one of the efﬁcient approaches for a large scale production of graphene. The estimation of the graphene ﬁlm thickness on
SiC substrate is necessary since the properties of graphene dependon its thickness. In general, there are several techniques, such as
scanning electron microscope (SEM) [11], Auger electron spectroscopy (AES) [12,13], X-ray photoelectron spectroscopy (XPS)∗ Corresponding author. Tel.: +81 8038233199.
E-mail addresses: akkawat@surf.nuqe.nagoya-u.ac.jp, u4605070@hotmail.com(A. Ruammaitree).
0169-4332/$ – see front matter © 2013 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.apsusc.2013.05.122[14], attenuation of substrate Raman intensity [14], angle-resolved
photoemission spectroscopy (ARPES) [1] and surface X-ray diffraction (SXRD) [15,17] to determine the layer number of graphenegrown on SiC. For the AES and XPS, the thickness determination
relies on the Si/C intensity ratio and the model which assumes
that graphene is grown uniformly on SiC substrate. Their accuracy
could suffer from the unrealistic model and the inaccurate knowledge of the inelastic mean free path of electrons [12–14,18]. In thecase of the estimation by attenuation of substrate Raman intensity,
the accuracy depends on the Raman intensity of SiC which varies
in position. In the case of ARPES, it can reveal the graphene band
structure which implies only the combination of graphene layer but
not respective coverages. The SXRD is a wonderful method which
can estimate the ﬁlm thickness. Nevertheless, this method is rather
complicated and time consuming, that is the SXRD needs hundredsof truncation rod intensity measurements (which takes tens ofhours) [16,17] and also needs many ﬁtting parameters (such as
3-dimensional atomic positions of each atoms including interface
and SiC layers and surface roughness) for structural analysis [15].
In particular, large number of parameters causes many candidatesof best ﬁt parameter sets as well as time consuming analysis. Low
accelerating voltage SEM (LV-SEM) is a technique which can locallydistinguish the relative graphene thickness regions by differencein contrast but it cannot exhibit the absolute graphene thickness
unless contrast-thickness relation for each sample is obtained.
In this report, an X-ray diffraction (XRD) pattern around agraphene peak was used for layer number distribution determination of non-uniform graphene layers on SiC substrate. The XRD
pattern was analyzed by using a simple equation and few numbers

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A. Ruammaitree et al. / Applied Surface Science 282 (2013) 297–301

of parameters (such as layer spacing and layer coverage of grapheneﬁlm). The XRD results were compared with LV-SEM and ARPES for
conﬁrmation.
2. Experimental
N-type Si-terminated 6H-SiC (0 0 0 1) substrates were employed
for the graphene growth. The substrate was precleaned by ultrasonic in acetone. After acetone was evaporated, the substrate wasimmediately mounted on the sample holder and put in the mainchamber with the base pressure of ∼10−8 Pa followed by silicon
deposition (about 2 layers) on the substrate. After that the substrate was transferred to an argon chamber without exposure to
air and then annealed in argon gas with a pressure of 0.05, 0.3 and0.5 atm. The samples were named as the value of argon pressure
where they were annealed in. The annealing temperature was inrange from ∼900 ◦ C to graphitization temperature (1550 ◦ C for the
0.05 atm sample, 1675 ◦ C for the 0.3 atm sample and 1700 ◦ C for
the 0.5 atm.sample) with increasing temperature by ∼100 ◦ C. The
annealing time was about 10–15 min for each temperature to produce a few layered graphene. The sample heating was carried out
by direct current through the sample.
After annealing, an ex situ XRD measurement was carried out
at the beam line 4C, Photon Factory, KEK (Tsukuba, Japan). Diffraction data were collected at X-ray energy of 10.2 keV and incident
beam size of 1 mm at room temperature. An ARPES measurement
was also conducted at room temperature at the beam line 5U of
UVSOR-II in the Institute for Molecular Science, Okazaki, Japan. The
excitation photon energy was set to 80 eV. An ultra-high vacuum(UHV)-SEM (Omicron Nano Technology) observation with incident
beam of 1.7–2.2 keV was also carried out.
3. Results and discussion
Fig. 1 shows XRD proﬁles (blue dots) of graphene ﬁlms grown on
SiC under argon pressure of (a) 0.05 atm, (b) 0.3 atm, and (c) 0.5 atm.
As indicated in the ﬁgure, diffraction peaks of graphene layers and
SiC are observed at ∼20◦ and 27.8◦ , respectively. The d-spacings of
the SiC can be calculated from the peak position as about 2.51 Å,
which corresponds to SiC bilayer spacing (2.52 Å) [1].

To estimate graphene thickness from XRD proﬁles, Laue diffraction function were used. At ﬁrst, a simple model was assumed thatthe graphene was grown uniformly on SiC substrate. Under thisassumption, the following simple equation was used for proﬁlecalculation.


2
 N


 2  2 
F  ∝ f ()  eikaj j  .


 j=0


(1)

Here, F is a structure factor, N is the number of graphene layer,
and f() is an atomic scattering factor which can be taken from
Ref. [19]. kaj = (4dj sin )/ where dj is a lattice spacing (between
jth and (j − 1)th layers) perpendicular to the surface,  is an angle
between the incident ray and the scattering planes,  is a wavelength of X-ray. In order to avoid the effect of SiC substrate, theﬁtting was operated in the range of 2 from 10 to ∼22◦ . Green dotted line and red broken line in Fig. 1(a) are calculated curves from
Eq. (1) with graphene layer number (N) of 1 and 2, respectively.
The spacing d of 3.60 Å was employed. As shown in the ﬁgure, there
are large discrepancy between the calculated curve and the experimental one, i.e. too broad for N = 1 or too narrow for N = 2. Thissuggests that the number of graphene layers on the SiC substrate
is not uniform, but has a distribution.
In order to improve the ﬁtting, another model which includes
graphene thickness distribution was introduced as shown in Fig. 2.
With this model and the Laue functions, XRD intensity can be calculated as


2
 N


 2  2 
F  ∝ f ()  ˇj eikaj j  ,


 j=0


(2)

where ˇj is a occupancy of jth graphene layer (its value is between
0 and 1). Solid lines in Fig. 1(a)–(c) show results of ﬁtting by using
Eq. (2). Parameters (dj and ˇj ) used in those calculations are shownin Table 1. It is apparent that the curve obtained from the modiﬁed model exhibits better ﬁtting than those of the uniform model.
2 (= (O − E)2 /E; O is intensity from the calculation, E is thatfrom experiment) dependence on ˇj parameter change is shownin Fig. 1(d). It reveals steep valley which suggests the ﬁtting resolution is good enough (less than 2%). For the interlayer spacings dj ,Fig. 1. Experimental XRD proﬁles (blue dots) of graphene ﬁlms grown on SiC (0 0 0 1) surface, which was annealed under argon pressure of (a) 0.05, (b) 0.3 and (c) 0.5 atm. As
written in the ﬁgures, peaks at ∼20◦ and 27.8◦ correspond to graphene layers and SiC bilayers respectively. Green dotted line and red broken line in (a) are calculated results
using ﬁtting Eq. (1) with parameters N = 1 and N = 2, respectively. A solid line in each ﬁgure shows a calculated result using Eq. (2) and (d) the chi-squared (2 ) dependenceon ˇj parameters for 0.3 atm sample. (For interpretation of the references to color in this ﬁgure legend, the reader is referred to the web version of the article.)A. Ruammaitree et al. / Applied Surface Science 282 (2013) 297–301

299

Table 1
XRD ﬁtting parameters, dj ’s (inter layer spacing) and ˇj ’s (occupancy of jth graphene layer).
Ar pressure

0.05 atm

j

1

2

1

2

3

1

2

d (Å)
ˇ (%)

3.55 ± 0.05
47 ± 23.50 ± 0.05
14 ± 23.30 ± 0.05
75 ± 53.30 ± 0.05
35 ± 53.30 ± 0.05
10 ± 53.40 ± 0.10
90 ± 53.40 ± 0.05
36 ± 5

0.3 atm

0.5 atmthere is one thing to point out. d value for bulk graphite is known
as 3.35 Å and ﬁttings result for 0.3 and 0.5 atm.samples agree withthis value. While for 0.05 atm sample, calculated d values are about
3.5 Å and about 5% larger than that of the bulk value. The reasonof the increase in interlayer spacing of this sample is not clear but
similar values were also obtained by X. Weng group measured bya high-resolution high-angle annular-dark-ﬁeld (HAADF) scanning
TEM (STEM) [20]. Coverages of n-layers graphene regions ( n ) can
be calculated from ˇ values as  n = ˇn − ˇn+1 , and those results areshown in the “by XRD” line in Table 2.
To conﬁrm layer number distribution obtained by XRD analysis,
low acceleration UHV-SEM experiments were carried out. Fig. 3
shows respective SEM images for 0.05, 0.3 and 0.5 atm.samples. As
shown in the ﬁgure, there are clear contrasts on the sample surfaces(indicated by 0, 1, and 2 in the ﬁgure). As described in the introduction, SEM contrast corresponds to number of layer of graphene.
However, absolute values of numbers cannot be determined. To
overcome this weakness, the following procedure was carried out.
Samples used in this experiment were heated by direct current,so that sample area near electrode could not be heated as high as
graphitization temperature. Thus SiC surface remains in this area.
Therefore continuous observation from SiC area to graphitized area
gives contrast-layer number relation for each sample. As a result,it was conﬁrmed that area 0, 1 and 2 in SEM images correspondto buffer layer, monolayer and bilayer graphene regions. Unfortunately, it was impossible to distinguish more than 2 layers region
from bilayer region under our experimental condition (acceleration voltage, S/N etc.). It is also a problem to compare XRD and
SEM results that observation area is different, ∼1 mm for XRD and∼10 ␮m for SEM. Therefore SEM measurements were carried out
at several points within XRD measurement area, and area of eachcontrast was summed up. Coverage of n-layers graphene region
obtained by SEM images are show in “by SEM” line in Table 2. As
shown in the table, coverages determined by XRD analysis are ingood agreement with those measured by SEM.
For qualitative inspection, ARPES experiment was also carriedout and its result is shown in Fig. 4. The sample used in this experiment is graphene grown under 0.05 atm of Ar pressure, which
was determined as mixture of 33% monolayer and 14% bilayer
graphene using the XRD analysis. Here, the origin of the energy
axis is taken at the Fermi energy EF . The inset curves at the bottom

Fig. 2. Schematic of thickness distribution model used in Eq. (2). ˇ0 is assumed
as 1.

Fig. 3. Low accelerating voltage UHV-SEM images of (a) 0.05, (b) 0.3 and (c)0.5 atm.samples taken with accelerating voltage of 2.2, 2.2 and 1.7 kV, respectively.
There are 3 contrast levels in these images, bright (indicated 0 in the ﬁgure), darkgray (1), and black (2), those correspond to buffer layer, monolayer and bilayer
graphene, respectively. Inset ﬁgure in (a) is the magniﬁed image in the broken line
square. The image contrast was adjusted to make a distinction of graphene thickness
clearly.

54
58
10
4
10

Monolayer (1) (%)
Buffer (0) (%)
Trilayer (3) (%)
Bilayer (2) (%)

25
27
40
48

Monolayer (1) (%)

14
6

Buffer (0) (%)
Bilayer (2) (%)

53
53
By XRD
By SEM

33
41

Buffer (0) (%)
Layers (n)Monolayer (1) (%)

25
25

0.5 atm
0.3 atm
0.05 atm
Ar pressure

Table 2
Coverages of n-layers graphene regions determined by XRD and SEM.

36
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A. Ruammaitree et al. / Applied Surface Science 282 (2013) 297–301

Bilayer (2) (%)

300

Fig. 4. ARPES spectra of the 0.05 atm sample around the K point of graphene. Upperright illustration represents a schematic electronic band structure which originatedfrom a graphene monolayer. An inset at the bottom shows momentum distribution
curves of photoelectrons at the energies of −1.5, −2 and −2.5 eV. Broken lines in
the graph show the components of the monolayer electronic structures ﬁtted using
Gaussian functions. Vertical arrows indicate two of noise signal lines (both in ARPES
mapping and the inset graph).

of Fig. 4 display intensities of photoelectrons with energies of −1.5,−2 and −2.5 eV against wave number (the momentum distribution curve). The intensity proﬁle was ﬁtted by Gaussian functions,and the results were shown by broken lines. In this ﬁtting noise
peaks indicated by vertical arrows were ignored. The electronic
band obtained by ARPES experiment consists of a single branchas shown by the ﬁtting result, which implies this sample consistsof monolayer graphene [1]. However, the band apparently showsa band gap (∼0.3 eV) and binding energy shift (∼0.4 eV), which isdifferent from free standing graphene monolayer [5]. It is considered that the band gap opening and the energy shift are caused byinteraction (strain and/or doping) between monolayer grapheneand the substrate [21]. Since ARPES evaluates only graphene layers(but not a buffer layer). It can be said that majority of graphenearea is monolayer region. However, it is very difﬁcult to obtain
quantitative value of layer distribution. XRD analysis delivered that
70% (33/(33 + 14)) of graphene region of this sample is monolayer,
which is qualitatively consistent with the ARPES result.
4. Conclusion
In this report we offer the new method to deliver absolute andreliable information on graphene thickness distribution on SiC substrate using XRD experiments and simple Laue functions. Unlike
other methods like low acceleration SEM, this is a standardlessmethod i.e. you do not need a standard or a known sample to determine absolute values of layer number distributions. However, it still
has a limitation since the graphene peak is only considered. Thisapproach is, therefore, suitable for the sample on which at least 1
carbon layer (buffer layer) covers the whole area shone by an X-ray
beam.

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Acknowledgements
The XRD measurements were supported by Photon Faculty, HighEnergy Accelerator Research Organization, Tsukuba, Ibaraki Prefecture, Japan. The ARPES measurements were performed at theInstitute of Molecular Science, Okazaki, Aichi Prefecture, Japan.
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