Grain Boundary Structures and Electronic Properties of Hexagonal

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Grain boundary structures and electronic properties of hexagonal boron nitride on Cu (111) Qiucheng Li,1 Xiaolong Zou,2 Mengxi Liu,1 Jingyu Sun,1 Yabo Gao,1 Yue Qi,1 Xiebo Zhou,1,3 Boris I. Yakobson,*,2 Yanfeng Zhang,*,1,3 and Zhongfan Liu*,1 1 Center for Nanochemistry (CNC), Beijing Science and Engineering Center for Nanocarbons. Beijing National Laboratory for Molecular Sciences, College of Chemistry and Molecular Engineering, Academy for Advanced Interdisciplinary Studies, Peking University, Beijing 100871, People’s Republic of China 2 Department of Materials Science and NanoEngineering, Department of Chemistry, and the Smalley Institute for Nanoscale Science and Technology, Rice University, Houston, Texas, 77005, United States 3 Department of Materials Science and Engineering, College of Engineering, Peking University, Beijing 100871, People’s Republic of China ABSTRACT: Grain boundaries (GBs) of hexagonal boron nitride (h-BN) grown on Cu (111) were investigated by scanning tunneling microscopy/spectroscopy (STM/STS). The first experimental evidence of the GBs composed of square-octagon pairs (4|8 GBs) was given, together with those containing pentagon-heptagon pairs (5|7 GBs). Two types of GBs were found to exhibit significantly different electronic properties, where the band gap of the 5|7 GB was dramatically decreased as compared with that of the 4|8 GB, consistent with our obtained result from density functional theory (DFT) calculations. Moreover, the present work may provide a possibility of tuning the inert electronic property of h-BN via grain boundary engineering. 1

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KEYWORDS: boron nitride, chemical vapor deposition, STM/STS, grain boundary, electronic properties

Atomically thin h-BN, a typical sp2-hybridized two dimensional material, has great potential for numerous applications ranging from far-ultraviolet light emitting devices,1 oxidation-resistant coatings,2, 3

to transparent electronics4,

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and dielectric layers6, 7, owing to its unique band structure, chemical

inertness, good transparency, as well as atomically flat surface. Moreover, its combination with graphene to form in-plane8-11 or vertically stacked heterostructures12-15 has stimulated a growing interest mainly due to their potentials in developing novel functional graphene-based devices.16-18 To fully realize the application potentials of h-BN, chemical vapor deposition (CVD) routes have been widely adapted for sample synthesis, because of its ease of operation and scalability.19 Previous studies indicated that h-BN films produced by either low pressure or atmospheric pressure CVD methods were usually of polycrystalline nature with the presence of ubiquitous GBs.20, 21 And the GBs, composed of an array of dislocations, usually degrade the device performances of as-synthesis materials. Recent studies of graphene, a structure analogue to h-BN, have also demonstrated novel properties of GBs related to electronic,22, 23 magnetic,24 and mechanical25 aspects. And special attentions have been paid to the atomic structures and the peculiar properties of graphene’s GBs.26-28 In contrast, the investigations of the GBs/dislocations in h-BN are still in its infancy. The dislocation structures in h-BN were initially predicted by theoretical calculations, where the square-octagon pair (4|8) was revealed to possess lower energy than that of pentagon-heptagon pair (5|7).29 This can be explained by the fact that 5|7 contains unfavorable homo-elemental bonds (either BB or N-N), and that the out-of-plane buckling in monolayer h-BN greatly release the strain energy of 4|8.

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However, such theoretically stable 4|8 has so far not been experimentally observed, although a latest study by Zettl et al. reported the transmission electron microscopy (TEM) observations of GBs composed of 5|7s in CVD grown h-BN films.30 More intriguingly, theoretical calculations predicted that the existence of GBs could modify the local electronic properties of h-BN.29 The band gap can be strongly decreased relying on their atomic arrangements, which could possibly create optical peaks in the visible light range, or stimulate potential applications in h-BN electronics. In this regard, it is imperative to discover diversiform GB structures of h-BN for further property explorations. In this paper, we report the first-time experimental observation of GB composed of 4|8s (4|8 GB) on our CVD-grown monolayer h-BN films. The CVD synthesis of h-BN films was performed under ultrahigh vacuum (UHV) conditions on the Cu (111) substrate. Subsequent in-situ characterizations using atomic-resolved STM/STS allowed us to probe the intrinsic morphologies and electronic properties of 5|7 and 4|8 GBs. Further DFT calculations regarding the local density of states (LDOS) projected to the GBs enabled us to achieve a deeper understanding of the unique defect states of h-BN. RESULTS AND DISCUSSION A schematic diagram of h-BN growth on Cu (111) under UHV conditions is illustrated in Figure 1a and further described in Supporting Information Figure S1. The growth was performed in an UHV chamber with a base pressure of 1×10−10 mbar. The Cu (111) surface (MaTeck GmbH, 99.99% purity) was cleaned by repeated argon-ion sputtering at p(Ar) = 5 ×10−6 mbar and 16 µA ion current, followed by annealing in the vacuum at ∼1000 K. Herein, the ammonia borane (BN3NH3) molecule was used as precursor, which was kept in a steel cylinder and heated by a wrapped heating belt. At about 400K heating, ammonia borane usually decomposed into borazine (BHNH)3, hydrogen (H2), and polyiminoborane (BH2NH2)n.31 The vaporized borazine ingredient was then introduced into the UHV 3


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chamber with its flow rate regulated through a leak valve. After absorbed on the hot Cu (111) surface, the borazine reactants decomposed into B and N fragments, which migrated on the hot Cu (111) substrate and then evolved into h-BN films (Figure 1a). After synthesis, the h-BN sample was directly transferred into STM/STS chamber for atomic-scale characterizations. The formation of h-BN films were also confirmed by scanning electron microscopy (SEM), Raman spectroscopy, and X-ray photoemission spectroscopy (XPS), after transferring the sample out of the vacuum system (Figures S2). The as-achieved h-BN film was a continuous monolayer composed of differently rotated domains, which was further convinced by atomic force microscope (AFM) height profile measurements after transferred onto a 280 nm SiO2/Si substrate (see Supporting Information Figure S2e). A two-step growth method including low temperature absorption and growth followed with high temperature annealing was selected in this work, with the purpose of increasing the nucleation density of h-BN films. By exposing the 600K-heated substrate to 5×10-6 mbar gaseous precursors for 5 minutes, highly polycrystalline h-BN films were obtained with an average grain size of ~ 1 × 1 nm2 (Figure 1b). Within each tiny grain, periodic lattice structures with the same lattice constant of ~ 0.25 nm were observed to suggest the formation of h-BN. With increased thermal annealing time, the grain sizes of the polycrystalline h-BN films were enlarged significantly with the sacrifice of small grains, as observed by STM in Figures 1c-e. Figure 1e shows a small grain (marked by red circle) which is in a process of being swallowed by the surrounding grains, as also schematically illustrated by the inset model. This phenomenon can be explained by the Ostwald ripening of h-BN grains, which is usually mediated by dislocation migration.32 Such a thermodynamically favored process enables the decrease of the total GB areas and hence the increase of grain size in polycrystalline materials. Similar to the graphene scenario, the dislocation migration in h-BN was proposed to be realized through Stone-Wales bond rotating process by theoretical calculations.33 The activation energy for such bond rotation in freestanding h-BN was calculated to be 4.4 - 5.4 eV, depending on the detailed dislocation structures.34 Although the 4


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activation energy seems too high for such a bond rotation process to occur, the heated copper substrate may act as a catalyst to significantly lower the activation barrier, as evidenced by a recent study on graphene/Cu (111).27 Therein, the post-annealing process was also introduced to greatly enlarge the grain size of graphene, which possessed an even higher activation barrier of 6-10 eV.35 Based on the delicate control over the growth and annealing process, we are able to obtain diverse GB structures for further studies. Meanwhile, a broad distribution of relative rotation angles between hBN and Cu (111) was observed, with a dominant angle around 0° (Figure 1f). This indicates that, to some extent, the non-rotated or slightly rotated stacking of h-BN on Cu (111) should be energetically more favorable than that of greatly rotated. This stacking preference has been explained by DFT calculations, which show that the non-rotated h-BN grains on Cu (111) usually present higher binding energies than that of the rotated ones.36 From the viewpoint of h-BN synthesis, the preferred stacking registry may facilitate the growth of aligned h-BN grains and even single-crystalline monolayers through a delicate control of the CVD process. Rotations of h-BN grains with regard to Cu (111) usually result in different moiré superstructures, which provide a convenient way to recognize various grains in polycrystalline h-BN films with the aid of STM. The different moiré periods (D) are correlated with the rotation angles (θ) between h-BN and Cu (111) lattices by the following equation,

D=

(1 + δ )a 2(1 + δ )(1 − cos θ ) + δ 2

where a is the lattice constant of h-BN (~ 0.25 nm), and ߜ is the lattice mismatch (~ 2.0 %) between hBN and Cu (111).37 As a reference, the representative STM images of different moiré superstructures are shown in Supporting Information Figure S3.

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In polycrystalline films, diverse moiré superstructures can be stitched together with the formation of abundant GBs in between (green dashed lines in Figures 2a, b). GBs are usually viewed as an array of dislocation cores,26,

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as schematically illustrated in Figure 2c. In general, different GBs can be

characterized by the tilt angle (λ) of adjacent grains (i.e., relative lattice misorientation of adjacent grains), where a high λ value usually corresponds to a high dislocation density.39 To identify the atomic structures of h-BN GBs, atomic-scale STM studies have been carried out, with representative STM images presented in Figures 2d-f. In Figure 2d, two grains showing moiré patterns with periodicities of ~ 2.0 nm (upper left) and ~ 3.0 nm (lower right) are patched with rotation angles of θ= 7.2° and 4.7° relative to Cu (111), respectively. The tilt angle (λ) of the two grains can therefore be calculated to be ~ 2.5°. Even with a tilt angle, the h-BN lattice is stitched well across the GBs, as evidenced by corresponding zoom-in STM image in Figure 2g. Similar cases are presented in Figures 2e, h and Figures 2f, i, with tilt angles measured of 3.4° and 7.9°, respectively. It is noted that these GBs possess quite small tilt angles and hence quite low densities of dislocation cores, making it difficult to identify the detailed dislocation structures using STM (shown in Supporting Information Figure S4). When we turned our attention to the GBs evolved from neighboring h-BN grains with high tilt angles of ~ 24° and 32°, we caught both 4|8 and 5|7 like GBs as clearly shown in Figures 3a and b, respectively. For better understanding, the atomic models of these GBs are superimposed on the enlarged STM images in Figures 3c, d. The GB structures in h-BN were tentatively defined by the STM image and coincidence site lattice (CSL) theory.40 Following the CSL theory, the bisector 5|7 GB can be obtained by rotating two grains by 32.2°, which matches well with the experimental tilt angle (~32°) (determined from FFT analysis, inset in Figure 3b). On the other hand, the observed 4|8 GB in Figure 3a should correspond to 0° 6


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bisector GB by CSL theory. The large deviation between the theoretical GB tilt angle (0°) and the experimental one (~24°) suggests that, at a large scale, the 4|8s should be embedded in a sinuous GB structure.26,

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This deviation between the experimental tilt angle and the theoretical one would

inevitably introduce lattice distortion near the grain boundary, which is clearly observed near 4|8 GBs (within one nanometer length scale) in Figure 3a. On the other hand, the isolated 4|8 dislocation should possess higher strain energy on a planar substrate than that of freestanding, since the underling substrate may restrict its out-of-plane buckling.29 In the observed 4|8 GB structures, however, the strain energy can be significantly released with compressive 4 member rings and tensile 8 member rings located next to each other. It should be emphasized that, this work presents the first STM observation of the GB structures of h-BN. In comparison with graphene, the specific configurations of GBs in h-BN are more complicated due to their binary composition nature. STM is not capable of recognizing B or N atoms, and hence detailed elemental identity of h-BN GBs is thus far not clear. From our experimental observation and theoretical consideration, the possible atomic configurations for specific GB topologies in h-BN are sketched in Figures 3e, f. For the 4|8 GB, there exist two possible atomic models, representing either hetero-elemental (type I) or homo-elemental (type II) bonding structures as shown in Figure 3e. While for the 5|7 GB, three types of atomic arrangements can be proposed, the alternating B- and N-rich 5|7s with B-B and N-N bonds shared by 5 and 7 rings (type III), the N-rich 5|7s (type IV) and the B-rich 5|7s (type V), as shown in Figure 3f. To further unravel the elemental identities of the two types of GBs, LDOS measurements by STS combined with DFT calculations were performed. STS measurements on the perfect h-BN region reveal a band gap of ~ 5 eV (black line in Figure 4a), which is consistent with the reported electronic property of h-BN/Cu (111).42, 43, 44 The STS spectra shown in Figure 4a are arithmetic average of several spectra

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obtained along the 4|8 and 5|7 GBs (shown in Supporting Information Figure S5), respectively. Interestingly, the STS spectrum of the 4|8 GB depicts a slightly smaller band gap of ~ 4.3 eV (blue line in Figure 4a). This value is close to the data (~ 4.2 eV by DFT calculations) deduced from the simulated LDOS of type I structure (blue line in Figure 4b) with the predominant peaks introduced near the band edges. Regarding the type II structure with homo-elemental bonds, the corresponding LDOS shows deep-in-gap states with greatly reduced band gap of ~ 2.5 eV (pink line in Figure 4c), unmatching the observed dI/dV results. Consequently, the 4|8-GB is inferred to possess a type I atomic arrangement with hetero-elemental bonds. In contrast, the STS spectrum of 5|7 GB (red line in Figure 4a) displays several in-gap peaks, in accompany with a decreased band gap of ~ 3.4 eV. The in-gap feature is consistent with the simulated LDOS results of type III structure (four in-gap peaks and a band gap of ~ 3.2 eV, red line in Figure 4b). The conformity of the band gap values (from STS measurement and DFT calculation) is good but somehow accidental. The band gap of h-BN/Cu (111) system should be smaller than that of freestanding h-BN due to the weak adlayer-substrate interaction, as proved by related theoretical calculations43 and the STS measurements. On the other hand, our DFT calculations were performed on freestanding h-BN, and DFT are known to underestimate the band gap values. The theoretical in gap states (marked as 1-4 in Figure 4b) are mainly contributed by the homo-elemental bonds of B-B or N-N, as proved by further DFT calculations of the partial charge density distributions (Figure 4d (1)-(4), accordingly). In addition, the LDOS for other two 5|7 GBs show only two (type IV, green line in Figure 4c) or three (type V, orange line in Figure 4c) in-gap states, respectively, which cannot fit well with our experimental data by STS (Figure 4a). Notably, in the spatially resolved STS spectra along the 5|7 GB, the peak intensities vary with different acquisitions along the GB (Supporting Information Figure S5c, d), which is possibly mediated by the detailed GB structure with alternate homo-elemental bonds (Figure 4d, left panel) and their local charge density distributions (Figure 4d, (1)-(4)). Furthermore, in corresponding STM 8


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observations of the 5|7 GB, the in-gap electronic states from homo-elemental N-N bonds (peak 2 in Figure 4d) are incorporated into the STM imaging, leading to the bright line contrast decorated with pairs of bright protrusions in detail (see Supporting Information Figure S6 for more detailed discussions). Briefly, the detailed configuration of the 5|7 GB is thus assigned to type III structure based on the spatially averaged STS spectra and their comparison with DFT calculations. It is worth noting that, the decreased band gaps at GB areas were also reported in molybdenum disulfide (MoS2),45, 46 where an increased electrical conductivity was detected along the GBs featured with in-gap states.47 This indicates a unique pathway for creating GBs-based electronic devices in both MoS2 and h-BN. In summary, we report systematic STM/STS studies on the GBs of h-BN towards an understanding of their atomic configurations and electronic properties. We give the first experimental evidence of the theoretically-predicted 4|8 GBs in h-BN. The novel findings are the remarkably different electronic properties of the 4|8 and 5|7 GBs based on the combined analysis of STS measurement and DFT calculations. This work offers a deeper insight into the grain boundary structures formed in CVD-grown h-BN films, as well as a possibility of tuning the inert electronic property of h-BN via grain boundary engineering. Methods DFT calculations: Our density functional theory (DFT) calculations were performed with the Perdew– Burke–Ernzerhof parametrization (PBE)48 of the generalized gradient approximation (GGA) and projector-augmented wave (PAW) potentials,49, 50 as implemented in the Vienna Ab-initio Simulation Package (VASP).51, 52 Adopting periodic boundary condition, our models in a rectangular simulation cells contain two antiparallel grain boundaries (GBs) of opposite tilts, each consisting of equally spaced dislocations cores. The lattice constant in the direction perpendicular to the GB was about 6.5 nm, while 9


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the vacuum layer thickness is set to be larger than 10 Å. These settings were chosen to keep the elastic interaction between neighboring GBs and the spurious interaction between images negligible, respectively. All structures were fully relaxed using the plane-wave-based total energy minimization53 with maximum force convergence criterion of 0.01 eV/Å. All the DFT calculations were performed on freestanding h-BN. STM/STS measurements: Omicron VT-STM/STS system was used for STM characterization and STS measurements. All of the STM data were captured under a constant current mode with the sample hold at room temperature. The STS local differential conductance (dI/dV) spectra were measured at 77 K by recording the output of a lock-in system with the manually disabled feedback loop. A modulation signal of 5 mV, 932 Hz was selected under a tunneling condition of 3 V, 20 pA.

ASSOCIATED CONTENT Supporting Information. Experimental setups, sample characterizations, STM images for moiré superstructures, more experimental results of the spatially resolved dI/dV spectra along the GBs. This material is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author [email protected] [email protected] [email protected] ACKNOWLEDGMENT

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This work was financially supported by the National Natural Science Foundation of China (Grants 51290272, 51222201, 11304053, 51121091, 51472008), the Ministry of Science and Technology of China (Grants, 2011CB921903, 2012CB921404, 2013CB932603, 2011CB933003, 2012CB933404) and the Beijing Municipal Science and Technology Planning Project (Z141103004414103). The work at Rice was supported by the Department of Energy, BES Grant No. ER46598, and the US Army Research Office MURI Grant No. W911NF-11-1-0362. The computations were performed at the Data Analysis and Visualization Cyberinfrastructure funded by NSF under Grant OCI-0959097.

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17. Britnell, L.; Gorbachev, R. V.; Jalil, R.; Belle, B. D.; Schedin, F.; Mishchenko, A.; Georgiou, T.; Katsnelson, M. I.; Eaves, L.; Morozov, S. V.; Peres, N. M. R.; Leist, J.; Geim, A. K.; Novoselov, K. S.; Ponomarenko, L. A. Science 2012, 335 (6071), 947-950. 18. Levendorf, M. P.; Kim, C.-J.; Brown, L.; Huang, P. Y.; Havener, R. W.; Muller, D. A.; Park, J. Nature 2012, 488 (7413), 627-632. 19. Li, X. S.; Cai, W. W.; An, J. H.; Kim, S.; Nah, J.; Yang, D. X.; Piner, R.; Velamakanni, A.; Jung, I.; Tutuc, E.; Banerjee, S. K.; Colombo, L.; Ruoff, R. S. Science 2009, 324 (5932), 1312-1314. 20. Song, L.; Ci, L. J.; Lu, H.; Sorokin, P. B.; Jin, C. H.; Ni, J.; Kvashnin, A. G.; Kvashnin, D. G.; Lou, J.; Yakobson, B. I.; Ajayan, P. M. Nano Lett. 2010, 10 (8), 3209-3215. 21. Kim, K. K.; Hsu, A.; Jia, X. T.; Kim, S. M.; Shi, Y. S.; Hofmann, M.; Nezich, D.; Rodriguez-Nieva, J. F.; Dresselhaus, M.; Palacios, T.; Kong, J. Nano Lett. 2012, 12 (1), 161-166. 22. Yazyev, O. V.; Louie, S. G. Nat. Mater. 2010, 9 (10), 806-809. 23. Ma, C. X.; Sun, H. F.; Zhao, Y. L.; Li, B.; Li, Q. X.; Zhao, A. D.; Wang, X. P.; Luo, Y.; Yang, J. L.; Wang, B.; Hou, J. G. Phys. Rev. Lett. 2014, 112 (22). 24. Cervenka, J.; Katsnelson, M. I.; Flipse, C. F. J. Nat. Phys. 2009, 5 (11), 840-844. 25. Grantab, R.; Shenoy, V. B.; Ruoff, R. S. Science 2010, 330 (6006), 946-948. 26. Huang, P. Y.; Ruiz-Vargas, C. S.; van der Zande, A. M.; Whitney, W. S.; Levendorf, M. P.; Kevek, J. W.; Garg, S.; Alden, J. S.; Hustedt, C. J.; Zhu, Y.; Park, J.; McEuen, P. L.; Muller, D. A. Nature 2011, 469 (7330), 389-392. 27. Yang, B.; Xu, H.; Lu, J.; Loh, K. P. J. Am. Chem. Soc. 2014, 136 (34), 12041-12046. 28. Lahiri, J.; Lin, Y.; Bozkurt, P.; Oleynik, I. I.; Batzill, M. Nat. Nanotechnol. 2010, 5 (5), 326-329. 29. Liu, Y. Y.; Zou, X. L.; Yakobson, B. I. Acs Nano 2012, 6 (8), 7053-7058. 30. Gibb, A. L.; Alem, N.; Chen, J.-H.; Erickson, K. J.; Ciston, J.; Gautam, A.; Linck, M.; Zettl, A. J. Am. Chem. Soc. 2013, 135 (18), 6758-6761. 31. Kim, G.; Jang, A. R.; Jeong, H. Y.; Lee, Z.; Kang, D. J.; Shin, H. S. Nano Lett. 2013, 13 (4), 18341839. 32. Kurasch, S.; Kotakoski, J.; Lehtinen, O.; Skákalová, V.; Smet, J.; Krill, C. E.; Krasheninnikov, A. V.; Kaiser, U. Nano Lett. 2012, 12 (6), 3168-3173. 33. Yakobson, B. I. Appl. Phys. Lett. 1998, 72 (8), 918-920. 34. Zou, X.; Liu, M.; Shi, Z.; Yakobson, B. I. Nano Lett. 2015, 15 (5), 3495–3500. 35. Banhart, F.; Kotakoski, J.; Krasheninnikov, A. V. Acs Nano 2011, 5 (1), 26-41. 36. Song, X.; Gao, J.; Nie, Y.; Gao, T.; Sun, J.; Ma, D.; Li, Q.; Chen, Y.; Jin, C.; Bachmatiuk, A.; Rümmeli, M. R.; Ding, F.; Zhang, Y.; Liu, Z. Nano Res. DOI 10.1007/s12274-015-0816-9. 37. Joshi, S.; Ecija, D.; Koitz, R.; Iannuzzi, M.; Seitsonen, A. P.; Hutter, J.; Sachdev, H.; Vijayaraghavan, S.; Bischoff, F.; Seufert, K.; Barth, J. V.; Auwärter, W. Nano Lett. 2012, 12 (11), 58215828. 38. Yazyev, O. V.; Chen, Y. P. Nat. Nanotechnol. 2014, 9 (10), 755-767. 39. Xu, Z. W.; Li, H.; Fujisawa, K.; Kim, Y. A.; Endo, M.; Ding, F. Nanoscale 2012, 4 (1), 130-136. 40. Carlsson, J. M.; Ghiringhelli, L. M.; Fasolino, A. Phys. Rev. B 2011, 84 (16), 165423. 41. Zhang, Z. H.; Yang, Y.; Xu, F. B.; Wang, L. Q.; Yakobson, B. I. Adv. Funct. Mater. 2015, 25 (3), 367-373. 42. Hwang, B.; Kwon, J.; Lee, M.; Lim, S. J.; Jeon, S.; Kim, S.; Ham, U.; Song, Y. J.; Kuk, Y. Curr. Appl. Phys. 2013, 13 (7), 1365-1369. 43. Laskowski, R.; Blaha, P.; Schwarz, K. Phys. Rev. B 2008, 78, 045409. 44. Koitz, R.; Seitsonen, A. P.; Iannuzzi, M.; Hutter, J. Nanoscale 2013, 5 (12), 5589-5595. 45. Huang, Y. L.; Chen, Y.; Zhang, W.; Quek, S. Y.; Chen, C.-H.; Li, L.-J.; Hsu, W.-T.; Chang, W.-H.; Zheng, Y. J.; Chen, W.; Wee, A. T. S. Nat. Commun. 2015, 6, 6298. 46. Zou, X.; Liu, M.; Yakobson, B. I. Nano Lett. 2013, 13 (1), 253–258. 12


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47. van der Zande, A. M.; Huang, P. Y.; Chenet, D. A.; Berkelbach, T. C.; You, Y. M.; Lee, G. H.; Heinz, T. F.; Reichman, D. R.; Muller, D. A.; Hone, J. C. Nat. Mater. 2013, 12 (6), 554-561. 48. Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77 (18), 3865-3868. 49. Kresse, G.; Joubert, D. Phys. Rev. B 1999, 59 (3), 1758-1775. 50. Blochl, P. E. Phys. Rev. B 1994, 50 (24), 17953-17979. 51. Kresse, G.; Furthmuller, J. Comp. Mater. Sci. 1996, 6 (1), 15-50. 52. Kresse, G.; Furthmuller, J. Phys. Rev. B 1996, 54 (16), 11169-11186. 53. Ihm, J.; Zunger, A.; Cohen, M. L. J. Phys. C Solid. State. 1979, 12 (21), 4409-4422.

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Figure 1. (a) Schematic diagram of the h-BN CVD growth process. (b-e) Representative STM images showing the morphological evolution of h-BN films during the growth and annealing process. All the hBN films were synthesized by exposing 600K-heated Cu (111) to 5×10-6 mbar gaseous precursors for 5 min (b), followed by prolonged annealing at 1000 K from 1h to 6h, giving rise to increased grain sizes and improved film quality (c-e). The inset in (e) is schematic of the small grain swallowed by the surrounding grain through GBs migration. (Scanning conditions: (b) VT = - 0.002 V, IT = 1.095 nA; (c) VT = - 0.008 V, IT = 7.136 nA; (d) VT = - 0.002 V, IT = 4.574 nA; (e) VT = - 0.006 V, IT = 1.061 nA.) (f) Statistic histogram of the relative rotation between h-BN and Cu (111) by calculating the area ratio of ~120 grains.

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Figure 2. (a) STM image showing the coexistence of different moiré superstructures and GBs (as distinguished by green dashed lines). (b) Schematic illustration of GBs formation at the linking edge. (c) Atomic model of the grain boundary with a tilt angle of ~ 9°. (d, e, f) STM images of neighboring grains with ~ 2.5°, 3.4°, and 7.9° tilt angles, respectively. (g, h, i) Magnified views of the GBs in (d, e, f). (Scanning conditions: (a) VT = - 0.002 V, IT = 7.136 nA; (d, g) VT = - 0.002 V, IT = 11.861nA; (e, h) VT = - 0.002 V, IT = 17.373nA; (f, i) VT = - 0.003 V, IT = 17.367nA.)

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Figure 3. (a) High-resolution STM image of the 4|8 GB (inset: FFT showing a tilt angle of ~24°); (b) High-resolution STM image of the 5|7 GB (inset: FFT image exhibiting a tilt angle of ~32°); (c-d) Magnified STM images of (a-b) with the probable structural models superimposed, respectively. (Scanning conditions: (a, c) VT = - 0.005 V, IT = 2.423 nA; (b, d) VT = - 0.009 V, IT = 2.665 nA.) (e, f) Possible atomic configurations of B and N atoms in 4|8 and 5|7 GBs, respectively (pink and blue spheres represent B and N atoms, respectively).

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Figure 4. (a, b) Averaged dI/dV spectra and simulated LDOS of the 4|8 and 5|7 GBs, respectively, using the data from perfect h-BN as reference. (c) Simulated LDOS of other unmatched GBs for comparison. (d) Partial charge density distributions for the four in-gap states of 5|7 GB (type III, marked with (1)-(4)).

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Grain Boundary Structures and Electronic Properties of Hexagonal

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