Report. Annemarie Köhl. February 27, Supervisors: Prof. Alessandra Lanazara Prof. Ralph Claessen

Transcription

1 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

2 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 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 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 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

3 Contents 1 Introduction 4 2 Materials and methods General graphene properties Silicon carbide substrate Growth of epitaxial graphene Measurement techniques Characterization of epitaxial graphene Surface morphology by AFM Crystal structure by LEED Thickness estimation by AES Band structure by ARPES Experiment Sample growth with face-to-face method AFM measurements LEED measurements AES measurement ARPES measurements Results and discussion Determination of graphene thickness Temperature dependence Orientation dependence Surface quality of graphene Conclusion 32 3

4 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 characteristics 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 faceto-face growth, where two samples are brought geometrically very close together. The decreased 4

5 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 faceto-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

6 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 sp 2 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 E D is identical with the Fermi level E F. 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 SiO 2 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

7 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 (E gap = 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 = 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

8 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 ( )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. Emtsev 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 sp 2 conguration and develops the typical graphene like delocalized π-bands with neighboring carbon atoms. Additionally the 8

9 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 ( )R30 reconstruction on 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 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 cantilever experiences surface forces, which have an eect on the oscillation amplitude. The change 9

10 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] 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 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

11 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 E kin = E(K) E(L 1 ) E(L 2 ) 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 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 E kin = hν Φ E B where hν is the photon energy, Φ is the work function and E B is the binding energy of the emitted electron. 11

12 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 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 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 E kin, ϕ and ϑ nally allows to probe directly the band structure E B (k ) of a system. 12

13 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 typically have a small miscut and are therefore not completely at. After H 2 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 H 2 etching or preparing Si-rich surfaces have an eect on the surface morphology of graphene. 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

14 Surprisingly the overall coherent size of a graphene 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 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 Further annealing leads to the development of a ( )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

15 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 s 1 / s 2 and graphite overlayer c 1 / c 2. 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 ( )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 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 of these unit vectors are possible so that the whole ( )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

16 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 H 2 etching (no UHV preparation), (b) UHV anneal at 1150 C (LEED 3 3 pattern), (c) UHV anneal at 1350 C (LEED 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 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

17 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 structure 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 transfer charges to the topmost layer can systematically change the position of the Dirac point or 17

18 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

19 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 di erent orientations with respect to the miscut of the wafer. The necessary temperatures are obtained by resistive heating, but in a new con guration, 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 di usion 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 e ort into improvement of the surface quality. Technically the face-to-face con guration is obtained by cutting a L-shaped piece of tantalum foil (d = 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

20 Figure 13: Mounting of the sample, red is the SiC-substrate, blue tantalum foil pumped down to a base pressure of approximately 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 ɛ = 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 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 Torr. This temperature has proven to give good ARPES results in earlier studies without being believed to change the sample composition [35]. 20

21 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 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 faceto-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 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 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

22 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 temperature 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 E kin = 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

23 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

24 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. decelerated with the same xed factor. In Fixed Retardation Ratio (FRR) mode all particles are 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 of the intensity with increasing kinetic energy as I 1 E kin. 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

25 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 (E HeII = 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

26 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

27 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

28 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

29 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 resistance 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 stepdown. 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

30 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 C. At temperatures above 1500 C, which is identical with the onset of graphene growth, the trend turns around and the surface becomes 30