Structural studies of epitaxial graphene formed on SiC{0001} surfaces

Transcription

1 Carnegie Mellon University Research CMU Dissertations Theses and Dissertations Structural studies of epitaxial graphene formed on SiC{0001} surfaces Luxmi Carnegie Mellon University Follow this and additional works at: Recommended Citation Luxmi, "Structural studies of epitaxial graphene formed on SiC{0001} surfaces" (2010). Dissertations. Paper 21. This Dissertation is brought to you for free and open access by the Theses and Dissertations at Research CMU. It has been accepted for inclusion in Dissertations by an authorized administrator of Research CMU. For more information, please contact researchshowcase@andrew.cmu.edu.

2 Structural studies of epitaxial graphene formed on SiC{0001} surfaces Doctoral Thesis 2010 Luxmi Advisor Prof. R. M. Feenstra Department of Physics Carnegie Mellon University, Pittsburgh, PA 15213

3 Abstract In this thesis, we report on the structural studies of epitaxial graphene formed on polar faces of SiC; the (0001) and the ( 0001 ) surfaces (the so-called Si-face and C-face, respectively). Graphene films are prepared by heating the SiC substrates either in ultra-high vacuum (UHV) or in 1-atm-argon environment. Prior to graphitization, substrates are hydrogenetched for removing residual polishing damages. The resulting graphene films are characterized using atomic force microscopy (AFM), Auger electron spectroscopy (AES), low-energy electron diffraction (LEED), low-energy electron microscopy (LEEM), Raman spectroscopy, and electrical measurements. Field-effect mobilities of the transistors made from vacuum-annealed graphene films exceed 4000 cm 2 /Vs at room temperature. It is found, in agreement with other reports, that the graphene growth and properties are very different on the two polar faces of SiC. Graphene formation rate is faster on the C-face compared to the Si-face. For a given annealing temperature and time, thick film forms on the C-face compared to the Si-face. On the Si-face, graphene lattice vectors are rotated 30 with respect to the SiC lattice vectors as seen in the LEED pattern which shows a hexagonal arrangement of six distinct spots. However on the C-face, graphene films are rotationally disordered which gives rise to streaking in the diffraction pattern. We still observe six discrete spots in the pattern, but additional spots (streaks) are also seen located at angles of 30 ± ϕ relative to the six discrete spots. Angles of ϕ ranging from 6 to 13 have been observed, although most typically we find ϕ 7. We have examined the evolution of surface morphology of graphene films prepared in UHV as a function of annealing temperature on both the faces. The results for the Si-face graphene films are found to be in good agreement with what is reported by other groups. However, we present novel results for the morphology and structural properties of the C-face graphene films. On the Si-face graphene films, pits form during the initial stages of graphitization (due to the development of buffer layer) and steps-terraces, seen after hydrogen-etching, are not ordered. On the C-face graphene films, it is observed that a uniform step-terrace arrangement is preserved during the initial stage which develops into a terraced morphology at a later stage. Terraces of varying heights are seen and with further annealing, thicker films with ridges (possibly arising from a thermal expansion mismatch ii

4 between the SiC and the graphene) are formed. An additional aspect of the C-face graphene films morphology is found to be associated with the surface properties of the starting wafer. It is observed that for wafers which show large number of pits (after etching or graphitization), the surface is covered with large amounts of disordered graphene, also called nanocrystalline graphite (NCG). However for wafers which display fewer pits, the surface is found to be covered with little amounts of NCG. As investigated in LEEM, small areas of constant graphene thickness, which we call domains, are found to extend laterally over 1-2 µm on the C-face with variation of up to 5 monolayers between domains. This large variation in thickness is suggestive of threedimensional growth of graphene. In the case of the Si-face graphene films, larger domains are formed with variation in thickness of only 1 monolayer between domains (away from step bunches) suggestive of layer-by-layer graphene growth. We have interpreted the difference in the growth modes for the two faces in terms of limited surface kinetics. It is likely that for the C-face, lower temperatures employed in graphitization inhibit coarsening of adjacent domains. Correlated AFM and LEEM data on the C-face graphene films suggests that domains are bounded by step bunches which could possibly lead to discontinuities in the graphene films. Due to low temperatures, the driving force for the planarization of the morphology or for the uniform distribution of graphene thicknesses is missing on the C-face. Due to higher temperatures needed for obtaining graphene of comparable thickness on the Siface compared to the C-face, steps are more mobile leading to a flatter morphology and a layer-by-layer growth of graphene films is promoted on this face. At higher annealing temperatures, the films thickness on the C-face is much greater than for the Si-face, but both films display the characteristic ridges associated with strain relaxation and both surfaces display comparable amounts of step bunching. The reason for the thicker film on the C-face is, we believe, simply because the ( 0001 ) surface and ( 0001 )/graphene interface have higher energies (i.e. are more unstable), respectively, than the (0001) surface and (0001)/graphene interface. Additionally, more defects in the C-face films such as the discontinuities and/or rotational domain boundaries could lead to easier Si diffusion through the graphene, which would also favor thicker growth. Thus, the different morphologies between the Si- and C-faces found for films of the same thickness simply iii

5 arises from the lower graphene formation temperatures used in the latter case, which inhibits coarsening between adjacent domains. In order to increase the growth temperature for the C-face, while maintaining a fixed growth rate, we switched to an ambient atmosphere of argon from UHV, following other workers research, for annealing the SiC substrates. In the presence of argon, Si sublimation rate is significantly reduced which leads to an increase in the annealing temperature for producing graphene of given thickness. Increase in temperature enhances the mobility of diffusing species which in turn improves the homogeneity of the film. We have been successful in forming monolayer graphene with increased domain size on the Si-face of SiC in the presence of argon. However, for the C-face the morphology becomes much worse, with the surface displaying markedly inhomogeneous nucleation of the graphene. It is demonstrated that these surfaces are unintentionally oxidized, which accounts for the inhomogeneous growth. iv

6 Dedicated to My father v

7 Acknowledgements First and foremost, I would like to thank my advisor Prof. Randy Feenstra for giving me the opportunity to work in his group. He has been a constant source of inspiration and encouragement. The long hours that were spent in order to figure out an experimental data would always remain a cherished memory. Under his guidance, I have learnt how every piece of scientific information is crucial for understanding the big picture of a given project. I have grown to be a much disciplined and focused person under his supervision. Thanks Randy! A vote of thanks to my committee members; Prof. Bob Suter, Dr. Dave Ricketts and Dr. Kristina Woods for providing a very positive feedback during my annual reviews. Thanks are due to our collaborators; Gong Gu at Sarnoff Corporation, Jakub Kedzierski at MIT Lincoln Labs, and Yugang Sun at Argonne National Labs. Financial support from the National Science Foundation and the Defense Advanced Research Projects Agency is gratefully acknowledged. Now, I would like to thank the most efficient and wonderful staff of the Physics department. In particular, I am thankful to Donna Thomas, Chuck Gitzen, Al Brunk, Hilary Homer, Mary Jane Hutchison, Patrick Carr and Gary Wilkin. I am grateful to all the help received from my lab members. I would like to acknowledge the help from Sandeep Gaan and Shu Nie who helped me in getting familiarized with different experimental set-ups in the lab. Patrick Fisher and Guowei He deserve a ton of thanks for being a constant source of help. Life in Pittsburgh would not have been easy without the undemanding support of some of my friends. I am thankful to Kaustubh and Sonal for their help during the crucial first few months. A special thanks to Nishtha for those endless discussions that we had about being a TA, tough times in research or life in general. I would like to thank Mudi for being there whenever I needed a big brother around me. Thanks to Prabhanshu, Tristan, Sidd and Swathi for being around. The unconditional support of my family members cannot be acknowledged in words. Even though I am thousands of miles away from them but they are always there with me. In the end, I would like to thank the people who are closest to my heart, rather who define my existence: Maa, Annu di, Neelam di, Sumit and Saurabh. Life has been a roller coaster ride in their company and I look forward to many more years of fun and togetherness. vi

8 Contents Abstract ii 1 Introduction Graphene Structure of graphene Synthesis of graphene Structure of SiC Graphene on SiC Overview of the thesis 15 2 Experimental Setup Graphene preparation chamber Low-energy electron diffraction (LEED) Low-energy electron microscopy (LEEM) Auger electron spectroscopy (AES) Atomic force microscopy (AFM) 31 3 Graphene formation on the Si-face of SiC in UHV Experiments Results and Discussion Summary 46 4 Graphene formation on the C-face of SiC in UHV Experiments 48 vii

9 4.2 Results Discussion Conclusions 64 5 Switching environments: From UHV to 1-atm-argon Experiments Results Discussion Summary 72 6 Summary UHV annealed graphene films Argon annealed graphene films 77 Bibliography 78 viii

10 Chapter 1 Introduction 1

11 1.1 Graphene Graphene is a single sheet of carbon atoms tightly bound into a two-dimensional (2D) hexagonal network and is a basic building block for all other graphitic materials, as shown in Fig. 1.1 [1]. Theoretical properties of graphene were studied as early as in 1947 [2]. This strictly 2D system was believed not to exist in a free state since the Mermin-Wagner theorem predicts that there should be no long range order in 2D [3]. Experimentally, films were found to become thermodynamically unstable at thicknesses of few atomic layers [4]. However, in 2004, a group of researchers led by A. Geim and K. Noveselov at University of Manchester experimentally isolated graphene, and that achievement fascinated the scientific community [5]. The atomically thin sheets were found to be stable under ambient conditions, exhibiting high quality and continuity on a microscopic scale. Graphene films were prepared by mechanical exfoliation of highly ordered pyrolytic graphite. Films were transferred to an oxidized silicon substrate and were identified in an optical microscope. Interaction with the substrate might be a reason for the thermodynamic stability of the graphene [6, 7]. In the case of suspended graphene, corrugations in the third dimension are seen which could relate to the stability of the film [8]. Fig. 1.1 Graphene: building block for all graphitic forms. It can be rolled into 0D buckyballs, 1D carbon nanotubes and can be stacked to form 3D graphite. From Ref. [1]. 2

12 Graphene is found to possess many interesting properties. It exhibits pronounced ambipolar electric field effect with mobilites of charge carriers exceeding 15,000 cm 2 /Vs even at room temperature [5-7], ballistic transport, and anomalous quantum Hall effect [6, 9, 10, 11]. The origin of these unusual properties can be explained on the basis of π bands intersecting near K-points or Dirac points [2]. Charge carriers in graphene are described by the Dirac equation, used for describing relativistic quantum particles, rather than the Schrödinger equation [12, 13]. Near the Dirac points, the energy dispersion is linear and is given by E = hkvf where v F is Fermi velocity and is approximately equal to 1/300 of the speed of light. The band structure of graphene is discussed in the next section. 1.2 Structure of graphene As described earlier, graphene consists of a layer of carbon atoms arranged in a hexagonal network. Carbon atoms are bonded in a sp 2 configuration with three σ in-plane bonds and one partially filled p z orbital (π orbital) that extends perpendicular to the plane. A unit cell of graphene consists of two carbon atoms and is shown in Fig. 1.2(a). Lattice vectors a 1 and a 2 can be written as: a a 1 2 = = 3 2 [ 0, a] 1 a, a 2 where a = a = a nm is the lattice constant of graphene. A single layer of 1 2 = graphene consists of 38.0 carbon atoms/nm 2. Corresponding reciprocal lattice vectors can be written as: b b 1 2 = = 4π,0 3a 2π, 3a 2π 3a The shaded area in Fig. 1.2 (b) corresponds to the first Brillouin zone in graphene. The electronic structure of graphene can be derived using the tight-binding method involving only the nearest neighbor interactions. In the calculation, Bloch functions are constructed using linear combinations of the p z orbitals corresponding to two carbon atoms 3

13 Fig. 1.2 (a) Two-dimensional lattice structure of graphene containing two carbon atoms (marked grey and black) in a unit cell, and (b) Reciprocal lattice of graphene with shaded region showing the first Brillouin zone. From Ref. [14]. in the unit cell of graphene (a detailed description of these tight-binding calculations is provided in Ref. [15]). These linear combinations give rise to bonding π and antibonding * bands of graphene. The energy gap between the π band and the π band is found to be: 2 E( k, k ) = 2γ 1+ 4cos( 3k a / 2) cos( k a / 2) 4cos ( k / 2) (1.1) x y 0 x y + ya where γ eV is the nearest neighbor overlap integral [15, 16]. Figure 1.3 shows the band structure of graphene. * The π and π bands touch near the corners, K and K' points or Dirac points, of the first Brillouin zone. Hence graphene is a zero-bandgap semiconductor with bands intersecting at the Dirac points. Equation (1.1) can be expanded near K and K' points (K= using a Taylor expansion yielding: 0 k K * π 2π 2π, ) 3a 3a E( k) = 3γ a k (1.2) Thus, the dispersion relationship is linear near the K and K' points rather than the usual parabolic form seen in conventional semiconductors. These linear bands are responsible for the interesting properties of graphene mentioned in the previous section. However, for bilayer graphene with AB stacking the situation is altered. Due to the interlayer interaction, 4

14 additional bands arise. The linear dispersion near the K points is no longer seen, although the bands still touch near these points [11, 18]. By applying an electric field perpendicular to the bilayer, a band gap can be opened, and this has been proved experimentally by several groups [19, 20]. Another way of altering the properties of graphene is by making narrow strips of graphene, called graphene nanoribbons. These structures are shown to exhibit electronic properties that depend on the details of their orientation with respect to the graphene lattice, and are found to be metallic in some cases and semiconducting with width dependent band gap in others [21, 22]. Fig. 1.3 Band structure of graphene. Conduction and valence band intersect at K and K' points and the dispersion relation is linear near these points. From Ref. [17]. 1.3 Synthesis of graphene There are several ways of fabricating graphene. As mentioned in Section 1.1, graphene layers can be obtained by micromechanical exfoliation starting with highly ordered pyrolytic graphite. These graphene layers are then transferred to a Si substrate with an oxidized layer on it. Graphene films prepared by this manner are generally termed as exfoliated graphene. Field-effect transistors (FET) have been fabricated using these exfoliated graphene films and 5

15 their transport properties have also been studied extensively [5-7, 23-25]. The quality of these exfoliated graphene layers is found to be good; however their lateral extent is limited to few microns, thus making them unsuitable for large scale device applications. In order to make wafer scale graphene layers for practical applications, an alternate route for fabricating graphene was provided recently by Walt de Heer et al. [26-28]. This method involves decomposition of SiC at high temperatures under ultra-high vacuum (UHV) conditions. Si atoms were found to preferentially sublimate from the surface leaving behind C atoms which rearrange to form graphene. Decomposition of SiC substrates was studied earlier by other groups [29-34]. The purpose of those experiments was to characterize the graphite layers formed on SiC surfaces using different experimental tools. Electronic applications of graphene prepared by sublimation of Si from SiC, also called epitaxial graphene (EG), were not studied until the most recent work [26-28]. Since high-quality semiinsulating SiC substrates are readily available, fabricating graphene films on these substrates provides a feasible path for making graphene based electronic devices by employing conventional planar lithographic techniques. Macroscopic FET based on these graphene films using polystyrene dielectric layer were fabricated by Gong Gu et al. and mobilities for these devices were found to be around 500 cm 2 /Vs [35]. An order of magnitude increase in the mobilities was reported by other groups using different processing techniques and dielectric layers [36, 37]. The mobility values measured in EG are still lower than measured in exfoliated graphene [6, 9, 38]. It is found that the graphene films prepared in UHV exhibit rough morphology and show areas with different thicknesses which could potentially be responsible for the decreased mobilities reported for these films [35, 39-45]. In order to make wafer scale graphene films with uniform thickness, Virojanadara et al. reported on the formation of homogenous large area graphene films by annealing SiC substrates at a temperature of 2000 C in a 1-atm-argon environment [46]. Emtsev et al. also reported on the formation of thin and uniform graphene by heating SiC at 1650 C under 900 mbar of argon [47]. Other methods of graphene fabrication include deposition of carbon onto surfaces of transition metal carbides [48, 49], and segregation/deposition of carbon from/to metal surfaces such as Ni, Pt, Ru or Ir [50-55]. Recently, Li et al. fabricated high quality monolayer graphene films by chemical vapor deposition of carbon on copper foils. Production of 30 6

16 inch diameter graphene films by this method has been reported by Bae et al. [56, 57]. Due to the need to transfer graphene films from metal substrates to insulating substrates for electronic applications, starting with SiC substrates seems to be the best route for graphene fabrication. In this thesis, graphene films are prepared by decomposition of SiC substrates either in UHV or in 1-atm-argon environment. Before moving on to epitaxy of graphene on SiC, the structure of SiC is briefly reviewed in the next section. 1.4 Structure of SiC SiC is a wide band gap semiconductor used extensively in making high-temperature and high-power electronic devices [58]. In SiC, each Si (C) atom is bonded to four other C (Si) atoms in a tetrahedral arrangement as shown in Fig Two nearest Si (or C) planes are separated by a distance of 0.25 nm. A hexagonal bilayer consisting of a plane of Si atoms and a plane of C atoms, shown in Fig. 1.4(b), makes the building block for SiC structures. In order to maintain the tetrahedral arrangement, bonds in adjacent bilayers can overlap each other when viewed from the top or they can be rotated by 60 with respect to each other [59]. Fig. 1.4 Hexagonal bilayers of SiC (a) Top View, and (b) Side view. From Ref. [14]. 7

17 If all bilayers are stacked the same way, i.e. overlapping or rotated, the result is a wurtzite crystal structure or zinc-blende crystal structure, respectively. Different stacking arrangements occurring from one bilayer to the next (e.g. overlapping, rotated, overlapping, rotated,...) leads to a number of other crystal structures, also called polytypes. For SiC, more than 170 polytypes are found to exist. Most of the work for graphene on SiC is done on hexagonal polytypes, mainly 6H or 4H (H stands for hexagonal). A unit cell of 6H-SiC consists of 6 bilayers (with a height of 1.50 nm along c-direction) and a unit cell of 4H-SiC is made up of 4 bilayers (with height of a 1.00 nm along c-direction). The stacking arrangements for 4H-SiC and 6H-SiC are ABCB(ABCB) and ABCACB(ABCACB), respectively, and are shown in Fig Lattice constant for the SiC unit cell for both 6H and 4H type polytypes is 3.08 nm. Fig. 1.5 Stacking arrangement for (a) 4H-SiC, and (b) 6H-SiC. Si-atoms are denoted by big open circles and C-atoms are denoted by small filled circles. 8

18 SiC has two polar faces perpendicular to the c-axis, shown in Fig The face with outward normal in [0001] direction is the SiC(0001) surface, also called the Si-face of SiC, and the face with outward normal in [ ] direction is the SiC( ) surface, also known as the C-face of SiC. These two SiC{0001} surfaces have different properties like reactivity, surface reconstructions etc. [30, 60]. Graphene growth and its structural properties are found to be very different on these two faces and will be discussed later in this chapter. Fig. 1.6 SiC crystal showing (0001) and ( ) surfaces, also known as the Si-face and the C-face, respectively. From Ref. [14]. 1.5 Graphene on SiC Graphene formation on SiC has been studied by a number of groups over the past few years using different experimental techniques like low-energy electron diffraction (LEED) [29, 31-33, 40, 43, 60-62], Auger electron spectroscopy (AES) [29, 30], photoelectron spectroscopy (PES) [19, 30-33, 39, 62-67], scanning tunneling microscopy and spectroscopy (STM/S) [34, 40, 60, 68-78], transport measurements [26-28], X-ray diffraction [34, 79-81], atomic force microscopy (AFM) [39, 45, 82-85], Raman spectroscopy [86-92] and low-energy electron microscopy (LEEM) [41, 42, 64, 93-97]. Based on these studies, various structural models for graphene formation on both polar faces of SiC have been proposed and will be discussed in subsequent sections. Van Bommel et al. who first studied the graphitization of SiC{0001} surfaces proposed that the formation of a single layer of graphene involves decomposition of 9

19 three SiC bilayers since carbon density in three SiC bilayers, 36.5 atoms/nm 2, is very close to the carbon density in a single layer of graphene, 38.0 atoms/nm 2 [29]. Prior to graphene formation, well ordered SiC surfaces can be prepared either by chemical methods or by thermal treatment. A comprehensive list of different SiC preparation techniques is given in Ref [59]. No studies have been reported, thus far, on the effect of different SiC surface preparation methods on the structural quality of epitaxial graphene [44] Graphene formation on the Si-face of SiC The Si-face of SiC shows number of surface reconstructions when heated in vacuum, as seen in LEED patterns (a brief description of LEED is provided in Chapter 2). These surface reconstructions have been studied by a number of other groups [26, 29, 31, 39, 40, ], and also observed by us [14, 61]. Figure 1.7 shows a general picture of the evolution of different reconstructions on the Si-face of SiC when the surface is heated to different temperatures in vacuum. It should be mentioned that these values of temperatures are not absolute due to the difficulties involved in measuring the temperature of transparent samples. These values could also vary from one experimental group to another due to the use of different temperature measurement techniques employed by different groups. Fig. 1.7 Evolution of different reconstructions of the SiC(0001) surface when heated in vacuum. Figure 1.8 shows detailed LEED results from Si-face SiC, acquired at room temperature after annealing the surfaces at consecutive steps for the times and temperatures specified. The initial unreconstructed 1 1 pattern of the substrate, Fig. 1.8(a), is replaced by a 3 3-R30 reconstruction on heating to 900 C, Fig. 1.8(b). The 3 3-R30 pattern is associated with one Si adatom per 3 3 SiC unit cell [101]. On further heating to 1200 C this pattern then progresses to a R30 arrangement (6 3 for short), Fig. 1.8(c), with a six-fold arrangement of spots around all of the 3 and 1 1 SiC spots. At 1250 C, the graphene (1,0) primary spots first appear and concomitantly the 3 and 2 3 spots decrease in intensity, shown in Fig. 1.8(d). Note in particular that the 3 spots decrease in intensity compared to 10

20 their neighboring 6 3 satellite spots, which is a characteristic feature of the onset of graphene formation. Upon further annealing the intensity of the graphene pattern increases while that of the SiC decreases, shown in Fig. 1.8(e)-Fig. 1.8(g). A six-fold arrangement of 6 3 satellite spots can be seen around the primary graphene spots in Fig. 1.8(h), acquired at an energy of 70 ev which enhances the intensity of those spots. Fig. 1.8 LEED patterns shown in reverse contrast, acquired from Si-face SiC after the following consecutive annealing steps: (a) bare SiC, (b) 1 min at 900 C, (c) 2 min at 1200 C, (d) 5 min at 1250 C, (e) 20 min at 1350 C, (f) 5 min at 1400 C, (g) 5 min at 1450 C, (h) no further annealing. All patterns were acquired at 100 ev electron energy except for (h) which is at 70 ev. The inset in (h) shows an expanded view of the graphene spot indicated by the square. The primary (1,0) SiC and graphene spots are indicated, as are the SiC 3 and 2 3 spots. From Ref. [61]. The 6 3 arrangement acts as a precursor to graphene formation. The structure of this 6 3 phase has been studied and much debated in the literature. Van Bommel et al. first interpreted this arrangement in terms of a multiple diffraction pattern of the SiC substrate and a graphite top layer, rotated 30 with respect to the SiC lattice [29]. Based on their studies on graphitized β-sic(111) surfaces, Li and Tsong proposed a model that comprises of a ( =3.198 nm) graphite cell that matches up almost exactly with a ( =3.200 nm) SiC cell [102]. Earlier STM studies reported a 6 6 reconstruction instead of a 6 3 arrangement observed in LEED [98, 100, 102, 103]. However, recent STM 11

21 studies have confirmed the presence of the 6 3 pattern [40, 60, 68]. Northrup and Neugebauer, on the basis of their theoretical calculations, proposed that the 6 3 arrangement arises from a graphite monolayer resting on 3 3 array of Si adatoms and interacts weakly with it [101]. Forbeaux et al. also supported a similar model based on their experimental observations [31]. Based on their LEED and STM data, Mårtensson et al. proposed that the 6 3 pattern arises from surface containing mixtures of 6 6, 5 5 and 3 3 reconstructions. Upon further heating, graphite layers appear on top of a 6 6 reconstruction [98, 99]. Emtsev et al. studied the electronic properties of this 6 3 arrangement using angle-resolved photoemission spectroscopy and found them to be different from an isolated graphene layer [62]. The 6 3 structure shows graphene-like σ bands implying that the arrangement of atoms in this structure is similar to that of graphene, but it fails to exhibit graphene-like π bands near K points implying a strong covalent bonding with the underlying substrate. The presence of strong covalent bonding of the 6 3 layer, also called buffer layer, with the substrate is in agreement with theoretical results [104, 105]. Carbon layer on top of this 6 3 layer is found to possess the electronic properties of a graphene sheet. So, this 6 3 layer acts as an interface between the SiC(0001) surface and the graphene layers. The 6 3 layer provides a uniform template for the growth of graphene layers on SiC(0001) surface and forces the graphene layers to be oriented in one direction with respect to the underlying SiC substrate [62]. This orientation is determined by the covalent bonds between the buffer layer and the SiC substrate. After the formation of the 6 3 layer, further heating leads to decomposition of SiC bilayers underneath the 6 3 layer leading to nucleation of a new carbon layer. Now, this new carbon layer formed beneath the 6 3 layer forms covalent bonds with the substrate forming the new 6 3 layer and the original 6 3 layer is now decoupled from the substrate forming the first graphene layer interacting weakly with the newly formed 6 3 layer. A schematic of the above description for graphene formation is shown in Fig So, every graphene layer starts out as a 6 3 layer with an arrangement determined by the covalent bonds to the substrate. Hence, graphene layers on the SiC(0001) surface exhibit one fixed arrangement with respect to the SiC substrate as observed in LEED pattern. It is found that this buffer layer contains nearly a full graphene monolayer s worth of excess carbon [41]. 12

22 Fig. 1.9 Schematic of graphene formation on the Si-face of SiC. Upon heating at 1150 C, the 6 3 layer forms and is strongly bound to the substrate. Heating at 1300 C leads to the formation of first graphene layer. Since the buffer layer is covalently bonded to the substrate, it is found to significantly affect the transport properties of graphene films fabricated on the Si-face of SiC. It would be desirable to decouple the buffer layer from the substrate. In order to achieve this goal, some groups have recently reported on the exposure of epitaxial graphene to hydrogen [96, 106, 107]. It is found that the hydrogen could pass through the interface layer and make covalent bonds with the Si atoms of the surface. The buffer layer, then, isolates from the substrate and exhibits the electronic properties of a graphene layer. This method of decoupling the buffer layer could potentially lead to an improvement in the performance of graphene based devices Graphene formation on the C-face of SiC The C-face of SiC exhibits a completely different sequence of surface reconstructions as compared to the Si-face under identical preparation conditions. The set of surface reconstructions for the C-face is reported by a number of other groups [29, 32, 60, 62, 71, 103, 108], and also observed by us. Figure 1.10 shows LEED patterns acquired from the C- face of SiC at room temperature. The sample is hydrogen-etched, for removing polishing damages, prior to loading into the ultra-high vacuum chamber (UHV) and a 3 3-R30 arrangement is seen on the surface, shown in Fig. 1.10(a). The presence of the 3 3-R30 pattern is explained by Starke et al. in terms of a silicate layer on the surface [109]. Upon annealing at 1000 C, the 3 3 pattern transforms into a 3 3 pattern, Fig. 1.10(b). Upon further heating to 1200 C, diffraction streaks associated with graphite layers are observed, 13

23 Fig. 1.10(c). Forbeaux et al. reported a (2 2) C reconstruction prior to seeing graphene rings [32]. Other groups have reported a coexistence of the 3 3 and the (2 2) C reconstructions before observing streaks in the diffraction pattern [62, 108]. Recent STM studies have also shown the presence of graphene layers on top of the 3 3 and the (2 2) C reconstructions [71]. So, a uniform template similar to the 6 3 layer seen in the case of Si-face is missing on the C-face of SiC. Fig LEED patterns acquired from the C-face of SiC after following steps: (a) hydrogen-etching, (b) heating at 1000 C for 20 min, and (c) diffraction streaks marked by arrows, 1300 C for 20 min. Patterns (a) and (c) are acquired at 130 ev, and (b) at 145 ev. This data was obtained by Nishtha Srivastava from Prof. Feenstra s research group. The diffraction streaks in the LEED pattern were earlier interpreted in terms of polycrystalline graphite on the surface [29]. However, recent studies have shown that the diffraction streaks for the C-face films arise due to different rotational orientations of the graphene layers [28, 44]. Generally, six discrete spots located at 30 relative to the SiC spots in the pattern are observed, with additional streaks located at angles of 30 ± φ relative to the six discrete spots. Different values for φ have been reported by different groups, ranging from 2.2 to 25 [28, 71, 97]. This difference in φ values can be interpreted as arising from various possible nearly-commensurate arrangements of graphene monolayers on top of each other [110]. The existence of rotated domains indicates a weak coupling of graphene layers with the substrate, which is confirmed recently by photoemission and STM measurements [60, 62, 71] and ab intio calculations [111]. However, these measurements are at variance with previous 14

24 findings of inverse photoemission studies [32], X-ray reflectivity studies [81] and theoretical calculations [104, 105] which suggest a strong interaction between the first graphene layer and the substrate. Further investigations need to be carried out in order to resolve this discrepancy. Due to the presence of this rotational disorder for the C-face graphene films, there were few reports earlier dealing with the morphology or structural properties of these films. However, Hass et al. reported that that the electronic properties of thick graphene films on the C-face are similar to that of a single layer graphene [79]. These findings were interpreted in terms of the rotated stacking of the graphene layers which seems to decouple adjacent layers, hence preserving the electronic properties of a monolayer graphene. The mobility values are reported to be higher for the C-face graphene films than the Si-face films making the C-face graphene films a suitable candidate for carbon-based electronics [27, 112]. 1.6 Overview of the thesis The research work in this thesis mainly deals with structural characterization of epitaxial graphene films fabricated on both the Si- and C-faces of SiC. Graphene films are fabricated in our custom-built preparation chamber by heating the SiC substrates either in UHV or in 1- atm-argon environment. The resulting films are characterized using different surface sensitive techniques. Results for vacuum-annealed Si-face graphene films are consistent with what has been reported by other groups. However, we present novel results for the morphology and structural properties of the C-face graphene films prepared by annealing in vacuum. In the case of Ar-annealed films, our findings for both the Si- and C-faces are similar to other reports. Additional studies on the C-face films conclude that the surface is unintentionally oxidized in the presence of argon. Such results are unique and further investigations based on these results can contribute towards making uniform and thin graphene film on the C-face of SiC. Since higher mobilities are reported for devices fabricated using the C-face films than the Si-face, it is desirable to produce samples with large areas covered with monolayer graphene on the C-face [27, 112]. While the background and context of the thesis has been introduced in this chapter, the rest of this thesis is arranged as follows. A description of the preparation chamber and different characterization methods is provided in Chapter 2. In Chapter 3, structural 15

25 properties of graphene films prepared on the Si-face of SiC in UHV are discussed. The evolution of surface morphology of graphene films with temperature is studied using AFM. It is found that the surface after graphitization is not smooth and shows a number of features like pits and randomly-located steps. LEED pattern from these graphene films exhibits six discrete spots rotated 30 with respect to the substrate as expected for the Si-face graphene films. Thickness of the graphene films is measured using AES and LEEM. In LEEM, different areas on the surface are found to be covered with different number of graphene layers which is not desirable for electronic applications. With an increase in the annealing temperature, it is observed that constant thickness areas (we call them domains ) grow in size with lateral extent of many microns and are separated by step bunches. The areas between step bunches are covered with graphene ranging in thickness of only 1 monolayer (ML). Hence, for thicknesses > 2ML, the graphene is found to form in a layer-by-layer manner. Chapter 4 deals with the properties of graphene films prepared by annealing the C-face of SiC in UHV. In agreement with other reports, graphene formation rate is found to be faster on the C-face compared to the Si-face. For a given annealing temperature and time, thick film forms on the C-face compared to the Si-face. The C-face graphene films are rotationally disordered which gives rise to streaking in the LEED pattern. It is observed that the C-face graphene films maintain a uniform step-terrace arrangement, seen after hydrogen-etching, during the initial stages which develops into a terraced morphology at a later stage. Terraces of varying heights are seen and with further annealing, thicker films with ridges (possibly arising from a thermal expansion mismatch between the SiC and the graphene) are formed. These morphological features are at variance with what is observed on the Si-face graphene films. As investigated in LEEM, small domains extending laterally over 1-2 µm are seen on the C-face with variation of up to 5 ML between domains. This large variation in thickness is suggestive of three-dimensional (3D) growth of graphene as opposed to a layer-by-layer growth observed in the case of Si-face graphene films. We have interpreted the difference in the growth modes for the two faces in terms of limited surface kinetics. In Chapter 5, the influence of 1-atm-argon annealing environment on the resulting graphene morphology and homogeneity is studied. It is found that in the presence of argon, large domains covered with monolayer graphene are formed on the Si-face of SiC. However 16

26 for the C-face in argon, only 3D formation of islands is found during the initial stage of graphene formation, with these islands growing relatively thick before complete graphene coverage is achieved. It is found that the C-face surface is unintentionally oxidized in the presence of argon which seems to inhibit the graphene formation. Further investigation into these results can lead to an optimization of preparation parameters that would give uniform and thin film on the C-face of SiC. 17

27 Chapter 2 Experimental Setup 18

28 2.1 Graphene preparation chamber We produce graphene by sublimation of Si from SiC, using the well-known procedure of heating the SiC either in vacuum or in 1-atm-argon environment [26-34, 46, 47]. Use of semi-insulating SiC precludes heating by direct current, and a metal film (which would allow electron-beam heating) cannot be deposited on the backside of the wafer since this metal is found to migrate to the front of the wafer during heating. Furthermore, poor thermal contact between sample and heater (in the case of vacuum environment) and low optical absorption of the SiC (band gap 3.0 ev, depending on polytype) necessitates temperatures as high as 1850 C for the heater itself. To accomplish this heating we have developed a simple arrangement consisting of a graphite strip [45]. The graphite strip heater is contained in a dedicated ultra-high-vacuum (UHV) chamber with a base pressure of Torr, pumped by a 150 l/s turbo-molecular pump and a hydrogen-getter pump. The chamber, shown in Fig. 2.1, is custom-built and is made up of stainless steel. A graphite plate with thickness 1 mm and area mm2 is cut into a bow-tie shape, with a narrow neck of 20 mm length and 14 mm width. Two thick (dual, 9.5 mm diameter) water-cooled copper feedthroughs are used to transmit the current, mounted onto large copper clamps on the two 75 mm ends of the plate. Current is supplied by a transformer capable of supplying up to 250 A. Gate valves separate the turbo pump as well as the hydrogen-getter pump from the main chamber. Fig. 2.1 Graphene preparation chamber. 19

29 The material used to fabricate the graphite heater strip was obtained from Poco Graphite, and is Semiconductor Grade material. No measurable contamination as seen by residual gas analysis is found to be emitted during the graphitization (these measurements were performed only after the first few heating runs with the strip). The strip is found to be quite robust, surviving many tens of heating cycles before breaking. (Some evaporation of the carbon from the strip is observed, creating graphitic deposits on the backside of the sample; over time the neck of the strip gets thinner, and eventually cracks). Fig. 2.2 Graphite strip heater. Most of our experiments have been performed on nominally on-axis, semi-insulating 4Hor conducting 6H-SiC substrates that were purchased from Cree Corp. These substrates had been mechanically polished on both sides and they are epi-ready (i.e. with further polishing and a damage removal step) either on the (0001) surface or the ( ) surface. Samples measuring mm2 are cut from the wafers. As-received wafers are covered with scratches arising from the polishing process. Hydrogen-etching is performed in order to get rid of these scratches [113]. Etching is performed using % purity hydrogen with a flow rate of 10 lpm and at a temperature of 1550ºC for 3 min. Gate valves to the turbo and getter pumps are closed during etching. After the etching, hydrogen is evacuated through the roughing line. For making samples in vacuum, gate valves to the turbo and getter pumps are opened and we wait until the pressure reaches Torr, and the annealing to form the graphene is then performed. For preparing samples in argon, the chamber is filled with high 20

30 purity argon gas and the annealing to form the graphene is performed in a slow flow of argon. All results shown in the following chapters refer to the surface of the sample that is facing away from the heater strip. Temperature is measured with a disappearing filament pyrometer; the pyrometer is directed at the sample, although since the sample is transparent it is mainly the heater strip that is seen. In the case of vacuum annealing, the heater strip is much hotter than the sample and hence, a large discrepancy occurs between the heater temperature and the actual sample temperature. To improve our determination of sample temperature, we use a small graphite "cap" piece that sits on top of the sample. This cap, fabricated from 1 mm thick graphite, measures about mm 2 and has a small depression milled into it so that it fits over the mm 2 sample. A hole with diameter 6.35 mm is drilled through the center of the cap piece, thus allowing the sample surface over this area to be exposed to the vacuum. With this cap in place, we measure its temperature as well as that of the heater strip, using the pyrometer. For strip temperature of 2000 K (i.e., 1727 C) we find a cap temperature that is 315±15 K lower than the strip. Comparing with expectations from black-body radiation, the bottom of the cap will absorb radiation from the strip (the sample being transparent), and both the bottom and the top will radiate, so balancing the input and output powers we expect a cap temperature to be a factor 0.5 1/4 times that of the strip, corresponding to a temperature difference of 318 K. With the cap present, we do not expect the sample temperature to be lower than that of the cap, and we simply use the cap temperature as an estimate of the sample temperature. In the absence of the cap, we estimate the temperature difference between sample and strip simply by shifting our experimental data such that data points with and without the cap being present are aligned. We find that 450 C and 350 C shifts are appropriate for semi-insulating samples and conducting samples, respectively, and we use these correction factors for all data measured without the cap. 2.2 Low-energy electron diffraction (LEED) LEED is a standard technique for checking the surface structure of a crystalline material. In LEED, low-energy electrons in the range of 10 to 300 ev impinge on the surface and elastically backscattered electrons give rise to diffraction spots that are observed on a florescent screen. Due to their low energy, electrons are not able to penetrate deep into the 21

31 sample making LEED a surface sensitive technique. The diffraction pattern corresponds to the surface reciprocal lattice [114]. Kinematic theory, with only one scattering event, is sufficient for explaining essential features in LEED. An elastically diffracted spot occurs when the scattering vector component ' parallel to the surface ( K = k k ) is equal to a vector of the surface reciprocal lattice G. ' The possible elastically scattered beams ( k ) can be obtained using the well-known Ewald construction. To every surface reciprocal lattice point (h,k) a rod normal to the surface is assigned and a sphere with radius k (wave vector of the primary beam) is drawn. As shown in Fig. 2.3, the condition K = G is satisfied for every point at which the sphere crosses a reciprocal lattice rod. Fig. 2.3 Ewald construction for elastic scattering on a surface lattice. From Ref. [114]. 2.3 Low-energy electron microscopy (LEEM) The capability of low energy electrons for surface imaging was invented by E. Bauer in 1962, however, not fully developed (by E. Bauer and W. Telieps) until 1985 [115, 116]. The energy of the electrons is in the range of ev when they interact with the sample, hence rendering this method surface-sensitive. LEEM is a true/direct imaging technique, as opposed to a scanning technique, with a very high spatial resolution of about 10 nm. 22

32 The image is generated using diffracted low energy electrons (LEED) since the backscattering is relatively strong at low energies [121]. In order to use LEED beams for imaging in LEEM the illuminating beam must be separated from the imaging beam. This is achieved by using magnetic deflectors [ ]. At low energies, electron optics suffers from several aberrations and this issue is resolved by making use of a cathode lens where the specimen forms one electrode and is kept at the potential of the electron gun, and the objective lens forms the other electrode which is grounded. Cathode lens could be considered as a combination of a homogeneous accelerating field which produces a virtual image behind the sample and of an electrostatic or magnetic field which forms a real image of the sample. The electric field strength at the sample surface is very strong, about 10 kv/mm, which puts strict requirements for the sample holder. The design for the sample holder is discussed later. It was described by Bauer that the lateral resolution in the LEEM is inversely proportional to the electric field strength at the sample surface [115]. Stronger field gives better resolution. Electrons emitted from the electron gun, which is kept at a high potential of typically -20 kv, are focused at the back focal plane of the objective lens using condenser lenses and a highly collimated beam impinges on the specimen. The energy of the electrons is greatly reduced as they traverse the distance between the objective and the sample since the sample is kept at the same potential as the electron gun. These low energy electrons interact with the sample and are elastically back diffracted. The back diffracted electrons are accelerated again and form the LEED pattern in the back focal plane of the objective lens and a Gaussian image is formed in the center of the magnetic deflector. A transfer lens is used to transfer the diffraction pattern or the image at fixed locations in front of an intermediate lens. A contrast aperture is placed at this fixed location or conjugate diffraction plane and is used to select a particular beam for the image formation. Depending upon the excitation of the intermediate lens, either the diffraction plane or the LEEM image could be projected with the help of two projector lenses on a channel plate. We use a commercial LEEM III apparatus built by Elmitec. A schematic of different lenses in the apparatus is shown in Fig. 2.4 and a picture of the apparatus is shown in Fig Prior to LEEM, samples are outgassed at a temperature of 700 C. For the alignment of illumination and imaging columns, it is a good practice to get started with photoelectron emission microscopy (PEEM) since it allows us to work on a wide area of the sample. For 23

33 Fig.2.4 Arrangement of different lenses in the LEEM set-up. From Ref. [124]. Fig.2.5 Elmitec LEEM III set-up. 24

34 getting a good intensity in PEEM, Pb is deposited on the sample. Once the alignment is done, the Pb is removed by heating the sample to a high temperature (> 1200 C) for a few minutes. Once the Pb is removed, a clear LEED pattern is generally seen on the surface. The LEEM results presented in this thesis are done in bright-field mode. In the brightfield mode, the (0,0) diffracted beam is used for imaging. The selection is done using the contrast apertures in the conjugate diffraction plane. Use of contrast aperture also helps in cutting down the secondary emission and leads to a sharp LEEM image formation but at the cost of reduction of intensity in the image Description of the sample holder [From Ref. [125]] The base plate of the sample holder is made up of titanium. Most other components of this sample holder, shown in Fig. 2.6, are made up of molybdenum both to withstand high sample temperatures and to insure that the sample holder remains non-magnetic. Heating of the samples is achieved using a tungsten filament which is electrically isolated from the rest of the sample holder. Samples are heated indirectly by electron bombardment by applying a voltage between the filament and the sample. A molybdenum reflecting cup, beneath and around the filament, held at the same voltage as the filament, is used for directing all the current at the sample. Highly polished, smooth molybdenum cap is designed to decrease field-emission and maintains electric field homogeneity near the sample during imaging. A tungsten-rhenium thermocouple is attached to the molybdenum ring which supports the sample allowing to monitor the sample s temperature. Small loops of tungsten-rhenium foil form the electrical contacts for the sample (two for the filament and two for the thermocouple), making contacts with pins which protrude from the sample stage. Fig.2.6 Sample holder. 25

35 2.3.2 Graphene thickness determination using LEEM In 2008, Hibino et al. measured the thickness of thin graphene films formed on SiC(0001) using LEEM [42]. It was found that the reflectivity of low-energy electrons, in the range of 0 to 10 ev, from thin graphene films shows oscillations depending on the electron beam energy and the film thickness. These oscillations were explained on the basis of quantization of energy levels in the conduction band of graphene with wave vectors normal to the surface. The energy levels depend on the film thickness. When the energy of the incident electrons matches with one of the quantized energy levels, the reflectivity of the electron is reduced and a dip occurs in the reflectivity curve. The number of dips in the reflectivity curve equals the number of graphene layers on the surface. The conduction band energy levels can be calculated using tight-binding approximation. For m -layer-thick film, energy levels are given: E = ε 2 t cos[ πn /( m + 1)] where ε is the band center energy, t is the transfer integral and n = 1 to m. The value of t is estimated using first-principles calculations and is found to be 1.6 ev. We find a good match between the experimental and theoretical values for the energies of the reflectivity dips, as will be shown in Chapter Data analysis While taking LEEM data, a sequence of images is recorded starting with beam energy of 0 ev and incrementing it by 0.1 ev as we go from one image to another. From the sequence of images, we analyze the reflectivity data to obtain local graphene coverage as follows: (i) At each pixel a reflectivity curve extending between about 2.0 and 6.5 ev is extracted from the data: (ii) A quadratic background is subtracted: 26

36 (iii) A sinusoidal function with adjustable frequency and phase, A sin( ke + φ), is fitted to the curve. The process is repeated for all pixels and a scatterplot of the phase vs. frequency is constructed, with reflectivity curves associated with different number of monolayers (ML) occupying distinctly different regions in the plot. (iv) The number of counts in the different regions of the scatterplot then gives the fraction of the surface covered with the different integer ML of graphene. From this we can calculate the average graphene thickness for a given sample. Also, we can construct a color map of the local graphene thickness by assigning each pixel in the image a specific color associated with the region that its reflectivity curve falls in. 2.4 Auger Electron Spectroscopy (AES) AES is routinely used in surface science for determining the chemical composition of solid surfaces. The advantages of this technique are its high surface sensitivity, a rapid data acquisition speed and its ability to detect all elements above helium [114, 126, 127]. 27

37 In AES, the excitation process is induced by a primary electron beam, with energy of several kev, from an electron gun. This energy is sufficient to ionize a core level, such as a K shell. The vacancy thus produced is immediately filled by another electron from a higher shell, say L 1 shell. The energy released from this transition may be used in the emission of a characteristic X-ray photon or may be transferred to another electron lying either in the same shell or a higher shell, say L 2 shell. This electron is ejected from the atom as an Auger electron. The kinetic energy of the Auger electron is characteristic of the parent atom and is independent of the primary beam energy. The levels involved in the transition are reflected in the nomenclature of Auger transition. For example, the above described Auger transition is called KL 1 L 2. In a simple picture, the kinetic energy of this Auger electron would be given by a difference between the corresponding core-level energies: E= E K -E L1 -E L2. Additional Auger processes are shown in Fig At least two energy states and three electrons are needed for an Auger process to happen, implying that the detection of hydrogen and helium is not feasible by this technique. Fig. 2.7 Nomenclature for different Auger processes. From Ref. [114]. Our Auger system is equipped with an electron gun capable of supplying 5 kev primary beam energy, a VG Scientific Clam 100 hemispherical analyzer and a channel electron multiplier (channeltron). Because of the small Auger signal, AES is usually performed in the derivative mode to suppress the large background of secondary electrons. This is done by applying a small oscillatory voltage to the hemispheres of the analyzer and in-phase output signal from the channeltron is detected using a lock-in phase amplifier. 28

38 2.4.1 Graphene thickness determination using AES Sensitivity factors from Ref. [128] are used. However, these numbers are for total emission from a bulk material whereas we are interested in layer sensitivity factors. So, we convert the bulk sensitivity factors to layer sensitive factors using, = λ S x N s s, x R x where S is the bulk sensitivity factor, R x is the layer sensitivity factor, x atoms in the standard material used for measurement of N S is the density of S x, and λ S, x is the electron escape depth from that standard. The layer sensitivity factor is defined according to an equation for the contribution to the intensity from the J th layer located at a distance of surface, I = gr N exp( d / λ ) x, J x J J x d J from the film where g is an instrument response function, N J is the two-dimensional density of atoms in the J th layer and λ x is the electron escape depth from the material under study. An empirical form for the electron escape depth is used, λ x = A /( N Ex ) + BEx / N 1 2 where λ x is the escape depth in nm, N is the atomic density in atoms/nm 3, A = 538 ev 2 and B = 0.41 nm -1/2 ev -1/2 [129]. In the early stage of our work we analyzed the intensities of the C KLL line at 272 ev to the Si LMM line at 92 ev, using for calibration a spectrum obtained from the SiC(0001) 3 3-R30 surface. This surface has a known structure of Si adatoms sitting on top of a SiC bilayer with one adatom for each three SiC unit cells [101]. We then apply the analysis procedure to spectra obtained from the graphene on SiC. For this purpose we assume a model of uniform monolayers of graphene (ML = 38.0 carbon atoms/nm -2 ) on the SiC, with nm spacing between graphene layers and also between the uppermost SiC layer and the first graphene layer. The resulting relationship between Auger C:Si ratio and number of carbon layers is shown in Fig As described in Chapter 1, an interface layer exists on the Si-face of SiC which has recently been found to contain close to 1 graphene ML of excess carbon relative to surface terminated with a SiC bilayer [41]. We can therefore estimate the number of graphene layers to be simply one less than the number of carbon layers on the Si- 29

39 face of SiC. However, on the C-face of SiC, no such interface is found to occur and hence we conclude the number of graphene layers to be the same as the number of carbon layers. Fig. 2.8 Calibration curve relating C:Si Auger intensity ratio to the number of excess carbon monolayers (relative to a SiC bilayer) on the surface. A model consisting of graphene layers uniformly spaced at nm from the interface is assumed. The inset shows Auger electron spectra acquired from a UHV-prepared SiC(0001) 3 3-R30 surface, and from a graphitized surface prepared by annealing at 1150 C for 40 min. Fig. 2.9 Calibration of Auger data with graphene thicknesses measured using LEEM. 30

40 In our later work we started using the Si KLL line at 1619 ev instead of the Si LMM line at 92 ev for determining the thickness of graphene films; the relatively long escape depth of the former allows determination of thicknesses up to 20 monolayers (ML). Calibration of the Auger sensitivity factors is, now, accomplished using graphene thicknesses determined by LEEM and is shown in Fig Atomic force microscopy (AFM) G. Binning, C. F. Quate and Ch. Gerber first developed the AFM in 1986 in order to investigate the surfaces of insulators, since such materials could not be studied with the scanning tunneling microscope (STM) which requires conducting or semiconducting surfaces [130]. AFM has emerged as a very powerful technique for studying the surface topography and has recently been used in the manipulation of atoms on the surfaces [131, 132]. The fact that the images can be obtained in ambient conditions, unlike STM that needs a vacuum environment, makes the AFM apparatus very easy to work with (for both insulating or conducting surfaces). In AFM, the force between the atoms located at the apex of a sharp tip (mounted on a cantilever) and atoms at the sample surface is measured. Figure 2.10 shows a plot of interatomic forces as the distance between the tip and sample is varied [133]. At smaller distances, the force between the atoms is repulsive and this part of the curve is used in contact-afm. When the tip is brought in contact with the sample, it experiences a repulsive force that leads to the deflection of the cantilever. The deflection is measured using a laser signal that is bounced off from the cantilever and is detected using position-sensitive photo diodes (PSPD) as shown in Fig There are two modes of operation: Constant-force mode: Here the force between the tip and the sample is kept constant (called the set-point). Since the surface of the sample is not flat, the force between the tip and the sample varies due to the variation in the tip-sample distance. The difference between the setpoint and the actual force is called an error signal. This error signal is sent to a feedback circuit which then, commands the scanner (piezoelectric tube connected to the sample or the tip) to either extend or retract in order to make the error signal zero which in turn generates the height profile of the surface. 31

41 Fig Inter-atomic force as a function of tip-sample separation. From Ref. [133]. Fig Deflection of laser signal from the cantilever and its detection using the PSPD. From Ref. [133]. 32

42 Constant-height mode: Here the tip-sample height is kept constant. The feedback circuit is deactivated and the deflection of the cantilever maps out the interaction forces directly. This method is preferred for flatter samples. Soft cantilevers are used in the contact-mode in order to boost the deflection signal and also to prevent the sample damage. In order to image softer samples, non-contact AFM (NC-AFM) is used where the region of attractive forces in the force vs. distance curve is explored. Here the cantilever is vibrated near the surface of the sample at its resonant frequency. The resonant frequency and the vibration amplitude of the cantilever vary as the tip is brought closer to the sample and this variation in frequency or amplitude could be used in the feedback circuit to generate the surface topography. The cantilever used for NC-AFM should be stiff so that it doesn t get pulled into contact with the sample surface. A mode whose operation lies in between the modes of contact-afm and NC-AFM is known as "tapping mode" or "intermittent-contact" AFM. Here, the vibrating cantilever barely hits, or "taps", the sample at the lowest point in its vibration cycle. Most of the AFM work presented in this thesis is in tapping-mode using a Digital Instruments Nanoscope III, shown in Fig. 2.12, and is done in ambient conditions. The cantilevers used for imaging are made of Si doped with antimony. Fig Digital Instruments Nanoscope III set-up. 33

43 Chapter 3 Graphene formation on the Siface of SiC in UHV 34

44 In this Chapter, graphene films prepared on the Si-face of SiC in UHV are discussed. As mentioned in Chapter 1, the Si-face of SiC undergoes various surface reconstructions prior to graphitization, with R30 reconstruction (denoted 6 3 for short) acting as a precursor to the graphene formation [44, 60, 62]. This 6 3 reconstruction or buffer layer is found to be strongly covalently bonded to the substrate [62]. Nucleation of a new carbon layer starts beneath this buffer layer making this new layer bond with the substrate. The original buffer layer is then isolated from the substrate, and this isolated layer forms the first graphene layer. So every new graphene layer starts as a 6 3 layer with a fixed orientation, determined by the covalent bonding, with respect to the substrate. Hence, this buffer layer provides a uniform template for the subsequent growth of the graphene layers on the Si-face of SiC and acts as an interface between the SiC(0001) surface and the graphene layers. We have investigated the formation of graphene films by decomposition of the Si-face of SiC in UHV. Section 3.1 describes the experiments that are done for fabricating and characterizing these graphene films. Results focusing on the structural and electrical properties of these films are presented in section 3.2. A summary of all the results is presented at the end of this chapter. 3.1 Experiments Experiments are performed on nominally on-axis, n-type 6H-SiC or semi-insulating 4H-SiC wafers purchased from Cree Corp. The wafers are 2 or 3 inches in diameter, mechanically polished on both sides and epi-ready on the (0001) surface. The wafers are cut into 1x1 cm 2 samples and the samples are chemically cleaned in acetone and methanol before putting them into our custom built preparation chamber, described in Chapter 2. Samples are first etched in a 10 lpm flow of pure hydrogen for 3 min at a temperature of 1600 C. This H-etching removes the polishing scratches which arise during the mechanical polishing of the wafers, resulting in an ordered step-terrace arrangement on the surface which is suitable for graphene formation [113]. Before annealing, hydrogen is pumped away from the chamber and we wait until a desired pressure of 10-8 Torr is reached and then the samples are annealed for 10 to 40 min at temperatures ranging from C. The surface morphology of resulting graphene films is studied by AFM using a Digital Instruments Nanoscope III in tapping mode. 35

45 After studying the morphology in AFM, samples are transferred to an Elmitec LEEM III system. In LEEM, we look at the intensity of the reflected electrons from different regions of the sample as a function of the beam energy. As discussed in Chapter 2, reflectivity curves are used for determining the average graphene thickness and also for generating color-coded maps of local graphene thickness. For routine determination of graphene thickness, we also use the ratio of the 272 ev KLL C line to either 1619 ev KLL or 92 ev LMM Si line in the Auger spectrum (also described in Chapter 2). Raman measurements are performed by Yugang Sun at Argonne National Labs. Raman spectra are measured on a Raman microscope (Renishaw, invia) with excitation wavelengths of 514 nm. All spectra are measured using a 100 microscope objective to focus the laser excitation (10 mw) onto the samples as well as for collecting the scattered light. The measurements are performed at room temperature. We have done some preliminary electrical conductance measurements on these samples in our laboratory using two probes. Field-effect transistors (FET) based on the graphene films are fabricated and analyzed by researchers at MIT Lincoln Labs and at Sarnoff Corporation and some results are presented in this chapter. 3.2 Results and Discussion A. Evolution of surface morphology with temperature Figure 3.1 shows the temperature dependence of the thickness of our graphene films. The thickness of graphene films is calculated using the Auger model, mentioned in Chapter 2, which employs the intensities of C KLL line at 272 ev and Si LMM line at 92 ev. We first examine the data points in Fig. 3.1(a) shown by open circles, for which the annealing temperatures are obtained by viewing the sample directly with the pyrometer. Since the sample is transparent, the pyrometer sees mainly the heater in this case. As described previously, additional calibration of temperature is done using a graphite cap. The data points shown by filled circles are from the samples prepared with the graphite cap sitting on top of them and the temperature of the graphite cap is measured with the pyrometer. With the cap present, we do not expect the sample temperature to be lower than that of the cap, and we simply use the cap temperature as an estimate of the sample temperature. In the absence of the cap, we estimate the temperature difference between sample and strip simply by shifting 36

46 the data in Fig. 3.1(a) such that data points with and without the cap being present are aligned, as shown in Fig. 3.1(b). We find that a 450 C shift is appropriate, and we use this correction for all data measured without the cap. Fig. 3.1 Graphene thickness as a function of annealing temperature: (a) using raw pyrometry data for the temperatures, and (b) using a 450 C temperature correction for points measured without the graphite cap in place. Annealing time is 40 min for all data points. The morphology of graphene film prepared at various annealing temperatures is shown in Fig As mentioned earlier, substrates are hydrogen etched prior to annealing in order to remove the polishing scratches and this process also generates a uniform array of steps and terraces on the surface. When the substrate is annealed to about 1150 C, the overall step morphology is preserved (steps are running approximately vertically in the image) although pits are seen to form in the areas between the steps, as shown in Fig. 3.2(a). The origin of these pits is explained by Hannon and Tromp as resulting from the formation of the 6 3 layer [41]. This 6 3 layer forms prior to the formation of graphene, and graphene then forms on top of the 6 3 structure. At a higher temperature of around 1250 C, we find motion of the 37

47 steps such that the ordered step-terrace array is no longer seen on the surface, as shown in Fig. 3.2(b) and the surface pits formed have begun to coarsen. At higher annealing temperature near 1350 C, the steps undergo considerable motion forming surface regions microns in size and separated by step bunches. Figure 3.2(c) displays AFM image acquired from a relatively flat surface area. Two interesting morphological features are seen in this image: the white lines or ridges (1-2 nm high) occurring both near step edges and on terraces, and the snowflake-like pattern seen on many of the terraces. The ridges might arise due to thermal expansion mismatch between graphene and SiC [44]. These snowflake patterns, we believe, arise from excess carbon on the surface forming disordered, nano-crystalline graphite (NCG). At higher temperatures above about 1400 C we do not discern any of the snowflake-like patterns on the terraces, as seen in Fig. 3.2(d), presumably because of the thicker films in those cases. Also, for these surfaces, the pits on the surface continue to coarsen and grow in size, and they tend to act as pinning centers for the observed ridges. Electron diffraction from a film similar to that of Fig. 3.2(d) is shown in Fig (This data was acquired by Patrick Fisher by employing a molecular beam epitaxy apparatus). In LEED, Fig. 3.3(a), we see simply the hexagonal array of spots expected for the graphene film on the Si-face [26, 29, 31, 63]. The SiC substrate cannot be discerned in this pattern due to the thickness of the graphene. However, using reflection high-energy electron diffraction (RHEED) we can faintly resolve the substrate, as shown in Fig. 3.3(b). Vertical lines in that image mark the 0th and 1st order RHEED streaks; their spacing is 3 times that of Fig. 3.3(c) obtained with a 30 change in sample orientation, as expected for a hexagonal surface. The arrows in Fig. 3.3(b) point to faint streaks that are located at a fraction 0.46±0.01 of the 1st order graphene spacing (the intense dots superimposed on the streaks arise from an intersection of a Kikuchi line with the streak; the sample orientation was carefully adjusted to achieve this intersection in order to enhance the intensity of the streak itself). We expect a fractional spacing of a ( a 3) using lattice constants of a = 0. C 246 nm and C / SiC = a = SiC nm, in agreement with experiment. 38

48 Fig. 3.2 AFM images of graphene on SiC(0001) surfaces prepared under various annealing conditions: (a) 1150 C for 40 min resulting in graphene thickness of 0.5 ML, (b) 1285 C for 40 min resulting in graphene thickness of 1.0 ML, (c) 1390 C for 40 min resulting in graphene thickness of 1.9 ML, and (d) 1410 C for 40 min resulting in graphene thickness of 4.0 ML. Images are displayed with gray scale ranges of 4, 3, 3 and 9 nm, respectively. Fig. 3.3 (a) LEED pattern acquired at 133 ev, of a surface prepared by annealing at 1410 C for 40 min resulting in graphene thickness of 2.0 ML. (b) and (c), RHEED patterns of the same sample as in (a), with electron beam along < 1100 > and < 1120 > azimuths, respectively. Vertical lines indicate features from the graphene, and arrows show features from the underlying SiC. All diffraction patterns are shown in reverse contrast. 39

49 B. Raman spectroscopy on the Si-face graphene films Typical Raman spectra from our graphene films are shown in Fig Each spectrum shows the known fingerprint features associated with graphene: The weak D peak at 1357 cm -1 and intense G peak at 1583 cm -1 correspond to graphene zone-edge and zone-center phonons, respectively (the D peak is normally forbidden, and its presence indicates disorder in the film) [86, 134]. The intense 2D peak located at 2706 cm -1 is attributed to the doubly-resonant scattering from the zone-edge phonons. Spectral features from the SiC substrate are also observed in each spectrum: The peaks at 1519, 1690, and 1710 cm -1 (as well as features below the observed G peak) arise from double resonance of SiC optical phonons. The weak peak at 1415 cm -1 is not associated with bulk phonons of SiC but it nevertheless does arise from the substrate since we find its intensity to increase as the focus of the probing laser is moved away from the surface and into the substrate. This peak is not seen for all the SiC substrates we have studied, and we tentatively attribute it to some sort of defect in this particular substrate. The position of the graphene peaks are found to be quite uniform over the surface, but significant variations in peak intensities do occur, as seen by comparing the two spectra of Fig We tentatively attribute these variations to varying thickness of the graphene film. Fig. 3.4 Raman spectra acquired from a sample annealed at 1370 C for 40 min. Spectra acquired from two different locations on the sample are shown. 40

50 C. LEEM on the Si-face graphene films Figure 3.5 shows larger-scale AFM images together with LEEM results obtained from two samples. The top panel, Fig. 3.5(a) through 3.5(d), shows the data acquired from a 6H- SiC(0001) surface annealed at 1320 C for 10 min and the bottom panel, Fig. 3.5(e) through 3.5(h), shows the data for a 4H-SiC(0001) surface annealed at 1320 C for 40 min. The LEEM images in Fig. 3.5(b) and (f) show data acquired with 3.7 ev electrons incident on the surface, with the measured signal being the reflectivity (i.e. bright-field imaging) of the electrons. Reflectivity curves as a function of the beam energy are shown in Figs. 3.5(c) and 3.5(g). Fig. 3.5 AFM and LEEM results for graphene on SiC(0001), with (a)-(d) showing a sample prepared by annealing at 1320 C for 10 min and (e)-(h) showing a sample prepared by annealing in vacuum at 1320 C for 40 min. (a) and (e) AFM images, with (a) displayed using a gray scale range of 3 nm. For image (e) there is an 8-nm-high step bunch extending vertically across the image, indicated by the arrows, and hence a split gray-scale is used with 4 nm range for each of the terraces on either side of the step bunch. (b) and (f) LEEM images at an electron beam energy of 3.7 ev. (c) and (g) Intensity of the reflected electrons from different regions marked in (b) or (f) as a function of electron beam energy. (d) and (h) Color-coded maps of local graphene thickness, deduced from analysis of the intensity vs. energy at each pixel; blue, red, yellow, green, and cyan correspond to 1, 2, 3, 4, and 5 ML of graphene, respectively. Small white or black crosses mark the locations of the intensity vs. energy curves. Regions with no discernable oscillations are colored black. 41

51 For the relatively short annealing time of Fig. 3.5(b), the surface is found to be covered mainly with 2 ML of graphene, as seen in the map of Fig. 3.5(d). Not all of the 2 ML domains are equivalent, however, since their contrast in Fig. 3.5(b) appears to be quite mottled. This mottling arises from variation in the magnitude of the intensity maximum at 3.7 ev, as illustrated by curves B, C and D of Fig. 3.5(c). We have not investigated this intensity variation further, but presumably it is related to the nm-scale nature of the small graphene domains in this nucleation phase of the film formation. In any case, Fig. 3.5(d) also shows that, in addition to the 2 ML areas, there are few small regions with 1 or 3 ML of graphene coverage. Average graphene thickness for this sample is found to be 1.9 ML. With longer annealing time, the graphitized Si-face morphology undergoes considerable changes, as shown in Fig. 3.5(e). Step bunches form, one of which is marked by the arrows in Fig. 3.5(e). The color-coded map of the thickness is shown in Fig. 3.5(h), with this surface area having an average graphene thickness of 3.0 ML. Importantly, the thickest regions of graphene are found near step bunches, one of which extends in a zig-zag manner from top to bottom of Fig. 3.5(f) and Fig. 3.5(h). Away from the step bunches, the graphene thickness is predominantly 2 or 3 ML. Additional color-coded images of graphene thickness for this same surface are shown in Fig We associate all of the 4 or 5 ML regions with steps or step Fig. 3.6 Color-coded maps of local graphene thickness for the same sample (and with the same manner of display) as Fig. 3.5(h). 42

52 bunches on the surface, and we find a separation between bunches of 10 µm. On the flat terraces between step bunches we find that almost the entire surface has only 2 or 3 ML of graphene thicknesses. This type of thickness variation, restricted to a single ML, is indicative of layer-by-layer formation of the graphene on the areas between bunches. The occurrence of layer-by-layer graphene formation was also reported in a LEEM study by Hibino et al. of graphene on vicinal SiC surfaces [135]. D. Electrical properties The electrical conductance of our graphene films is measured, simply by measuring the resistance between two probes (bent copper wires) gently placed on two corners of the sample. Results are shown in Fig We find a sharp onset in the conductance occurring at a graphene thickness of 1.0 ML, with conductance values of about 1 (kohm) -1 for thicker films. Fig. 3.7 Conductance of graphene layers (measured with two probes across a mm 2 sample), as a function of graphene layer thickness. Open and closed symbols have the same meaning as in Fig Field-effect transistors (FETs) based on graphene films are fabricated by our collaborators at MIT Lincoln Labs and at Sarnoff Corporation. During the fabrication of these devices, patterning of the graphene layers is achieved by oxygen plasma etch. Source/drain layers are directly deposited on the graphene layer and consist of 2 nm Ti and 20 nm Pt. A high k 43

53 dielectric hafnium dioxide (HfO 2) of thickness 40 nm is deposited using thermal evaporation. In the end, 20 nm Pt gate layer is deposited. A schematic of the device structure is shown in Fig Fig. 3.8 Schematic of the graphene based FET. Figure 3.9(a) shows drain current vs. gate voltage (I d -V g ) curve for transistor fabricated using the Si-face graphene film. All measurements are done at room temperature. For both positive and negative gate voltages, graphene device shows an increase in the drain current. At negative gate voltages, holes are responsible for electrical conduction and at positive gate voltages electrons dominate the conduction. Conductivity (σ d ) is calculated using drain current, drain voltage and device geometry and is plotted as a function of the gate voltage in Fig. 3.9(b). It can be seen that at certain gate voltages, conduction is minimum. This minimum conductivity determines I on /I off ratio of a device. The higher the ratio the easier it is to turn off a device. In our graphene devices, the minimum value of the conductivity is found to be around 1 ms. Calculations of field-effect mobility (µ) are done using ( dσ / dv )( WL / C) where the derivatives are measured from the σ d -V g curves, W is the graphene width, L is the channel length and C is the graphene to gate capacitance. Highest mobility for the data set shown above is around 2000 cm 2 /Vs. Histogram of the mobilites is shown in Fig We have observed highest mobility to be around 4000 cm 2 /Vs in a set of devices fabricated using another Siface graphene sample [136]. These values for mobilities are comparable to what have been reported for epitaxial Si-face graphene films [36, 37]. Well, the device yield is found to be d g 44

54 not so high and gate shorts are observed in a number of cases. These gate shorts might arise due to pits or other unwanted morphological features, as discussed in section 3.1 A. 2.5m 2.0m V d = 0.1V V d = 1.0V Graph G W4R2C10 T HfO2 = 40nm W=5µm, L=10µm 10.0m 9.0m 8.0m 7.0m GraphG W4 T HfO2 = 40nm W=5µm, L=10µm 1.5m 6.0m I d (A) 1.0m σ d (Ohm -1 ) 5.0m 4.0m 3.0m 500.0µ 2.0m 1.0m I dmin V g (V) V g (V) Fig. 3.9 (a) I d -V g curves for two drain voltages, and (b) σ d -V g for a set of devices processed under identical conditions. Devices / Histogram Bin Device Set W=5µm, L=10µm Wafer 4 e-like µ h-like µ 0 0 1k 2k 3k 4k 5k Mobility (cm 2 /Vs) Fig Histogram of mobilities for a set of device fabricated from a given Si-face graphene sample. 45

55 3.3 Summary We have fabricated graphene films on the Si-face of SiC by heating the SiC crystals in UHV. The structural properties of resulting graphene films are studied using AFM, electron diffraction, LEEM and Raman spectroscopy. It is found that the surface after graphitization is not smooth and shows a number of features like pits, randomly-located steps and snowflakelike pattern. We observe areas of different graphene thicknesses on a given sample. As the annealing temperature is increased, constant thickness areas (we call them domains ) grow in size with lateral extent of many microns and are separated by step bunches. The areas between step bunches are covered with graphene ranging in thickness of only 1 ML. Hence, for thicknesses > 2ML, the graphene is found to form in a layer-by-layer manner. FETs fabricated using the Si-face graphene films are found to have mobilities as high as 4000 cm 2 /Vs. 46

56 Chapter 4 Graphene formation on the C- face of SiC in UHV 47

57 This chapter deals with the structural properties of graphene films fabricated by annealing the C-face of SiC in UHV. As described in Chapter 1, the interface between the SiC C-face and graphene is not so well understood. There have been reports of (3 3) or (2 2) C surface reconstructions on the C-face prior to graphitization [32, 62, 71, 108]. A uniform template similar to the 6 3 layer seen in the case of Si-face is missing on the C-face of SiC. Due to the absence of a uniform template, graphene layers are found to be rotationally disordered on the C-face of SiC as opposed to the Si-face graphene films where the graphene layers have a fixed orientation with respect to the SiC substrate. Due to this rotational disorder, LEED patterns on the C-face films shows streaking. The presence of this streaking in the LEED pattern led early researchers in believing that the film is not ordered and hence its structural properties and electronic properties were not studied until recently. In 2008, Hass et al. reported that that the electronic properties of thick graphene films on the C-face do not deviate from that of a single layer graphene [79]. These findings were interpreted in terms of the rotational disorder seen in these graphene films which seems to decouple adjacent graphene layers, hence preserving the electronic properties of a monolayer graphene. The mobility values are found to be higher for the C-face graphene films than the Si-face films making the C-face graphene films a suitable candidate for carbon-based electronics [27, 112]. Some groups have reported that the method of annealing in UHV does not produce homogeneous graphene on the C-face [80, 137]. However, we have been able to form high quality graphene on the C-face by annealing in UHV. Field-effect mobilities of the transistors fabricated from these films exceed 4000 cm 2 /Vs at room temperature [136]. Section 4.1 briefly describes the experiments that are done for fabricating and characterizing the C-face graphene films. Results are presented in section 4.2. Differences between the C-face and the Si-face graphene films are also mentioned and the reasons as to why graphene forms differently in the two cases are also discussed. 4.1 Experiments Samples measuring 1 1 cm 2, using both semi-insulating 4H-SiC and n-type 6H-SiC C-face material, are prepared in our custom built preparation chamber. In order to remove polishing damages on the as-received wafer surfaces, samples are heated in 1 atm of hydrogen at 1500 C for 3 min. After etching, the hydrogen is pumped away and the samples are heated at 48

58 temperatures above 1100 C, for 20 min in a background pressure of 10-8 Torr. The resulting films are characterized by AFM, LEED, LEEM and Raman spectroscopy. Thickness of the graphene films is determined by using either AES or LEEM. As described in Chapter 2, Pb is deposited on the surface of the sample for aligning the LEEM set-up. Once the alignment is done, Pb is removed by heating the sample to about 1200 C for few minutes. This heating could lead to an increase in the carbon content on the surface. Occasionally, an increase of about 0.5 ML in the graphene thickness is noticed for thin films after doing LEEM. 4.2 Results A. Morphology of C-face graphene films Figure 4.1 shows the plot of graphene thickness as a function of annealing temperature for graphene grown on the C-face of SiC. For comparison, data for the Si-face graphene films is also presented. In agreement with prior reports, we find that graphene starts to form at a significantly lower temperature on the C-face compared to the Si-face, about 1100 C for the former and 1250 C for the latter [29, 30, 66]. At a given temperature, thicker graphene film forms on the C-face than the Si-face. It can be seen that about 9 ML are formed on the C-face at about 1250 C while only one monolayer is formed on the Si-face. The data for the Si-face Fig 4.1 Graphene thickness as a function of annealing temperature for 6H-SiC{0001} surfaces, showing results for C-face (anneal time 20 min) and Si-face (anneal time 40 min). 49

59 is in agreement with our previous report for that surface, with an uncertainty of ±50 C in the temperatures which can be attributed to difficulties associated with measuring the temperature of a transparent sample accurately with optical pyrometry [45]. Figure 4.2 shows AFM images of samples annealed at different temperatures. After annealing at about 1120 C, we can see in Figs. 4.2(a) and (b) that the overall step-terrace pattern, as seen after H-etching [113], is maintained along with some small changes in the morphology. On the terraces, small domains ( 200 nm in extent) of varying gray-contrast are seen; these domains are similar to those reported in scanning tunneling microscopy studies of C-face graphene, and attributed to differing underlying interface structure between the graphene and the SiC [71]. After annealing at 1190 C, the morphology further evolves, forming raised and lowered terraces as seen in Fig. 4.2(c). The small domains are still faintly seen, and the shape of the terraces now deviates from the original step structure of the H- etched surface. It should be noted that those original steps can still be discerned in Figs. 4.2(a)-(c) by the lines of white deposits [ 1 nm high and vertically aligned in Fig. 1(c)]. After annealing at 1240 C, Fig. 4.2(d), the surface is fully transformed into a morphology with distinct terraces of differing heights. All the terraces still have faint white lines extending over them. These lines perhaps delineate domains in the graphene, or alternatively they could be related to the larger (higher) raised ridges or "puckers" seen in Fig. 4.2(e). In that image, obtained after annealing at 1320 C, the puckers are believed to arise from thermal expansion mismatch between the substrate and the graphene films [44]. The features seen in Fig. 4.2 for graphene on C-face graphene films are quite different than those observed on Si-face graphene films. On the Si-face graphene films, small pits are seen on the surface even during the early stages of graphitization (refer Chapter 3). The origin of these pits is recently explained in terms of the development of the 6 3 layer between the SiC and the graphene [41]. This interface layer apparently acts as a template for subsequent graphene formation, with the graphene forming from the 6 3 layer and the 6 3 structure moving downwards as Si sublimates from below it. For the C-face, however, the graphene/sic interface can consist of various different structures, and apparently any sort of uniform templating behavior analogous to that of the 6 3 does not occur [62, 71, 108]. We hypothesize that the different graphene/sic interface structures observed to occur for the C- face may have varying efficacy for producing graphene, as shown in Fig The interface 50

60 Fig. 4.2 AFM images of graphene formed on C-face 6H-SiC by annealing at temperatures of (and forming graphene thicknesses of): (a) and (b) 1120 C (1.2 ML), (c) 1190 C (4 ML), (d) 1240 C (9 ML), and (e) 1320 C (16 ML). Images are displayed with gray scale ranges of 2 nm, 2 nm, 4 nm, 13 nm, and 15 nm respectively. structure for the C-face would thus still act as a template for Si release and resulting graphene formation, but different structures would have varying rates for this process. Different thicknesses of graphene would form on the surface, at least initially, which could account for the varying contrast seen in the small domains of Figs. 4.2(a)-(c).This result is also consistent with the above hypothesis of having different interface structures between the graphene and the SiC which produce differing graphitization rates for different areas of the surface. Fig. 4.3 Schematic of graphene formation on the C-face of SiC: (a) Surface before graphitzation, and (b) Different interface structures with varying efficacy for graphene production (Assuming a faster Si sublimation rate for the 2 2 surface than the 3 3 surface for demonstration). 51

61 To further probe the nature of the terraced morphology seen for the C-face, scanning Auger microscopy studies are carried out. Figure 4.4(a) shows an AFM image of a C-face graphene film and Fig. 4.4(b) shows a scanning electron microscope (SEM) image from the same sample. The morphology as seen by AFM consists of raised terraces over a minority of the surface area, similar to that of Fig. 4.2(d). Examining the SEM image, we see that it displays just the same type of morphology, and we therefore associated the white portions of the SEM image with raised terraces. Now, examining the individual spectra of Fig. 4.4(c), acquired from the locations marked in Fig. 4.4(b), we see that the white (raised) area in the SEM image shows a Si peak with greater amplitude than that from the darker (lower) area on the surface. Similar results were obtained at multiple locations over the surface, and we conclude that the raised areas in the topography actually have a thinner coverage of graphene, with the lower areas having thicker coverage. This conclusion is consistent with an expectation of a lower morphology and concomitantly thicker graphene in areas where more Si has left the surface, i.e. assuming that the Si leaves the SiC by diffusing through the overlying graphene without significantly redistributing itself, as shown in Fig. 4.3 and will also be discussed in the subsequent section. Fig. 4.4 (a) AFM image of graphene on C-face 4H-SiC prepared by annealing at 1320 C, forming 8 ML of graphene. The image is displayed with a gray-scale range of 10 nm. (b) SEM image of same sample (different surface area). (c) Auger electron spectra acquired from the surface locations indicated in (b). 52

62 We mention here one additional aspect of the morphology of the C-face graphene films that we have observed for certain wafers. Figure 4.5(a) shows a sample prepared in an identical manner as described above. This sample displays two types of surface morphology: a low (black) topography covered by small domains, similar to those of Fig. 4.2(d), and a high (light gray) topography. The latter is quite disordered and rough, as seen in the inset of Fig. 4.5(a). The optical micrograph of Fig. 4.5(b) is taken from the same sample as Fig. 4.5(a), and the characteristic hexagonal-shaped disordered areas are again evident. Figure 4.5(c) shows spatially resolved Raman spectra, one acquired from within a disordered area inside a hexagon and the other from an ordered area between hexagons. Both spectra show characteristic peaks associated graphene, marked as D, G, and 2D [86, 134]. However, the spectrum from the disordered area differs from that of the ordered area in that it reveals a higher intensity of the defect-related D peak at 1360 cm -1 and its G peak is shifted by 10 cm -1 to 1610 cm -1. This type of shift is known to be associated with the occurrence of nanocrystalline graphite (NCG), and we therefore attribute the disordered areas of the surface to the presence of NCG [138]. Fig. 4.5 (a) AFM image of graphene on C-face 6H-SiC prepared by annealing at 1220 C. The inset shows an expanded view of the higher (light gray) surface area. Gray-scale ranges are 9 nm for the main image and 2 nm for the inset. (b) Optical micrograph of same sample (different surface area). (c) Raman spectra, with the solid and dashed lines showing spectra acquired from the locations indicated in (b). The inset shows an expanded view of the G-line. 53

63 We find that the amount of NCG that forms is dependent on the starting wafer that we use. We have studied five different wafers, with 5 15 samples studied from each wafer. Excellent sample-to-sample reproducibility is found for samples cut from a given wafer. Some wafers produce little amounts of NCG and some large; the former display in their morphology (after hydrogen-etching) a well-ordered array of parallel, straight steps edges (arising from unintentional miscut of the surface), as shown in Fig. 4.6(a), whereas the latter display numerous spiral steps (asociated with screw dislocations intersecting the surface), as shown in Fig. 4.6(b). We believe that this formation of the NCG is related to the inhomogeneous nucleation of graphene discussed by Camara et al., who observe both intrinsic and extrinsic graphene formation, with the latter arising from dislocations intersecting the surface [137, 139]. Their extrinsic graphene forms in an ordered manner, whereas we find disordered NCG, but the growth temperatures employed by Camara et al. are considerably higher than ours and we believe that that could account for this difference. Fig. 4.6 AFM images of H-etched C-face surfaces showing (a) well-ordered steps, and (b) spiral steps. Graphene films have a fixed rotational orientation with respect to the SiC substrate on the Si-face as seen in their LEED patterns which display a hexagonal arrangement of six clear, distinct spots. However on the C-face, there is a rotational disorder in the graphene layers giving rise to streaking in the diffraction pattern, as illustrated in Fig We still observe six discrete spots in the pattern, seen weakly at the maximal angles indicated in the figure, but additional spots (streaks) are also seen located at angles of 30 ± ϕ relative to the six 54

64 discrete spots. Angles of ϕ ranging from 6 to 13 have been observed, although most typically we find ϕ 7. Overall our patterns are quite similar to those reported by Hass et al., although their angle ϕ was only 2.2 [79]. We interpret this difference as arising from the various possible nearly-commensurate arrangements of graphene monolayers atop each other [110]. Fig. 4.7 LEED pattern for graphitized SiC( 0001 ) surfaces, obtained at the energies of (a) 133 ev (using a VG Scientic LEED apparatus) and (b) 44 ev (using an Elmitec LEEM III). Samples were prepared by annealing for 20 min, (a) 4H-SiC( 0001 ) surface at 1370 C and (b) 6H-SiC( 0001 ) surface at 1235 C. The faint streak indicated by the arrow in (a) is an artifact (optical reflection) of the video acquisition system. The black lines indicate diffraction features over a 60 range of angles, with the outer peaks of this range being orientated at 30 relative to primary SiC (1,0) spots. B. LEEM on the C-face graphene films Figure 4.8(a) shows an AFM image of 6H-SiC( 0001 ) graphitized at 1100 C for 20 min. The surface has preserved the uniform step-terrace arrangement as seen after hydrogen-etching, with terraces showing small domains of varying gray-contrast. These steps can also be discerned in the LEEM image shown in Fig. 4.8(b). This image shows the reflected electron intensity, at an electron energy of 3.3 ev. As described by Hibino et al., areas of the graphene with different thickness interact differently with the incident electrons, thus producing varying contrast for the graphene films as a function of energy [42]. Plots of the reflected intensity as a function of energy are shown in Fig. 4.8(c), for the specific locations A-G indicated in Fig. 4.8(b). Secondary electrons produce the large reflectivity below about 1.5 ev. The number of minima in the curves A-D above that energy corresponds to the local thickness in ML of the graphene film. Thus, for curve B, acquired from the distinctly white 55

65 contrast region of Fig. 4.8(b), there are 2 ML of graphene. This type of contrast extends over roughly half of Fig. 4.8(b), and the remainder having a darker, but somewhat mottled, contrast. Reflectivity curves from those types of areas reveal a combination of 1 ML and 3 ML graphene coverage, as illustrated by the curves A and C. Finally, a few small regions of this surface reveal 4 ML graphene thickness, as shown by the curve D. Regions marked E-G show no well-defined oscillations, as seen in the reflectivity plot of Fig. 4.8(c). These regions might contain very small domains (<50 nm) of varying thicknesses. LEEM images acquired at different beam energies are analyzed pixel by pixel to generate a color-coded map of local graphene thickness, as shown in Fig. 4.8(d). It can be seen that the sample is covered with domains of different graphene thicknesses, mainly 2 ML. Fig. 4.8 Results from graphitized 6H-SiC( ) surfaces prepared by heating in vacuum under conditions of (a)-(d) 1100 C for 20 min, yielding an average thickness of 2.0 ML of graphene, and (e)-(h) 1150 C for 20 min, yielding 3.9 ML of graphene. (a) and (e) um2 AFM images, displayed with gray scale ranges of 3 and 4 nm, respectively. (b) and (f) LEEM images at an electron beam energy of 3.3 ev with 15 µm field-of-view. (c) and (g) Intensity of the reflected electrons from different regions marked in (b) or (f) as a function of electron beam energy (curves are shifted vertically, for ease of viewing). (d) and (h) Color-coded maps of local graphene thickness, deduced from analysis of the intensity vs. energy at each pixel; blue, red, yellow, green, cyan, magenta, and gray correspond to 1 7 ML of graphene, respectively. Small white or black crosses mark the locations of the intensity vs. energy curves. Regions with no discernable oscillations are colored black. 56

66 It is important to realize that, as the graphene forms, the surface of the sample will recede since Si atoms are leaving (assuming limited interdiffusion of the Si and C atoms, as demonstrated below) [62]. The carbon content in a single graphene monolayer (38.0 atoms/nm 2 ) is very close to that in three SiC bilayers (36.5 atoms/nm 2 ). The latter constitutes 0.75 nm of height in its SiC form, whereas the graphene monolayers are spaced by about 0.34 nm from each other and have similar spacing to the SiC (for the C-face) or the 6 3 layer (for the Si-face) [140]. Thus, for each additional ML of graphene, the top surface must recede by about 0.4 nm. The data of Fig. 4.8(d) showing a mixture of 1, 2, 3 and 4 ML graphene thickness is consistent with the nm variation in surface height across the terraces on this surface as seen in Fig. 4.8(a) [an exceptionally low region is marked by the arrow in Fig. 4.8(a) and it is likely associated with the 4 ML graphene thickness]. With further annealing, the morphology of the surface changes. Figure 4.8(e) shows an AFM image of a surface graphitized at 1150 C for 20 min. Its surface morphology is quite different than that of Fig. 4.8(a). We now see that the step edges are somewhat irregular, with flat regions of the surface now forming large irregularly-shaped µm-sized regions separated from their neighboring terraces by step bunches. Traces of the original step edges from the hydrogen-etched surface are still visible in the Fig. 4.8(e); these traces are small deposits, likely carbon in the form of NCG, that form at the steps edges during the initial graphitization and these persist even during subsequent graphitization. Examining now the morphology of the graphene film for the surface prepared at 1150 C, Figs. 4.8(f) 3 (h), we find domains with 1-3 µm lateral extent and having a wide range of graphene thicknesses, from 2 ML to 7 ML. We note that the reflectivity curves provide a faithful measure of the graphene thickness over this entire range. In Fig. 4.9 we compare the measured location of the minimum of the reflectivity curves together with a simple prediction based on a tight-binding model for a one-dimensional chain, using the same parameters as in Ref. [42] but with central energy of 3.2 ev above the vacuum level (0.2 ev higher than used in Ref. [42], but that work discusses the Si-face whereas our data is for the C-face). We can see that there is a reasonably good match between theory and experiment. Below 1.5 ev the reflectivity curves show an intense shoulder due to secondary electrons, which affects the location of minima near that energy. Even accounting for that, the match 57

67 Fig. 4.9 Location of local minima in the reflectivity curves from Fig. 6(g), compared with theoretical expectations based on a tight-binding model. between experiment and theory is still somewhat better for the upper half of the curves (above 3.2 ev) than for the lower half. However, as pointed out by Hibino et al., this discrepancy is likely due to the fact that the true bandwidths differ above and below this central energy (an effect that is not present in the tight-binding model, but is seen in firstprinciples computations) [42]. The situation we find for the C-face, with graphene domains having a very wide range of thicknesses is much different from that found for the Si-face for which only a 1 ML range in graphene thickness is found over most of the surface, as shown in the previous chapter. This large range in graphene thicknesses for the C-face, essentially a three-dimensional (3D) growth phenomenon, is expected to have significant deleterious effects on electrical behavior of the films and it is therefore of interest to identify the source of this 3D morphology. One possibility is that the limited step motion on the C-face surface could, in some way, lead to the limited lateral extent of the graphene domains. In particular, there could possibly be some correlation between the location of the surface terraces, Fig. 4.8(e), and the graphene domains, Fig. 4.8(h), and thus one might be influencing the other. To further investigate this we have performed AFM and LEEM imaging over identical surface areas. Figure 4.10(a) shows a LEEM image acquired with 8.6 ev electron energy and Fig. 4.10(b) shows an AFM image of the same surface region. A large defect located off of the 58

68 right-hand side of the images, together with smaller defect indicated by the arrows and trenches indicated by crosses, permit precise alignment of the images. Analyzing the graphene thickness, a color-coded map is shown in Fig. 4.10(c). The areas colored gray and white have graphene thicknesses of 7 and 8 ML, respectively. These areas are outlined by dashed lines, and those dashed lines are superimposed on the AFM image of Fig. 4.10(d). We see that these areas of thick graphene correspond reasonably quite well to the areas of lower Fig AFM and LEEM images acquired from identical surface areas of a graphitized 6H- SiC( 0001 ) surface [same sample as in Figs. 4.8(e) 4.8(h)]. (a) LEEM image acquired at 8.5 ev. (b) AFM image, with relative surface height represented by a gray scale ranging from 0 nm (black) to 10.5 nm (white). Arrows in (a) and (b) indicate a surface defect, and crosses indicate trenches in the surface morphology. (c) Color-coded map of local graphene thickness, presented in same manner as Fig. 4.8(h) and with white areas indicating 8 ML of graphene. (d) Same AFM image as (b), but now with areas of gray and white from (c) indicated with dashed lines. (e) Solid lines show cross-sectional cuts along the black/white dashed lines indicated in (d). Black/white dashed lines at identical locations are also shown in (c), revealing the local thickness of the graphene, as indicated by dashed lines in (e). 59

69 (darker) surface height. We thus conclude that there is indeed limited interdiffusion of C and/or Si within the SiC during the graphitization, so that regions from which Si has left then convert locally into graphene, and the surface height recedes accordingly. The data of Fig shows 2 nm lower (darker) surface regions where the graphene is locally several ML thicker than its surroundings, which is consistent with our expected 0.4 nm drop in surface height per graphene ML. We find that many of the edges of the graphene domains in Fig. 4.10(c), particularly those that correspond to 2 ML of thickness change, are located at the position of step bunches as seen in Fig. 4.10(d). This correlation is illustrated in Fig. 4.10(e), where we have shown cross-sectional cuts of the AFM topography along the lines shown in Fig. 4.10(d). These same lines are shown in Fig. 4.10(c), and from that data we can obtain the local graphene thickness. The solid lines of Fig. 4.10(e) show the surface topography from AFM, and the dashed lines show the depth of the graphene below the surface (in many cases on the lower terrace there are small deposits of NCG on the surface, as discussed above, and we ignore that NCG in placing the dashed lines for the graphene/sic interface). For cut C-C, across a 3.5-nm-high step bunch, the graphene thickness is 5 ML on the upper terrace and 7 ML on the lower. For B-B, across a 4.0 nm bunch, the graphene thickness is 3 ML on the upper terrace (directly adjoining the step bunch) and 5 ML on the lower. For A-A, across a 3.2 nm bunch, the graphene thickness is 6 ML on the upper terrace and 4 ML on the lower (although along a cut slightly above A-A the thickness is 4 ML on both sides of the step bunch). In all cases, the depth of the graphene on the upper terrace is less than the height of the step bunch, and this relationship also holds true for most other step bunches found on the surface. The correlation found between the locations of the step bunches and the boundaries between graphene constant-thickness domains suggests that, indeed, the formation of the step bunches and the graphene domains are somehow coupled. Apparently the limited step motion on the surface at these temperatures (< 1200 C) also produces some limitation in the extent of the graphene domains. It appears from the data that adjacent graphene domains do not planarize (i.e. establish coincident upper surfaces and/or lower graphene/sic interfaces), and this inability to planarize seems to be related to the existence of the step bunches at the boundaries between domains. 60

70 The "domains" that we have discussed above refer to areas of constant graphene thickness. These are not necessarily the same as a grain size (i.e. crystallographic domain size) in the graphene, and indeed, prior measurements indicate that the grain size is much smaller than our domain size, typically 100 nm [80]. To check this value for our own samples, we have performed selected-area LEED. We employed a sample similar to that of Fig. 4.8(e), with 4.3 ML average graphene thickness and having constant-thickness domains with lateral extent of 3-4 µm. We acquired LEED patterns using an illumination aperture of the LEEM that corresponded to an area on the sample of about 2 µm in diameter. The patterns resembled those of Fig Examining the patterns at scores of locations over the surface, spaced by about 5 µm from each other, we do not find any observable variation from location to location in the pattern. This result implies that either the crystallographic orientation is unchanged over the surface, or that the grain size is much smaller than the 2 µm sampling size. The former is impossible since the streaks themselves observed in the LEED patterns demonstrate multiple orientations of the grains, so we conclude, consistent with prior works, that the grain size is much less than 2 µm. As previously discussed, we do observe in our samples at low graphene coverage 200-nm-sized areas that display varying contrast in AFM, and these areas likely are different crystallographic domains in the graphene [82]. We have discussed graphene films on the C-face with average thickness less than about 4 ML, formed by annealing at temperature <1200 C. Higher temperature annealing produces thicker films, as shown in Fig. 4.2(e). A large size AFM image of the same sample, formed at 1320 C. is shown in Fig Step bunches, 3-6 nm high, are clearly visible in the topographic cut taken through the image. A striking difference between this image and those of our 4 ML graphene films [Figs. 4.8(e) or 4.10(b)] is that Fig displays very prominent ridges (white lines) in the image, arising from strain relaxation of the film. These features are characteristic of films that extend continuously (carpet-like) over the step bunches so that elastic strain relaxation of the film produces the raised ridges [44, 76]. The continuity of the ridges over step edges in Fig provides evidence of the continuous growth of the graphene over the edges (indeed, transmission-electron microscopy (TEM) of 61

71 such films directly reveals this type of carpet-like growth of step edges [136]). In contrast, our graphene films prepared at 1170 C do not display any such strain-induced ridges. Fig (a) AFM image of graphene film prepared on 6H-SiC( 0001 ) by annealing at 1320 C for 20 min, resulting in an average film thickness of 16 ML. (b) Topographic cut, along the dashed line in (a). We take the absence of the ridges in the 1170 C-prepared films to indicate that the strain in these films is relieved in some other manner, e.g. at boundaries between the constantthickness domains. Coupled with our observation that many of those domain boundaries occur at step bunches, we conclude that the films may well be somewhat discontinuous at the bunches. This discontinuity does not necessarily mean that no graphene is formed at the step bunches, but rather, just that the carpet-like growth of the graphene over the boundaries that occurs for the higher-temperature C- and Si-face films does not appear to proceed so well for these 1170 C-prepared C-face films. 62

72 4.3 Discussion For our in vacuo results, it appears that the initial graphene formation on the C-face is not so different than on the Si-face. In both cases the initial lateral extent of constant-thickness (1 or 2 ML) domains of the graphene is 100 nm. With subsequent annealing the C-face graphene morphology coarsens, forming large areas (several µm) with 2 ML coverage, as well as small areas with 3 ML coverage. This process continues, with the several-µm-sized domains of graphene becoming thicker. However, the lateral extent of the domains does not further increase for the C-face, even for thickness up to 8 ML [Fig. 4.8(h)], and the range of thicknesses on the C-face is about 5 ML whereas it is limited to a single ML (away from step bunches) for the Si-face. If we compare the Si-face and C-face graphene morphologies for a fixed film thickness, then they are very different. But if we instead compare them at fixed temperatures, the differences become understandable. At 1320 C, the films thickness on the C-face is much greater than for the Si-face (16 vs. 2 ML), but both films display the characteristic ridges associated with strain relaxation and both surfaces display comparable amounts of step bunching. The reason for the thicker film on the C-face is, we believe, simply because the ( 0001 ) surface and ( 0001 )/graphene interface have higher energies (i.e. are more unstable), respectively, than the (0001) surface and (0001)/graphene interface. Additionally, more defects in the C-face films such as the discontinuities and/or rotational domain boundaries could lead to easier Si diffusion through the graphene, which would also favor thicker growth [135, 141]. Turning to the C-face graphene prepared at 1170 C, and comparing that to the higher-temperature C-face graphene, it seems clear that the 1170 C-prepared material has lower structural quality, due to kinetic limitations from the reduced growth temperature. Thus, the different morphologies between the Si- and C-faces found for films of the same thickness simply arises from the lower graphene formation temperatures used in the latter case, which inhibits coarsening between adjacent domains. We believe that the fundamental growth mode is 2D, i.e. with the graphene wetting the SiC surface, for both the Si-face and the C-face. 63

73 4.4 Conclusions In summary we have studied the formation of graphene in UHV on the SiC ( 0001 ) surface (the C-face) using AFM and LEEM. By comparison of the results with our prior measurements for the (0001) surface (the Si-face) we are able to understand certain aspects of the formation kinetics. For in vacuo preparation and coverage of < 2 ML we find that the morphology of the graphene is similar on both surfaces, comprising small areas 100's of nm in extent of given thickness. We refer to these areas of fixed thickness as domains of the graphene. Further formation of the graphene produces coarsening of the domains, but the process is very different on the C-face compared to the Si-face. For the C-face the domains grow laterally up to an extent of only several microns. Importantly, for average thickness of 4 ML, the variation in thickness over the surface is quite large, with thinnest and thickest regions differing by 5 ML. The graphene thus forms a 3-dimensional type of morphology. In contrast, for the Si-face at coverage > 2 ML, the graphene domains coarsen considerably forming areas with extent of many microns or more. The variation in thickness over the surface (away from step bunches) is limited to 1 ML, so that the graphene is seen to form in a layer-by-layer manner. For a fixed graphene thickness, the morphology of steps on the surface are quite different between the C-face and the Si-face, with the 150 C higher graphitization temperature for the Si-face leading to much greater step motion. On the C-face, with formation temperatures of about 1170 C yielding average graphene film thicknesses of 4 ML, we observe characteristic terraces in the surface morphology with lateral extent of 1-3 µm. The size of the graphene constant-thickness domains seen in LEEM is similar, and we suggest a connection between the two. Correlated AFM and LEEM imaging reveals that many of the boundaries between constant thickness domains (particularly for relatively thick domains) occur at the location of the step bunches, from which we propose that the graphene films are somewhat discontinuous at the step bunches. This discontinuity would then tend to inhibit the formation of a more uniform thickness distribution in the C-face graphene film, since the disconnected areas have no driving force for forming a flat, continuous graphene/sic interface across domains. We thus argue that the 3D morphology found for C-face graphene is a consequence of kinetic limitations due to its relatively low growth temperature. 64

74 Chapter 5 Switching environments: From UHV to 1-atm-argon 65

75 In this Chapter, we investigate the effect of an argon annealing environment on the morphology and homogeneity of the graphene films prepared on both the Si- and C-faces of SiC. Graphene formation is achieved by sublimation of Si atoms from the surface of SiC. In the presence of argon, the sublimation rate of Si from the SiC is reduced compared to the sublimation rate in vacuum since the Si atoms leaving the surface get reflected back to the surface with a finite probability when they collide with argon atoms [46, 47]. Hence, the annealing temperature needed to form the graphene of given thickness is increased significantly, as compared to the temperature used for fabricating graphene of the same thickness in vacuum. This increased temperature leads to improved kinetics in the graphene formation process, at least on the Si-face of SiC. However, for the C-face the morphology becomes much worse, with the surface displaying markedly inhomogeneous nucleation of the graphene. Possible reasons of this inhomogeneity are discussed in this chapter. 5.1 Experiments Both C-face and Si-face samples, measuring 1 1 cm 2, are annealed at a temperature of 1600 C for 15 to 30 min in a 1-atm environment of argon (99.999% purity). Prior to the argon annealing, the sample is hydrogen-etched which gives rise to an ordered array of steps and terraces on the surface. Resulting graphene films are characterized using AFM and LEEM. 5.2 Results A. Graphene Formation in argon on the Si-face of SiC We have succeeded in forming a single uniform monolayer of graphene on the Si-face of SiC by annealing in 1-atm-argon, as shown in Fig As a result of the argon annealing the steps undergo considerable motion, and we see in the AFM image of Fig. 5.1(a) large flat terraces separated by step bunches. A LEEM image of this sample, acquired at 2.8 ev, is shown in Fig. 5.1(b). Reflectivity curves from areas marked A E in the LEEM image show only a single minimum thus demonstrating that the surface is covered with graphene of monolayer thickness. Even though the surface is found to be covered with a single layer of graphene, we nevertheless see some contrast in the LEEM image of Fig. 5.1(b). This contrast might arise due to slight phase difference in the reflected electrons leading to a variation in 66

76 their intensity [142]. LEEM images from other regions on the surface revealed some areas that were covered with bilayer graphene, but those accounted for only a few % of the total surface area. In contrast to the results of Fig. 5.1, we observe for vacuum annealed samples of thickness 1 ML many small pits on the surface [i.e. similar to Fig. 3.2(a)]. We do, however, observe a few relatively large pits on the surface for samples prepared in argon, as seen in Fig. 5.1(a). These pits could possibly arise from preferential sublimation at dislocations. Further studies are needed to clarify this point. In any case, compared with a vacuum annealed sample of thin coverage, the samples prepared in argon are found to have much larger domains of uniform graphene thickness. Fig. 5.1 Results of graphene prepared on SiC(0001), by annealing at 1600 C for 30 min in 1 atm of argon. (a) AFM image with gray scale range of 8 nm, (b) LEEM image at beam energy of 2.8 ev, (c) Intensity of the reflected electrons from different regions marked in (b) as a function of electron beam energy, and (d) Color-coded maps of local graphene thickness, deduced from analysis of the intensity vs. energy at each pixel; blue corresponds to 1. The surface is covered uniformly with monolayer thick graphene. B. Graphene formation in argon on the C-face of SiC To achieve a narrower distribution of the thickness-domains on the C-face, while maintaining a relatively thin film, it seems clear that higher formation temperature in an argon environment is needed. We have attempted in eight experimental runs to form thin graphene on the C-face under 1 atm of argon. About half of those attempts resulted in nearly no graphene at all (as detected by AES), and the other half produced very thick (>15 ML) graphene films. However, in two cases for samples that displayed no graphene over most of their surface, there were a few isolated 0.1-mm-sized areas that were graphitized. These areas are easily visible under an optical microscope. 67

77 AFM and LEEM studies near the edge of one such area are shown in Fig In the AFM image, Fig. 5.2(a), there are many ridges or "puckers" (white lines at various angles) extending over the surface on the right and left-sides of the images. These features are well known to be characteristic of the presence of graphene on the surface, and they arise from the mismatch in thermal expansion coefficients between the graphene and the SiC as discussed previously. However, near the center of the image (to the right of the step bunch) no such ridges are seen, thus suggesting that no graphene is present there. This inhomogeneous coverage of the graphene is consistent with the AES measurements just mentioned, and also consistent with the LEEM results described below. Figure 5.2(b) shows a LEEM image acquired at 5.2 ev, and reflectivity curves from the associated sequence of images are shown in Fig. 5.2(c). Curves C-G correspond to 1 5 monolayers, respectively. Curve C actually has an additional shallow minimum, marked by the dashed line at 6.8 ev, and this same feature is weakly seen in curve D. But, other than that, the other minima in all the curves match up very well with the results already presented in Chapter 4 (the curves in Fig. 5.2(c) are shifted upwards by about 0.5 ev, but this can be the result simply of a different alignment of the electron beam in the LEEM). A color-coded map of the graphene thicknesses is shown in Fig. 5.2(d), revealing an average graphene thickness (over the area covered by graphene) of 3.0 ML. On the left-hand side of the LEEM image of Fig. 5.2(b) is seen a black region, with reflectivity given by curve A. The reflectivity is seen to be nearly featureless over the range 3 10 ev, without the characteristic oscillations of the graphene. It should be noted in this regard that, in addition to the oscillations in the range 2 7 ev, the reflectivity from graphene also increases over the energy range 8 10 ev because of additional band structure effects [93]. This increase at higher energies is also not seen for curve A. The same reflectivity as in curve A was found over the vast majority of the surface. Thus, we can be certain that the surface, at location A in Fig. 5.2(b) and over the vast majority of the sample, is not covered with any graphene at all. Figure 5.3 provides additional LEEM results from the same sample, with Figs. 5.3(a) and 5.3(b) showing data acquired near the edge of an island, and Figs. 5.3(c) and 5.3(d) showing data acquired near the center of an island. These results are consistent with those of Fig. 5.2, revealing the average thickness of the graphene islands of about 4.1 ML near the island edge 68

78 Fig. 5.2 Results of graphene prepared on SiC( 0001 ), by annealing at 1600 C for 15 min in 1 atm of argon yielding an average thickness of 3.0 ML of graphene (for this image, including only the areas where graphene covers the surface). (a) AFM image with gray scale range of 16 nm, (b) LEEM image at beam energy of 5.2 ev and with 25 µm field-of-view. (c) Intensity of the reflected electrons from different regions marked in (b) as a function of electron beam energy, and (d) Color-coded map of local graphene thickness, presented in same manner as for Figs. 6(d) and 6(h).. Fig. 5.3 LEEM results from the same sample and using the same manner of display as Fig. 4.7, showing results near the edge of a graphene island [(a) and (b)] with average graphene thickness of 4.1 ML in this portion of the island, and near the center of an island [(c) and (d)] with average graphene thickness 4.9 ML. (a) and (c) Color-coded maps of local graphene thickness; (b) and (d) reflectivity curves acquired from the locations indicated in (a) and (b), respectively. 69

79 and increasing to 4.6 ML near the island center. The anomalous minimum near 6.8 ev is also seen in the reflectivity curves for 1 ML and 2 ML thickness near the edge of the island, Fig. 5.3(b), although not at the center of the island, Fig. 5.3(d). Returning for a moment to Fig. 5.2(c), the reflectivity curve B has a shape never before seen by us nor reported by others. This reflectivity curve exists only over the small area colored black in Fig. 5.2(d) near location B, although we have found identical curves on other sample areas. The origin of this new reflectivity as well as the extra minima seen in the 2 and 3 ML curves is not known at present, although we note that the latter resemble the additional minima produced in reflectivity curves obtained on Si-face graphene when it is intercalated by H [106]. As described below, our samples annealed in argon turn out to be unintentionally oxidized, with a silicate layer (Si 2 O 3 ) on their surface. Perhaps this silicate layer is affecting the reflectivity curves and producing the new features we observe, although the details of this effect are not understood at present. In any case the main conclusion from the data of Figs. 5.2 and 5.3 is clear: This surface, prepared at high temperatures under 1 atm of argon, is covered only in a few areas by graphene, and there the graphene is many ML thick. Elsewhere on the surface no graphene is present. Thus, we find islanding of the graphene, similar to that reported recently by both Camara et al. [139], and Tedesco et al [143]. LEED obtained from areas of the Ar-annealed samples that do not have any graphene display clear SiC 1 1 spots together with faint 3 3-R30º spots (the latter vary in intensity over the surface). This same pattern is found for the measurement performed ex situ or in situ. In Fig. 5.4(b) we display one of these patterns and compare it to a 3 3 LEED pattern formed by annealing a C-face sample in vacuum, Fig. 5.4(a). The surfaces prepared in vacuum or argon are clearly very different. We have measured LEED intensity vs. energy spectra for the 3 3-R30º pattern, as shown in Fig. 5.4(c). The results agree very well with the known spectra for a silicate (Si 2 O 3 ) layer on SiC( 0001 ), with residual oxygen present during the Ar annealing apparently oxidizing the surface [109]. However, it should be noted in this regard that, in vacuum, the silicate layer is unstable at temperature above about 1200 C, at least for the Si-face [144]. This fact raises the possibility that the oxidation observed on our argon-annealed sample might have occurred while the sample was cooling down to room temperature, or during evacuation of the Ar gas. To 70

80 investigate this we have taken a C-face 3 3 surface formed by annealing in vacuum, exposed it for 10 min at various temperatures to a 1-atm Ar environment, and measured the resulting LEED pattern. For room temperature annealing we find that the LEED pattern becomes noticeably dimmer but that the 3 3 spots are still faintly visible; no trace of any 3 3-R30º spots are seen. But, after annealing in the Ar to > 700 C, the 3 3-R30º spots appear. This pattern grows markedly in intensity as the temperature is increased to 1000 C, and then it maintains a constant intensity as the temperature increases to 1550 C. For annealing at 1650 C we find that the 3 3-R30º disappears, and that the surface is graphitized. Thus, we find that the silicate is stable, in the Ar environment, for temperature up to 1600 C. Fig. 5.4 LEED data acquired from SiC( 0001 ) surfaces: (a) 3 3 pattern acquired at 100 ev from a sample prepared by annealing at 1000 C in vacuum, with the primary SiC (1,0) spot indicated; (b) 3 3-R30 pattern acquired at 100 ev from a sample prepared by annealing in 1-atm argon at 1400 C, with the (1,0) and (2/3, 2/3) spots indicated; (c) and (d) Intensity vs. energy characteristics for the two spots marked in (b). (This data was obtained by Guowei He from Prof. Feenstra's research group). For the C-face in vacuum we found that it graphitizes easier than the Si-face, indicating a higher surface energy of the C-face. Now, in argon, we find that the C-face surface is more resistant to graphitization than the Si-face, indicative of a lower surface energy for the C- face. The presence of the oxide layer on the C-face surface accounts for this difference in the 71