Growth of epitaxial graphene on 6H-SiC(0001) with

face-to-face technique

Report

by

Annemarie Köhl

February 27, 2009

Supervisors:

Prof. Alessandra Lanazara

Prof. Ralph Claessen

Lawrence Berkeley Laboratory

Materials Sciences Division

Abstract

In this work a new technique to grow epitaxial graphene on 6H-SiC(0001) silicon carbide wafers is

employed to achieve a better controllable growth and higher quality samples. Epitaxial graphene

is a reliable candidate for all kind of applications as it has similar properties to carbon nanotubes

and exfoliated graphene but is more appropriate for the design of electronic devices as it can

be grown in wafer-sized pieces. However, to this date it is still a big issue to control graphene

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 of terrace size as well as graphene 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 elec-

tron 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 of carbon on the sample, which is related to

the number of graphene layers. LEED and ARPES are useful tools to estimate the number of

graphene layers and give a sense of the sample quality.

The graphene thickness is studied extensively as a function of the growth temperature. The

overall temperature which is necessary for the formation of graphene with the face-to-face method

is considerably higher than for the usual growth of graphene in UHV. A closer analysis reveals

a clear relation between growth temperature and graphene thickness with an increasing number

of graphene layers at increasing temperatures. Actually the measurements suggest that in the

interesting range of monolayer to few-layer graphene the growth temperature is a very sensitive

parameter.

In the temperature range 1500− 1550 C several samples with mono- to trilayer graphene 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 of the new

technique and support the further development of the face-to-face method. As an unwanted

side eect a dierence in graphene thickness has been observed between the middle and the

border of the sample. Beside the temperature dependence the inuence of the relative direction

of the heating current to the vicinal miscut of the substrate has been studied. No signicant

dependence of the relative orientation has been observed at our samples.

2

Contents

1 Introduction 4

2 Materials and methods 6

2.1 General graphene properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2 Silicon carbide substrate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.3 Growth of epitaxial graphene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.4 Measurement techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3 Characterization of epitaxial graphene 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 of graphene thickness . . . . . . . . . . . . . . . . . . . . . . . . . 27

5.2 Temperature dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

5.3 Orientation dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

5.4 Surface quality of graphene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

6 Conclusion 32

3

1 Introduction

The two dimensional (2D) honeycomb lattice of carbon atoms, which is widely referred to as

graphene, has received great interest during the last 5 years [1, 2, 3]. Although it has been

known as a building part of 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 graphene 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 of a linear energy-momentum

dispersion. The electrons and holes behave like massless Dirac fermions with a speed of light

of c ≈ 10−6 m/s and reveal a pseudospin due to two carbon sublattices. Besides this insight into

theoretical questions graphene has many possible applications.

Due to its unique electronic properties graphene is a candidate to replace silicon in all kind

of 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 of

a graphene sheet by manipulating the boundary conditions is interesting for applications [6, 8].

For example it would be possible to engineer a complete device consisting of semiconducting and

conducting parts out of one material [1]. Moreover bilayer or trilayer graphene, which consists

of 2 or 3 layers of carbon atoms respectively, reveal dierent properties and gain increasing

interest. Bilayer graphene 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 of normal 2D lithographic techniques - and the high stability of graphene

under processing as well as in air is encouraging from a technical point of view [10].

Mechanically exfoliated akes, which are peeled o of bulk graphite, have desirable charac-

teristics like a high crystal quality and extremely weak coupling to the supporting substrate

and therefore have widely been used for basic research. However, epitaxially grown graphene is

the more promising candidate for large scale applications [8]. Epitaxial graphene is grown on

a silicon carbide (SiC) wafer by evaporation of silicon. It exhibits the typical 2D behavior of

graphene, but has the big advantage of being available on wafer sized pieces. On the other hand

till now the quality in terms of homogeneity of the number of carbon layers as well as terrace size

of epitaxial graphene is poor and a lot of research is performed in order to produce high quality

samples [11, 12].

In this project a new technique of growing epitaxial graphene samples has been employed in

order to improve the sample quality. The goal was to produce samples of a specic thickness of

graphene, concentrating on mono- and bilayer graphene, with big terrace sizes. The principle

idea behind the new method is to increase the partial silicon pressure in proximity of the sample,

which slows down the growth process. The high silicon pressure is achieved by the so-called face-

to-face growth, where two samples are brought geometrically very close together. The decreased

4

speed of the growing process allows one to use higher temperatures, which generally leads to a

better ordered surface [11].

To characterize quality and thickness of 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 of 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 of terrace size.

The later three methods give a characteristic signal for a dierent number of layers and can be

used to determine the graphene 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 of the properties of graphene and the substrate SiC.

Subsequently the growth process of epitaxial graphene, the measurement techniques and the face-

to-face method are introduced. Afterwards literature data is presented for later characterization

of the samples. Finally the results are presented, discussed and compared with the literature.

5

2 Materials and methods

2.1 General graphene properties

A sheet of graphene is made of a 2D honeycomb structure of carbon atoms [1, 3]. The single

atomic layer of graphene can be seen as the mother of 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 of aG = 2.46 Å [13]. The two sublattices give

rise to some special graphene properties as for example the pseudospin.

In plane the carbon atoms are bonded by sp2 bonds in a hexagon. Out of plane delocalized π-

electrons give rise to the interesting electronic properties of graphene. Two of the high symmetry

points of the hexagonal Brillouin zone are the Γ-point in the center and the K-point in the

corner of the hexagon. Whereas nearly everything in condensed matter physics is described by

the Schroedinger equation, graphene shows an unusual behavior. In contrast to the ordinary

parabolic dispersion of a free electron, graphene exhibits a linear dispersion in the vicinity of 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 of the two cones is therefore called the Dirac point. For undoped graphene the

energy of the Dirac point ED is identical with the Fermi level EF . Thus, freestanding graphene

is called a semi-metal or zero-gap semiconductor.

Figure 1: Left: Atomic structure of graphene [3] Right: Electronic structure of graphene [14]

There are two common approaches for the production of graphene. Exfoliated graphene is

peeled o a graphite crystal with tape [6]. The critical point for the discovery of exfoliated

graphene was the usage of an interference eect on a 300nm SiO2 wafer, which allows one to

identify few-layer-pieces with an optical microscope. Even though exfoliated graphene is the

more natural form and was mainly used to answer initial questions, the problem of small pieces

in applications lead to increased interest on epitaxial graphene. The growth of epitaxial graphene

by thermal decomposition of a SiC substrate will be described in more detail in the following

sections. In contrast to exfoliated graphene epitaxial graphene 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

6

caused by lattice mismatch, or a shift of the Dirac point below the Fermi level due to doping

[3]. Therefore one must strictly distinguish between the two dierent types of graphene. As this

work is exclusively about epitaxial graphene the term graphene is used synonymical for epitaxial

graphene in the following parts of 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 of SiC in ultrahigh vacuum (UHV)

leads to evaporation of silicon, which leaves behind a carbon-rich surface. Later it has been

proven that these carbon layers order into a graphene structure [8, 18]. This instance together

with the fact that SiC is a well known wide-gap semiconductor (Egap = 3 eV) has lead to the

majority of research about epitaxial graphene 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 of dierent orientations of adjacent bilayers is nearly

degenerated, SiC grows in more than 100 dierent polytypes. Nevertheless for the purpose of

growing graphene 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 of 6H-SiC is described by the unit cell vectors aSiC = 3.08 Å and cSic = 15.11 Å [2, 19].

Figure 2: Crystal structure of 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

of the crystal. The SiC(0001) surface is called Si-face and is terminated by silicon atoms, while

7

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 of rotational disordered graphene on the C-face leading

to thick (5 to 100 layers) graphene. However, graphene on the Si-face is rotationally ordered

and well aligned under an angle of 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 of the early

research concentrated on the Si-face, although by now the C-face receives new interest. The

group of de Heer has argued that some small rotation of adjacent graphene sheets leads to a very

weak coupling between each set of 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 of SiC(0001), but one should

always keep in mind that the C-face would give dierent results.

2.3 Growth of epitaxial graphene

Although the process of silicon evaporation on SiC was known since 1975 [17], this graphitized

SiC surface did not gain a lot of interest. The big boom started when Berger et al. [8] showed

that this thin graphite exhibits 2D electron gas behavior. The growth of epitaxial graphene is

based on thermal decomposition of 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 of the background pressure in the vacuum chamber has been conducted

[2]. From the molar densities one can calculate that approximately 3 bilayers of SiC are necessary

to set free enough carbon atoms for the formation of one graphene 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 graphene [21, 22]. However, unlike graphene one third of the

carbon atoms of this reconstruction layer has covalent bonds to underlying silicon atoms of 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 graphene as for example the lack of π-bands at the Fermi level and the

presence of a band gap.

In order to obtain graphene the annealing temperature must be increased above 1150 C. Emt-sev et al.[22] propose a growth mechanism on SiC(0001) where new graphene 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 sp2 conguration and develops

the typical graphene like delocalized π-bands with neighboring carbon atoms. Additionally the

8

evaporating silicon atom leaves behind three dangling bonds of carbon atoms in the topmost

layer of the substrate. These connect to each other to form an interface layer of covalently bound

graphene, whose structure is identical to the reconstruction layer.

Now the former reconstruction layer has evolved into a graphene layer which only interacts with

the interface layer through weak Van der Waals forces and all the typical graphene properties can

be observed. The next graphene layer grows in the same manner under the interface layer with

converting the interface layer into a graphene layer and the topmost substrate layer into a new

interface layer. This growth of new layers under the rst layer also explains the good rotational

order of graphene 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 of the dangling bonds [22]. This leads to a weak interaction of

graphene 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 of carbon atoms with

covalent bonds is called reconstruction layer to refer to the bare (6√

3×6√

3)R30 reconstructionon the substrate and is called interface layer to refer to the actual interface between SiC and

graphene 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 graphene 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 of the sample holder or the lament of 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 of the sample holder [2]. Therefore the possibility of

direct comparison of temperature values of 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 of 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 can-

tilever experiences surface forces, which have an eect on the oscillation amplitude. The change

9

of 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 of the surface. The necessary adjustments of the

height of 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 of the

sample.

Figure 3: Schematics of 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 of 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 of the diraction spots can be used to determine reciprocal

unit vectors, symmetries and surface reconstructions. In a layered structure the comparison

of intensities of dierent spots allows an estimation of layer thickness. The sharpness of spots

can nally give a sense of the sample quality in terms of 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 of a given sample.

10

2.4.3 Auger electron spectroscopy (AES)

Auger electrons arise from the Auger eect which is the non-radiative decay of a hole in the

core levels of an atom [26, 27, 28]. When a sample is bombarded by high energy electrons in

the range of keV, core level electrons are removed, leaving behind a hole. This unstable state

decays by an electron of 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 - of 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 of the L shell, which gives the energy to another electron of the L shell.

The kinetic energy of this Auger electron depends of 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

Ekin = E(K)− E(L1)− E(L2)

with E(K/L) being the binding energy of 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 of a KLL Auger process

2.4.4 Angle-resolved photoemission spectroscopy (ARPES)

Angle-resolved photoemission spectroscopy is an extremely useful tool of 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 of

Ekin = hν − Φ− |EB|

where hν is the photon energy, Φ is the work function and EB is the binding energy of the

emitted electron.

11

Figure 5: Illustration of ARPES geometry [30]

Figure 5 shows the experimental setup of an ARPES measurement. The hemispherical electron

energy analyzer measures the energy Ekin. 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 of 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 of the angles and therefore any point of the Brillouin zone.

Detecting Ekin, ϕ and ϑ nally allows to probe directly the band structure EB(k||) of a system.

12

3 Characterization of epitaxial graphene

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 typ-

ically have a small miscut and are therefore not completely at. After H2 etching the substrates

show well ordered terraces of several µm [2]. However, the graphitization in UHV environment

causes surface roughening, so that the graphene surface shows random steps and valleys (compare

gure 6). The achieved average terrace size after the graphene 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 of 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 of a UHV grown nominally 1 ML graphene sample on 6H-SiC [11]

Recent progress in the growth of better ordered surfaces has been made by Hupalo et al.[12]

by growing graphene in short heating ashes of 30 seconds and lead to 150 nm terraces. Emtsev

et al.[11] performed growing of graphene in an argon environment and succeeded in growing

terraces of a width of 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 H2 etching or

preparing Si-rich surfaces have an eect on the surface morphology of graphene. For example a

recent study suggested that H2 etching even worses the quality as the step borders are necessary

starting points for the growth process [12].

13

Surprisingly the overall coherent size of a graphene sheet as determined by transport mea-

surements is bigger than the terrace size [2]. This is explained by the observation in scanning

tunneling microscope (STM) images that graphene sheets can grow over substrate steps as well

as over graphene steps [2, 32, 12] (see gure 7).

Figure 7: STM image of a graphene sheet growing over a SiC step [12]

3.2 Crystal structure by LEED

The LEED pattern of the graphitized Si-face of SiC has been studied widely [3, 8, 18, 33]. During

step by step heating to higher temperatures dierent surface reconstructions are observed. While

some of the early patterns depend on preparation techniques, all groups agree in the observation

of a (√

3 ×√

3)R30 pattern for temperatures in the range of 1050. Further annealing leads

to the development of a (6√

3 × 6√

3)R30 reconstruction. [18, 22]. The LEED pattern of one

monolayer of graphene 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

graphene 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 of graphene compared

to SiC in real space. This ts well to the real space unit vectors of 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 of one monolayer graphene. Orange arrows indicate SiC-spots,

white arrows indicate graphite spots [3].

Right: Schematic LEED pattern with unit vectors of reciprocal lattice for SiC ~s1/~s2

and graphite overlayer ~c1/~c2. Additional spots are due to sum vectors. [18]

The mismatch of the unit cells gives rise to a coincidence lattice with a large hexagonal unit cell

of a (6√

3× 6√

3)R30 periodicity [2, 22]. In the reciprocal space this is observed as a hexagonal

set of 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 of sum vectors of

~s1, ~s2,~c1,~c2. The spot a in gure 8 is for example at the position ~c1 +~c2 − ~s2, spot b at position

~s1 + ~s2 − ~c1. Theoretically all dierent combinations of these unit vectors are possible so that

the whole (6√

3 × 6√

3)R30 mesh would appear, but as double diraction is involved most of

them are extremely faint and therefore invisible.

3.3 Thickness estimation by AES

AES has been used to identify the presence of 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 of the intensities of the silicon and the carbon peak as a function of the

number of graphene 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 of silicon atoms

of 1/3 the atom density of a SiC-bilayer, a analogous interface layer with carbon atoms, or the

growth of graphene directly on the substrate. As discussed in section 2.3, the most likely model

for the interface between SiC and graphene is the existence of an interface layer which consists of

15

Figure 9: Model of Si:C Auger peak intensity ratio versus number of graphene layers for SiC(0001)

substrates. Solid line: Model with interface layer of C adatoms at 1/3 their bilayer

density. Dotted line: Model with interface layer of 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 H2 etching (no UHV preparation), (b) UHV anneal

at 1150 C (LEED√

3×√

3 pattern), (c) UHV anneal at 1350 C (LEED 6√

3× 6√

3pattern) [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 of atoms of a given element. The interface layer has the same atom density as

graphene 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 of carbon

is the interface layer. Therefore the axis at the graph should be called number of carbon layers

and the number of actual graphene layers is always n-1. For example at a ratio of Si:C=0.1 two

carbon layer are measured which corresponds to a monolayer of graphene. A recent review states

that AES usually overestimates the number of graphene layers by one to two layers if Li's model

is used [2]. Therefore the existence of the interface layer could explain this systematical error.

16

3.4 Band structure by ARPES

Figure 10 shows the band structure of graphene. The direction of k|| within the Brillouin zone

is indicated by the green inset. The observation of the band structure allows one to observe the

whole development of the surface from the bare substrate to the formation of graphene. Whereas

the reconstruction layer only exhibits the σ-bands, monolayer graphene reveals the typical linear

dispersion of the π-bands close to the K-point as one can see in gure 10. One branch of 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 of graphene 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 of graphene layers. One can see a signicant development of the band struc-

ture with thickness which is also reproduced by the theoretical calculations. The most obvious

dierence is the appearance of additional bands for more graphene layers which is explained by

interlayer splitting [34]. Moreover one can observe a shifting of the Dirac point. Due to charge

transfer from the substrate the Dirac point of monolayer graphene is shifted below the Fermi

level. As this substrate eect decreases for increasing thickness the Dirac point approaches the

Fermi level for more graphene layers. Adsorption of alkali atoms like potassium which will trans-

fer charges to the topmost layer can systematically change the position of the Dirac point or

17

even open and close the gap in the bilayer band structure [3]. Comparing the number of bands

and the position of the Dirac point can be used to identify the thickness of a given sample.

Figure 11: ARPES data and theoretical calculations close to the Dirac point show clear variations

depending on the graphene 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

graphene develops. This work presents a new technique for growing epitaxial graphene, which

can lead to more ordered surfaces than the usual growth in UHV.

Commercial, nominally on-axis oriented wafers of 6H-SiC with a vicinal miscut of less than

±0.06 and a polished Si-face are purchased from Cree Research, Inc. The resistivity of the N-

doped wafer is ρ ≈ 0.1 Ωcm. Pieces of 4.5 cm x 6.5 cm were cut with a diamond saw in dierent

orientations with respect to the miscut of 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 of big terraces is more likely. This is similar to the approach

of growing graphene on SiC(0001) under an argon atmosphere [11] or the RF-furnace growth

of graphene on SiC(0001) [2, 20]. In both cases a better ordered surface compared to UHV-

grown 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 of the surface quality.

Technically the face-to-face conguration is obtained by cutting a L-shaped piece of 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 of 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 of 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 of the sample, red is the SiC-substrate, blue tantalum foil

pumped down to a base pressure of approximately 8 × 10−7 Torr. Afterwards the sample is

heated to 700 C for approximately 4 hours to clean the surface of contaminations like oxygen

and water. The temperature is measured with an pyrometer at ε = 0.96.After the wrapping the sample sandwich has a very high resistance in the range of several

100 kΩ, which can be explained by a bad contact between the substrate and the tantalum foil.

However, in the rst minute of the cleaning process the resistance drops into the range of 100 Ω.This is probably due to improvement of 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 of the wrap, which also support this theory.

After these preparations the sample is heated to a specic temperature for 20 minutes. The

necessary increase of the current leads to a further drop of the resistance into the range of several

10 Ω. The temperature is the main parameter which has been varied in this work. During the

project in total 14 sets of 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 of 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 DimensionTM 3100 Atomic Force Microscope from Digital

Instruments in tapping mode. An AFM image of the bare SiC substrate as it looks like before

any kind of treatment is shown in gure 14.

Figure 14: AFM image of a SiC substrate (surface polished, no further treatment)

The surface is quite at on a height scale of 8nm with some scratches which originate from

the polishing process. Some white spots are visible which are probably pieces of dirt. One face-

to-face set has only been wrapped and heated to 700 C in order to examine the eect of 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 of the polishing are still visible.

For all samples which are heated above 1200 C a change compared to the bare substrate ap-

pears. 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 of 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 of the same set are roughly similar and show terraces in

the middle of 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 of the same wafer the only critical point is the wrapping of 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 of the foil to the two samples is dierent. This

could be supported by the observation that the overall resistance of the sample sandwich drops

during the rst minute of the cleaning process. Perhaps even if the initial contact is similar,

this improvement of the contact is dierent for the two samples. For example if the contact

21

Figure 15: Trend of terrace size to increase for temperature range 1200 C-1400 C

becomes signicantly better on one side, most of 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 of the semiconducting SiC substrate.

On the other hand one would normally expect thermal radiation to be very high at this temper-

ature and therefore due to the small distance of 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 of the

electron gun is in the order of one millimeter, the images are always average images of a large

area of the sample. A kinetic energy of Ekin = 98.9 eV has been used and a camera has been

employed to take pictures of the uorescent screen. Figure 16 shows images which are taken at

dierent samples and illustrate dierent steps in the graphene growth process.

Pattern a) shows only the bulk SiC spots. In this case no considerable amount of graphene 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 graphene

layers than sample b). A drop in the intensity of the SiC spots can be observed because the

22

Figure 16: LEED pattern at dierent stages of graphene growth. Orange circle marks SiC spot,

white circle marks graphite spot.

a) SiC substrate b) Reconstruction layer/Monolayer c) Bilayer d) 5-6 layers of

graphene

additional graphene 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 graphene layers. For more than 6-8 graphene layers the LEED image is identical to that

of graphite as the electrons don't probe the SiC surface any more.

Although LEED is a very fast tool to get a sense of the surface structure it is hard to achieve

accurate thickness estimations based on LEED images. Firstly the intensity of 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 of an intensity ratio of the spots is very

error-prone as background intensity, adjustment of the lenses and the size of 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 of 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 of 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 of 3 keV. The data is taken with the medium

area lens mode and a pass energy of 15 eV. After the measurement the data is averaged over

the angle and dierentiated to decrease the eect of 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 of 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 of gure 17 for example exhibits monolayer to bilayer graphene as

23

Figure 17: AES data of a sample with a thickness of 1-2 layer graphene. 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 of Si : C ≈ 0.1 if the

interface layer is taken into account or Si : C ≈ 0.3 otherwise. This is an order of magnitude

smaller than the measured ratio of 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 ∝ Ekin. In the Fixed Analyzer Transmission (FAT) mode the energy

resolution is kept constant for all energies. This leads to an decrease of the intensity with

increasing kinetic energy as I ∝ 1Ekin

. Due to experimental limitations of 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 of the derivative. The use of 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 of

this eect leads to a smaller Si:C ratio but it is still not comparable to the literature data. A

development of the experimental conditions is under way so an experimental test of the dierent

analyzer modes can be performed soon.

Another dierence between a CMA and a hemispherical analyzer is the geometry of 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 of 42. However, in our

case the electron gun is mounted under an angle while the analyzer is orientated vertically.

Reconstruction of 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 of 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 of parameters like the resolution or the modulation voltage.

Therefore it is still not clear what causes the dierence of 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 of two reference samples has been determined

by ARPES measurements (compare chapter 4.5). A sample with 1.5 ML of graphene showed a

Si:C ratio of Si : C ≈ 2.4 and a sample with approximately 3 layers of graphene had a ratio of

Si : C ≈ 1.1. These two samples are sucient to give a rough estimate of the graphene 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 of the number of 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 of 10 eV and the low angular dispersion

lens mode. The excitation of the photoelectrons steams from a Helium lamp, where the HeII

signal was used (EHeII = 40.81 eV). One sample was measured at the Advanced Light Source,

Beamline 10.

Figure 18: ARPES data of a sample between monolayer and bilayer graphene

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 of 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 of 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 of gure 11 which has been taken at a

synchrotron with a smaller spot size and probably better base pressure. Therefore the quality of

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 of

dierent areas which exhibit monolayer and bilayer graphene or if the whole surface is covered

by a mono- and bilayer mixture.

26

5 Results and discussion

5.1 Determination of graphene thickness

As explained in previous sections, LEED, AES and ARPES can be used to characterize the

number of graphene layers. Although some techniques don't allow to give an exact number of

graphene layers, it is always possible to compare the results of the dierent samples relatively

and order these by less, more or equal graphene thickness. Independent analysis of 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 of layers.

Therefore the qualitative trends are determined by three independent methods whereas the

quantitative number of 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 of the

reference data in the literature. Therefore the face-to-face method does not change the electronic

or crystal properties of graphene but only introduces changes into the surface quality.

As well as all methods agree on dierent graphene thickness on dierent samples, they also

show uniformly a position dependence of the thickness on one sample. One usually nds more

layers of graphene at the border of the sample. The dierence between center and border of the

sample can be as big as 2 layers. To nd a possible explanation for this eect one must consider

a special feature of 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 of the substrate. At the border

of the sample the evaporated silicon atoms can escape the small gap between the two facing

samples. Therefore it is reasonable that in the area of the borders of 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 of the

number of estimated graphene layers as a function of the growth temperature. Since the samples

don't exhibit a constant graphene thickness at all positions, the graphic shows the range of

graphene 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 of 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 of position dependent estimated graphene thickness for variable

temperature

The overall trend in gure 19 is clearly visible. At a higher temperature more graphene layers

are grown during the same period of time. This is an expected result as a higher temperature

causes an eectively higher silicon evaporation rate which will lead to more graphene layers.

The overall temperature of the onset of graphene 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 of face-to-face growth, which predicts a decrease of 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 of graphene grows in 20 minutes, at 1550 C three

layers of graphene develop in the same amount of 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 of the thickness.

As this graphic shows even samples which are grown at the nominally same parameters can

exhibit a dierent amount of graphene, as it is most striking if one compares the blue and the

dark green sample. These are samples of 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 of 10 C between the purple (1525 C) and dark green/blue (1535 C) is

28

controllable with this technique. Moreover instabilities of 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 of 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 of 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 of a set.

At the same time, eort should be put into improvement of the mechanical implementation of

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 of the molybdenum material. Moreover

technical problems showed up with the handling of many small pieces and an overall higher resis-

tance of the sample sandwich. Nevertheless further improvement of this design or development

of a new one is necessary to gain reproducible results.

5.3 Orientation dependence

The reorganization of surfaces and the formation of 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 of a force on the diusing adatoms on the surface by the

conducting electrons. The step bunching only occurs in a special orientation of the current

relative to the steps of the vicinal miscut, which are normally described as step-up and step-

down. Sometimes the direction of 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

graphene growth as most of the heating is performed by e-beam heating. In this work samples

have been grown in controlled orientations of the original step direction, as induced by the miscut,

and the direction of 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 of the surface morphology have been observed in the AFM images. As explained in

section 3.1 the surface morphology of a given sample varies signicantly with position. Due to

the small number of samples which are tested under consideration of 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 of high quality samples.

5.4 Surface quality of graphene

As the goal of this project was to grow mono- and bilayer graphene 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 of the probing sources

of LEED, AES and ARPES is around 1mm whereas the AFM shows images of 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 of the measurement very accurate. Nevertheless it is possible

to clearly discriminate between the middle and the border of the samples.

Broad, uniform terraces of up to 2 µm width as in gure 15c can only be observed on the

middle of samples with very low graphene thickness. The border of the samples as well as

samples which show a considerable amount of graphene (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 of a place with approximately 2ML of graphene

The assumption of well ordered surfaces at low temperatures and roughened surfaces at higher

temperatures or the border of the samples can be veried for all studied samples. Therefore

one is forced to believe that the big terraces don't carry graphene but are still SiC or at most

the reconstruction layer. The trend of an increasing terrace width at increasing temperatures in

gure 15 is only true for the range of 1200− 1400 C. At temperatures above 1500 C, whichis identical with the onset of graphene 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 graphene 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 face-

to-face method is an improvement although it is disappointing that the roughening during the

graphene 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 graphene

under an argon atmosphere lead to an even higher surface quality [11]. This group succeeded in

growing uniform terraces of 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 of epitaxial graphene has been presented. The face-to-

face 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 of 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 of graphene layers.

All measurement techniques gave consistent results in comparison of the data with each other

as well as with the literature. Similar to the growth of graphene 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 of

monolayer to trilayer graphene have been grown at temperatures between 1500 C − 1550 C.Graphene samples exhibit terraces of 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 of only 50 nm. This is further supported

by the observation of quite a sharp band structure. The results don't indicate a dependence of

the surface quality from relative orientation of 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 of the technical implementation of the method is necessary. It would also

be a promising route to change the annealing time which has been kept constant for all samples

of this project.

Further studies should additionally consider the use of 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 graphene 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 of graphene on the sample. This would allow to determine the quality of 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 graphene samples of promising quality can be grown. The use of four dierent techniques

allowed broad characterization of the samples and showed that the method gives rise to an

improved surface quality while the graphene properties remain unaltered. With some further

work the face-to-face method will hopefully become a way to grow high quality samples of

epitaxial graphene.

32

References

[1] A. K. Geim and K. S. Novoselov. The rise of graphene. Nat Mater, 6(3):183191, March

2007.

[2] J. Hass, De W. A. Heer, and E. H. Conrad. The growth and morphology of epitaxial

multilayer graphene. Journal of Physics: Condensed Matter, 20(32):323202+, 2008.

[3] Th Seyller, A. Bostwick, K. V. Emtsev, K. Horn, L. Ley, J. L. Mcchesney, T. Ohta, J. D.

Riley, E. Rotenberg, and F. Speck. Epitaxial graphene: a new material. Physica status

solidi (b), 245(7):14361446, 2008.

[4] Eduardo Fradkin. Critical behavior of disordered degenerate semiconductors. II. Spectrum

and transport properties in mean-eld theory. Phys. Rev. B, 33(5):32633268, Mar 1986.

[5] L. D. Landau. Zur Theorie der Phasenumwandlungen II. Phys. Z. Sowjetunion, 11:2635,

1937.

[6] K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V.

Grigorieva, and A. A. Firsov. Electric Field Eect in Atomically Thin Carbon Films. Science,

306(5696):666669, 2004.

[7] K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grig-

orieva, S. V. Dubonos, and A. A. Firsov. Two-dimensional gas of massless dirac fermions in

graphene. Nature, 438(7065):197200.

[8] Claire Berger, Zhimin Song, Tianbo Li, Xuebin Li, Asmerom Y. Ogbazghi, Rui Feng, Zhent-

ing Dai, Alexei N. Marchenkov, Edward H. Conrad, Phillip N. First, and Walt A. de Heer.

Ultrathin epitaxial graphite: 2d electron gas properties and a route toward graphene-based

nanoelectronics. J.Phys.Chem., 108:19912, 2004.

[9] Taisuke Ohta, Aaron Bostwick, J. L. Mcchesney, Thomas Seyller, Karsten Horn, and Eli

Rotenberg. Interlayer interaction and electronic screening in multilayer graphene inves-

tigated with angle-resolved photoemission spectroscopy. Physical Review Letters, 98(20),

2007.

[10] Walt A. de Heer, Claire Berger, Xiaosong Wu, Phillip N. First, Edward H. Conrad, Xuebin

Li, Tianbo Li, Michael Sprinkle, Joanna Hass, Marcin L. Sadowski, Marek Potemski, and

Gérard Martinez. Epitaxial graphene. Solid State Communications, 143(1-2):92100, July

2007.

[11] Konstantin V. Emtsev, Aaron Bostwick, Karsten Horn, Johannes Jobst, Gary L. Kellogg,

Lothar Ley, Jessica L. McChesney, Taisuke Ohta, Sergey A. Reshanov, Eli Rotenberg, An-

dreas K. Schmid, Daniel Waldmann, Heiko B. Weber, and Thomas Seyller. Atmospheric

pressure graphitization of SiC(0001) - A route towards wafer-size graphene layers. ArXiv

e-prints, 2008.

33

[12] M. Hupalo, E. Conrad, and M. C. Tringides. Growth mechanism for epitaxial graphene on

vicinal 6H-SiC(0001) surfaces. ArXiv e-prints, September 2008.

[13] Pauling L. Kukesh J. S. The problem of the graphite structure. American Mineralogist,

35:125125, 1950.

[14] http://www.magnet.fsu.edu/inhouseresearch/condensedmatter/electroninteraction.html

accessed on 01/19/09.

[15] Dong S. Lee, Christian Riedl, Benjamin Krauss, Klaus von Klitzing, Ulrich Starke, and

Jurgen H. Smet. Raman spectra of epitaxial graphene on SiC and of epitaxial graphene

transferred to SiO2. Nano Lett., November 2008.

[16] Nicola Ferralis, Roya Maboudian, and Carlo Carraro. Evidence of structural strain in

epitaxial graphene layers on 6H-SiC(0001). Physical Review Letters, 101(15):156801, 2008.

[17] A. van Bommel. LEED and Auger electron observations of the SiC(0001) surface. Surface

Science, 48:463472, March 1975.

[18] I. Forbeaux, J.-M. Themlin, and J.-M. Debever. Heteroepitaxial graphite on 6H-

SiC(0001): Interface formation through conduction-band electronic structure. Phys. Rev.

B, 58(24):1639616406, Dec 1998.

[19] Tianbo Li. Characteristics of graphite lms on silicon- and carbon-terminated faces of silicon

carbide. Doctoral thesis, 2006.

[20] Walter A. de Heer. Epitaxial graphene: A new platform for nanoelectronics. Seminar talk,

2008.

[21] K. V. Emtsev, Th Seyller, F. Speck, L. Ley, P. Stojanov, J. D. Riley, and R. G. C. Leckey.

Initial stages of the graphite-SiC(0001) interface formation studied by photoelectron spec-

troscopy. Mater. Sci. Forum, 556-557:525, 2007.

[22] K. V. Emtsev, F. Speck, Th. Seyller, L. Ley, and J. D. Riley. Interaction, growth, and order-

ing of epitaxial graphene on SiC(0001) surfaces: A comparative photoelectron spectroscopy

study. Physical Review B (Condensed Matter and Materials Physics), 77(15):155303, 2008.

[23] Scanning probe microscopy training notebook. Digital instruments Veeco Metrodgy Group,

2000.

[24] M.A. Van Hove, W.H. Weinberg, and C.-M. Chan. Low Energy Electron Diraction.

Springer-Verlag, Berlin, XVII edition, 1986.

[25] Michael P. Marder. Condensed Matter Physics. Wiley-Interscience, January 2000.

[26] Wolfgang Demtröder. Experimentalphysik 3: Atome, Moleküle und Festkörper. Springer,

Berlin, 2005.

34

[27] M. P. Seah D. Briggs. Practical Surface Analysis: By Auger and X-ray Photo-electron

Spectroscopy. Wiley, 3rd edition, 1983.

[28] Lawrence E. Davis. Handbook of Auger Electron Spectroscopy: A Reference Book of Standard

Data for Identication and Interpretation of Auger Electron Spectroscopy Data. Physical

Electronics Industries, 2 edition, 1976.

[29] St. Hüfner. Photoelectron Spectroscopy. Springer, Berlin, Heidelberg, 2nd edition, 1996.

[30] Andrea Damascelli. Probing the electronic structure of complex systems by arpes. Physica

Scripta, T109:6174, 2004.

[31] J. B. Hannon and R. M. Tromp. Pit formation during graphene synthesis on SiC(0001):

In situ electron microscopy. Physical Review B (Condensed Matter and Materials Physics),

77(24):241404, 2008.

[32] Th. Seyller, K.V. Emtsev, K. Gao, F. Speck, L. Ley, A. Tadich, L. Broekman, J.D. Ri-

ley, R.C.G. Leckey, O. Rader, A. Varykhalov, and A.M. Shikin. Structural and electronic

properties of graphite layers grown on SiC(0001). Surface Science, 600(18):3906 3911,

2006.

[33] E. Rollings, G.-H. Gweon, S.Y. Zhou, B.S. Mun, J.L. McChesney, B.S. Hussain, A.V. Fe-

dorov, P.N. First, W.A. de Heer, and A. Lanzara. Synthesis and characterization of atom-

ically thin graphite lms on a silicon carbide substrate. Journal of Physics and Chemistry

of Solids, 67(9-10):2172 2177, 2006.

[34] Taisuke Ohta, Aaron Bostwick, J. L. Mcchesney, Thomas Seyller, Karsten Horn, and Eli

Rotenberg. Interlayer interaction and electronic screening in multilayer graphene inves-

tigated with angle-resolved photoemission spectroscopy. Physical Review Letters, 98(20),

2007.

[35] David A. Siegel. Personal communication, 2008.

[36] Manual for Hemispherical Energy Analyzer Series, Phoibos 150. SPECS, 2.08 edition, 2006.

[37] B.J. Gibbons, S. Schaepe, and J.P. Pelz. Evidence for diusion-limited kinetics during

electromigration-induced step bunching on Si(111). Surface Science, 600(12):2417 2424,

2006.

35