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Structural and electronic properties of interfaces in graphene and hexagonal boron nitride lateral heterostructures Junfeng Zhang, Weiyu Xie, Xiaohong Xu, Shengbai Zhang, and Jijun Zhao Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.6b01764 • Publication Date (Web): 05 Jul 2016 Downloaded from http://pubs.acs.org on July 7, 2016

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Chemistry of Materials

Structural and electronic properties of interfaces in graphene and hexagonal boron nitride lateral heterostructures Junfeng Zhang1, Weiyu Xie2, Xiaohong Xu1*, Shengbai Zhang2, Jijun Zhao3,4* 1

Key Laboratory of Magnetic Molecules and Magnetic Information Materials of Ministry of Education, Shanxi Normal University, Linfen, 041004, China 2

Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, Troy, NY 12180, USA

3

Key Laboratory of Materials Modification by Laser, Ion and Electron Beams (Dalian University of Technology), Ministry of Education, Dalian 116024, China 4

Beijing Computational Science Research Center, Beijing 100089, China

ABSTRACT: The in-plane heterostructures composed of graphene and hexagonal boron nitride (G/BN), as the first kind of two-dimensional (2D) metal/semiconductor heterostructures of one-atom thickness, are attractive for both fundamental low-dimensional physics and nanoscale devices because of the tailorable electronic properties. The atomic structures and electronic properties of interfaces in lateral G/BN heterostructures are investigated by first-principles calculations. The symmetric armchair (AC) interfaces have similar formation energy but larger band gap compared with the nonsymmetric ones. G/BN heterostructures with zigzag (ZZ) type interfaces constructed under the guide of Clar’s rule are found to possess lower formation energy than those with abrupt interface and open a finite band gap. In addition to the zigzag and armchair interfaces, other misorientated interfaces with pentagon and heptagon rings are also stable with low formation energies of 4.4~6.8 eV/nm. These theoretical results are important to clarify the correlation between atomic structures and electronic properties of in-plane G/BN heterostructures and establish a fundamental picture for further theoretical studies and device design.

1. Introduction As the first fabricated monolayer two dimensional (2D) material, graphene possesses peculiar electronic properties and become focus of intensive studies during the past decade 1. However, many potential device applications are hindered by the semimetal (zero-gap) nature of graphene 2 . Substituting B and N atoms into the honeycomb lattice of graphene can modify the electronic properties with controllable band gap, and transform graphene from intrinsic semimetal to n- or p- type semiconductors 3, 4. The BCN hybrid systems with separated h-BN and C phases are thermodynamically stable and have been fabricated in experiment 5. Recently, there is a growing trend to directly merge graphene and h-BN into in-plane graphene/h-BN (G/BN) heterostructures with well controlled shape and size of domains 5-17. Using a two-step chemical vapor deposition (CVD) method, Ajayan and coworkers 5 firstly synthesized the large-scale monolayer h-BNC sheets, consisting of hBN and graphene domains with tunable compositions between pure h-BN to pure graphene. Levendorf 6 proposed a “patterned regrowth” method that allows for spatially controlled synthesis of lateral heterostructures by graphene and h-BN, in which the size and shape of graphene and h-BN domains are controllable. Soon later, several groups fabricated in-plane G/BN heterostructures

and characterized them using various experimental means such as scanning electron microscope (SEM) 7-9, 11, scanning tunneling microscope (STM) 7, 8, 11, atomic force microscope (AFM) 10, 11, Raman 10, X-ray photoelectron spectroscopy (XPS) 8, DUV-via-NIR hyperspectral microscope 9, transmission electron microscope (TEM) 9, 11, 18, nano-Auger electron spectroscopy (AES) 7. It is noteworthy that G/BN heterostructures have been recently fabricated on a wide-band-gap semiconductor SiC substrate, which makes the direct application easier 19. Parallel to experiments, extensive theoretical calculations using density functional theory (DFT) have been performed to explore the electronic 14, 20-27, transport 28, 29, magnetic 22, thermal 30, and optoelectronic 31 properties of in-plane G/BN hybrid systems. It was predicted that different interfaces in G/BN heterostructures possess comparable thermal stability 5, 24 but distinct electronic properties. For example, a band gap is opened at the armchair (AC) interfaces 21, 23, in contrast to the metallic zigzag (ZZ) ones 20, 21, 23, 24. Meanwhile, the thermal 30 and electronic 28, 29 transport behaviors of these heterostructures also strongly rely on the interfacial type. For the polycrystalline monolayer materials of pure graphene or h-BN, misorientation angles between neighboring domains and consequently the existence of defective rings (such as pentagons and heptagons) on the grain

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boundary (GB) are almost inevitable 32-37, which can significantly affect their electronic and transport properties, e.g., opening an electronic or transport gap in graphene GB 38, 39. In experimental fabrication of in-plane G/BN heterostructures, it was observed that h-BN domain starts nucleation from the edge of graphene domain 6, 7, 9, while nucleation of graphene can be either at the edge of h-BN domain 8, 10 or away from h-BN flakes 10. Both the atomically sharp interfaces of ZZ or AC type 7, 8 and the defective interfaces 14 have been observed. Similar to the case of graphene or h-BN GBs, other types of interfaces with misorientation angle and defective rings are expected as a natural consequence of various ways of nucleation growth during experimental fabrication 6-10. All these aforementioned progresses open new opportunities in integrating 2D monolayer devices with precisely tailored physical properties. However, so far the theoretical studies considered the G/BN heterostructures with pure ZZ and AC interfaces only, while the possible existence of defective rings has been neglected. It is crucial to elucidate the interplay between interface structures and electronic properties. In this paper, we constructed a series of structural models for G/BN interfaces of different misorientation angles and defective rings. The detailed site occupations of B, N and C atoms on the interface have been investigated to elucidate the stability and electronic properties of lateral G/BN heterostructures. Our results not only have explained some existing experimental observations, but also would serve as useful guideline for future design of 2D materials and devices using lateral G/BN heterostructures. 2. Computational methods The atomic structures and electronic properties of the in-plane interfaces in G/BN heterostructures were computed using DFT and projector-augmented wave method (PAW) 40, as implemented in the Vienna ab initio simulation package (VASP) 41, 42. The Perdew-Burke-Ernzerhof (PBE) 43 functional was used to describe the exchangecorrelation interactions and the plane-wave basis was expanded up to a cutoff energy of 550 eV. A series of 2D periodic supercells were used with individual G/BN layers separated by a vacuum space of 2 nm thickness. To avoid the interaction between adjacent interfaces resulted from the periodic boundary condition, the in-plane distance perpendicular to the interfaces (which is half of the supercell length in x direction) was set to be about 2 nm. The 2D Brillouin zones were sampled by a series of k point grids with a constant separation of 0.015 Å-1. The inplane atomic coordinates were fully relaxed until the forces on the atoms are less than 0.01 eV/Å. 3. Results and discussion 3.1 Atomic structures, formation energies and stability

Figure 1. (a) Schematic diagram of the 2D supercell used in this calculation. The solid line stand for the ZZ direction and  is the misorientation angle between h-BN and graphene domains. (b) G/BN heterostructure with AC type interface. (c) Abrupt pure ZZ type interface. (d) Pure ZZ interface constructed with Clar’s rule. (e) AC-dominated interface with misorientation angle 21.8°. (f) ZZ-dominated interface with misorientation angle 38.2°.

The lateral G/BN heterostructure supercell is constructed by merging a half h-BN domain and a half graphene domain into one supercell, as shown in Figure 1a. The lattice parameters of the G/BN hybrid system are adapted as the graphene’s values, since the lattice mismatch between honeycomb lattices of graphene and h-BN is only about 1.7%. Our test calculations show that fully relaxation of lattice parameters would only systematically increase the formation energy of an interface by about 0.4 eV/nm but has little impact the relative stability and electronic properties of these interfaces. Inside the supercell, two domains may have different orientations, which can be labeled by a misorientation angle () measured from the change of ZZ direction from h-BN domain to graphene domain (Figure 1a). In the cases of =0° and 60°, the interfaces become pure AC and ZZ types, respectively


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(see Figure 1b and 1c). Between these two limits (0° 2.13 nm. Actually, such kinds of substitution has been found in STM measurement 8, in which the defective rings and atomic permeation can be observed at the G/BN interface region. Therefore, we can conclude that Clar’s rule is an effective guidance in determining the stable atomic structure of 1D interface in lateral G/BN heterostructures. For G/BN with AC interface, the Clar’s rule is not applicable because all carbon atoms are already well saturated by the C-B or C-N bonds (see Figure 1b). However, according to whether one interface is the mirror of another one in a supercell or not, the AC interfaces can be categorized into symmetric and non-symmetric types, as shown in the insets of Figure 3. Both symmetric and nonsymmetric AC interfaces have Eform ranging from 2.35 to 1.88 eV/nm with supercell length from 1.48 to 9.84 nm, consistent with the value ~2.2 eV/nm 21 from previous calculation. Figure 3 also suggested the comparable thermodynamic stability because of the small difference in Eform (~0.02 eV/nm) between the symmetric and nonsymmetric AC interfaces. In the experimentally synthesized G/BN, ZZ and AC interfaces are usually dominant since graphene (or h-BN)

prefer grows at the edges of pre-grown h-BN (or graphene) flakes 7, 8. However, it was also observed that graphene starts nucleation away from the h-BN flakes 8, which would probably lead to the defective rings 14 or misorientated interfaces. For the misorientated interfaces with pentagonal and heptagonal rings, we considered six misorientation angles: 9.4°, 13.2°, 21.8°, 32.2°, 38.2°, 42.1° (see Figure 1e and Figure 1f as two representatives). Here, only pentagon and heptagon have been considered in this work, other defective rings like quadrilaterals, octagons, or nonagons were ruled out because they usually have higher formation energy 35 and make the interface structure more complicated. With aid of the Clar’s rule, the unsaturated electrons in C atoms can be effectively diminished by B/N substitutions. For a given misorientated interface, there are different ways of substitutions to obtain the Clar’s interface. Figure 4 presents five possible Clar’s interfaces for G/BN with the same misorientation angle of 32.2º. All of them obey the Clar’s rule, but their Eform range from 4.42 to 5.26 eV/nm. A comparison of these isomeric interfaces further argues that one must select fewer C atoms to substitute in order to achieve thermodynamically more favorable Clar’s interface. Based on this observation, we construct other misorientated interfaces with relatively high stability and summarize their Eform in Table 1. Interestingly, the Eform of G/BN interfaces are comparable to those of graphene GBs (2.6~7.3 eV/nm) 45, 52 . Compared to the AC and ZZ ones, defective interfaces possess higher Eform by ~ 2 eV/nm. Therefore, there is certain probability for the emergence of misorientated interfaces in G/BN hybrid systems that can be observed in


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Table 1. Formation energies (Eform) and band gaps (Eg) of perfect and defective G/ BN heterostructures with graphene ribbon width ~2 nm and different misorientation angles. AC

pZZ

cZZ

9.4°

13.2°

21.8°

32.2°

38.2°

42.1°

Eform (eV/nm)

2.2

2.8

2.9

5.6

5.6

4.7

4.4

5.0

6.8

Eg (eV)

0.43

0.75

--

0.52

0.50

0.59

0.52

0.68

0.48

the metallic 23 and semiconducting interfaces 12, 13 have been observed in the G/BN hybrid monolayer on the Ir(111) substrate. The main difference of them lies in the intercalated Au in the former experiment 23, which may account for the enhanced metallic interfacial states. Compared with previous computational studies 21, 23, 25, 31, cZZ is the first semiconducting ZZ interface for lateral G/BN. Moreover, as plotted in Figure 7a and 7b, the partial projected conductance band minimum (CBM) and valence band maximum (VBM) are only contributed by the

Figure 5. (left) Density of state (DOS) and (right) band structure of G/BN heterostructures with symmetric AC (upper) and non-symmetric AC (lower) interface. future experiment. Moreover, for a given misorientation angle, the theoretical Eform of G/BN interface (for both AC and ZZ) slightly reduces with increasing supercell width (see Figure 2). 3.2 Electronic properties Previous theoretical studies 21, 23, 25, 31 suggested metallic behavior for hybrid G/BN systems with ZZ interface and semiconducting behavior for those with AC interface. For G/BN with AC interfaces (either symmetric or nonsymmetric), semiconducting behavior is also found in the present calculation as shown in Figure 5. For hybrid G/BN system with ~2 nm wide graphene ribbons, a band gap of 0.156 eV for non-symmetric or 0.333 eV for symmetric AC interface is achieved, which is consistent with that of 0.3~0.5 eV calculated for graphene nanoribbon 53, 54. Note that symmetric and non-symmetric AC systems have similar Eform but distinct band gap, which is a consequence of the non-vanishing eigenstates of Dirac fermions in non-symmetric system due to broken symmetry 47. For lateral G/BN heterostructures with ZZ type interface, with aid of the Clar’s rule, all C atoms with nonbonding electrons on cZZ interface are eliminated through B(N) substitution (see Figure 1). In contrast to the metallic pZZ, semiconducting characteristic is found for cZZ with band gap ~0.8 eV determined from electron density of states (DOS) and band structures, as shown in Figure 6a and Figure 7, respectively. Interestingly, both

Figure 6. DOS of lateral G/BN heterostructures with (a) ZZ and misorientated system with (b)  = 21.8° and (c) 38.2°. The solid lines are of the interfaces constructed with the guide of Clar’s rule, and the dotted lines are of the abrupt interfaces. unsaturated carbon atoms of pZZ, leading to the metallic behavior and less stability of pZZ. In contrast, CBM (Figure 7d) and VBM (Figure 7e) states of cZZ are both delocalized in the entire graphene region, suggesting all of the unsaturated electrons have been well eliminated in cZZ. From the projected band structure (Figure 7c and 7f), we can see that both CB and CN interfaces of pZZ are metallic, while the local gap opened at B-rich and N-rich cZZ interfaces are 0.82 eV and 0.8 eV, respectively. Consistently, experimental measurement of STM also demon-



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strated that the electronic characteristic transits gradually from the semi-metallic behavior for graphene to insulating behavior for h-BN, without obvious interface states 12, 13 . We can thus conclude that cZZ is more stable than pZZ from both thermodynamic and experimental points of view.

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heterostructures with embedded graphene nanoribbons. Most importantly, the electronic properties of a G/BN heterostructure rely sensitively on the detailed chemical composition of the interface, leading to new opportunities of tailoring the physical properties of G/BN hybrid materials.

AUTHOR INFORMATION Corresponding Author * Corresponding authors. Email: [email protected] (Jijun Zhao), [email protected] (Xiaohong Xu).

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENT

Figure 7. Partial projected conductance band minimum (CBM), valence band maximum (VBM) and band structure for G/BN heterostructures with pZZ (d-f) and cZZ (gi) ZZ interface. The Fermi energy is set as zero. Figure 6b and 6c display electron DOS of two representative misorientated interfaces (= 21.8° and 38.2°). Similar to cZZ, the misorientated systems with Clar’s interfaces also exhibit finite band gap of 0.44~0.68 eV (Table 1), whereas those non-Clar’s ones are all metallic. Again, such difference between Clar’s and non-Clar’s interfaces indicates that the electronic states of G/BN interface are significantly influenced by the detailed atomic structure and composition. In principle, gap opening and removal of unsaturated electrons are more favorable. The semiconducting feature from scanning tunneling spectroscopic measurements 12, 13 and the transition width of ~0.5 nm from STM observation 12 support the existence of Clar’s interfaces in the experimental samples of Graphene/h-BN heterostructures. Therefore, we argue that all stable G/BN interfaces should be semiconducting as long as the unsaturated atoms on interface are carefully treated. 4. Conclusions To summarize, we have explored the atomic structures and electronic properties of interfaces in G/BN heterostructures. Compared with the non-symmetric AC interfaces, the symmetric ones have comparable stability but larger band gap because of the reserved symmetry. For ZZ type interfaces, Clar’s sextet rule plays a crucial role in lowering the formation energies and eliminating the unsaturated electrons, and opens a finite gap in cZZ. The semiconducting misorientated interfaces constructed under the Clar’s rule are found thermodynamically stable with formation energies close to those of graphene grain boundaries. All these results demonstrate that the guidance of Clar’s rule is necessary for deeply investigating the

Work in China was supported by the National Natural Science Foundation of China (11304191, 11134005, 11574040 and 61434002), the Fundamental Research Funds for the Central Universities of China (DUT16LAB01), and the Natural Science Foundation of Shanxi province (2015021011). WYX was supported by the US-NSF under Award No. 1104786, while SBZ was supported by the US-DOE under Grant No. DESC0002623. The supercomputer time by NERSC under DOE contract No. DE-AC02-05CH11231 and by the CCI at RPI are also acknowledged.

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