In situ atomic-scale observation of monolayer graphene growth from SiC

Transcription

1 Nano Research 2018, 11(5): In situ atomic-scale observation of monolayer graphene growth from SiC Kaihao Yu 1,, Wen Zhao 2,4,, Xing Wu 1,5,, Jianing Zhuang 4, Xiaohui Hu 1,6, Qiubo Zhang 1, Jun Sun 1, Tao Xu 1, Yang Chai 9, Feng Ding 2,3,4 ( ), and Litao Sun 1,7,8 ( ) 1 SEU-FEI Nano-Pico Center, Key Laboratory of MEMS of Ministry of Education, School of Electronic Science and Engineering, Southeast University, Nanjing , China 2 Center for Multidimensional Carbon Materials, Institute for Basic Science, Ulsan , Republic of Korea 3 School of Materials Science and Engineering, Ulsan National Institute of Science and Technology, Ulsan , Republic of Korea 4 Institute of Textiles and Clothing, The Hong Kong Polytechnic University, Hong Kong , China 5 Shanghai Key Laboratory of Multidimensional Information Processing, Department of Electrical Engineering, East China Normal University, Shanghai , China 6 College of Materials Science and Engineering, Nanjing Tech University, Nanjing , China 7 Center for Advanced Carbon Materials, Southeast University and Jiangnan Graphene Research Institute, Changzhou , China 8 Center for Advanced Materials and Manufacture, Joint Research Institute of Southeast University and Monash University, Suzhou , China 9 Department of Applied Physics, The Hong Kong Polytechnic University, Hong Kong , China Kaihao Yu, Wen Zhao, and Xing Wu contributed equally to this work. Received: 18 September 2017 Revised: 23 October 2017 Accepted: 3 November 2017 Tsinghua University Press and Springer-Verlag GmbH Germany 2017 KEYWORDS graphene, epitaxial growth, in situ, transmission electron microscopy ABSTRACT Because of its high compatibility with conventional microfabrication processing technology, epitaxial graphene (EG) grown on SiC shows exceptional promise for graphene-based electronics. However, to date, a detailed understanding of the transformation from three-layer SiC to monolayer graphene is still lacking. Here, we demonstrate the direct atomic-scale observation of EG growth on a SiC (11 00) surface at 1,000 C by in situ transmission electron microscopy in combination with ab initio molecular dynamics (AIMD) simulations. Our detailed analysis of the growth dynamics of monolayer graphene reveals that three SiC (11 00) layers decompose successively to form one graphene layer. Sublimation of the first layer causes the formation of carbon clusters containing short chains and hexagonal rings, which can be considered as the nuclei for graphene growth. Decomposition of the second layer results in the appearance of new chains connecting to the as-formed clusters and the formation of a network with large pores. Finally, the carbon atoms released from the third layer lead to the disappearance of the chains and large pores in the network, resulting in a whole graphene layer. Our study presents a clear picture of the epitaxial growth of the monolayer graphene from SiC and provides valuable information for future developments in SiC-derived EG technology. Address correspondence to Litao Sun, slt@seu.edu.cn; Feng Ding, f.ding@unist.ac.kr

2 2810 Nano Res. 2018, 11(5): Introduction In view of its high room-temperature carrier mobility of ~ 10 4 cm 2 V 1 s 1, graphene, a one-atom thick carbon layer packed into a two-dimensional (2D) honeycomb lattice, is considered to be one of the most promising candidates for next generation electronics [1]. Several methods have been demonstrated for preparing graphene, including mechanical exfoliation, liquid-phase exfoliation, reduction of graphene oxide, chemical vapor deposition, and epitaxial growth on SiC [2, 3]. Among these methods, the growth of epitaxial graphene (EG) on SiC is the most promising for electronic applications since it meets the stringent requirements of quality, and ease of patterning; additionally, a complicated transferring process is not required. Using these advantages, Berger et al. have applied conventional lithographic techniques to prepare a high-mobility graphene transistor in a top-gate configuration [4], while Lin et al. have demonstrated a graphene-based broadband radio frequency mixer working up to 10 GHz by integrating all the circuit components on a SiC wafer [5]. EG on a SiC surface is obtained by the formation of a carbon layer from the released carbon atoms during the sublimation of Si at an elevated temperature. EG is commonly fabricated on the polar surfaces of SiC ((0001) or (111) for the hexagonal or cubic polytypes) [4, 6 14]. A clean and un-reconstructed (0001)/(111) surface that is terminated by silicon atoms is named as the Si-face and the corresponding (0001 )/(1 1 1) surface is called the C-face. The number of layers of the grown EG on the Si-face can be more easily controlled, but the graphene formed by this method interacts strongly with the substrate through a carbon buffer layer, which has the periodicity of ( )R30, with respect to the substrate surface [4, 15 17]. Because of the electrically inert buffer layer, the EG is n-type doped with a density of ~ cm 2 and the mobility is ~ 1,000 cm 2 V 1 s 1 at room temperature [9, 18 20]. Although the EG grown on the C-face is always multi-layered, it preserves the electrical properties of the monolayer because of a rotational stacking fault between the layers [17, 21 23]. To understand the growth mechanism, many ex situ experiments using scanning probe microscopes and other surface characterization methods have been performed [9, 21, 24 31]. On the Si-face, EG nucleates at a step and then grows to cover the terraces mainly in a reverse step-flow manner [9, 24 28], whereas on the C-face, multilayer EG islands nucleate at defective sites and coalesce during lateral expansion [21, 29 31]. However, so far only ex situ experiments have been conducted to investigate the discrete growth stages. Based on these discontinuous and indirect observations, EG growth mechanisms have been proposed [9, 21, 24 31]. Theoretical simulations have served to fill this gap by revealing that six-membered rings start to form at 1,300 1,500 K, larger graphene domains appear above 2,000 K, and amorphous 3D carbon structures form if some carbon atoms bond to the substrate [32 34]. Although great efforts have been dedicated to understand the mechanism of EG formation from the SiC surface, there are still many unsolved puzzles; for example, there is no experimental evidence to verify the exact number of SiC layers required to form single layer graphene and the nature of the intermediate layers between graphene and the substrate remain unknown. Apart from the two polar surfaces, the EG growth from the two low-index nonpolar surfaces, namely, the m-plane (11 00) and the a-plane (112 0) have also drawn attention. At high temperatures, the etching rates along <11 00> and <112 0> are higher than that along <0001> [35] because of the larger packing density in the (0001) plane. Therefore, step bunching occurs on the polar (0001) surfaces at high temperature or under H-etching. High temperature normally leads to a larger step height as well as the resistance of the grown graphene, due to the inhomogeneity in carrier density caused by the steps [36]. The fast etching rate in turn causes thicker, smaller, and rougher EG growth on nonpolar surfaces [35]. Steps play an important role during graphene nucleation on the Si-face and the vertical surfaces of these steps always have nonpolar surfaces. Among these two nonpolar surfaces, the (11 00) surface has a faster etching rate [35], which indicates that graphene actually grows fast on it. In addition, its interplanar spacing is 0.26 nm, the carbon density is approximately one third of that of graphene, similar to that of the (0001) surface but larger than that of the (112 0). EG on the (11 00) surface has rotational stacking faults but no buffer layer exists as that on the Si-face [37],

3 Nano Res. 2018, 11(5): and the large structural symmetry mismatch between the EG and SiC (11 00) surface causes weaker scattering from the SiC substrate [38]. However, the mechanism of transformation from SiC to graphene on (11 00) surfaces, which is known to be free from step bunching, has never yet been revealed. To investigate the graphene growth mechanism on a SiC (11 00) (m-plane) surface at atomic resolution, we carried out in situ heating experiments in an aberration-corrected transmission electron microscope (Titan ) equipped with an Aduro 100 heating system (Protochips Inc.). Our experimental results reveal that the SiC decomposes layer by layer and three SiC (11 00) layers transform to one graphene layer. To further understand the growth process, ab initio molecular dynamics (AIMD) simulations have been performed. It has clearly shown that the sublimation of one and two SiC layers only produces carbon clusters and a carbon network, respectively; a complete graphene layer is seen after the third SiC layer was decomposed. for 33 min to minimize the thermal drift and identify an appropriate sample zone (Fig. 1(a)). Deng et al. reported that the onset of silicon single detection in the exhaust was at 850 C for a pressure of ~ 10 7 Torr [39]. The pressure in the microscope chamber stayed at ~ 10 7 Torr, which implies that silicon sublimation can be ignored at 800 C. A SiC particle with the [0001] orientation was chosen to investigate graphene growth on the (11 00) surface (Figs. 1(b) and 1(c)). Since we are interested only in the (11 00) surface, the polarity of <0001> was ignored. The evaporation rate of silicon increases with increasing temperature, resulting in a higher graphene growth rate [8]. Muehlhoff et al. showed that the evaporation rate of silicon at 1,027 C under ultrahigh vacuum is Si(gas) atoms cm 2 s 1, which indicates 2 Results and discussion 2.1 Preparation of a clean surface of SiC 6H-SiC particles (several hundred nanometers in size) were first etched by oxygen plasma for 5 min to remove contaminants and subsequently transferred to the Aduro 100 heating system. This heating system consists of an external power supply, a controller, and a specimen holder. The conventional 3 mm copper grid is replaced by a micro-electro-mechanical system device clamped at the holder tip (Fig. 1(a)). The key element in the device is a 0.5 mm 0.5 mm-area and ~ 120 nm-thick free-standing conductive ceramic membrane suspended at the center of a 4 mm 5.8 mm silicon chip. Joule heating occurs when electrical current is forced through the membrane. In order to ensure electron transparency, 7 7 through holes that are 6 μm in diameter are patterned on the ceramic membrane. A holey carbon film is coated on the ceramic membrane to support the specimen (Fig. 1(a)). Compared to a conventional heating system, the Aduro 100 enables a very fast heating rate up to 1,000 C ms 1 with an extremely low thermal drift even at high temperatures (1,000 C in this work). The chip was firstly heated to 800 C in 98 s and then the temperature was maintained Figure 1 Experimental set up and atomic structure of a SiC surface before and after graphene growth. (a) Annealing procedure and schematic diagram of the specimen holder. (b) HRTEM image of a 6H-SiC particle edge at 1,000 C before graphene growth; the inset illustrates the crystal orientation. The electron beam is incident along the c-axis of SiC. (c) FFT of (b) showing the [0001] zone axis. ((d), (e)) and ((f), (g)) Filtered HRTEM images and corresponding structural models showing, respectively, the atomic structures of the SiC (11 00) surface before and after graphene growth. The blue and red arrows indicate the orientations of SiC and graphene respectively and the SiC in ((e) and (g)) have the same orientation. The interstitial atoms between graphene and SiC have been omitted to highlight graphene. The scale bars in both (d) and (f) are 0.5 nm. Nano Research

4 2812 Nano Res. 2018, 11(5): that 2.7 layers of SiC will be lost after 5 min of annealing [40]. This decomposition rate is appropriate for the observation of graphene growth and therefore, the temperature was increased and stabilized at 1,000 C (Fig. 1(a)). Surface cleanness is quite important for EG growth on SiC; however, the initial surface was always covered with contaminants even after 5 min of oxygen plasma etching prior to insertion into the microscope chamber. A convergent electron beam was applied to clean the surface of the substrate and to remove all possible contaminations (Fig. S4 in the Electronic Supplementary Material (ESM)). Figures 1(d) and 1(e) show the highresolution transmission electron microscopy (HRTEM) images and atomic models of the clean (11 00) 6H-SiC surface before graphene growth. The inter-planar spacing at the (11 00) surface is 0.26 nm, the same as that in bulk and very close to that (0.25 nm) observed between the (0001) planes. The error bar for all distances measured from the HRTEM images is ± 0.02 nm. Due to the fact that atoms in the (11 00) plane are located in different sublayers, the crystal can be terminated by different surface structures (Fig. S1 in the ESM). On these surfaces, there are two types of atoms, type I with one dangling bond and type II with two dangling bonds. The structure D in Fig. S1 (in the ESM) consisting only of type I atoms has the minimum number of dangling bonds among the different possible structures and hence is the most stable due to its minimized surface energy [41, 42]. Seyller et al. reported that the hydrogen saturated 4H-SiC (11 00) surface did not reconstruct and contained only monohydrides, which meant that the silicon and carbon atoms on this surface had just one dangling bond [43]. This stable structure has a surface lattice that is nearly sp 2 trigonal (Fig. 1(e)) and shows a zigzag structure along the [0001] direction (Fig. S1 in the ESM) that can be imaged when an incident beam travels along the [112 0] azimuth (Fig. S3 in the ESM). Here, it is worth noting that this surface consists of two nanofacets, the Si-face and the C-face (Fig. 1(e)), both inclined at approximately 20 with respect to the surface (Fig. S2 in the ESM). Figure 2 Graphene growth process and mechanism at SiC (11 00) surface. (a) (l) HRTEM images and schematic diagrams show the overall process of graphene growth at the surface. (m) False color HRTEM images illustrate the detailed structures corresponding to areas enclosed by the dashed white rectangles. Numbers without superscripts (e.g., 1, 2, 3 ) indicate the perfect SiC layers and numbers with superscripts (1, 2, 3, 4 ) represent partially decomposed SiC layers. The distance between the initially formed graphene and SiC is 0.30 nm, which is smaller than 0.36 nm between SiC and the quasi-free-standing graphene. The fringes with spacing of 0.21 nm in (m) VI correspond to graphene lattice constant.

5 Nano Res. 2018, 11(5): Growth process of graphene Figures 1(f) and 1(g) illustrate the HRTEM image and structure of epitaxial monolayer graphene on the SiC (11 00) surface. The distance between graphene and SiC is 0.36 nm, which is much larger than that between the SiC (11 00) planes, but is very close to that reported in a previous study [37]. The fringes shown in Fig. 1(f) correspond to the (11 00) plane in graphene and this implies that the SiC [0001] direction is parallel to the graphene [112 0] (Fig. 1(g)), which is also consistent with the previous observation [38]. Since the carbon density in one 6H-SiC (11 00) layer is ~ 1/3 of that in graphene, it is necessary to decompose at least three (11 00) layers to form one complete graphene layer. Figure 2 shows the frames extracted from Movie S1 in the ESM, showing the growth of monolayer graphene at the SiC (11 00) surface. Silicon atoms are sublimated layer by layer and the carbon atoms that remain in each layer rearrange to form different structures. Owing to the deficiency in the number of carbon atoms, only carbon dimers, short chains, and some rings are formed and bonded to the surface (represented by small red balls in Fig. 2(c)), and are observed after the complete decomposition of the first (11 00) layer. Although these carbon structures cannot be directly imaged by HRTEM, they can influence the changes occurring in the second layer (Fig. 3). With the atomic details revealed by the AIMD simulation, it is possible to model the evolution of the surface structure (Figs. 4(a1) 4(a3)). Sublimation of the second layer doubles the number of carbon atoms at the surface but this is still insufficient to form a complete graphene layer. Instead, a random carbon network appears (Fig. 2(g)). This carbon network is labeled as C in Fig. 2(m) III and shows a disordered structure in contrast to the inner layer of SiC, which implies that it is highly defective. The distance between this carbon network and the SiC surface is ~ 0.26 nm, identical to the SiC (100) lattice spacing. The carbon network is unstable and can quickly collapse into the third layer (Movie S1 in the ESM), forming a hybrid C structure (Fig. 2(h) and Fig. S6 in the ESM) which is a combination of the carbon network and a partially decomposed SiC layer. An atomic step appears during the decomposition of the second layer and a small piece of the graphene domain is seen at this step (Fig. 2(e)). This is consistent with the conclusion from previous works, that the steps are the energetically favorable sites for graphene formation [9, 44]. As mentioned above, the decomposition of the two SiC (11 00) layers cannot result in graphene growth (Figs. 2(e) 2(g)). Some new graphene domains appear but quickly vanish after the step moves away, as shown in Movie S1 in the ESM. In Fig. 2(f), the third layer underlying the graphene domain evaporates and the released C atoms cause the graphene to expand and bridge the adjacent SiC layers. The decomposition of three SiC layers produces just enough carbon atoms to form a complete graphene layer. Simultaneously, another graphene domain is formed (Movie S1 in the ESM). As shown in Fig. 2(m) IV, the spacing between this graphene and the SiC surface is 0.30 nm, which is larger than that of SiC (11 00). Although the carbon density of the three (11 00) layers is Å 2, which is a bit higher than that in graphene (0.382 Å 2 ), a quasifree-standing graphene is not seen due to the dangling bonds at the SiC surface. Some carbon atoms in the graphene are bonded to the surface (Fig. 4(c3)), which introduces defects in graphene and increases the interaction between graphene and SiC. Single layer graphene cannot prevent the sublimation of silicon atoms from the surface and the subsequent layers can continue to decompose. Figures 2(j) 2(k) present the disintegration of the fourth layer, which is similar to that of the first layer in producing only carbon clusters between graphene and SiC. These carbon atoms saturate the dangling bonds and promote the detachment of the graphene layer from SiC. The distance between this graphene layer and the SiC surface increases to 0.36 nm (Fig. 2(m) IV VI), which is greater than the spacing between graphene layers. This graphene has a very weak interaction with the SiC and hence we refer to it as a quasi-free-standing graphene. In Fig. 2(m) VI, graphene (11 00) fringes with a spacing of 0.21 nm are observed, confirming that the outermost layer is graphene. Also, the decomposition of the fourth layer coincides with the beginning of the second graphene layer and a complete second layer should be formed along with the sublimation of the subsequent layers. However, the electron beam with an energy of 300 kev can create several vacancies in graphene, and these vacancies rapidly anneal with the newly released C Nano Research

6 2814 Nano Res. 2018, 11(5): atoms at 1,000 C [45], thus suppressing the growth of the second graphene layer. Figures 2(i) 2(l) show how a defect nucleates, grows, and breaks the graphene to finally vanish. Figure S7 in the ESM shows the decomposition of subsequent SiC layers under the first graphene layer without the formation of a second graphene layer. In other areas, away from the influence of electron irradiation, multi-layer graphene is observed (Fig. S8 in the ESM). It is interesting to note that the Si-face and C-face nanofacets of the SiC (11 00) surface (Fig. 1(e)) have surface energies of 2,200 and 300 mj m 2, respectively [46]. Hence, the Si-face sublimates faster than the C-face, and the decomposition of one SiC (11 00) layer may be accompanied by the formation of intermediate structures, which implies that the SiC does not vanish all at once. In our experiment, two transitional structures during the sublimation of the first layer (1,1 ), and one transitional structure (2,3,4 ) during the decomposition of the subsequent layers were recorded. Figures 3(a) 3(d) illustrate the full decomposition sequences of the first SiC layer, where the contrast of layer 1 gradually decreases and vanishes in the end (Fig. 3(i)). During the transformation to structure 1, a clear decomposition front is observed, indicated by a red arrow in Movie S1 in the ESM, but the mechanism is still unclear. Although 1 and 1 have lower contrast, they show a structural order similar to the bulk SiC layer (Fig. 2(m) I and Fig. 3). The other transitional layers (2, 3, and 4 ) show lower contrast but have slightly disordered structures (Fig. 3 and Fig. S5 in the ESM). It is worth noting that the contrast of the second layer is apparently enhanced when layer 1 transforms to structure 1 and is nearly constant even after the vanishing of the first layer according to the line profiles in Fig. 3(i). The contrast decreases in the partially decomposed SiC layer due to the sublimation of silicon atoms and the increased disorder in the arrangement of the carbon atoms. The increase in contrast in the second layer may arise from stress due to the reconstruction (Fig. 4(a3)) induced by the atoms in the first layer, which can be treated as ad-atoms [41]. The fact that the contrast of the inner layers remains unchanged excludes influences due to the variation of microscope parameters such as defocus and spherical aberration. At the atomic scale, the thermal decomposition process implies breaking of bonds and the displacement of atoms from lattice sites. Figure 3(l) demonstrates that the C C bond is stronger than the Si C bond, and the Si Si bond is the weakest [47 50]. Therefore, after the breaking of Si C bonds, carbon atoms are more likely to bond with other carbon atoms whereas silicon atoms prefer to leave Figure 3 The contrast changes during decomposition of the SiC (1 100) layers. (a) (h) HRTEM images at different stages clearly showing structure changes in the first, second, and fourth (1 100) layer. Numbers with superscripts represent the transition structures. (i) (k) Average line profiles of the rectangular areas in (a) (h) showing an apparent decrease in contrast of the transition structures. In (i) a contrast increase can be seen in layer 2. (l) Bond lengths and bond energies of the different bond types between silicon and carbon.

7 Nano Res. 2018, 11(5): the surface. Due to the insufficiency of carbon atoms, only a few rings are formed that remain adsorbed at the surface (Fig. 4(a3)) after the complete decomposition of one (11 00) layer. Since the C C bond is more stable, these carbon rings prefer to stay at the C-faces. Figure 4 AIMD simulation of the graphene growth process from a SiC (11 00) surface upon layer by layer removal of silicon atoms. (a) (c) After the removal of silicon atoms from each atomic layer, three snapshots are taken during the annealing process to represent the initial, middle, and final structures obtained by the AIMD simulation. The grey dashed lines show the supercell lattices. In addition to the top (the lower panels) and front (the upper panels) views of each structure, the number of pentagons, hexagons, heptagons, and octagons are counted and labeled in orange, magenta, blue, and green, respectively. Polygons containing both carbon and silicon atoms are excluded. (d) The number of pentagons, hexagons, heptagons, and octagons in each of the final structures obtained by AIMD simulation after the removal of silicon atoms from the 1st, 2nd, and 3rd layer of SiC. The orientation for the top panels of (a1) (c3) is [112 0], and that for the bottom panels is [11 00]. The longer sides of the top and bottom panels are parallel to the [0001] direction. The carbon atoms on the surface are highlighted in red and the SiC substrates in the top views are concealed. 2.3 Theoretical calculations of the growth process For a deep understanding of these experimental observations, it is essential to study in depth, the process of graphene growth from SiC on the atomic scale during the sublimation of silicon atoms at high temperature. For this purpose, based on the well-accepted mechanism of graphene growth from SiC through silicon sublimation, we performed AIMD simulations to explore the structural evolution of carbon atoms on the SiC (1 100) surface after the layer-by-layer removal of silicon atoms. The temperature is deliberately chosen to be 2,800 K, which is much higher than the realistic experimental temperature of ~ 1,273 K; this assumption is essential to accelerate the atomic evolution in AIMD simulation in order to observe a full annealing process in a short simulation time (~ 10 ps). During the simulation, silicon atoms in four atomic layers were removed in sequence, and the AIMD simulation was performed for a certain time period after the removal of silicon atoms until the structure was stabilized. Figure 4 shows the structures obtained by AIMD simulation after the removal of silicon atoms from each layer at the initial, middle (~ 1 ps), and final stages in the time period of 10 ps. After removing silicon atoms from the first layer, the dispersed carbon atoms anneal quickly and a carbon chain is formed along the [11 20] direction (Fig. 4(a1)). Further annealing leads to ring formation (one pentagon and two hexagons are recognized) (Fig. 4(a2)). Due to the presence of dangling carbon bonds in these structures, all the carbon atoms are tightly bonded to the second SiC layer. This is very different from the formation of carbon clusters on metal surfaces, e.g., Ni(111) [51 53], Rh(111) [53, 54], Cu(111) [54, 55], and Ru(0001) [54] surfaces, wherein the carbon atoms are tightly bonded to each other and can diffuse quickly, which renders the carbon chain highly stable until the number of carbon atoms reaches ~ 10. The carbon chain formation becomes very stable in a few picoseconds and in the final stage (Fig. 4(a3)), we can identify two high quality and pure carbon hexagons, which can be considered as the initial nuclei of graphene. Some hexagons containing carbon and silicon atoms can also be seen in Fig. 4(a3), but they are unstable and can be excluded from the statistics of rings (Fig. 4). Most of these carbon atoms attach to the C-face due to the stronger C C bond. In Nano Research

8 2816 Nano Res. 2018, 11(5): Fig. 4(a3), it can be seen that the second layer also undergoes some structural change, which may be responsible for the contrast enhancement observed in HRTEM (Fig. 3). The simulation results show that the low coverage of carbon atoms on the SiC favors sp 2 - or sp 3 -hybridization on the SiC substrate in order to effectively passivate the dangling bonds of the system. After the removal of silicon from the second SiC layer, the carbon atoms of the second layer bridge the formed carbon structure to the SiC substrate (Fig. 4(b1)). Since such a formation is highly unstable, it is quickly transformed into a structure in which all the carbon atoms are tightly attached to the SiC surface (Fig. 4(b2)). In the final stage, (~ 6.50 ps, Fig. 4(b3)), the polygons in the as-formed graphene nuclei increase and carbon chains connect these nuclei forming a network with large pores on the SiC surface. This carbon network is highly disordered compared to graphene and the HRTEM images in Fig. 2(m) confirm this disorder. Obviously, the number of carbon atoms in the first two SiC layers is not enough to form a complete graphene layer on the SiC surface. After the removal of silicon atoms from the third layer SiC, the number of carbon atoms is just enough to form a single atomic layer of graphene. The annealed structure (Fig. 4(c3)) covers the SiC surface with a few small pores and most of the carbon atoms in it are sp 2 -hybridized. The quality of the carbon formation is much improved as evidenced by the significant increase in the number of polygons and disappearance of chains and large pores in the structure. Due to the greatly improved quality of the sp 2 network, the interaction between the graphene layer and the substrate becomes weaker and only a few bonds connect it to the SiC surface, with a large part of the structure floating on the surface. This result strongly supports the experimental observation that the sublimation of silicon from three SiC layers is essential to form a complete single layer of graphene on the SiC surface and the spacing is larger than that of the carbon network. Due to the very short simulation time (24.33 ps in total), it is not surprising that the structure obtained by the AIMD simulation still has many defects such as dangling bonds, and pentagons. To further investigate the possibility of forming a high-quality graphene layer, we adopted the recently developed energy driven kinetic Monte Carlo (EDKMC) method [56, 57]. This method was used to further anneal the obtained carbon structure and prove that a perfect graphene layer could be obtained if the simulation time was long enough (Fig. S10 and Movie S4 in the ESM), that is, as long as in real experiments (a few minutes). To further confirm the necessity to sublimate three layers of SiC to form a complete graphene, we studied the carbon formation that resulted after the removal of silicon atoms from the fourth SiC layer. It is found that the carbon atoms beneath the top layer graphene (Fig. S11 in the ESM) form a structure which is very similar to the configuration in Fig. 4(a), that is, they attach to the SiC substrate forming sporadic rings and have an average spacing ~ 0.3 nm from the top layer graphene. This implies the nucleation of the second graphene layer and indicates that the further removal of silicon atoms would lead to the formation of the second layer of graphene. The distance between graphene and SiC in Fig. S11(c) is larger than that in Fig. 4(c3), which agrees with the experiment result shown in Fig. 2(m). The evolution of structures and energy along the whole AIMD steps can be found in Movies S2(a) S2(d) and Fig. S12 in the ESM. 3 Conclusions In situ HRTEM and AIMD simulations have been used to investigate the growth mechanism of EG on a 6H-SiC (11 00) surface consisting of two inclined nanofacets, namely, the Si-face and the C-face. SiC decomposes layer by layer and each layer forms transition structures before total decomposition. A large area graphene layer is seen following the sublimation of the third SiC layer. Less stable carbon clusters and a network are formed as transition structures during sublimation of the first and second layers. These carbon clusters, which consist of hexagonal rings, serve as nuclei for graphene growth and remain strongly bonded to the surface. As the number of surface carbon atoms increases, more rings can be seen in the clusters and some carbon chains connect to these clusters forming a carbon network with large pores. A large graphene layer results when chains transform to rings and pores are filled with carbon atoms. A detailed understanding of the growth process of monolayer EG on SiC is an important step in the production of high quality homogeneous EG

9 Nano Res. 2018, 11(5): films for electronic applications. 4 Methods 4.1 Sample preparation The SiC micro powder was purchased from Shangdong Qingzhou Micropower Co., Ltd., and particles with several hundred nanometers were selected by blowing. These particles were first etched by oxygen plasma for 5 min before dispersing in ethanol. After sonication for 5 min, a drop (~ 10 μl) of the suspension was placed at the center of the heating chip and dried under ambient conditions. 4.2 HRTEM observation In situ HRTEM was conducted on a Titan transmission electron microscope equipped with image corrector and monochromator, operating at 300 kv with resolution up to 80 pm. First the temperature was ramped up from room temperature to 800 C at a rate of ~ 10 C s 1. One SiC particle with the [0001] orientation was chosen for the investigation of graphene growth on its (11 00) surface. Next, the temperature was increased to 1,000 C for graphene growth at an average rate of ~ 2 C s 1. Once the sample was stable, a convergent beam with a current of ~ 20 na was used to etch the edge of the particle until a clean (11 00) surface was acquired (Fig. S4 in the ESM). The temperature control and monitoring was carried out using the Aduro 100 heating system and each chip was calibrated in the factory with a temperature accuracy of 0.5%. During the observation, the electron beam current density was maintained at ~ A m 2 and the chamber pressure was stabilized at ~ 10 7 Torr. The image was recorded using a Gatan US1000 CCD camera with the exposure time about 0.5 s. 4.3 Theoretical calculations AIMD simulations were performed using the Vienna Ab initio Simulation Package (VASP) [58]. Considering the time consuming nature of the AIMD, the exchangecorrelation functional is described by the local density approximation (LDA) [59], the core region by the projector augmented wave (PAW) method [60], the plane-wave cutoff is set to be 00 ev, and the 3Brillouin zone is sampled at the Γ point only, because of the relatively large size of the unit cell. All AIMD trajectories were run with the canonical ensemble (NVT) using a Nosé thermostat [61] at the temperature of 2,800 K. The time step of the AIMD simulation is 0.5 fs. The total time scales of the trajectories are from several to tens of picoseconds (ps). A SiC (11 00) slab containing six atomic carbon- silicon layers with the bottom layer fixed and saturated by hydrogen is used as the initial structure and around 15 Å vacuum space is maintained in the direction perpendicular to the basal plane. To simulate the sublimation process of SiC for graphene growth, silicon atoms were artificially removed layer by layer during the AIMD simulation and the leftover carbon atoms were allowed to gradually aggregate into carbon chains, clusters, and eventually to form single layer graphene. Due to the very high computational time of AIMD simulations time scale (~ 10 ps), though accurate and reliable, its time scale does not allow us to describe completely, the real growth process that occurs on macroscopic time scales (from seconds to hours). Therefore, the carbon layer obtained from AIMD is further annealed using the energy-driven kinetic Monte Carlo (EDKMC) method [56, 57] with the second-generation reactive empirical bond order (REBO2) potential [62] at a temperature of 3,500 K. Acknowledgements This work was supported by the National Natural Science Foundation of China (Nos , , , , , and ) and the Fundamental Research Funds for the Central Universities (Nos K41039, MTEC-2015M03, and NJ ) and the Natural Science Foundation of Jiangsu Province (No. BK ). W. Z. and F. D. acknowledge the support of Institute for Basic Science, Republic of Korea (No. IBS-R019-D1). X. W. would like to acknowledge support from the Projects of Science and Technology Commission of Shanghai Municipality (No. 14DZ ). Electronic Supplementary Material: Supplementary material (additional details of the experiments conditions, surface treatment, simulations and complete growth Nano Research

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