Growth of epitaxial graphene on 6H-SiC(0001) with face-to ... - Physics

<strong>Growth</strong> <strong>of</strong> <strong>epitaxial</strong> <strong>graphene</strong> on 6H-SiC(0001) with
face-to-face technique
Report
by
Annemarie Köhl
February 27, 2009
Supervisors:
Pr<strong>of</strong>. Alessandra Lanazara
Pr<strong>of</strong>. Ralph Claessen
Lawrence Berkeley Laboratory
Materials Sciences Division

Abstract
In this work a new technique to grow <strong>epitaxial</strong> <strong>graphene</strong> on 6H-SiC(0001) silicon carbide wafers is
employed to achieve a better controllable growth and higher quality samples. Epitaxial <strong>graphene</strong>
is a reliable candidate for all kind <strong>of</strong> applications as it has similar properties to carbon nanotubes
and exfoliated <strong>graphene</strong> but is more appropriate for the design <strong>of</strong> electronic devices as it can
be grown in wafer-sized pieces. However, to this date it is still a big issue to control <strong>graphene</strong>
thickness and to achieve large domains. The new face-to-face growing method, which is based
on a higher partial silicon pressure during the growth, is believed to improve the homogeneity in
terms <strong>of</strong> terrace size as well as <strong>graphene</strong> thickness. In this project samples have been grown in
this new geometry at many dierent temperatures and for dierent substrate orientations.
The samples have been characterized using atomic force microscopy (AFM), low energy electron
diraction (LEED), Auger electron spectroscopy (AES) and angle resolved photoemission
spectroscopy (ARPES). AFM measurements provide information about surface morphology and
terrace size. AES is used to determine the amount <strong>of</strong> carbon on the sample, which is related to
the number <strong>of</strong> <strong>graphene</strong> layers. LEED and ARPES are useful tools to estimate the number <strong>of</strong>
<strong>graphene</strong> layers and give a sense <strong>of</strong> the sample quality.
The <strong>graphene</strong> thickness is studied extensively as a function <strong>of</strong> the growth temperature. The
overall temperature which is necessary for the formation <strong>of</strong> <strong>graphene</strong> with the face-to-face method
is considerably higher than for the usual growth <strong>of</strong> <strong>graphene</strong> in UHV. A closer analysis reveals
a clear relation between growth temperature and <strong>graphene</strong> thickness with an increasing number
<strong>of</strong> <strong>graphene</strong> layers at increasing temperatures. Actually the measurements suggest that in the
interesting range <strong>of</strong> monolayer to few-layer <strong>graphene</strong> the growth temperature is a very sensitive
parameter.
In the temperature range 1500 − 1550 ◦ C several samples with mono- to trilayer <strong>graphene</strong> have
successfully been grown. AFM as well as ARPES measurements conrmed a improved surface
quality compared to UHV grown samples. These promising results ratify the idea <strong>of</strong> the new
technique and support the further development <strong>of</strong> the face-to-face method. As an unwanted
side eect a dierence in <strong>graphene</strong> thickness has been observed between the middle and the
border <strong>of</strong> the sample. Beside the temperature dependence the inuence <strong>of</strong> the relative direction
<strong>of</strong> the heating current to the vicinal miscut <strong>of</strong> the substrate has been studied. No signicant
dependence <strong>of</strong> the relative orientation has been observed at our samples.
2

Contents
1 Introduction 4
2 Materials and methods 6
2.1 General <strong>graphene</strong> properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Silicon carbide substrate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 <strong>Growth</strong> <strong>of</strong> <strong>epitaxial</strong> <strong>graphene</strong> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.4 Measurement techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3 Characterization <strong>of</strong> <strong>epitaxial</strong> <strong>graphene</strong> 13
3.1 Surface morphology by AFM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.2 Crystal structure by LEED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.3 Thickness estimation by AES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.4 Band structure by ARPES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4 Experiment 19
4.1 Sample growth with face-to-face method . . . . . . . . . . . . . . . . . . . . . . . 19
4.2 AFM measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.3 LEED measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.4 AES measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.5 ARPES measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
5 Results and discussion 27
5.1 Determination <strong>of</strong> <strong>graphene</strong> thickness . . . . . . . . . . . . . . . . . . . . . . . . . 27
5.2 Temperature dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5.3 Orientation dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
5.4 Surface quality <strong>of</strong> <strong>graphene</strong> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
6 Conclusion 32
3

1 Introduction
The two dimensional (2D) honeycomb lattice <strong>of</strong> carbon atoms, which is widely referred to as
<strong>graphene</strong>, has received great interest during the last 5 years [1, 2, 3]. Although it has been
known as a building part <strong>of</strong> graphite, carbon nanotubes and fullerenes for quite a long time, it
has been believed that no free state exist as this was supposed to be energetically unstable [4, 5].
Therefore it was quite a surprise when Novoselov et al. [6] succeeded in producing <strong>graphene</strong> just
a few years ago and found it to be stable with remarkable characteristics [7].
Graphene shows several unusual properties like a minimum conductivity, an integer-quantum
Hall eect at half-integer lling factors and anomalous Shubnikov-de Haas oscillations [1, 7].
These eects are theoretically understood and explained in terms <strong>of</strong> a linear energy-momentum
dispersion. The electrons and holes behave like massless Dirac fermions with a speed <strong>of</strong> light
<strong>of</strong> c ≈ 10 −6 m/s and reveal a pseudospin due to two carbon sublattices. Besides this insight into
theoretical questions <strong>graphene</strong> has many possible applications.
Due to its unique electronic properties <strong>graphene</strong> is a candidate to replace silicon in all kind
<strong>of</strong> devices. Beside the high carrier mobility, ballistic transport at room temperature and the
possibility to use the electrical eld eect, especially the possibility to control the properties <strong>of</strong>
a <strong>graphene</strong> sheet by manipulating the boundary conditions is interesting for applications [6, 8].
For example it would be possible to engineer a complete device consisting <strong>of</strong> semiconducting and
conducting parts out <strong>of</strong> one material [1]. Moreover bilayer or trilayer <strong>graphene</strong>, which consists
<strong>of</strong> 2 or 3 layers <strong>of</strong> carbon atoms respectively, reveal dierent properties and gain increasing
interest. Bilayer <strong>graphene</strong> for example exhibits a tunable band gap, which is extremely promising
for industrial use [3, 9]. Finally the advantage over other carbon based devices like carbon
nanotubes - the use <strong>of</strong> normal 2D lithographic techniques - and the high stability <strong>of</strong> <strong>graphene</strong>
under processing as well as in air is encouraging from a technical point <strong>of</strong> view [10].
Mechanically exfoliated akes, which are peeled o <strong>of</strong> bulk graphite, have desirable characteristics
like a high crystal quality and extremely weak coupling to the supporting substrate
and therefore have widely been used for basic research. However, <strong>epitaxial</strong>ly grown <strong>graphene</strong> is
the more promising candidate for large scale applications [8]. Epitaxial <strong>graphene</strong> is grown on
a silicon carbide (SiC) wafer by evaporation <strong>of</strong> silicon. It exhibits the typical 2D behavior <strong>of</strong>
<strong>graphene</strong>, but has the big advantage <strong>of</strong> being available on wafer sized pieces. On the other hand
till now the quality in terms <strong>of</strong> homogeneity <strong>of</strong> the number <strong>of</strong> carbon layers as well as terrace size
<strong>of</strong> <strong>epitaxial</strong> <strong>graphene</strong> is poor and a lot <strong>of</strong> research is performed in order to produce high quality
samples [11, 12].
In this project a new technique <strong>of</strong> growing <strong>epitaxial</strong> <strong>graphene</strong> samples has been employed in
order to improve the sample quality. The goal was to produce samples <strong>of</strong> a specic thickness <strong>of</strong>
<strong>graphene</strong>, concentrating on mono- and bilayer <strong>graphene</strong>, with big terrace sizes. The principle
idea behind the new method is to increase the partial silicon pressure in proximity <strong>of</strong> the sample,
which slows down the growth process. The high silicon pressure is achieved by the so-called faceto-face
growth, where two samples are brought geometrically very close together. The decreased
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speed <strong>of</strong> the growing process allows one to use higher temperatures, which generally leads to a
better ordered surface [11].
To characterize quality and thickness <strong>of</strong> the samples four dierent measurement techniques are
employed to get a broad picture. An atomic force microscope (AFM) is used to study the surface
morphology in real space. In contrast, low energy electron diraction (LEED) measurements
probe the reciprocal space and therefore the crystal structure. Auger electron spectroscopy
(AES) is used to gain information about the chemical composition <strong>of</strong> the topmost layers. Angle
resolved photoemission spectroscopy (ARPES) nally allows one to measure the electronic band
structure. The AFM images are used to determine the sample quality in terms <strong>of</strong> terrace size.
The later three methods give a characteristic signal for a dierent number <strong>of</strong> layers and can be
used to determine the <strong>graphene</strong> thickness by comparison with data in the literature. Moreover
ARPES and LEED can also help to determine the overall sample quality.
This report starts with a short summary <strong>of</strong> the properties <strong>of</strong> <strong>graphene</strong> and the substrate SiC.
Subsequently the growth process <strong>of</strong> <strong>epitaxial</strong> <strong>graphene</strong>, the measurement techniques and the faceto-face
method are introduced. Afterwards literature data is presented for later characterization
<strong>of</strong> the samples. Finally the results are presented, discussed and compared with the literature.
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2 Materials and methods
2.1 General <strong>graphene</strong> properties
A sheet <strong>of</strong> <strong>graphene</strong> is made <strong>of</strong> a 2D honeycomb structure <strong>of</strong> carbon atoms [1, 3]. The single
atomic layer <strong>of</strong> <strong>graphene</strong> can be seen as the mother <strong>of</strong> all carbon based materials. It can be
stacked into 3D graphite, rolled up into 1D carbon nanotubes or with some minor modications
be wrapped into 0D fullerenes. The honeycomb is built up by a hexagonal lattice with two atoms
per unit cell (see gure 1) with a unit cell vector <strong>of</strong> aG = 2.46 Å [13]. The two sublattices give
rise to some special <strong>graphene</strong> properties as for example the pseudospin.
In plane the carbon atoms are bonded by sp 2 bonds in a hexagon. Out <strong>of</strong> plane delocalized π-
electrons give rise to the interesting electronic properties <strong>of</strong> <strong>graphene</strong>. Two <strong>of</strong> the high symmetry
points <strong>of</strong> the hexagonal Brillouin zone are the Γ-point in the center and the K-point in the
corner <strong>of</strong> the hexagon. Whereas nearly everything in condensed matter physics is described by
the Schroedinger equation, <strong>graphene</strong> shows an unusual behavior. In contrast to the ordinary
parabolic dispersion <strong>of</strong> a free electron, <strong>graphene</strong> exhibits a linear dispersion in the vicinity <strong>of</strong> the
fermi surface [7]. This is illustrated in the band structure as seen in gure 1. This band structure
can best be described by the Dirac equation as the electrons mimic massless Dirac fermions. The
crossing point <strong>of</strong> the two cones is therefore called the Dirac point. For undoped <strong>graphene</strong> the
energy <strong>of</strong> the Dirac point E D is identical with the Fermi level E F . Thus, freestanding <strong>graphene</strong>
is called a semi-metal or zero-gap semiconductor.
Figure 1: Left: Atomic structure <strong>of</strong> <strong>graphene</strong> [3] Right: Electronic structure <strong>of</strong> <strong>graphene</strong> [14]
There are two common approaches for the production <strong>of</strong> <strong>graphene</strong>. Exfoliated <strong>graphene</strong> is
peeled o a graphite crystal with tape [6]. The critical point for the discovery <strong>of</strong> exfoliated
<strong>graphene</strong> was the usage <strong>of</strong> an interference eect on a 300nm SiO 2 wafer, which allows one to
identify few-layer-pieces with an optical microscope. Even though exfoliated <strong>graphene</strong> is the
more natural form and was mainly used to answer initial questions, the problem <strong>of</strong> small pieces
in applications lead to increased interest on <strong>epitaxial</strong> <strong>graphene</strong>. The growth <strong>of</strong> <strong>epitaxial</strong> <strong>graphene</strong>
by thermal decomposition <strong>of</strong> a SiC substrate will be described in more detail in the following
sections. In contrast to exfoliated <strong>graphene</strong> <strong>epitaxial</strong> <strong>graphene</strong> is grown on a substrate which
gives rise to an interaction. Although this interaction has been found to be quite small some
dierences have been observed like a blueshifted Raman Spectrum [15, 16], probably due to stress
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caused by lattice mismatch, or a shift <strong>of</strong> the Dirac point below the Fermi level due to doping
[3]. Therefore one must strictly distinguish between the two dierent types <strong>of</strong> <strong>graphene</strong>. As this
work is exclusively about <strong>epitaxial</strong> <strong>graphene</strong> the term <strong>graphene</strong> is used synonymical for <strong>epitaxial</strong>
<strong>graphene</strong> in the following parts <strong>of</strong> the work, but the reader should always be aware about this
dierence.
2.2 Silicon carbide substrate
As early as in 1975 van Bommel et al.[17] found that heating <strong>of</strong> SiC in ultrahigh vacuum (UHV)
leads to evaporation <strong>of</strong> silicon, which leaves behind a carbon-rich surface. Later it has been
proven that these carbon layers order into a <strong>graphene</strong> structure [8, 18]. This instance together
with the fact that SiC is a well known wide-gap semiconductor (E gap = 3 eV) has lead to the
majority <strong>of</strong> research about <strong>epitaxial</strong> <strong>graphene</strong> being focused on SiC as a substrate.
In a SiC crystal each silicon atom is tetrahedrally bonded to four carbon atoms and vice versa
[2, 19]. These SiC clusters in turn are arranged in a hexagonal bilayer structure with a carbon
and silicon sublayer. As the total energy <strong>of</strong> dierent orientations <strong>of</strong> adjacent bilayers is nearly
degenerated, SiC grows in more than 100 dierent polytypes. Nevertheless for the purpose <strong>of</strong>
growing <strong>graphene</strong> most groups use the hexagonal 4H-SiC or 6H-SiC. These polytypes are build up
by Si-C bilayers which are stacked ABCB... or ABCACB... respectively and give rise to an overall
hexagonal structure. In this work 6H-SiC has been used. The unit cell is illustrated in gure 2.
The Si-C bond length is 1.89 Å and the distance between two bilayers is 2.52 Å. The hexagonal
unit cell <strong>of</strong> 6H-SiC is described by the unit cell vectors aSiC = 3.08 Å and cSic = 15.11 Å [2, 19].
Figure 2: Crystal structure <strong>of</strong> 6H-SiC. Big purple balls represent silicon atoms, small green balls
represent carbon atoms [19].
6H-SiC has a polar c-axis, which results in two dierent bulk terminations on opposite sides
<strong>of</strong> the crystal. The SiC(0001) surface is called Si-face and is terminated by silicon atoms, while
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the SiC(0001) surface is called C-face and is terminated by carbon atoms (see also gure 2). It is
extremely important to note this dierence as the two faces show dierent chemical and physical
properties.
Early studies revealed a fast growth <strong>of</strong> rotational disordered <strong>graphene</strong> on the C-face leading
to thick (5 to 100 layers) <strong>graphene</strong>. However, <strong>graphene</strong> on the Si-face is rotationally ordered
and well aligned under an angle <strong>of</strong> 30 ◦ in respect to the substrate. Moreover the growing process
is slower and usually easy to terminate after a few layers [3, 10]. Therefore most <strong>of</strong> the early
research concentrated on the Si-face, although by now the C-face receives new interest. The
group <strong>of</strong> de Heer has argued that some small rotation <strong>of</strong> adjacent <strong>graphene</strong> sheets leads to a very
weak coupling between each set <strong>of</strong> two layers. Therefore even as many as 100 layers can exhibit
single layer behavior [2, 20].
In this work all growth processes and analysis have been performed on the Si-face. Unless
particular mentioned in the following the term SiC is used instead <strong>of</strong> SiC(0001), but one should
always keep in mind that the C-face would give dierent results.
2.3 <strong>Growth</strong> <strong>of</strong> <strong>epitaxial</strong> <strong>graphene</strong>
Although the process <strong>of</strong> silicon evaporation on SiC was known since 1975 [17], this graphitized
SiC surface did not gain a lot <strong>of</strong> interest. The big boom started when Berger et al. [8] showed
that this thin graphite exhibits 2D electron gas behavior. The growth <strong>of</strong> <strong>epitaxial</strong> <strong>graphene</strong> is
based on thermal decomposition <strong>of</strong> the SiC substrate. Both e-beam heating as well as resistive
heating have been used, but no dierence seems to arise from the dierent heating methods [2].
In order to avoid contaminations the heating is usually performed in UHV environment. Similar
results have been observed for high and low base pressure growth but till now no comparative
study about the inuence <strong>of</strong> the background pressure in the vacuum chamber has been conducted
[2]. From the molar densities one can calculate that approximately 3 bilayers <strong>of</strong> SiC are necessary
to set free enough carbon atoms for the formation <strong>of</strong> one <strong>graphene</strong> layer [17].
If SiC is heated to temperatures between 1050 ◦ C and 1150 ◦ C, silicon starts to evaporate and
a (6 √ 3 × 6 √ 3)R30 ◦ reconstruction evolves. The latest theory suggests that this is a carbon layer
with a honeycomb structure like <strong>graphene</strong> [21, 22]. However, unlike <strong>graphene</strong> one third <strong>of</strong> the
carbon atoms <strong>of</strong> this reconstruction layer has covalent bonds to underlying silicon atoms <strong>of</strong> the
topmost SiC layer. Therefore, although this reconstruction layer shows some graphitic properties
and structure, it strongly interacts with the substrate. This leads to electronic properties which
are totally dierent from <strong>graphene</strong> as for example the lack <strong>of</strong> π-bands at the Fermi level and the
presence <strong>of</strong> a band gap.
In order to obtain <strong>graphene</strong> the annealing temperature must be increased above 1150 ◦ C. Emtsev
et al.[22] propose a growth mechanism on SiC(0001) where new <strong>graphene</strong> layers are formed
beneath already existing reconstruction layers. If a silicon atom below the reconstruction layer
evaporates, the covalent bond to the substrate is cut. As this dangling bond is unstable and can't
connect to any other atoms the carbon atom rehybridizes into a sp 2 conguration and develops
the typical <strong>graphene</strong> like delocalized π-bands with neighboring carbon atoms. Additionally the
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evaporating silicon atom leaves behind three dangling bonds <strong>of</strong> carbon atoms in the topmost
layer <strong>of</strong> the substrate. These connect to each other to form an interface layer <strong>of</strong> covalently bound
<strong>graphene</strong>, whose structure is identical to the reconstruction layer.
Now the former reconstruction layer has evolved into a <strong>graphene</strong> layer which only interacts with
the interface layer through weak Van der Waals forces and all the typical <strong>graphene</strong> properties can
be observed. The next <strong>graphene</strong> layer grows in the same manner under the interface layer with
converting the interface layer into a <strong>graphene</strong> layer and the topmost substrate layer into a new
interface layer. This growth <strong>of</strong> new layers under the rst layer also explains the good rotational
order <strong>of</strong> <strong>graphene</strong> on SiC(0001) as the former covalent bonds to the substrate cause a rotational
xed position. In contrast, no reconstruction layer is formed on SiC(0001) due to dierences in
surface polarity and properties <strong>of</strong> the dangling bonds [22]. This leads to a weak interaction <strong>of</strong>
<strong>graphene</strong> with the substrate and a dierent growth mechanism, which can explain the observed
azimuthal disorder.
Although the structure is identical for clarity the honeycomb layer <strong>of</strong> carbon atoms with
covalent bonds is called reconstruction layer to refer to the bare (6 √ 3×6 √ 3)R30 ◦ reconstruction
on the substrate and is called interface layer to refer to the actual interface between SiC and
<strong>graphene</strong> layers. To avoid confusion it shall be noted at this point that some publications
furthermore use the term buerlayer for this conguration as this carbon layer acts as a buer
to isolate the <strong>graphene</strong> from the substrate.
One should note that the given temperatures need to be treated with caution. Absolute
growth temperatures may dier from one experimental group to another due to measurement
diculties. As SiC is transparent for infrared light, measurements with pyrometers can get
inuenced by light <strong>of</strong> the sample holder or the lament <strong>of</strong> the e-beam heating behind the sample.
Moreover dierent groups tend to use dierent emissivities, which also changes the measured
temperatures. Thermocouples don't have this problem but they can't be at the exact same place
as the sample and the further away the thermocouple is mounted the more the temperature is
underestimated due to a thermal gradient <strong>of</strong> the sample holder [2]. Therefore the possibility <strong>of</strong>
direct comparison <strong>of</strong> temperature values <strong>of</strong> dierent groups with each other or with this study is
limited. Nevertheless temperature measurements at the same setup are consistent and one can
study and compare the relative values.
2.4 Measurement techniques
2.4.1 Atomic Force Microscopy (AFM)
Information about the surface morphology like surface roughness, terrace size and step height
can be obtained with an atomic force microscope (AFM) (see gure 3). Central part <strong>of</strong> an AFM
is the oscillating cantilever with a small tip at the end. The measurements in this work have been
performed in tapping mode, where the cantilever is excited to oscillations close to his resonance
frequency [23]. During the oscillation the tip slightly taps on the sample surface and the cantilever
experiences surface forces, which have an eect on the oscillation amplitude. The change
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<strong>of</strong> the amplitude due to these surface forces is determined by a laser signal which is reected
from the cantilever and measured by photodiodes. A feedback loop maintains the oscillation
amplitude to be constant during the scanning <strong>of</strong> the surface. The necessary adjustments <strong>of</strong> the
height <strong>of</strong> the cantilever to maintain these constant amplitude and therefore constant tip-sample
distance is saved for each (x,y) data point and can be displayed as a topographic image <strong>of</strong> the
sample.
Figure 3: Schematics <strong>of</strong> an AFM setup [23]
2.4.2 Low energy electron diraction (LEED)
Low energy electron diraction (LEED) is a commonly used technique for surface analysis [24, 25].
Low-energy electrons with an energy <strong>of</strong> 10 − 1000 eV are focused onto a crystalline surface,
diracted and subsequently observed on a uorescent screen. As LEED is based on diraction
the measurement can only be performed on ordered surfaces and provides information about
the reciprocal space. The position <strong>of</strong> the diraction spots can be used to determine reciprocal
unit vectors, symmetries and surface reconstructions. In a layered structure the comparison
<strong>of</strong> intensities <strong>of</strong> dierent spots allows an estimation <strong>of</strong> layer thickness. The sharpness <strong>of</strong> spots
can nally give a sense <strong>of</strong> the sample quality in terms <strong>of</strong> rotational order, crystal faults and
contamination. As the electron mean free path at this energy is only around a few Å, LEED
measurements are very surface sensitive and probe only the rst few layers <strong>of</strong> a given sample.
10

2.4.3 Auger electron spectroscopy (AES)
Auger electrons arise from the Auger eect which is the non-radiative decay <strong>of</strong> a hole in the
core levels <strong>of</strong> an atom [26, 27, 28]. When a sample is bombarded by high energy electrons in
the range <strong>of</strong> keV, core level electrons are removed, leaving behind a hole. This unstable state
decays by an electron <strong>of</strong> an outer shell lling the hole in the core level. The additional energy
which is set free can be emitted as a photon (which is observed as X-ray uorescence) or given
to another electron - called Auger electron - <strong>of</strong> the outer shell which subsequently leaves the
crystal. Figure 4 illustrates an Auger process with a hole in the K shell. The hole is lled by an
electron <strong>of</strong> the L shell, which gives the energy to another electron <strong>of</strong> the L shell.
The kinetic energy <strong>of</strong> this Auger electron depends <strong>of</strong> all the dierent energy levels which are
involved into this process and is therefore unique for each element. In this simple picture the
kinetic energy can be calculated by
E kin = E(K) − E(L 1 ) − E(L 2 )
with E(K/L) being the binding energy <strong>of</strong> an electron in the K/L-shell. The unique kinetic
energy can be used to identify the chemical elements on the surface and to determine their
relative amount.
Figure 4: Illustration <strong>of</strong> a KLL Auger process
2.4.4 Angle-resolved photoemission spectroscopy (ARPES)
Angle-resolved photoemission spectroscopy is an extremely useful tool <strong>of</strong> surface sciences [29]. In
a very simple picture it can be explained by the photoelectric eect where a photon is absorbed
and transfers its energy to an electron. If the photon energy is high enough the electron will
leave the crystal with a kinetic energy <strong>of</strong>
E kin = hν − Φ − |E B |
where hν is the photon energy, Φ is the work function and E B is the binding energy <strong>of</strong> the
emitted electron.
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Figure 5: Illustration <strong>of</strong> ARPES geometry [30]
Figure 5 shows the experimental setup <strong>of</strong> an ARPES measurement. The hemispherical electron
energy analyzer measures the energy E kin . Using geometric considerations the information about
the angles ϑ and ϕ can be used to extract information about the momentum ⃗ k. As the translation
invariance is broken at the surface <strong>of</strong> the crystal only k || can be determined, but for 2D surface
states this is the mainly important value. Sample and analyzer can be rotated versus each other
to achieve any possible combinations <strong>of</strong> the angles and therefore any point <strong>of</strong> the Brillouin zone.
Detecting E kin , ϕ and ϑ nally allows to probe directly the band structure E B (k || ) <strong>of</strong> a system.
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3 Characterization <strong>of</strong> <strong>epitaxial</strong> <strong>graphene</strong>
3.1 Surface morphology by AFM
As scattering at terrace steps has an inuence on the electronic transport properties, great eort
has been made in order to achieve an ordered surface. Even nominally on-axis SiC substrates typically
have a small miscut and are therefore not completely at. After H 2 etching the substrates
show well ordered terraces <strong>of</strong> several µm [2]. However, the graphitization in UHV environment
causes surface roughening, so that the <strong>graphene</strong> surface shows random steps and valleys (compare
gure 6). The achieved average terrace size after the <strong>graphene</strong> growth is approximately 50nm
[2, 12]. The kinetic processes behind the growth are still not clear and under extensive research
[12, 31]. The studies agree on the fact that the growth process starts at surface steps and that
pits form due to dierent retraction speed <strong>of</strong> the steps. A fast high-temperature annealing is
supposed to lead to a higher nucleation density and therefore better surface quality.
Figure 6: AFM image <strong>of</strong> a UHV grown nominally 1 ML <strong>graphene</strong> sample on 6H-SiC [11]
Recent progress in the growth <strong>of</strong> better ordered surfaces has been made by Hupalo et al.[12]
by growing <strong>graphene</strong> in short heating ashes <strong>of</strong> 30 seconds and lead to 150 nm terraces. Emtsev
et al.[11] performed growing <strong>of</strong> <strong>graphene</strong> in an argon environment and succeeded in growing
terraces <strong>of</strong> a width <strong>of</strong> up to 3 µm. They also conrmed that these bigger terraces give rise
to a higher carrier mobility. Whereas these modications during the growth process lead to
promising results, it is to this date uncertain if pregraphitization procedures like H 2 etching or
preparing Si-rich surfaces have an eect on the surface morphology <strong>of</strong> <strong>graphene</strong>. For example a
recent study suggested that H 2 etching even worses the quality as the step borders are necessary
starting points for the growth process [12].
13

Surprisingly the overall coherent size <strong>of</strong> a <strong>graphene</strong> sheet as determined by transport measurements
is bigger than the terrace size [2]. This is explained by the observation in scanning
tunneling microscope (STM) images that <strong>graphene</strong> sheets can grow over substrate steps as well
as over <strong>graphene</strong> steps [2, 32, 12] (see gure 7).
Figure 7: STM image <strong>of</strong> a <strong>graphene</strong> sheet growing over a SiC step [12]
3.2 Crystal structure by LEED
The LEED pattern <strong>of</strong> the graphitized Si-face <strong>of</strong> SiC has been studied widely [3, 8, 18, 33]. During
step by step heating to higher temperatures dierent surface reconstructions are observed. While
some <strong>of</strong> the early patterns depend on preparation techniques, all groups agree in the observation
<strong>of</strong> a ( √ 3 × √ 3)R30 ◦ pattern for temperatures in the range <strong>of</strong> 1050 ◦ . Further annealing leads
to the development <strong>of</strong> a (6 √ 3 × 6 √ 3)R30 ◦ reconstruction. [18, 22]. The LEED pattern <strong>of</strong> one
monolayer <strong>of</strong> <strong>graphene</strong> is illustrated in gure 8.
In gure 8 orange arrows indicate spots which are due to the SiC substrate and reveal the
hexagonal symmetry as expected from the hexagonal unit cell in real space (compare section
2.2). White arrows indicate spots which can be explained by a thin graphite overlayer, which
also exhibits a hexagonal symmetry. The fact that sharp peaks are visible, indicates that the
<strong>graphene</strong> overlayer is rotationally well aligned. The angle between the SiC and the graphite
reciprocal vectors is 30 ◦ and corresponds to a 30 ◦ rotation between substrate and overlayer in
real space. Moreover one can observe that the graphite spots appear further outside on the LEED
pattern. This larger reciprocal unit vector corresponds to a smaller unit cell <strong>of</strong> <strong>graphene</strong> compared
to SiC in real space. This ts well to the real space unit vectors <strong>of</strong> graphite (aSiC = 2.46 Å,
compare section 2.1) and SiC (aSiC = 3.08 Å, compare section 2.2).
14

Figure 8: Left: LEED pattern <strong>of</strong> one monolayer <strong>graphene</strong>. Orange arrows indicate SiC-spots,
white arrows indicate graphite spots [3].
Right: Schematic LEED pattern with unit vectors <strong>of</strong> reciprocal lattice for SiC ⃗s 1 /⃗s 2
and graphite overlayer ⃗c 1 /⃗c 2 . Additional spots are due to sum vectors. [18]
The mismatch <strong>of</strong> the unit cells gives rise to a coincidence lattice with a large hexagonal unit cell
<strong>of</strong> a (6 √ 3 × 6 √ 3)R30 ◦ periodicity [2, 22]. In the reciprocal space this is observed as a hexagonal
set <strong>of</strong> spots close to the (0,0) spot. The unit cell in reciprocal space is very small and marked
gray in the schematic LEED pattern. Finally spots are visible at positions <strong>of</strong> sum vectors <strong>of</strong>
⃗s 1 , ⃗s 2 ,⃗c 1 ,⃗c 2 . The spot a in gure 8 is for example at the position ⃗c 1 + ⃗c 2 − ⃗s 2 , spot b at position
⃗s 1 + ⃗s 2 − ⃗c 1 . Theoretically all dierent combinations <strong>of</strong> these unit vectors are possible so that
the whole (6 √ 3 × 6 √ 3)R30 ◦ mesh would appear, but as double diraction is involved most <strong>of</strong>
them are extremely faint and therefore invisible.
3.3 Thickness estimation by AES
AES has been used to identify the presence <strong>of</strong> carbon on the SiC substrate [8, 10, 16, 17]. The
Si-LVV Auger peak is located at 92 eV and the C-KLL peak at 271 eV [28]. Li [19] has calculated
theoretically the ratio <strong>of</strong> the intensities <strong>of</strong> the silicon and the carbon peak as a function <strong>of</strong> the
number <strong>of</strong> <strong>graphene</strong> layers, based on the attenuation in each layer, the backscattering factor,
sensitivity factors and mole fractions.
These calculations used dierent models for the interface: an interface layer <strong>of</strong> silicon atoms
<strong>of</strong> 1/3 the atom density <strong>of</strong> a SiC-bilayer, a analogous interface layer with carbon atoms, or the
growth <strong>of</strong> <strong>graphene</strong> directly on the substrate. As discussed in section 2.3, the most likely model
for the interface between SiC and <strong>graphene</strong> is the existence <strong>of</strong> an interface layer which consists <strong>of</strong>
15

Figure 9: Model <strong>of</strong> Si:C Auger peak intensity ratio versus number <strong>of</strong> <strong>graphene</strong> layers for SiC(0001)
substrates. Solid line: Model with interface layer <strong>of</strong> C adatoms at 1/3 their bilayer
density. Dotted line: Model with interface layer <strong>of</strong> silicon adatoms at 1/3 their bilayer
density. Dashed line: Model with bulk terminated SiC(0001). Inset shows Auger
spectra obtained after (a) ex-situ H 2 etching (no UHV preparation), (b) UHV anneal
at 1150 ◦ C (LEED √ 3 × √ 3 pattern), (c) UHV anneal at 1350 ◦ C (LEED 6 √ 3 × 6 √ 3
pattern) [10]
carbon atoms in a honeycomb structure with covalent bonds to the substrate. Although dierent
binding congurations can change the AES signal slightly, the signal height is mainly determined
by the amount <strong>of</strong> atoms <strong>of</strong> a given element. The interface layer has the same atom density as
<strong>graphene</strong> although the binding conguration is dierent [22]. Therefore it is most accurate to
use the bulk terminated model (dashed line) and take into account that the rst layer <strong>of</strong> carbon
is the interface layer. Therefore the axis at the graph should be called number <strong>of</strong> carbon layers
and the number <strong>of</strong> actual <strong>graphene</strong> layers is always n-1. For example at a ratio <strong>of</strong> Si:C=0.1 two
carbon layer are measured which corresponds to a monolayer <strong>of</strong> <strong>graphene</strong>. A recent review states
that AES usually overestimates the number <strong>of</strong> <strong>graphene</strong> layers by one to two layers if Li's model
is used [2]. Therefore the existence <strong>of</strong> the interface layer could explain this systematical error.
16

3.4 Band structure by ARPES
Figure 10 shows the band structure <strong>of</strong> <strong>graphene</strong>. The direction <strong>of</strong> k || within the Brillouin zone
is indicated by the green inset. The observation <strong>of</strong> the band structure allows one to observe the
whole development <strong>of</strong> the surface from the bare substrate to the formation <strong>of</strong> <strong>graphene</strong>. Whereas
the reconstruction layer only exhibits the σ-bands, monolayer <strong>graphene</strong> reveals the typical linear
dispersion <strong>of</strong> the π-bands close to the K-point as one can see in gure 10. One branch <strong>of</strong> the
symmetrical cone (compare section 2.1) is suppressed due to matrix elements if the image is
taken along the ΓK direction. A measurement where k || is perpendicular to the ΓK direction
would reveal both branches with equal intensity.
Figure 10: ARPES <strong>of</strong> <strong>graphene</strong> for the whole Brillouin zone [3]
As states close to the Fermi level are mainly responsible for the electronic properties, most
interest is focused on this area. Figure 11 shows the band structure close to the Fermi level for
dierent numbers <strong>of</strong> <strong>graphene</strong> layers. One can see a signicant development <strong>of</strong> the band structure
with thickness which is also reproduced by the theoretical calculations. The most obvious
dierence is the appearance <strong>of</strong> additional bands for more <strong>graphene</strong> layers which is explained by
interlayer splitting [34]. Moreover one can observe a shifting <strong>of</strong> the Dirac point. Due to charge
transfer from the substrate the Dirac point <strong>of</strong> monolayer <strong>graphene</strong> is shifted below the Fermi
level. As this substrate eect decreases for increasing thickness the Dirac point approaches the
Fermi level for more <strong>graphene</strong> layers. Adsorption <strong>of</strong> alkali atoms like potassium which will transfer
charges to the topmost layer can systematically change the position <strong>of</strong> the Dirac point or
17

even open and close the gap in the bilayer band structure [3]. Comparing the number <strong>of</strong> bands
and the position <strong>of</strong> the Dirac point can be used to identify the thickness <strong>of</strong> a given sample.
Figure 11: ARPES data and theoretical calculations close to the Dirac point show clear variations
depending on the <strong>graphene</strong> thickness [3]
18

4 Experiment
4.1 Sample growth with face-to-face method
As explained in section 2.3 it is commonly known that during heating SiC silicon evaporates and
<strong>graphene</strong> develops. This work presents a new technique for growing <strong>epitaxial</strong> <strong>graphene</strong>, which
can lead to more ordered surfaces than the usual growth in UHV.
Commercial, nominally on-axis oriented wafers <strong>of</strong> 6H-SiC with a vicinal miscut <strong>of</strong> less than
±0.06 ◦ and a polished Si-face are purchased from Cree Research, Inc. The resistivity <strong>of</strong> the N-
doped wafer is ρ ≈ 0.1 Ωcm. Pieces <strong>of</strong> 4.5 cm x 6.5 cm were cut with a diamond saw in dierent
orientations with respect to the miscut <strong>of</strong> the wafer. The necessary temperatures are obtained by
resistive heating, but in a new conguration, which we call the face-to-face method. The principle
idea is to bring two samples facing each other very close together, which will give rise to a higher
silicon pressure between the samples. This will in turn cause higher growing temperatures,
which normally increases the mobility. Therefore the diusion is enhanced and the ordering in
the energetically most stable state <strong>of</strong> big terraces is more likely. This is similar to the approach
<strong>of</strong> growing <strong>graphene</strong> on SiC(0001) under an argon atmosphere [11] or the RF-furnace growth
<strong>of</strong> <strong>graphene</strong> on SiC(0001) [2, 20]. In both cases a better ordered surface compared to UHVgrown
samples has been achieved. For the samples which are grown in the argon atmosphere
an enhanced carrier mobility was measured as expected due to the reduced scattering. This
supports that it is worth putting eort into improvement <strong>of</strong> the surface quality.
Technically the face-to-face conguration is obtained by cutting a L-shaped piece <strong>of</strong> tantalum
foil (d = 0.025 mm), where the short end is put between the two samples to provide a small
distance and the long side is wrapped around the two samples several times to x the tantalum
foil in this place (see gure 12). The polished Si-face <strong>of</strong> the wafers which are used for the growth
are looking at each other, which gives the name face-to-face. As the two samples are very close
together the evaporating silicon is captured in the small gap and gives rise to a higher silicon
pressure.
Figure 12: Pictures <strong>of</strong> wrapping procedure
This sample-sandwich is subsequently clamped between two nuts on a rod on both sides (see
gure 13). The rods are connected to a electrical feedthrough which provides the possibility
to perform resistive heating. This mounting part is inserted into a little vacuum chamber and
19

Figure 13: Mounting <strong>of</strong> the sample, red is the SiC-substrate, blue tantalum foil
pumped down to a base pressure <strong>of</strong> approximately 8 × 10 −7 Torr. Afterwards the sample is
heated to 700 ◦ C for approximately 4 hours to clean the surface <strong>of</strong> contaminations like oxygen
and water. The temperature is measured with an pyrometer at ɛ = 0.96.
After the wrapping the sample sandwich has a very high resistance in the range <strong>of</strong> several
100 kΩ, which can be explained by a bad contact between the substrate and the tantalum foil.
However, in the rst minute <strong>of</strong> the cleaning process the resistance drops into the range <strong>of</strong> 100 Ω.
This is probably due to improvement <strong>of</strong> the electrical contact between the foil and the substrate
by running a current through the contact points. Sometimes bright spots or even sparks can be
observed at places close to the border <strong>of</strong> the wrap, which also support this theory.
After these preparations the sample is heated to a specic temperature for 20 minutes. The
necessary increase <strong>of</strong> the current leads to a further drop <strong>of</strong> the resistance into the range <strong>of</strong> several
10 Ω. The temperature is the main parameter which has been varied in this work. During the
project in total 14 sets <strong>of</strong> samples have been grown with dierent parameters. After the sample
has cooled down the chamber is vented and the sample is unwrapped. For further measurements
the two facing samples are analyzed independently.
In order to perform LEED, AES and ARPES the samples are attached to a molybdenum puck
by spotwelding two tantalum stripes. The samples are brought into a UHV chamber with a
base pressure below 5 × 10 −10 Torr. Prior to performing the measurements, the samples are
heated by e-beam heating to a temperature <strong>of</strong> T = 1000 ◦ C with the pressure being kept below
5×10 −8 Torr. This temperature has proven to give good ARPES results in earlier studies without
being believed to change the sample composition [35].
20

4.2 AFM measurements
All samples are examined with a Dimension T M 3100 Atomic F orce Microscope from Digital
Instruments in tapping mode. An AFM image <strong>of</strong> the bare SiC substrate as it looks like before
any kind <strong>of</strong> treatment is shown in gure 14.
Figure 14: AFM image <strong>of</strong> a SiC substrate (surface polished, no further treatment)
The surface is quite at on a height scale <strong>of</strong> 8nm with some scratches which originate from
the polishing process. Some white spots are visible which are probably pieces <strong>of</strong> dirt. One faceto-face
set has only been wrapped and heated to 700 ◦ C in order to examine the eect <strong>of</strong> the
cleaning procedure. It turns out, that at 700 ◦ C the surface does not change signicantly. After
the cleaning the white spots disappear but the scratches <strong>of</strong> the polishing are still visible.
For all samples which are heated above 1200 ◦ C a change compared to the bare substrate appears.
However, the surface morphology is not identical at all positions. Places on the substrate,
which were covered with Ta-foil are usually very rough. The middle <strong>of</strong> the sample is normally
the best ordered place with at terraces while places close to the border show some roughening.
For low temperatures both samples <strong>of</strong> the same set are roughly similar and show terraces in
the middle <strong>of</strong> the sample. The terrace size increases towards higher temperatures as illustrated
in gure 15.
At temperatures above 1500 ◦ C the situation becomes more diverse. One sample typically
shows terraces while the other one is very rough with many pits and holes. As the two samples are
grown under nominally identical conditions this is quite surprising. In order to nd a explanation
for the dierent properties one needs to nd a dierence between the two samples. As they are
cut in the same way out <strong>of</strong> the same wafer the only critical point is the wrapping <strong>of</strong> the sample
into the face-to-face geometry. As this is done by hand it is not possible to control the wrap
perfectly. One could imagine that the contact <strong>of</strong> the foil to the two samples is dierent. This
could be supported by the observation that the overall resistance <strong>of</strong> the sample sandwich drops
during the rst minute <strong>of</strong> the cleaning process. Perhaps even if the initial contact is similar,
this improvement <strong>of</strong> the contact is dierent for the two samples. For example if the contact
21

Figure 15: Trend <strong>of</strong> terrace size to increase for temperature range 1200 ◦ C-1400 ◦ C
becomes signicantly better on one side, most <strong>of</strong> the current will run through this sample so the
mechanism which initially improved the contact won't work for the second sample.
If a dierent current is running through the samples this could cause a dierent temperature
which would explain a dierent surface morphology. Moreover this eect could be self-energizing
as a higher temperature will further decrease the resistance <strong>of</strong> the semiconducting SiC substrate.
On the other hand one would normally expect thermal radiation to be very high at this temperature
and therefore due to the small distance <strong>of</strong> the two samples a similar temperature should
be at both samples. The temperature reading with the pyrometer will always give the highest
temperature as SiC is transparent for the infrared light and can't shield the radiation.
So far the reason for the discrepancy between the two samples couldn't be determined. Further
studies to investigate this question are necessary. Due to the restricted time usually only one
sample was introduced into the UHV chamber and analyzed. For this purpose it has always been
chosen the sample with the better ordered surface.
4.3 LEED measurements
LEED measurements characterize the surface structure and crystal order. As the spot size <strong>of</strong> the
electron gun is in the order <strong>of</strong> one millimeter, the images are always average images <strong>of</strong> a large
area <strong>of</strong> the sample. A kinetic energy <strong>of</strong> E kin = 98.9 eV has been used and a camera has been
employed to take pictures <strong>of</strong> the uorescent screen. Figure 16 shows images which are taken at
dierent samples and illustrate dierent steps in the <strong>graphene</strong> growth process.
Pattern a) shows only the bulk SiC spots. In this case no considerable amount <strong>of</strong> <strong>graphene</strong> is
grown. In pattern b)/c) SiC spots as well as graphite spots and reconstruction spots are visible
(compare chapter 3.2). While in b) the graphite spots are very weak they are even brighter
than the SiC spots in pattern c). Therefore one can conclude that sample c) has more <strong>graphene</strong>
layers than sample b). A drop in the intensity <strong>of</strong> the SiC spots can be observed because the
22

Figure 16: LEED pattern at dierent stages <strong>of</strong> <strong>graphene</strong> growth. Orange circle marks SiC spot,
white circle marks graphite spot.
a) SiC substrate b) Reconstruction layer/Monolayer c) Bilayer d) 5-6 layers <strong>of</strong>
<strong>graphene</strong>
additional <strong>graphene</strong> layers prevent the electrons to reach the SiC layers due to the nite mean
free path at 98.9 eV. Pattern d) nally shows nearly undetectable SiC spots. This corresponds
to many <strong>graphene</strong> layers. For more than 6-8 <strong>graphene</strong> layers the LEED image is identical to that
<strong>of</strong> graphite as the electrons don't probe the SiC surface any more.
Although LEED is a very fast tool to get a sense <strong>of</strong> the surface structure it is hard to achieve
accurate thickness estimations based on LEED images. Firstly the intensity <strong>of</strong> a LEED spot
is energy dependent. Therefore one can only compare patterns which have been taken at the
same energy. As the LEED patterns in the literature are taken at many dierent energies direct
comparison is not possible. Moreover the determination <strong>of</strong> an intensity ratio <strong>of</strong> the spots is very
error-prone as background intensity, adjustment <strong>of</strong> the lenses and the size <strong>of</strong> the measured spot
can change the calculated intensity. Nevertheless LEED is an useful tool for rough estimations.
The human eye can quite easily give an estimation <strong>of</strong> the ratio which allows relative statements
between images taken in the exact same manner. If some samples are characterized by other
methods, the thickness can be classied in terms <strong>of</strong> similar, more or less than a given reference
sample.
4.4 AES measurement
AES measurements are performed with a SPECS Phoibos 150 hemispherical analyzer and an
electron gun which provides electrons at an energy <strong>of</strong> 3 keV. The data is taken with the medium
area lens mode and a pass energy <strong>of</strong> 15 eV. After the measurement the data is averaged over
the angle and dierentiated to decrease the eect <strong>of</strong> the background. Moreover this allows to
compare the data with reference AES data which has been taken with a cylindric mirror analyzer
(CMA).
Figure 17 shows an example <strong>of</strong> the data. In order to get a consistent value for the Si:C
ratio a t with an exponential background and two Lorentzian peaks is performed. Comparison
with the literature data (section 3.3) shows that our data have a distinctly higher silicon peak
than expected. The sample <strong>of</strong> gure 17 for example exhibits monolayer to bilayer <strong>graphene</strong> as
23

Figure 17: AES data <strong>of</strong> a sample with a thickness <strong>of</strong> 1-2 layer <strong>graphene</strong>. The inset shows the
raw data and the main graph gives the derivate (red) and the t function (blue).
determined by LEED and ARPES and should therefore have a ratio <strong>of</strong> Si : C ≈ 0.1 if the
interface layer is taken into account or Si : C ≈ 0.3 otherwise. This is an order <strong>of</strong> magnitude
smaller than the measured ratio <strong>of</strong> Si : C = 2.4.
Several explanations for this dierence have been suggested. A contribution to the dierence is
denitely the analyzer mode. The signal intensity as measured by an electron energy analyzer is
not independent from the kinetic energy [36]. Two dierent operation modes with two dierent
energy dependences are possible. In Fixed Retardation Ratio (FRR) mode all particles are
decelerated with the same xed factor. This causes the measured intensity to increase with
the kinetic energy as I ∝ E kin . In the Fixed Analyzer Transmission (FAT) mode the energy
resolution is kept constant for all energies. This leads to an decrease <strong>of</strong> the intensity with
increasing kinetic energy as I ∝ 1
E kin
. Due to experimental limitations <strong>of</strong> our system, data could
only be acquired in FAT mode. In contrast, most Auger data is taken with a CMA which uses
FFR and direct acquisition <strong>of</strong> the derivative. The use <strong>of</strong> this dierent modes will change the
measured peak ratios. Knowing the energy dependences, one can calculate the dierence in the
ratio which will arise due to this dierence in data acquisition. The mathematical treatment <strong>of</strong>
this eect leads to a smaller Si:C ratio but it is still not comparable to the literature data. A
development <strong>of</strong> the experimental conditions is under way so an experimental test <strong>of</strong> the dierent
analyzer modes can be performed soon.
Another dierence between a CMA and a hemispherical analyzer is the geometry <strong>of</strong> incoming
electrons and Auger electrons. In a CMA the electron gun is mounted normal to the sample
surface and the detected electrons leave the sample under an angle <strong>of</strong> 42 ◦ . However, in our
case the electron gun is mounted under an angle while the analyzer is orientated vertically.
Reconstruction <strong>of</strong> Li's calculation with our geometry showed that this dierence has only a
minor eect and can be neglected at this point.
Another possible explanation could be that the growth process leaves additional silicon at
the sample, which might sound reasonable, as everything is held under high silicon pressure.
24

However, this can probably be ruled out as well as a sample which was produced without the
use <strong>of</strong> the face-to-face method gave a similar signal.
Even for identical samples, geometry and analyzer mode quantitative AES measurements
are inuenced by a large number <strong>of</strong> parameters like the resolution or the modulation voltage.
Therefore it is still not clear what causes the dierence <strong>of</strong> the peak ratio in literature and our
results. In order to use AES measurements despite this, even now unsolved problem, our own
reference samples have been used. The thickness <strong>of</strong> two reference samples has been determined
by ARPES measurements (compare chapter 4.5). A sample with 1.5 ML <strong>of</strong> <strong>graphene</strong> showed a
Si:C ratio <strong>of</strong> Si : C ≈ 2.4 and a sample with approximately 3 layers <strong>of</strong> <strong>graphene</strong> had a ratio <strong>of</strong>
Si : C ≈ 1.1. These two samples are sucient to give a rough estimate <strong>of</strong> the <strong>graphene</strong> thickness
in the considered range.
4.5 ARPES measurements
Due to limited experimental time only few samples have been measured by ARPES although this
gives the best estimate <strong>of</strong> the number <strong>of</strong> layers and can at the same time provide information
about the sample quality. The ARPES measurements are nevertheless extremely important as
they have been used as references for LEED and AES. ARPES measurements were conducted
with a SPECS Phoibos 150 analyzer at a pass energy <strong>of</strong> 10 eV and the low angular dispersion
lens mode. The excitation <strong>of</strong> the photoelectrons steams from a Helium lamp, where the HeII
signal was used (E HeII = 40.81 eV). One sample was measured at the Advanced Light Source,
Beamline 10.
Figure 18: ARPES data <strong>of</strong> a sample between monolayer and bilayer <strong>graphene</strong>
25

Figure 18 shows the band structure as measured at the K point in ΓK direction. The image
shows two bands but still has intensity at the Dirac point. Moreover the Dirac point is around
−0.3 eV. Comparison with gure 11 shows that this is produced by adding the monolayer and
bilayer bands.
The sharpness <strong>of</strong> the band gives information about the sample quality. Unfortunately the base
pressure for this measurement was quite high, no cooling was used and the measurement has
been performed with the Helium lamp with a very big spot size. Therefore a lot <strong>of</strong> additional
broadening originates from these parameters, which makes it hard to estimate the quality. It is
encouraging that quite sharp bands have been observed despite this problematic circumstances.
The quality is already comparable to the reference data <strong>of</strong> gure 11 which has been taken at a
synchrotron with a smaller spot size and probably better base pressure. Therefore the quality <strong>of</strong>
the band structure might be even sharper if measured under better conditions. Due to the big
spot size it is till now also uncertain if the signal originates from the simultaneous probing <strong>of</strong>
dierent areas which exhibit monolayer and bilayer <strong>graphene</strong> or if the whole surface is covered
by a mono- and bilayer mixture.
26

5 Results and discussion
5.1 Determination <strong>of</strong> <strong>graphene</strong> thickness
As explained in previous sections, LEED, AES and ARPES can be used to characterize the
number <strong>of</strong> <strong>graphene</strong> layers. Although some techniques don't allow to give an exact number <strong>of</strong>
<strong>graphene</strong> layers, it is always possible to compare the results <strong>of</strong> the dierent samples relatively
and order these by less, more or equal <strong>graphene</strong> thickness. Independent analysis <strong>of</strong> the three
techniques gave consistent results for all 8 studied samples. This conrms that the measurements
are performed and analyzed correctly. As only ARPES can give an exact number, the three
samples which are measured by ARPES are used to calibrate the results by the number <strong>of</strong> layers.
Therefore the qualitative trends are determined by three independent methods whereas the
quantitative number <strong>of</strong> layers is basically xed on a few reference samples, which are measured
by ARPES. It is also worth noting that the measurements reproduce the general structure <strong>of</strong> the
reference data in the literature. Therefore the face-to-face method does not change the electronic
or crystal properties <strong>of</strong> <strong>graphene</strong> but only introduces changes into the surface quality.
As well as all methods agree on dierent <strong>graphene</strong> thickness on dierent samples, they also
show uniformly a position dependence <strong>of</strong> the thickness on one sample. One usually nds more
layers <strong>of</strong> <strong>graphene</strong> at the border <strong>of</strong> the sample. The dierence between center and border <strong>of</strong> the
sample can be as big as 2 layers. To nd a possible explanation for this eect one must consider
a special feature <strong>of</strong> the face-to-face method. As explained in section 4.1 the face-to-face method
is used to increase the partial silicon pressure in the proximity <strong>of</strong> the substrate. At the border
<strong>of</strong> the sample the evaporated silicon atoms can escape the small gap between the two facing
samples. Therefore it is reasonable that in the area <strong>of</strong> the borders <strong>of</strong> the sample a lower silicon
pressure is present which leads to a faster growth with more nal layers.
5.2 Temperature dependence
Samples have been grown at many dierent temperatures. Figure 19 gives a summary <strong>of</strong> the
number <strong>of</strong> estimated <strong>graphene</strong> layers as a function <strong>of</strong> the growth temperature. Since the samples
don't exhibit a constant <strong>graphene</strong> thickness at all positions, the graphic shows the range <strong>of</strong>
<strong>graphene</strong> thickness which has been found on the sample. This graphic is only a best attempt
and not a denitive plot, as it was necessary to combine all methods to one number and to
calibrate the thickness axis by few ARPES measurements.
The orange sample has one special feature. As the face-to-face method should work the
better the smaller the gap between the two samples is, it seemed logical to try to grow samples
with a nominally d=0 gap. The rst test at 1400 ◦ C worked well as illustrated but for higher
temperatures the surface <strong>of</strong> the sample was destroyed and extremely rough. This is probably an
eect where the samples are glued together at the growth temperature and destroyed if taken
apart afterwards. As it was not possible to achieve a high quality surface for a d=0 gap, it has
been given up quite soon and returned to the Ta-foil as a distance piece.
27

Figure 19: Illustration <strong>of</strong> position dependent estimated <strong>graphene</strong> thickness for variable
temperature
The overall trend in gure 19 is clearly visible. At a higher temperature more <strong>graphene</strong> layers
are grown during the same period <strong>of</strong> time. This is an expected result as a higher temperature
causes an eectively higher silicon evaporation rate which will lead to more <strong>graphene</strong> layers.
The overall temperature <strong>of</strong> the onset <strong>of</strong> <strong>graphene</strong> growth (≈1500 ◦ C) is considerably higher for
the face-to-face method as compared to the growth in UHV environment (≈1200 ◦ C). This is
also in good agreement with the theory <strong>of</strong> face-to-face growth, which predicts a decrease <strong>of</strong> the
growth speed compared to the UHV growth. To reinforce the growth it is therefore necessary to
apply higher temperatures. One should also note that the growth process is very temperature
sensitive. Whereas at 1500 ◦ C one layer <strong>of</strong> <strong>graphene</strong> grows in 20 minutes, at 1550 ◦ C three
layers <strong>of</strong> <strong>graphene</strong> develop in the same amount <strong>of</strong> time. Therefore the evaporation rate triples
while only increasing the temperature by 50 ◦ C. Thus it is very important to achieve a close
temperature control in order to obtain a close control <strong>of</strong> the thickness.
As this graphic shows even samples which are grown at the nominally same parameters can
exhibit a dierent amount <strong>of</strong> <strong>graphene</strong>, as it is most striking if one compares the blue and the
dark green sample. These are samples <strong>of</strong> dierent sets which are grown at the nominally same
temperature. The reason for this eect is still under discussion. There could be diculties with
the temperature measurement as the pyrometer is not very accurate and it is questionable if
the nominal dierence <strong>of</strong> 10 ◦ C between the purple (1525 ◦ C) and dark green/blue (1535 ◦ C) is
28

controllable with this technique. Moreover instabilities <strong>of</strong> the power supply could be responsible
for dierences between dierent growing procedures as the power supply has been used above
the ocial range. Finally the mechanical problems <strong>of</strong> the wrap and the contact between the
Ta-foil and the substrate need to be taken into account. As explained in section 4.2 this could
cause dierences between the two samples <strong>of</strong> one set. In the same way this could also introduce
a dierence between dierent sets as perhaps it is once tighter or looser than the other time.
Therefore overall resistance and overall current could dier or the dierence between the two
partners could be smaller or bigger. More research is necessary at this point which would include
measuring both samples <strong>of</strong> a set.
At the same time, eort should be put into improvement <strong>of</strong> the mechanical implementation <strong>of</strong>
the face-to-face method. One design with several molybdenum plates, which are held together
by rods and nuts, failed due to the additional heating <strong>of</strong> the molybdenum material. Moreover
technical problems showed up with the handling <strong>of</strong> many small pieces and an overall higher resistance
<strong>of</strong> the sample sandwich. Nevertheless further improvement <strong>of</strong> this design or development
<strong>of</strong> a new one is necessary to gain reproducible results.
5.3 Orientation dependence
The reorganization <strong>of</strong> surfaces and the formation <strong>of</strong> big macro terraces at high temperatures
is called step bunching as the single layer steps, due to the vicinal miscut, bunch together to
form macro steps [11]. If resistive heating is performed this can be induced by electromigration
[37]. Electromigration is the eect <strong>of</strong> a force on the diusing adatoms on the surface by the
conducting electrons. The step bunching only occurs in a special orientation <strong>of</strong> the current
relative to the steps <strong>of</strong> the vicinal miscut, which are normally described as step-up and stepdown.
Sometimes the direction <strong>of</strong> the current which is necessary for step bunching even changes
for dierent temperature ranges [37].
To this date no literature can be found if electromigration induced step bunching occurs during
<strong>graphene</strong> growth as most <strong>of</strong> the heating is performed by e-beam heating. In this work samples
have been grown in controlled orientations <strong>of</strong> the original step direction, as induced by the miscut,
and the direction <strong>of</strong> the electrical current. Three samples have been grown in dierent directions
(step-up, step-down and along the original steps) at similar temperatures. No extremely striking
dierences <strong>of</strong> the surface morphology have been observed in the AFM images. As explained in
section 3.1 the surface morphology <strong>of</strong> a given sample varies signicantly with position. Due to
the small number <strong>of</strong> samples which are tested under consideration <strong>of</strong> this aspect and this big
variance within one sample it hasn't been possible to attribute any signicant change to the
dierent orientation. Nevertheless one can not denitely exclude that electromigration might
have an eect based on this results.
One interesting point should be noted about the sample, where the current is running along the
original steps. The nal steps are orientated perpendicular to the current. Therefore the terraces
have completely reorganized and are mainly inuenced by the electrical current rather than the
vicinal miscut. Moreover, although the results are not statistically good enough to give a denite
29

answer about the best orientation, this sample seemed to have a slightly improved surface. More
work will be necessary to understand the mechanism behind this eect and perhaps utilize it for
the growth <strong>of</strong> high quality samples.
5.4 Surface quality <strong>of</strong> <strong>graphene</strong>
As the goal <strong>of</strong> this project was to grow mono- and bilayer <strong>graphene</strong> with a high surface order, one
nally needs to combine the thickness data with the surface morphology. This is quite challenging
and can't be done with perfect accuracy. On the one hand the spot size <strong>of</strong> the probing sources
<strong>of</strong> LEED, AES and ARPES is around 1mm whereas the AFM shows images <strong>of</strong> 10 µm x 10 µm.
Therefore the thickness from spectroscopic estimates is averaged over quite a large area while
the surface morphology can only be identied for small places. Moreover the experimental setup
does not allow to identify the spot <strong>of</strong> the measurement very accurate. Nevertheless it is possible
to clearly discriminate between the middle and the border <strong>of</strong> the samples.
Broad, uniform terraces <strong>of</strong> up to 2 µm width as in gure 15c can only be observed on the
middle <strong>of</strong> samples with very low <strong>graphene</strong> thickness. The border <strong>of</strong> the samples as well as
samples which show a considerable amount <strong>of</strong> <strong>graphene</strong> (at least one monolayer) in the middle
usually look worse. The terraces are smaller and not longer at, but exhibit pits and holes as
demonstrated in gure 20. The terraces can be up to 1 µm wide but they are littered with pits.
Figure 20: AFM image <strong>of</strong> a place with approximately 2ML <strong>of</strong> <strong>graphene</strong>
The assumption <strong>of</strong> well ordered surfaces at low temperatures and roughened surfaces at higher
temperatures or the border <strong>of</strong> the samples can be veried for all studied samples. Therefore
one is forced to believe that the big terraces don't carry <strong>graphene</strong> but are still SiC or at most
the reconstruction layer. The trend <strong>of</strong> an increasing terrace width at increasing temperatures in
gure 15 is only true for the range <strong>of</strong> 1200 − 1400 ◦ C. At temperatures above 1500 ◦ C, which
is identical with the onset <strong>of</strong> <strong>graphene</strong> growth, the trend turns around and the surface becomes
30

less ordered. Therefore the face-to-face method proves itself by giving rise to a well ordered SiC
surface but can't prevent the surface roughening during the <strong>graphene</strong> growth.
Comparison with the literature data nevertheless shows an improvement. The UHV grown
sample (compare section 3.1, gure 6) has an even worse surface quality. Therefore the faceto-face
method is an improvement although it is disappointing that the roughening during the
<strong>graphene</strong> growth still shows up even if the eect is less important than for UHV growth. On the
other hand one must note that a recent trial to improve the surface quality by growing <strong>graphene</strong>
under an argon atmosphere lead to an even higher surface quality [11]. This group succeeded in
growing uniform terraces <strong>of</strong> up to 3 µm. Future investigations will show if a improved face-to-face
method can be used to achieve this quality.
31

6 Conclusion
In this work a new method for the growth <strong>of</strong> <strong>epitaxial</strong> <strong>graphene</strong> has been presented. The face-t<strong>of</strong>ace
method is dened by a special geometric design which increases the silicon pressure during
the growth process. Due to the higher silicon pressure a higher growth temperature can be used
which is supposed to give rise to better surface ordering. 14 samples have been grown by this
technique at dierent temperatures and substrate orientations. Extensive characterization <strong>of</strong> the
samples has been conducted by AFM to study the surface morphology and terrace sizes. ARPES,
LEED and AES have been used to identify the number <strong>of</strong> <strong>graphene</strong> layers.
All measurement techniques gave consistent results in comparison <strong>of</strong> the data with each other
as well as with the literature. Similar to the growth <strong>of</strong> <strong>graphene</strong> in UHV the thickness can
be controlled by the temperature with increasing thickness at higher temperatures. However
the overall temperature is higher for the face-to-face method. Several samples in the range <strong>of</strong>
monolayer to trilayer <strong>graphene</strong> have been grown at temperatures between 1500 ◦ C − 1550 ◦ C.
Graphene samples exhibit terraces <strong>of</strong> up to 1 µm width with some small pits. Although the
small pits indicate that surface roughening is still present, the overall surface quality is better
than for UHV growth as this leads to average terraces <strong>of</strong> only 50 nm. This is further supported
by the observation <strong>of</strong> quite a sharp band structure. The results don't indicate a dependence <strong>of</strong>
the surface quality from relative orientation <strong>of</strong> electrical current to the initial step direction.
Till now the method is not perfectly controlled, which can sometimes result in quite big
dierences between samples with nominally similar parameters. Further work with special eort
into the improvement <strong>of</strong> the technical implementation <strong>of</strong> the method is necessary. It would also
be a promising route to change the annealing time which has been kept constant for all samples
<strong>of</strong> this project.
Further studies should additionally consider the use <strong>of</strong> other characterization methods. Due to
the reduced scattering an improved surface quality is expected to give rise to improved transport
properties as for example a higher carrier mobility. Transport measurements would be a route to
conrm this and to estimate the domain size. As <strong>graphene</strong> sheets can grow uninterrupted over
substrate steps this domain size can be signicantly bigger than the terrace size. On the other
hand STM measurements can show if this uninterrupted growth is also possible over the big
steps which come along with the big terrace size. LEEM measurements can be used to image the
thickness <strong>of</strong> <strong>graphene</strong> on the sample. This would allow to determine the quality <strong>of</strong> the thickness
control. Finally Raman measurements could be interesting due to the small spot size which
allows to probe single terraces independently.
In this project it was shown that the principle idea behind the face-to-face method is working
and that <strong>graphene</strong> samples <strong>of</strong> promising quality can be grown. The use <strong>of</strong> four dierent techniques
allowed broad characterization <strong>of</strong> the samples and showed that the method gives rise to an
improved surface quality while the <strong>graphene</strong> properties remain unaltered. With some further
work the face-to-face method will hopefully become a way to grow high quality samples <strong>of</strong>
<strong>epitaxial</strong> <strong>graphene</strong>.
32

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