This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and

Transcription

1 This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier s archiving and manuscript policies are encouraged to visit:

2 Surface Science 605 (2011) Contents lists available at ScienceDirect Surface Science journal homepage: locate/susc Formation of wide and atomically flat graphene layers on ultraprecision-figured 4H-(0001) surfaces Azusa N. Hattori a,, Takeshi Okamoto b, Shun Sadakuni b, Junji Murata b, Kenta Arima b, Yasuhisa Sano b, Ken Hattori c, Hiroshi Daimon c, Katsuyoshi Endo a, Kazuto Yamauchi a,b a Research Center for Ultra-Precision Science and Technology, Graduate School of Engineering, Osaka University, Yamada-oka 2-1, Suita, Osaka , Japan b Department of Precision Science and Technology, Graduate School of Engineering, Osaka University, Yamada-oka 2-1, Suita, Osaka , Japan c Graduate School of Materials Science, Nara Institute of Science and Technology, Takayama , Ikoma, Nara , Japan article info abstract Article history: Received 5 August 2010 Accepted 19 December 2010 Available online 30 December 2010 Keywords: Graphene Scanning probe microscopy Low-energy electron diffraction Reflection high-energy electron diffraction Surface flatness Ultraprecision figuring Damaged layers and polishing haze exist on substrate surfaces owing to abrasion during figuring processes, which deteriorate surface integrity. We have developed a novel damage-free ultraprecision figuring technique and obtained atomically flat and damage-free (0001) surfaces with a domain size of nm. Using ultraprecision-figured 0 -off 4H-(0001) surfaces as substrates, we demonstrated the formation of graphene layers upon them and successfully produced atomically flat monolayer graphene with a domain size of over 300 nm on entire ultraprecision-figured surfaces by annealing in ultra high vacuum without any Si flux. The quality of the graphene layers on the ultraprecision-figured surfaces was markedly higher than that of layers on non-figured surfaces. This indicates that the damaged surface layers with scratches, defects, and so on, enhance roughness on surfaces, and reduce the quality of graphene films. In addition, we found a new phenomenon:step terraces of 500 nm width exhibited erosion at step edges, leading to the creation of hexagonal pits at terraces, while step terraces of 300 nm width exhibited hardly any erosion. A graphitization mechanism was discussed Elsevier B.V. All rights reserved. 1. Introduction Perfect surfaces are expected to upgrade the quality of films grown on them. As discussed in this paper, graphene layers of excellent quality can be grown upon an atomically flat and defect-free surface. In other words, imperfect surfaces degrade the property of the surfaces themselves and the performance of the integrated materials upon them. In general, wafers (or substrates) are bought, then clean surfaces are prepared on them by annealing, sputtering, wet etching, and so on. In standard wafer manufacturing, surfacefiguring processes are introduced to obtain a flat surface after slicing a wafer from an ingot. As a figuring process of wafers, chemical mechanical polishing (CMP) with a SiO 2 or diamond abrasive is generally used [1]. CMP techniques have been modified and are now well established, particularly for Si wafers [2]; however, it was reported that damaged layers result from the abrasion, the thickness of which is commonly about one-fourth of the abrasive particle size (typically nm in manufacturing processes) [3]. Surface cleaning procedures are useful for removing native oxides and surfactants on a Si surface for improving the surface flatness, but they cannot remove Corresponding author. Present address: Nanoscience and Nanotechnology Center, The Institute of Scientific and Industrial Research, Osaka University, 8-1, Mihoga-oka, Ibaraki, Osaka , Japan. address: a-hattori@sanken.osaka-u.ac.jp (A.N. Hattori). damaged layers completely. CMP techniques have also been used for other materials under certain modifications based on the conditions used for Si wafers. For wafers, a lot of micro scratches and considerable subsurface damage, which deteriorate surface integrity, are inevitably generated on their surface, due to the physical hardness and chemical inertness of [4,5]. Therefore, it is difficult to obtain sufficient surface integrity for the growth of epitaxial films on commercial wafers. In order to obtain ideal surfaces, CMP-alternative and novel surface-figuring techniques are desired. Commercial wafers contain many scratches with an average depth of a few nm even after CMP, as shown in the typical atomic force microscope (AFM) image in Fig. 1(a). Recently, we have developed a catalyst-referred etching (CARE) method as a novel damage-free technique for the planarization of substrates [6], which was used to obtain an atomically flat surface on an entire 2-inch wafer [7 10]. Fig. 1(b) shows a typical AFM image of a CARE-treated (0001) on-axis surface without subsequent annealing in UHV. The AFM image shows a step-terrace structure without inhomogeneous structures such as scratches. has been focused on for its use in next-generation semiconductor power devices because of its excellent properties, for instance, wide band-gap energy, high thermal conductivity, high saturated electron-drift velocities, and high breakdown electric fields. It is well known that graphene films can be grown on surfaces [11 21] /$ see front matter 2011 Elsevier B.V. All rights reserved. doi: /j.susc

3 598 A.N. Hattori et al. / Surface Science 605 (2011) Fig. 1. (a) (c) Typical AFM images with LEED patterns (insets) and (d) (f) RHEED patterns for 0 -off 4H-(0001) surfaces: (a) and (d) as-received commercial wafers, (b) and (e) CARE-treated wafers, and (c) and (f) wet-treated CMP wafers without any treatment in UHV. The incident electron energies for RHEED and LEED were 15 kev and 65 ev, respectively. (g), (h), and (i) Spot intensity profiles of A-A, B-B, and C-C in (d), (e), and (f), respectively. Graphene has attracted considerable attention and interest owing to its unconventional two-dimensional electron gas and electron transport properties [11,21 23]. Epitaxial graphene layers can be grown on (0001) surfaces by solid-state graphitization during the sublimation of decomposed Si atoms, where the number of graphene layers is controlled by the annealing temperature and duration under ultrahigh vacuum (UHV) condition [11 20] or atmosphere condition [21]. A technique for forming monolayer graphene on (0001) has been searched, and the structure and physical properties of graphene layers have been actively studied. One of the general preparation methods to obtain graphene under UHV condition is the Si-flux method: the thermal etching of with the deposition of Si atoms to reduce Si sublimation at areas with damage due to surface polishing [11 17,19,20]. Recently, Emtsev et al. proposed the atmospheric-pressure graphitization of and succeeded in forming high-quality graphene [21]; the ex-situ graphitization of (0001) without Si flux but in an argon atmosphere produces monolayer graphene films with considerably higher quality and larger domain size compared with the graphene films prepared by vacuum annealing. However, the growth of a specific number of large wellordered graphene layers on (0001) in UHV was not achieved in previous studies. At present, graphene layers grown on (0001) surfaces in UHV have a domain size of at most 100 nm, and the graphene domains exist on only part of the substrate rather than the entire substrate [11 17,19,20,24,25], because the decomposition of is not a self-limiting process and, as a result, regions of different film thicknesses coexist. Roughness on surfaces, which increases as a result of scratches [26], defects [27], inhomogeneity [13,14], and so on reduces the quality of graphene films. Therefore, we expect that graphene layer of excellent quality can be formed upon an atomically flat and defect-free surface even by vacuum annealing. In this paper, we report the formation and quality of graphene layers on CARE- and wet-treated CMP- surfaces subsequently annealed in UHV. We found that the graphene layers grown on CARE- was markedly high, while the quality of the graphene on wet CMP- was considerably degraded. We also found that the Si desorption started at almost the same temperature for both CARE- and wet CMP- surfaces, however, the graphitization temperature for wet CMP- surfaces was approximately 200 C higher than that for CARE-. On graphitized CARE- surfaces, step terraces of ~500 nm width exhibited erosion at step edges and hexagonal pits on terraces, while step terraces of ~300 nm width exhibited hardly any erosion and pit. Here, we emphasize that CARE should become one of widelyused surface-figuring techniques in the wafer manufacturing process, as CMP, in future. 2. Experimental Two-inch wafers of commercial CMP 4H-(0001) with a 0 -off (±0.5, on-axis oriented) Si face (N-doped, 0.02 Ω cm) were used. The wafers were planarized by the CARE technique [6,8 10], where a Pt plate was used as a catalyst in HF solutions. Each substrate was dipped in a sulfuric peroxide mixture (SPM) solution [28] for 10 min, dipped in HF for 10 min, planarized in HF for 5 10 h, dipped in SPM solution for 10 min, dipped in aqua regia for 20 min, and dipped in HF for 10 min. After every process, the substrate was rinsed with flowing

4 A.N. Hattori et al. / Surface Science 605 (2011) ultrapure water [29]. To confirm the advantageous effect of surface planarization on the graphene quality, we prepared a reference CMP- sample without CARE planarization; another 2-inch wafer was kept in HF for 6 h instead of being subjected to the planarization process but was subjected to all the other processes. Here, we denote samples treated with and without the CARE planarization process as CARE- and wet-treated CMP-, respectively. After the wet procedures, samples of 2 7 mm 2 area were cut from the wafers and introduced into a UHV chamber with a base pressure of less than Pa. [30 32]. The graphitization of (0001) was performed in UHV by annealing; the samples were degassed at 300 C for 3 5 h and annealed at C for 5 s 10 min at a pressure below Pa. In-situ low-energy electron diffraction (LEED), in-situ reflection high-energy electron diffraction (RHEED), in-situ scanning tunneling microscopy (STM), ex-situ X-ray photoelectron spectroscopy (XPS), ex-situ Raman spectroscopy (HORIBA, LabRAM HR-800), exsitu Temperature Programmed Desorption (TPD), and ex-situ AFM (Digital Instruments, D3110) were used for the surface characterization. All experiments except the TPD were performed at room temperature (RT), and all experiments except the RHEED and Raman spectroscopy were performed in a class 1 clean room. AFM and Raman spectroscopy were performed under atmosphere pressure. Almost all the obtained STM images were topographic except Fig. 5(a), which is a current image. All the obtained AFM images were in non contact mode. Raman spectroscopy was performed using an excitation laser with a photon energy of 2.37 ev. 3. Results and discussions 3.1. Surface structures of CARE- Fig. 1 shows typical AFM images, and LEED, and RHEED patterns of (0001) 0 -off surfaces of as-received commercial (CMP), CAREtreated, and wet-treated CMP wafers. The AFM image of the asreceived commercial wafer (Fig. 1(a)) showed many scratches on the surface with an average depth of a few nm, as mentioned before. The LEED and RHEED patterns (the insets in Fig. 1(a) and (d), respectively) of the as-received exhibited diffused 1 1 patterns with a high background, arising from a native oxide layer of nm thickness [33], implying poor surface crystallinity after surface-figuring treatment (for example, CMP, etc.) [34]. For the CARE-(0001) surfaces without subsequent annealing in UHV (Fig. 1(b), (e), and (h)), the AFM image showed a step-terrace structure with a terrace width of ~ nm, and the LEED and RHEED patterns exhibited sharp and intense 1 1 spots. The spot profiles of the RHEED patterns (Fig. 1(g) (i)) show obvious differences in spot intensities among the differently treated surfaces [35]. The RHEED pattern in Fig. 1(e) with sharp and intense Kikuchi lines demonstrates that the CARE- surface is ideally flat. This surface has an inert property due to surface termination [33], that is, surface oxidation does not progress even in air. The CARE technique is highly reproducible, which makes it possible to repeatedly obtain atomically flat terraces with uniform and straight steps on the surfaces [6,8 10]. On the other hand, for the wet CMP- surface (Fig. 1(c), (f), and (i)), LEED and RHEED patterns exhibited sharper and more intense 1 1 spots than those for the as-received surface (Fig. 1(a), (d), and (g)) but more diffuse and weaker spots than those for the CARE surface (Fig. 1(b), (e), and (h)), while the AFM image showed similar features to those observed for the as-received. This suggests that surface damage including scratches was not removed, although the native oxide layer (SiO x ) was dissolved and the surface was terminated by dipping in HF solution [36]. After the CARE treatment, an entire wafer surface has a terracestep structure without scratches [6 10,37]. Fig. 2 shows typical AFM images of a CARE-treated (0001) 0 -off wafer. All AFM images show terrace-step structures without scratches, and we can see the different step densities depending on the area of the wafer. This is caused by the poor slicing accuracy within the error range (±0.5 ) in the manufacturing process [10,34,37]. In this case, the average terrace width was ~140 nm, corresponding to the average off-angle ~0.10. It was confirmed that the CARE technique can lead to atomically flat terrace-step surfaces independent of the off-angle and the quality of the initial wafer [8,10,37]. In the CARE process, the surface conditions of the initial wafer, such as surface crystallinity, morphology, the thickness of the damaged layer, scratches, carrier densities, and so on, do not affect the final surface condition, but affect the etching speed and total etched volume of. Usually in order to prepare flat surfaces, H 2 annealing treatment (H 2 etching), which can produce the terrace-step surfaces without scratches, has been used for CMP treated surfaces [38 40]. The H 2 etching is an etching without arbitrary reference planes, which is different from CMP or CARE figuring method. The reaction (etching) area and depth are not self-limited and the etching controllability is lower than CARE method. Indeed, the surfaces prepared by the H 2 etching contained facet boundaries at the step edges [38], tilted (not straight) steps [40], and remained (screw) dislocations [40]. Anisotropic step bunching is also induced by H 2 etching [40]. These factors which decline the total surface smoothness on surfaces, were not observed on the CARE surface [7,8,10,37]. We consider CARE treatment as a final figuring technique alternative to CMP treatment, and emphasize that the substrate surfaces with CARE treatment require no more complex surface treatment, such as H 2 etching and Si flux, to obtain clean and flat surfaces and graphene films, as shown in a following section. As mentioned before, damaged layers and polishing haze exist on commercial wafer surfaces resulting from the abrasion during the figuring processes. The CARE reaction automatically stops after removing a certain amount (about nm) of the surface layers [7,8]. Since the CARE reaction is truly a chemical and autonomous reaction, CARE treatment can remove damaged layers completely, resulting in perfect surfaces. Hara et al. studied the crystallographic properties of 4H-(0001) surfaces before/after CARE treatment using cross-section transmission electron microscopy (TEM) [7]. Their TEM images show disordered arrangements due to the damaged layers in the surface region of an as-received commercial (CMP) sample. On a CARE- sample, however, such disordered arrangements were removed and well-ordered arrangements remained. Although the mechanism of the CARE reaction is not clear yet, the CARE technique can reproduce damage-free terrace-step surface structures. Moreover, this method has generality; it has been successfully applied to not only but also GaN surfaces [41 43] Graphene layers grown on surfaces Fig. 3(a) shows a typical LEED pattern for a CARE-(0001) surface annealed at 900 C for 5 min in UHV without Si flux, which clearly displays a ( )R30 (hereafter 6 3) reconstruction pattern. The 6 3 reconstruction has been pointed out to be a prerequisite but not a sufficient condition for the formation of a uniform graphene film [12]. Considering the periodicities of both graphite and, 13 times the graphite lattice constant (a graphite =0.246 nm) coincides with 6 3 times the lattice constant (a =0.308 nm) 3.20 nm. The initial stage of graphitization on surface is the 6 3 reconstruction and graphene layers are grown on the buffer layer at higher annealing temperatures and/or longer annealing times, keeping a 6 3 periodicity. It is known that the specific properties of graphene develop from only the first graphene layer on the 6 3 buffer layer [44]. We found that the 6 3 sample in Fig. 3 is monolayer graphene by analyzing the results of LEED, XPS (not shown), and Raman spectroscopy, as discussed below. The surface structure on the CARE-(0001) changed from 1 1 to 3 3 with increasing annealing temperature, and the 6 3

5 600 A.N. Hattori et al. / Surface Science 605 (2011) Fig. 2. Typical AFM images of the CARE-treated 4H-(0001) 0 -off 2-inch wafer with the same scale. There is a distribution of step density, i.e., terrace width, because of the difference of off-angles on the same wafer within the slicing accuracy; the off-angles are (a) ~0.08, (b) ~0.15, (c) ~0.02, and (d) ~0.06. structure appeared at 900 C [33]. On non-care-(0001) surfaces prepared using Si flux, 3 3, 3 3, 6 6, or structures appear depending on the preparation conditions [11 21,25]. The LEED pattern of the 900 C-annealed CARE- (Fig. 3(a)) showed only the 6 3 reconstruction without the other phases. The pure 6 3 phase was confirmed by the chemical shifts and the areal ratio of Si 2p and C 1s in XPS spectra for the 1 1, 3 3, and phases [45]. The RHEED pattern also showed clear 6 3 reconstruction (Fig. 4(a)). An STM image of the annealed CARE-(0001) surface (Fig. 3(c)) showed a rhombic unit with a length of ~1.8 nm (note that the distortion observed here is due to thermal drift). Although the atomic crystallographic structure was not completely resolved, the periodicity of ~1.8 nm can be attributed to the 6 6 reconstruction. In STM, the structure is often imaged with an apparent 6 6 periodicity, particularly at a high tunneling bias [12], as shown in Fig. 3(c) and (e). Depending on the bias voltage, this quasi -6 6 corrugation appears as rings in a honeycomb pattern (Fig. 3(c)) and as a hillock structure (Fig. 3(e)). So far, at least four types of 6 3 structure, the buffer layer underneath mono-, bi-, and tri-layer graphene, and the buffer layer without the graphene layer [12], have been confirmed on (0001) surfaces through the graphitization. Recently, Starke and Riedl estimated the thickness of graphene layers on from dispersion curves obtained by angular-resolved photoelectron spectroscopy, and suggested a strong correlation between the thickness and the intensities of some LEED spots [12]. This suggestion enables us to determine the number of layers approximately by comparing the relative intensity of the graphite spot with that of the satellite spots in the 6 3 pattern at 126 ev, as shown in Fig. 3(b). From the LEED fingerprints in Ref. [12], we estimated that the graphene in Fig. 3 had roughly monolayer thickness [30]. This method of thickness estimation based on the LEED pattern is easy to use under in-situ conditions; however, it is not a quantitative method. Therefore, we also confirmed the monolayer thickness of graphene from XPS [30] and Raman spectroscopy for the same CARE- sample annealed at 900 C for 5 min. The chemical shifts in the C 1s core-level spectra [30] showed that the surface region includes three inequivalent types of carbon atoms; those in the graphene layer (graphic peak), those in the underneath 6 3 buffer layer (buffer peak), and those in the substrate (bulk peak) [12,15]. We estimated the overlayer thickness from the intensity ratio of the surface and bulk components [15,30] to be 0.33±0.06 nm, assuming a simple layer attenuation model. This value is close to the interlayer distance in graphite (0.335 nm). The graphene thickness estimated from the results of XPS is consistent with the thickness determined from the LEED intensity profile. We found that the thickness of graphene layers grown on CARE- can be easily controlled by tuning the annealing temperature and duration. For further-annealed samples at 1000 C for 2 min, we also estimated a bilayer graphene film by XPS and LEED [30]. Moreover, these methods also showed the formation of monolayer graphene on 8 -off CARE- surfaces by annealing at 900 C for 2 min [30]. Fig. 4(b) shows the Raman spectra of D, G, and G bands [46 55] for the 6 3 sample of Fig. 3. The G band around 1580 cm 1 (1598 cm 1 in Fig. 4(b)) is first-order Raman scattering and the Raman active mode of graphene or graphite, corresponding to the doubly degenerate phonon mode at the Brillouin zone (BZ) center [46]. The graphene film thickness [53,55] can be estimated by the Raman shifts of the G band. The G band around 2700 cm 1 (2691 cm 1 in Fig. 4(b)) and the D band around 1350 cm 1 (1368 cm 1 in Fig. 4(b)) correspond to the double resonance of the incident laser excitation energy around K points in BZ; the G band is allowed in graphene without any kind of

6 A.N. Hattori et al. / Surface Science 605 (2011) disorder or defects [47], and the D band appears due to some structural disorder in a graphene sample [48,49]. We can see the intense and sharp G band appearing at 1598 cm 1. Since the bulk contributed peak appears at around 1570 cm 1 [55], we consider that the tail of the peak D around 1570 cm 1 would correspond to the elements, and the G peak could be fitted by single-lorentzian with a full width at half maximum (FWHM) of 18 cm 1. The G band was observed at 1586 cm 1 for the exfoliated monolayer graphene [53], at 1608 cm 1 for a 1.5 monolayer graphene film grown on a (0001) surface [55], Fig. 4. (a) Typical RHEED pattern for the ( )R30 reconstruction for a CARE- (0001) hsurfaceiafter annealing at 900 C for 5 min in UHV. The incident 15 kev beam was in the 1100 direction. (b) Raman spectrum with 2.37 ev laser excitation for the CARE- in Fig. 3. The spectrum shows a G band at ~1598 cm 1 and a G band at ~2691 cm 1. The G and G peaks were almost symmetric and described by one Lorentzian (red lines) with an FWHM of 18 cm 1 and 45 cm 1, respectively. The small D band is shown around 1370 cm 1. and at 1578 cm 1 for highly oriented pyrolytic graphite (HOPG) [55]. Röhrl et al. [55] reported that the scattered Raman peak shift of the G and G bands happened even among samples with the same graphene thickness. They suggested that strains in film samples fabricated by different methods mainly cause the Raman shift. The observed G peak frequency is consistent with that in previous reports on monolayer graphene on substrates within the expected range of the shift due to the strain. The identification of the number of graphene layers by Raman spectroscopy is also established using the G bands [50,52]. For monolayer graphene, a symmetric G band is observed and fitted by one Lorentzian. For bi-, tri-, and quad-layer graphenes, and HOPG samples, the G peaks become broader and asymmetric, and are fitted Fig. 3. (a) A typical LEED pattern at 135 ev displaying the ( )R30 reconstruction for a CARE-(0001) surface after annealing at 900 C for 5 min in UHV. First-order fundamental diffraction spots from the (0001) substrate and graphene are indicated by yellow and green circles, respectively. The satellite spots around the fundamental spot of the graphene at 126 ev are shown in (b), which enable us to determine the graphene-layer thickness [12]. (c) (e) Topographic STM images of graphene on the same CARE- surface; the sample bias voltage is +2.8 V and the tunneling current is 0.5 na. (c) Typical (6 6) (cyan) rhombic unit with ~1.8 nm unit length but hardly any atomic-scale protrusions due to the poor tip condition in this case. (d) Atomically flat and homogeneous surface with wide flat terraces with a width of over 250 nm, an arm chair (ac) edge at the upper left, and a zig-zag (zz) edge at the upper right. (e) A magnified image of (d) with zig-zag edge. Note that the curved feature of the arm chair step in the upper part of (d) is caused by thermal or piezotuberesponse drift.

7 602 A.N. Hattori et al. / Surface Science 605 (2011) by four, six, three, and two Lorentzians, respectively. The observed G band (Fig. 4(b)) is almost symmetric and fitted by one Lorentzian (red line) at 2691 cm 1 with an FWHM of 45 cm 1 ; this is a characteristic feature of monolayer graphene. Therefore, we can conclude that the observed 6 3 sample was almost monolayer graphene, which is consistent with the LEED and XPS results as mentioned before. Note that there is still a possibility that bi- and tri-layer graphene partially exist in the graphene, since LEED, XPS, and Raman results showed the average information, and no microscopically resolved measurements have been conducted in this study. We can also see a small D band (1368 cm 1 ) at about half the frequency of the G band. In general, a D band appears in samples with structural disorders that break the translational symmetry (e.g., impurities, edges, finite size effects, etc.) [48,49,51,52]. The intensity of the D band in CARE- is quite smaller than that in the previous samples [25,51,52], implying the high crystallinity of graphene on the CARE- surfaces, probably because the graphitization temperature for the CARE- samples (900 C) was considerably lower than temperatures for non-care- surfaces ( C) [18,25]. From the Raman spectrum (Fig. 4(b)), Refs. [25] and [51] suggested that the estimation of the grain size, L a,of nanographite films using the I D /I G ratio in the empirical formulas. Here, I D and I G are the integral intensities of the D and G bands, respectively. The obtained values of I D /I G were for the monolayer graphene, corresponding to the in-plane domain size of ~ nm and ~ nm, by the formulas in Refs. [25] and [51], respectively. Here, we should notice the width of the G band peak; less quality graphene has wider width due to stress by imperfection, multiple layers, and so on. In particular, the multiple layers leading to multiple peaks, similar to the G band, would result in the increase of I G extraneously. The observed G band (Fig. 4(b)), indeed, is quite narrower (18 cm 1 in FWHM) than those in Fig. 2 in Ref. [25] and Fig. 3 in Ref. [51]. Moreover, the observed D band is small as noise level, which indicates a high-quality graphene. Therefore, we doubt the generality of the proposed empirical formulas for L a at present, though only one laser-energy was used in our study. The monolayer graphene formed on CARE- was remarkably uniform and consisted of wide terraces and steps. Fig. 3(d) shows a wide-scale STM image of the 6 3 phase on the CARE- of Fig. 3(a) (c). The STM image exhibits a wide uniform surface; the ordered 6 3 terrace has an area of at least nm 2, and there are no defects or inhomogeneous structures except for dust from the STM tip. Moreover, the STM images showed that the 6 3 protrusion arrangement was maintained in entire terraces ( 250 nm in size), that is, no domain boundaries appeared on the terraces. The step in the upper left of Fig. 3(d) is straight but h partially i rounded near the bottom. This straight edge is parallel to 1210, which corresponds to an arm chair (ac) edge [54]. Fig. 3(e) shows a typical STM image including h ia zig-zag (zz) step edge, where the straight edge is parallel to The step heights in Fig. 3(d) and (e) were ~0.25 nm, which corresponds to the height of a bilayer of 4H-(0001) (0.251 nm). Fig. 5(a) and (b) shows STM images around the domain boundaries for the 6 3 phase on the same CARE-. We can confirm that these are domain boundaries but not steps from Fig. 5(c), which shows that the terrace height is the same on both sides of each boundary. We did not observe a domain enclosed by boundaries or steps in the area of nm 2, that is the maximum scan area in our STM system, at over ten different positions on the surface. This indicates that the domain size of the monolayer graphene on CARE- exceeded 300 nm. The diffraction spot profiles in LEED and RHEED supported the estimation of the domain size roughly, though the finite incident-beam size prevented the accurate estimation. The sharper LEED, RHEED spots and Raman peaks, however, indicate that the CARE- can be produced the high-quality graphene films. AFM images also showed a uniform graphene layer grown on CARE-. Moreover, the images revealed the considerable erosion of Fig. 5. (a) A current STM image and (b) a topographic STM image of graphene including domain boundary on monolayer graphene for the same CARE- as in Fig. 3; the sample bias voltage is (a) +2.3 V and (b) 3.0 V, and the tunneling current is 0.5 na. (b) A magnified image of (a) (6 6) (cyan) rhombic unit with ~1.8 nm unit length and a domain boundary. (c) A cross-sectional profile through the line in (b). steps and the creation of pits on wide terraces, but there was little erosion and few pits on narrow terraces of graphene. Fig. 6(a) and (b) shows typical AFM images of the same CARE-(0001) sample as that in Figs. 3 and 5 but after exposure to air. The fluctuation of the offangle within the cutting accuracy on the as-received substrate surface [34,37,56] induces different terrace widths on the CARE- surface [37], which should also lead to different terrace widths for the annealed sample with monolayer graphene. We observed 17 different

8 A.N. Hattori et al. / Surface Science 605 (2011) other hand, on the wide (~500 nm) terrace in Fig. 6(b), we can see dominant arm chair edge and roundish (finger-like) step edges and also many characteristic hexagonal pits, the edge directions of which are those of the arm chair edges. We found that the depths of the pits had discrete values, ~0.50nm, ~0.75nm, and ~1.00nm, corresponding to the heights of two, three, and four bilayers of 4H- (0001), respectively, within the margin of error. Similar hexagonal pits on the terraces of a graphene layer on surfaces have been reported [57,58]; Bolen et al. suggested that the creation of pits supplies the carbon atoms to form graphene on [57]. The quality of the graphene layers on wet-treated CMP- surfaces was considerably lower than that of layers on CARE- surfaces. Annealing temperatures above 1100 C were required to obtain 6 3 LEED patterns on wet CMP- surfaces. Fig. 7(a) and (b) show a typical LEED pattern and an AFM image of graphene on a wet CMP- surface after annealing at 1100 C for 5 min, respectively. Weak and diffused 6 3 spots with a higher background than that in the case of a CARE- surface, appeared in the LEED pattern, for instance, the satellite spots in the green square in Fig. 7(a) are much Fig. 6. AFM images of monolayer graphene on CARE- after annealing in UHV. The average graphene terrace widths in (a) and (b) are ~300 nm and ~500 nm, which correspond to local off-angles of 0.05 and 0.03, respectively. (a) The surface with narrow terraces has steps with mainly zig-zag (zz) edges and a few arm chair (ac) edges. (b) The surface with wide terraces has hexagonal pits and eroded steps. regions for two monolayer graphene samples (900 C for 5 min) by AFM. Roughly, two types of the regions could be classified. Majority was narrow terrace (11 regions) and minority was wide terrace (6 regions), as follows. The graphene surfaces in Fig. 6(a) and (b) have average terrace widths of ~300 nm and ~500 nm, corresponding to local off-angles on of h 0.05 iand 0.03, respectively, both of which are the direction of Although a uniform monolayer graphene formed on both narrow (Fig. 6(a)) and wide (Fig. 6(b)) terraces, different features of the graphene can be observed depending on the terrace width. Fig. 6(a) shows that most h of the i steps in the narrow terrace area have zig-zag edges along the 1010 direction, while the minority of steps have arm chair edges along the 1120 directions. The inset of Fig. 6(a) displays few small pits (defects) in a μm 2 region on the narrow (~300 nm) terrace. The average step height was ~0.25 nm, which is consistent with the STM results within the margin of error. Since the STM results (Figs. 3 and 5) indicate that the 6 3 domain covers entire terraces without domain boundaries over an area of ~ nm 2, the wide-scan AFM image in Fig. 6(a) should also display the growth of an atomically flat monolayer graphene over a domain size of ~300 nm with few defects. On the Fig. 7. (a) A LEED pattern at 135 ev for the ( )R30 reconstruction of wettreated CMP-(0001) (non-care) after annealing at 1100 C for 5 min in UHV and (b) corresponding AFM image. The fundamental spots (one is marked by a green circle) and the 6 3 satellite spots (in a green square) of graphene were much weaker and diffused than those on CARE-. The AFM image shows an inhomogeneous surface with many pits. Some pits have characteristic hexagonal shapes.

9 604 A.N. Hattori et al. / Surface Science 605 (2011) weaker than those in Fig. 3(a). The corresponding AFM image shows a nonuniform layer with many hexagonal pits (Fig. 7(b) inset); step and terrace structures are hardly seen. These results imply that it is difficult to grow well-ordered graphene with a specific number of layers on wet CMP- surfaces, in contrast to growth on CARE- surfaces. Though the formation mechanism of graphene on surfaces is still unclear, the processes of decomposition, Si sublimation, C diffusion, and graphene formation have been suggested [13,18,24,57,59,62]. To obtain a monolayer graphene on surfaces, the desorption of at least three Si layers is required [13,24,57]; carbon must be released from approximately three bilayers to produce a single graphene layer. The conditions of steps on or 6 3 buffer layer surfaces [13,24,57] and also the buffer layer surface morphology [18] affect the formation of graphene and its qualities. Ohta et al. reported that decomposition started from the step edges and that carbon atoms are emitted onto the terrace [18]. These carbon atoms coalesce and nucleate a graphene ribbons (islands) at step edge, and the graphene islands enlarge along the etched step edge. They considered that the rate-determining factor was the carbon diffusion process (i.e., carbon concentration), which governs the features of graphene steps. We confirmed the reproducible formation of a uniform and atomically flat monolayer graphene with dominant zigzag edges and few defects, and the average terrace width of ~300 nm at the narrow terrace regions, while ~500 nm at the wide terrace regions. Graphitization started at 900 C on the CARE- in UHV; monolayer graphene was produced at 900 C for 5 min and bilayer graphene was produced at 1000 C for 2 min, while it started at 1100 C on the wet CMP-, where the 6 3 spot intensity was weak and graphene films could not form on entire substrate. The temperature of 900 C is much lower than that ( C) in previous reports [11 17,19,20] on the graphitization of. Fig. 8(a) shows typical TPD curves for Si intensity from CARE- and wet CMP- samples. The detected species including Si in the quadruple mass spectrometer were 28, 29, 30, 31, and 32 in mass number, and the cracking ratio was taken into account for the Si intensities. The Si desorption started at 800 C both on the CARE- and wet CMP-, but there was ~200 C difference for the graphitization temperature: 900 C for the CARE-, and 1100 C for the wet CMP-. The TPD intensities were normalized by sample weight, thus, the intensities are comparable. We can see the larger amount of Si desorption from the wet CMP- than the CARE-. For the graphitization, it has been suggested the process of the nucleation of graphene sheets (islands or ribbons) at the Si desorbed area, resulting in the excess of carbon atoms forming sp 2 hybridization network [18,24,59,60]. Theoretically, the desorption rate increases with increasing surface roughness, i.e., surface area [61], which is consistent with our result (Fig. 8(a)). This indicates that much more carbon atoms, forming the nucleation centers exist on the rough surfaces (wet CMP-) than that on the CARE surfaces, above the desorption temperature. On the rough surfaces, we consider that many nucleation centers restrict the domain size of the graphene sheets, some of which would not be parallel to the (0001) plane due to the roughness and defects. Indeed, the angle between the plane of the graphene sheet and the substrate was reported to be 14±2 for the bilayer-like thin graphene sheets on 6H-(0001) surfaces [62]. We speculate that higher temperature require to overcome the activation barriers to enlarge the domain size, and/or to form the sp 2 network itself using diffused carbon atoms, arising from the rough surface configurations. On the other hand, on the atomically flat CARE surfaces, the Si desorption and graphitization would start smoothly at the step edges mainly, and form the uniform and wide domains on terraces at the lower temperature, as shown in Fig. 6. A small amount of defects on terraces would initiate the graphitization also; the hexagonal pit formation is influenced by the competition between the carbon supply from the step edges and that from the defects on the terraces. On the wide terraces, the sufficient size of the pits would be grown before the graphitization from the step edges. More stable arm chair step edges would be formed by the release of many carbon atoms from the edges before the graphitization of the terraces. In contrast, on the narrow terraces, sufficient number of carbon atoms should be supplied before the terrace graphitization. The surface roughing factors, such as, scratches, dislocations and so on, induce much excess Si desorption from, and would prevent the nucleation growth of graphene, resulting in the facet boundaries at step edges [38], tilted (not straight) steps [40], and remained (screw) dislocations, anisotropic step and so on. So far, Si flux have been required for the graphitization process in UHV condition on the surfaces prepared by H 2 etching [11 17,19,20]; the role of Si flux is to compensate for the excess desorbed Si. However, the Si flux is not needed on CARE- even for the graphene prepared by vacuum annealing. We consider that substrate uniformity and flatness is one of the key factors in achieving uniform, wide, and thicknesscontrolled graphene layers on substrates. 4. Conclusion Fig. 8. (a) TPD curves of Si from CARE- (black curve) and wet-treated CMP- (red curve) samples. TPD intensities were normalized by sample weight; the intensities are comparable. The temperature was ramped up at a rate of 1.0 K/s. (b) Schematic phase diagrams for CARE- and wet CMP- surfaces treated by annealing. Damage-free and atomically flat 4H-(0001) surfaces with terrace-step structures were prepared by a novel planarization method, catalyst-referred etching. We demonstrated the formation of graphene films on ultraprecision-figured 4H-(0001) surfaces (CARE-); almost monolayer graphene films were successfully formed with wide and atomically flat terraces and few defects on entire CARE-treated 4H-(0001) surfaces by annealing in UHV. We could control the number of graphene layers on CARE- by changing the annealing temperature and duration. The graphene on CARE- surfaces displayed clear step and terrace structures with an average domain size of over 300 nm in almost entire area, while that on non- CARE- (wet CMP-) surfaces hardly showed the structures. In the graphene on CARE-, the narrow terraces of ~300 nm width mainly had zig-zag step edges and few pits, while the wide terraces of ~500 nm had a significant number of arm chair step edges and many hexagonal pits. We emphasize that the surface uniformity and flatness

10 A.N. Hattori et al. / Surface Science 605 (2011) of the substrate, in other words, the perfection of the surface, strongly affect the graphene quality. Wide and flat graphene domains with few defects are expected to be important and useful for studies on the fundamental properties and applications of graphene films. For instance, a domain wider than the electron coherent length in LEED (~30 nm) makes detailed structure analyses possible. Such a domain can reduce the uncertainty of momentum in photoelectron spectroscopy. In conductivity measurements, it can reduce extrinsic scattering factors. Of course, wide and high-quality graphene is required for applications such as metallic transistors. We can fabricate a higher-quality monolayer graphene on CARE- surfaces in UHV by the simple method of annealing without any Si flux. This study demonstrates one of the advantages of ultraprecision-figured 4H-(0001) surfaces. The CARE technique can remove the damaged layers on substrate surfaces independent of the initial surface conditions. We consider that damage-free samples can be used to produce higher-quality epitaxial grown films, which have excellent properties. We believe that the CARE technique will become an indispensable basic technique to support future nano-scale technologies. Acknowledgements This study was partly supported by a grant of the Global COE Program, Center of Excellence for Atomically Controlled Fabrication Technology from the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan, the Industrial Technology Research Grant Program in 2005 from the New Energy and Industrial Technology Development Organization (NEDO) of Japan, and Kyoto- Advanced Nanotechnology Network under sponsorship from MEXT, Japan. One of the authors (ANH) was supported in part by Special Coordination Funds for Promoting Science and Technology from MEXT for the Osaka University Program for the Support of Networking among Present and Future Women Researchers. References [1] E. Mandel, Solid State Technol. 10 (1967) 27. [2] B. Mullany, G. Byrne, J. Mater. Process. Technol. 132 (2003) 288 and references therein. [3] Y. Liu, K. Zhang, F. Wang, W. Di, Microelectron. Eng. 66 (2003) 438. [4] L. Zhou, V. Audurier, P. Pirouz, J. Electrochem. Soc. 144 (1997) L161. [5] V.D. Heydemann, W.J. Everson, R.D. Gamble, D.W. Snyder, M. Skowronski, Mater. Sci. Forum (2004) 805. [6] H. Hara, Y. Sano, H. Mimura, K. Arima, A. Kubota, K. Yagi, J. Murata, K. Yamauchi, J. Electron. Mater. 35 (2006) L11. [7] H. Hara, Y. Sano, H. Mimura, K. Arima, A. Kubota, K. Yagi, J. Murata, K. Yamauchi, Mater. Sci. Forum 556 (2007) 749. [8] K. Yagi, J. Murata, A. Kubota, Y. Sano, H. Hara, T. Okamoto, K. Arima, H. Mimura, K. Yamauchi, Surf. Inter. Anal. 40 (2008) 998. [9] K. Arima, H. Hara, J. Murata, T. Ishida, R. Okamoto, K. Yagi, Y. Sano, H. Mimura, K. Yamauchi, Appl. Phys. Lett. 90 (2007) [10] T. Okamoto, Y. Sano, H. Hara, K. Arima, K. Yagi, J. Murata, H. Mimura, K. Yamauchi, Mater. Sci. Forum (2009) 835. [11] C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A.N. Marchenkov, E.H. Conrad, P.N. First, W.A. de Heer, Science 312 (2006) [12] U. Starke, C. Riedl, J. Phys. Condens. Matter 21 (2009) [13] J. Hass, W.A. de Heer, E.H. Conrad, J. Phys. Condens. Matter 20 (2008) [14] J. Hass, R. Feng, T. Li, X. Li, Z. Zong, W.A. de Heer, P.N. First, E.H. Conrad, C.A. Jeffrey, C. Berger, Appl. Phys. Lett. 89 (2006) [15] J. Penuelas, A. Ouerghi, D. Lucot, C. David, J. Gierak, H.E. Szwarckopf, C.A. Vignolle, Phys. Rev. B 79 (2009) [16] C. Berger, Z. Song, T. Li, X. Li, A.Y. Ogbazghi, R. Feng, Z. Dai, A.N. Marchenkov, E.H. Conrad, P.N. First, W.A. de Heer, J. Phys. Chem. B 108 (2004) [17] H. Hibino, H. Kageshima, F. Maeda, M. Nagase, Y. Kobayashi, H. Yamaguchi, Phys. Rev. B 77 (2008) [18] T. Ohta, N.C. Bartelt, S. Nie, K. Thürmer, G.L. Kellogg, Phys. Rev. B 81 (2010) [19] T. Ohta, F.E. Gabaly, A. Bostwick, J.L. McChesney, K.V. Emtsev, A.K. Schmid, Th. Seyller, K. Horn, E. Rotenberg, New J. Phys. 10 (2008) [20] P. Lauffer, K.V. Emtsev, R. Graupner, Th. Seyller, L. Ley, S.A. Reshanov, H.B. Weber, Phys. Rev. B 77 (2008) [21] K.V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G.L. Kellogg, L. Ley, J.L. McChesney, T. Ohta, S.A. Reshanov, J. Röhrl, E. Rotenberg, A.K. Schmid, D. Waldmann, H.B. Weber, Th. Seyller, Nat. Mater. 8 (2009) 203. [22] K.S. Noboselov, A.K. Ceim, S.V. Morozov, D. Jiang, M.I. Katsnelson, I.V. Grigorieva, S.V. Dubonos, A.A. Firsov, Nature 438 (2005) 197. [23] Y. Zhang, Y.-W. Tan, H.L. Stormer, P. Kim, Nature 438 (2005) 201. [24] M. Hupalo, E.H. Conrad, M.C. Tringides, Phys. Rev. B 80 (2009) (R)8 and references therein. [25] L.G. Cançado, K. Takai, T. Enoki, M. Endo, Y.A. Kim, H. Mizusaki, A. Jorio, L.N. Coelho, R. Magalhães-Paniago, M.A. Pimenta, Appl. Phys. Lett. 88 (2006) [26] Th. Seyller, K.V. Emtsev, K. Goa, F. Speck, L. Ley, A. Tadich, L. Broekman, J.D. Riley, R.C.G. Leckey, O. Rader, A. Varykhalov, A.M. Shikin, Surf. Sci. 600 (2006) [27] N. Ferralis, R. Naboudian, C. Carraro, Phys. Rev. Lett. 101 (2008) [28] K. Kobayashi, H. Unno, H. Takizawa, S. Adachi, Jpn. J. Appl. Phys. 35 (1996) [29] We used ultrapure water with a low dissolved oxygen content (#1 ppb) for all experiments. In ultrapure water, the total organic carbon (TOC) concentration measured by a TOC meter was 8 ppb, and inductively coupled plasma mass spectroscopy showed that the final content of each metal (Mg, Al, Ca, Cr, Mn, Fe, Ni, Cu, K, and Zn) in the water was reduced to less than 5 ppt. [30] A.N. Hattori, T. Okamoto, S. Sadakuni, J. Murata, H. Oi, K. Arima, Y. Sano, K. Hattori, H. Daimon, K. Endo, and K. Yamauchi, J. Nanosci. Nanotechnol. (in press). [31] A.N. Hattori, K. Endo, K. Hattori, H. Daimon, Appl. Surf. Sci. 256 (2010) [32] A.N. Hattori, F. Kawamura, M. Yoshimura, Y. Kitaoka, Y. Mori, K. Hattori, H. Daimon, K. Endo, Surf. Sci. 604 (2010) [33] A.N. Hattori, T. Okamoto, S. Sadakuni, J. Murata, K. Arima, Y. Sano, K. Hattori, H. Daimon, K. Endo, and K. Yamauchi, unpublished. [34] H. Yashiro, T. Fujimoto, N. Ohtani, T. Hoshino, M. Katsuno, T. Aigo, H. Tsuge, M. Nakabayashi, H. Hirano, K. Tatsumi, Mater. Sci. Forum (2009) 819. [35] When the RHEED patterns were measured under the same conditions, the peak intensities were comparable. Note that the intensity was so intense that the CCD camera was saturated in Fig. 1(h). We cannot estimate the peak widths exactly, because of the finite size of the incident beams. [36] D. Schmeiβer, D.R. Batchelor, R.P. Mikalo, P. Hoffmann, A. Lloyd-Spetz, Appl. Surf. Sci. 184 (2001) 340. [37] T. Okamoto, Y. Sano, K. Tachibana, K. Arima, A.N. Hattori, K. Yagi, J. Murata, S. Sadakuni, and K. Yamauchi, J. Nanosci. Nanotechnol. (in press). [38] V. Ramachandran, M.F. Brady, A.R. Smith, R.M. Feenstra, D.W. Greve, J. Electron. Mater. 27 (1998) 308. [39] S. Nie, C.D. Lee, R.M. Feenstra, Y. Ke, R.P. Devaty, W.J. Choyke, C.K. Inoki, T.S. KUan, G. Gu, Surf. Sci. 602 (2008) [40] A. Nakajima, H. Yokoya, Y. Fujikawa, H. Yonezu, J. Appl. Phys. 97 (2005) [41] S. Sadakuni, J. Murata, K. Yagi, Y. Sano, K. Arima, A.N. Hattori, T. Okamoto, K. Yamauchi, Mater. Sci. Forum 795 (2010) 645. [42] J. Murata, A. Kubota, K. Yagi, Y. Sano, H. Hara, K. Arima, T. Okamoto, H. Mimura, K. Yamauchi, J. Cryst. Growth 310 (2008) [43] J. Murata, A. Kubota, K. Yagi, Y. Sano, H. Hara, K. Arima, T. Okamoto, H. Mimura, K. Yamauchi, Mater. Sci. Forum (2009) 815. [44] C. Riedl, U. Starke, J. Bernhardt, M. Franke, K. Heinz, Phys. Rev. B 76 (2007) [45] Si 2p 3/2 peak shifts were observed when the 1 1 as-care sample was changed to 3 3 and phases [33]. The Si 2p 3/2 peak shifted toward a higher binding energy when the phase was changed from 3 3 to The C 1s peak has three components at the phase [30], while the peaks were fitted by one component at the 1 1 and 3 3 phases. We evaluated the pure phase based on the magnitudes of the Si 2p chemical shift and the C 1s components. [46] L.M. Malard, M.A. Pimenta, G. Dresselhaus, M.S. Dresselhaus, Phys. Rep. 473 (2009) 51. [47] L.M. Malard, J. Nilsson, D.C. Elias, J.C. Brant, F. Plentz, E.S. Alves, A.H. Castro Neto, M.A. Pimenta, Phys. Rev. B 76 (2007) [48] F. Tuinsra, J.L. Koening, J. Chem. Phys. 53 (1970) [49] F. Tuinsra, J.L. Koening, J. Compos. Mater. 4 (1970) 492. [50] L.M. Malard, M.H.D. Guimarães, D.L. Mafra, M.S.C. Mazzoni, A. Jorio, Phys. Rev. B 79 (2009) [51] S. Kurita, A. Yoshimura, H. Kawamoto, T. Uchida, K. Kojima, M. Tachibana, P. Molina-Morales, H. Nakai, J. Appl. Phys. 97 (2005) [52] L.G. Cançado, A. Reina, J. Kong, M.S. Dresselhaus, Phys. Rev. B 77 (2008) [53] D. Graf, F. Molitor, K. Ensslin, C. Stampfer, A. Jungen, G. Hierold, L. Wirtz, Nano Lett. 7 (2007) 238. [54] M. Maruyama, K. Kusakabe, S. Tsuneyuki, K. Akagi, Y. Yoshimoto, J. Yamauchi, J. Phys. Chem. Solids 65 (2004) 119. [55] J. Röhrl, M. Hundhausen, K.V. Emtsev, Th. Seyller, R. Graupner, L. Ley, Appl. Phys. Lett. 92 (2008) [56] C.-T. Lin, C.-W. Chang, C.-B. Chen, Int. J. Adv. Manuf. Technol. 30 (2006) 388. [57] M.L. Bolen, S. Harrison, L.B. Biedermann, M.A. Capano, Phys. Rev. B 80 (2009) [58] G.F. Sun, J.F. Jia, Q.K. Xue, L. Li, Nanotechnology 20 (2009) [59] H. Kageshima, H. Hibino, M. Nagase, H. Yamaguchi, Appl. Physiol. Express 2 (2009) [60] C. Tang, L. Meng, H. Xiao, J. Zhong, J. Appl. Phys. 103 (2008) [61] K. Akaishi, J. Plasma Fusion Res. 79 (2003) 581. [62] K. Kim, H. Lee, J.-H. Choi, H.-K. Lee, T.-H. Kang, B. Kim, S. Kim, J. Phys. Condens. Matter 20 (2008)