Atomic Structure, Electronic Properties, and Reactivity of In-Plane

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Atomic Structure, Electronic Properties and Reactivity of InPlane Heterostructures of Graphene and Hexagonal Boron Nitride Radisav S. Krsmanovic, and Zeljko Sljivancanin J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp501581g • Publication Date (Web): 25 Jun 2014 Downloaded from http://pubs.acs.org on July 3, 2014

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The Journal of Physical Chemistry

Atomic Structure, Electronic Properties and Reactivity of In-Plane Heterostructures of Graphene and Hexagonal Boron Nitride Radisav S. Krsmanovi´c,† and Željko Šljivanˇcanin∗,‡ Faculty of Natural Sciences and Mathematics, University of Montenegro, ME-21000 Podgorica, Montenegro, and Vinˇca Institute of Nuclear Sciences (020), P.O.Box 522, RS-11001 Belgrade, Serbia E-mail: [email protected]

Phone: +381 116442611.

∗ To

whom correspondence should be addressed of Natural Sciences and Mathematics, University of Montenegro, ME-21000 Podgorica, Montenegro ‡ Vinˇ ca Institute of Nuclear Sciences (020), P.O.Box 522, RS-11001 Belgrade, Serbia

† Faculty

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Abstract We applied density functional theory (DFT) to investigate structural and electronic properties, as well as the reactivity of in-plane heterostructures composed of graphene and hexagonal boron nitride (h-BN). The calculations demonstrate a strong tendency of graphene and h-BN to minimize the number of C-N and C-B bonds and thus to segregate into homogeneous domains. A simple bond model, with parameters obtained from DFT calculations, is used to describe trends in the formation energies of the studied heterostructures. We show that the electronic properties of the BN clusters embedded into graphene qualitatively resemble those of graphene antidot lattices. The calculations also reveal that the h-BN monolayer doped with small graphene clusters is a material with the band gap tunable over an energy range of several electron volts, since the band gap values strongly depend on the size of embedded graphene quantum dots. The reactivity of the graphene/h-BN heterostructures is quantified using H atoms as a probe. We found a strong increase of the H binding energy in the heterostructures where localized electronic states appear in the vicinity of the Fermi level. The highest value of 2.31 eV, calculated for the ideal zigzag graphene/h-BN interface, is approximately three times larger compared to the H atom binding energy at an infinite graphene sheet. Keywords: DFT, 2D materials, nanoribbons, quantum dots, edge states, catalysis.

1 Introduction Despite of the remarkable physical properties of graphene, 1–3 its utilization as a key material in post-silicon electronic devices is to large extend hampered by difficulties in converting this two dimensional crystal from a semimetal to a semiconductor. Two the most promising approaches employed to address this issue are graphene cutting into nanoribbons (GNR) 4–7 and its hydrogenation. 8–11 It turns out that the GNRs with nearly perfect edges must be produced in order to preserve high electron mobility of graphene. However, this is still a challenging task even when the cutting-edge experimental techniques for synthesis and manipulation of nanostructured materials were used. On the other hand the controlled graphene functionalization with hydrogen has


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been realized only for graphene sheets supported by transition or noble metals. 10–12 The transfer of hydrogenated graphene to an insulating substrate needed for the majority of the applications in electronic devices is likely to be accompanied with a degradation in the quality of produced hydrogen patterns. A monolayer of hexagonal boron nitride (h-BN) is another two-dimensional material with the honeycomb lattice which recently attracted considerable interest. 13–15 At variance to graphene, composed of two equivalent sublattices of C atoms, the B and N atoms in the h-BN form chemically non-equivalent sublattices, which gives rise to a large band gap of ∼5.5 eV. The same crystal structure shared by graphene and h-BN and similar lattice constants which differ less than 2%, enable combination of graphene and h-BN into variety of the nanostructures with peculiar mechanical and electronic properties. 16 The tuning of the C to BN ratio in these heterostructures is expected to open new routes for tailoring band gaps in graphene based materials in an energy range from 0 to several eV. Due to relatively low reactivity of pure graphene it is mostly utilized as a two dimensional catalytic supports, rather than considered as an active catalyst. 17 Yet, in-plane graphene/h-BN heterostructures could show qualitatively different behaviour since the boundaries between surfaces with different atomic structure and chemical composition are known to be the special catalytic sites with enhanced reactivity. 18 Increased reactivity is usually caused by their peculiar electronic properties. The first experimental realization of in-plane heterostructures of graphene and h-BN, together with their characterization at the atomic scale was reported by Ci et al.. 19 The study indicated tendency of the BN and C to separate into two-dimensional domains which was confirmed by Song et al.. 20 The band-gap engineering of graphene doped with the BN was also investigated applying X-ray photoelectron spectroscopy. 21 The measurements revealed a band-gap opening of 0.6 eV in the graphene films doped with only 6% of the BN, in agreement with theoretical predictions that hybrid structures of graphene and h-BN are predominantly semiconductors. 22,23 Single-layer core/shell structures of graphene and h-BN is another example of two-dimensional heterostructures with the electronic properties which can be tuned by changing their size and geometrical shape, as



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demonstrated in the first-principles study of Cahangirov and Ciraci. 24 A tight-binding study of the electronic properties of graphene quantum dots embedded in the h-BN revealed that the band gaps in these structures could vary in a range from 0.3 to 3 eV, depending on the size of the quantum dots. 25 Recently, Liu et al. adapted concept of two-dimensional epitaxy to grow a single layer, in-plane heterostructure of graphene and h-BN which allows to control the type of the boundaries between two materials. 26 Unlike in free GNRs, produced edges in graphene/h-BN sheets are robust against reconstruction due to formation of the strong C-N and C-B bonds, and thus the graphene/hBN heterostructures are promising candidates for fabrication of the graphene-based nanostructures with stable, ideal armchair and zigzag edges. Even though various two-dimensional graphene/h-BN heterostructures were recently studied combining different experimental and computational methods, 15,19–21,27–30 a detailed description of their physical and chemical properties is still missing. Here, we apply DFT to elucidate the effects of the in-layer coupling between graphene and h-BN on the energetics of formed heterostructures and their electronic properties. We thoroughly investigated occurrence of the edge states confined to the interfaces between graphene and h-BN, the band gap opening in the graphene doped with small BN islands, as well as the electron localization within graphene quantum dots embedded into h-BN monolayer. To the best of our knowledges there are now any reports describing the reactivity of such boundaries within planar graphene/h-BN heterostructures. Therefore, one of the focuses of the present study was to address this issue using as a measure of the local reactivity the H atom binding energies. From DFT calculations we found three-fold increase in the binding energies of H atoms at C sites near zigzag edges of graphene patches coupled to h-BN domains compared to the values calculated for C atoms at perfect graphene sheet. The enhancement in the reactivity is correlates with the edge electronic states, positioned in the vicinity of the Fermi level. The manuscript is organized as follows. In Section 2 we describe the methodology and computational details used in our DFT study. The results of the calculations, combined with the discussion are presented in Section 3. Finally, the summary of the main results, together with concluding


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remarks are provided in Section 4.

2 Computational methods All DFT calculations were performed using the GPAW computer code, 31 based on real space grid implementation of the projector augmented wave (PAW) method. 32,33 The effects of electronic exchange and correlations were described by the Perdew Burke Ernzerhof functional (PBE). 34 The unit cells used for modeling several graphene/h-BN heterostructures and the Monkhorst Pack 35 kpoint meshes employed for the sampling of the corresponding Brillouin zones are listed in Table 1. The calculations were performed with the grid spacing of 0.15 Å, imposing two-dimensional peTable 1: The list of graphene/h-BN heterostructures, description of the corresponding unit cells and the Brillouin zone k-point samplings used in the calculations. heterostructure

No. of atoms per unit cell

k-points

armchair interface zigzag interfaces BN and graphene clusters

56 [Figure 1a] 32 [Figure 1b,c] 96 [Figure 2a, Figure 3a]

2×16 2×16 2×2 2×2

riodic boundary conditions parallel to the honeycomb sheet. The open boundary conditions were used in the direction perpendicular to the surface with 9 Å of vacuum separating the graphene/h-BN layer from the cell boundaries. The relaxation of the atomic positions of all atoms was performed by the BFGS algorithm. 36

3 Results and Discussion Description of the results and the corresponding discussion will start with the subsection 3.1 devoted to the structural properties of studied hetersotructures, and then in subsection 3.2 we will show effect of the atomic structure on the electronic properties. Finally, in subsection 3.3 will be 5 ACS Paragon Plus Environment


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demonstrated that the reactivity of the graphene/h-BN heterostructures is governed by their electronic structure.

3.1 Structural properties of in-plane heterostructures The in-plane structures of graphene and the h-BN considered in this article include their ideal interfaces as well as small clusters of graphene embedded in an infinite layer of h-BN or vice versa. The extended interfaces are relevant for modeling edges in the heterostructures with large graphene and h-BN domains. Small BN clusters in graphene or tiny graphene clusters in h-BN are likely to form when the synthesis of the heterostructures occurs under the C-rich and C-poor conditions, respectively. In addition to a description of the results from DFT calculations we will present a simple bond model which is used to elucidate trends in the stability of studied heterostructures.

3.1.1 Ideal interfaces between graphene and h-BN We limited the investigation of extended boundaries between graphene and h-BN to the armchair and zigzag interfaces since they are thermodynamically the most stable types of the edges which occur in the structures with the honeycomb lattice. The unit cell used in the study of armchair grahene/h-BN interface is depicted in Figure 1(a). According to our calculations the formation of this interface is accompanied with the energy cost of 0.22 eV/Å. We studied two different zigzag interfaces, denoted as zz-A and zz-B, shown in Figure 1(b) and Figure 1(c), respectively. The formation energy of the zz-A interfaces of 0.29 eV/Å is considerably lower than the value of 0.69 eV/Å calculated for the zz-B structure. According to the bond model, 29 the total energy of a planar C-BN heterostructure i can be expressed in terms of the first-neighbour bond energies εx−y (x, y ∈ {C, B, N}), corresponding to the bonds present in the studied structure: i Etot = ∑ nixy εx−y , x,y


(1)

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a) armchair

b) zz−A

c) zz−B

Figure 1: (color online) The atomic structure of (a) armchair, (b) zigzag-A (zz-A) and (c) zigzag-B (zz-B) interfaces of graphene and h-BN. The C, N and B atoms are represented by light gray, blue and orange spheres, respectively. The surface unit cells are marked with dashed lines. where nixy denotes the number of the x-y bonds. The parameters εc−c and εb−n corresponding to the C-C and B-N bonds in graphene/h-BN heterostructures, are determined from DFT calculations of a pure graphene and a pure h-BN monolayer. Since we consider only in-plane heterostructures with the B/N ratio of one, in Eq. 1 only appears the sum of the εc−n and εc−b . Hence these two parameters can be combined together into a single parameter, determined from DFT results for graphene/h-BN interfaces. We have chosen it as a mean value of the results found for armchair and zz-A interfaces, i.e. a a + εc−b ), εc−b,n = 1/4 ∑(εc−n

a ∈ {armchair, zz − A}.

a

This definition reduces Eq. 1 to a simple, three term expression i Etot = nicc εc−c + nibn εb−n + (nicb + nicn ) εc−b,n .


(2)


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The calculated values of the parameters are presented in Table 2. The energy cost to substitute Table 2: The bond energy parameters obtained combining DFT calculations of pure graphene, pure h-BN monolayer, and their interfaces in Figure 1(a,b). The ∆ε is the energy cost of replacing a pair of C −C and B-N bonds with a pair of C-N and C-B bonds. All values are in eV.

εc−c

εb−n

εc−b,n

∆ε

-6.16

-5.88

-5.43

1.19

a pair of C-C and B-N bonds by a pair of C-N and C-B bonds is ∆ε = 2εc−b,n − (εc−c + εb−n ) = 1.19 eV, in an excellent agreement with the result reported in Ref. 29 A large, positive value for ∆ε clearly demonstrates the tendency of graphene and h-BN to minimize the interface region and thus segregate into compact domains. This parameter plays an important role in understanding the stability of two-dimensional heterostructures described in the text below. 3.1.2 Heterostructures with small clusters In this subsection we focus on the graphene/h-BN heterostructures where small domains of one honeycomb crystal are embedded into an infinite layer of the other one. We start with the DFT results obtained for h-BN clusters in graphene. The studied structures, depicted in Figure 2, vary in size from a single BN ring (Figure 2a) to the cluster with twelve BN dimers (Figure 2v). The clusters formation energies E f , which are used to quantify their stability, are defined by standard expression E f = Etot − nc µc − nbn µbn ,

(3)

where Etot is the total energy of a studied heterostructure obtained either from DFT calculations or using Eq. 2. The nc and nbn are the corresponding numbers of C atoms and BN dimers. The µc and

µbn are chemical potentials of a C atom and a BN dimer in ideal graphene and h-BN monolayer, respectively, calculated at T = 0 K. The DFT results for formation energies, calculated per BN dimer, are provided in Table 3. The calculated values clearly indicate a decrease in the formation energy per BN dimer with an increase in the size of the clusters embedded into graphene. The 8 ACS Paragon Plus Environment

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Figure 2: (color online) The atomic structure of BN clusters embedded in graphene. The color scheme of the atoms is the same as in Figure 1. The surface unit cell is marked by dashed lines in panel (a). comparison of the clusters with the same size shows that the lowest formation energies are found in the BN islands with the smallest number of the C − N and C − B bonds. A new type of heterostructures, derived from those in Figure 2 can be constructed if graphene host is replaced by h-BN monolayer, and species from BN clusters substituted by carbon atoms. The obtained structures of small graphene quantum dots embedded in h-BN monolayer, shown in Figure 3, are likely to form if the graphene/h-BN heterostructures are synthesized under the C-poor conditions. Their formation energies (see Table 3) follow the same trend as those of the BN clusters in graphene, i.e. the E f per C atom decreases with an increase in the number of C atoms within clusters. The relative stability of clusters in Figure 2 and Figure 3 found from DFT calculations can be understood applying bond model described by Eq. 2. It is convenient to rewrite Eq. 3 in terms of



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Table 3: The DFT results for formation energies of the clusters presented in Figure 2 and Figure 3. The calculated values for BN and graphene clusters are in eV per BN dimer and eV per C atom, respectively. BN clusters config. Ef (eV/BN) Figure 2a 1.15 Figure 2b 0.94 Figure 2c 0.95 Figure 2d 0.84 Figure 2e 0.88 Figure 2f 0.89 Figure 2g 0.77 Figure 2h 0.84 Figure 2i 0.80 Figure 2j 0.81 Figure 2k 0.80 Figure 2l 0.77 Figure 2m 0.76 Figure 2n 0.72 Figure 2o 0.73 Figure 2p 0.76 Figure 2q 0.78 Figure 2r 0.79 Figure 2s 0.75 Figure 2t 0.78 Figure 2u 0.81 Figure 2v 0.62

graphene clusters config. Ef (eV/C) Figure 3a 0.52 Figure 3b 0.43 Figure 3c 0.43 Figure 3d 0.38 Figure 3e 0.39 Figure 3f 0.40 Figure 3g 0.34 Figure 3h 0.38 Figure 3i 0.36 Figure 3j 0.36 Figure 3k 0.35 Figure 3l 0.34 Figure 3m 0.32 Figure 3n 0.33 Figure 3o 0.34 Figure 3p 0.35 Figure 3q 0.34 Figure 3r 0.35 Figure 3s 0.36 Figure 3t 0.27


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Figure 3: (color online) The atomic structure of graphene clusters embedded in h-BN monolayer. The color scheme of the atoms is the same as in Figure 1. The calculations are preformed with the surface unit cell highlighted in panel (a). the parameter ∆ε and the number of C-N and C-B bonds present in the studied structure: E model = ∆ε (ncb + ncn )/2. f

(4)

The model accurately reproduces DFT results for BN clusters in graphene. However, it turns out that Eq. 4, when applied to graphene clusters embedded in h-BN, overestimates formation energies obtained from DFT calculations. The parameters in Eq. 4 are determined from DFT calculation performed for the interfaces between a semimetal (graphene) and a wide band gap semiconductor (h-BN) and thus can by successfully applied to the BN clusters in graphene. However the electronic properties of small graphene clusters are qualitatively different from those of an infinite graphene layer since the clusters are nanostructures with the band gaps of several electron volts. The small graphene clusters in h-BN are heterostructures composed of two materials with significant band gaps, which can not be accurately modeled with the parameters calculated for the boundaries between a semimetal and a wide band gap semiconductor. To account for these quantum size effects 11 ACS Paragon Plus Environment


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in small graphene clusters embedded in the h-BN we introduce a correction of 0.5 eV per cluster and modeled the formation energies of the structures in Figure 2 and Figure 3 using the following formula: E model = ∆ε (ncb + ncn )/2 − Ec, f where

   0.0 eV, Ec =   0.5 eV,

for BN clusters in graphene

(5)

(6)

for graphene clusters in BN.

The comparison of DFT results with those produced applying Eq. 5 is presented in Figure 4. The formation energies are given in eV per C atom for graphene clusters in h-BN monolayer, or in eV per BN dimer for BN clusters embedded into graphene. The plot clearly demonstrates the ability of the simple bond model to reproduce trends in the cluster formation energies calculated using DFT. Thus the model can be applied to accurately estimate formation energies of any in-plane graphene/h-BN heterostructure with the B/N ratio of one. This includes the structures with the sizes of the domains well beyond those which can be directly calculated by DFT-based methods.

3.2 Electronic properties of in-plane heterostructures 3.2.1 Ideal interfaces between graphene and h-BN Two-dimensional graphene/h-BN interfaces considered in our study are actually periodic arrays of nanoribbons of graphene and h-BN. Since the h-BN is an insulator, the electronic states in the vicinity of the Fermi level either resemble those in GNRs or they represent a new type of the interface states. In the vicinity of the Fermi level the electronic bands of the armchair interface, presented in Figure 5a show similar dispersion near Γ-point as the ones of the free armchair GNRs. For this interface we calculated the band gap of 0.41 eV, by 0.2 eV larger compared to the band gap of the free armchair GNR with the same width. The states near the Fermi level originate exclusive from the π network of the C-2p states.


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1.4 BN in graphene graphene in BN

1.2

Emodel (eV)

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1.0 0.8 0.6 0.4 0.2 0.2

0.4

0.6

0.8 1.0 EDFT (eV)

1.2

1.4

Figure 4: (color online) Comparison of the E f (per C atom or BN dimer) obtained from DFT calculations and using Eq. 5. At variance to the in-plane heterostructure with armchair edges the electronic properties of the zigzag interfaces are qualitatively different from those of the zigzag GNRs. We restricted investigation of the electronic structure of zigzag heterostructures to the zz-A interface, identified from DFT calculations as considerably more favorable than the zz-B structure. Its band structure is depicted in Figure 5b. A weak spin polarization of the states in close proximity of the Fermi level induces magnetic moments at the atoms near the interface. Yet, their values are smaller than 0.1

µB . According to our calculations free zigzag GNRs of the same size are semiconductors with the band gap of 0.45 eV. Closer inspection of the states near the Fermi level reveals that the states from the highest occupied band are located at the C-N edge of the interface. They are composed of the C and B 2p spin majority states, with dominant the C-2p character. The states from the lowest unoccupied band, located on the opposite edge of the graphene strip, are a mixture of the C and N 2p spin minority states. The hybridization of the states at the graphene/h-BN edges results in 13 ACS Paragon Plus Environment


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-3

Figure 5: (color online) The band structure plot of (a) armchair and (b) zigzag graphene/h-BN interfaces depicted in Figure 1a and Figure 1b, respectively. The spin majority and spin minority bands in the right panel are represented by black and brown lines, respectively. the broadening of the valence and conduction bands and thus reduced band gaps compared to the values found for free zigzag GNRs of the same size. However, we did not find similar reduction of the band gap in the armchair GNR embedded in the h-BN, probably due to the lack of the states confined at graphene edges, which would be sensitive to the interaction with the h-BN. The coupling of the electronic states from atoms with different electronegativity is accompanied with significant charge transfers. Employing Bader charge analysis 37 we found that ∼ 0.6 electrons was transfered from B atoms at the armchair edges to the nearest C atoms. On the other hand, the C atoms bonded to N sites are positively charged due to ∼0.4 electrons transfered to nearby N atom (Figure S1a in the Supporting information). The same effect is also observed at the zigzag graphene/h-BN interface, as depicted in Figure S1b in the Supporting Information. The values of the charge transfers calculated with the Bader method are in general larger compared to the results produced applying Mulliken population analysis. 38 The results obtained from GGA calculations 14 ACS Paragon Plus Environment

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can also be affected by the well know band gap problem of the standard GGA.

3.2.2 Heterostructures with small clusters Adjustment of the C/BN ratio during fabrication of in-plane graphene/h-BN heterostructures is a method to tune their electronic structure from semimetallic to semiconducting. In this subsection we will examine electronic properties of the heterostructures depicted in Figure 2 and Figure 3. The BN clusters in Figure 2 are likely to form when the C/BN ratio is much larger than one. The periodic structures of these clusters embedded into graphene are examples of the graphene antidot lattices, know as a novel class of graphene based materials with controllable electronic and optical properties. 39,40 Previous DFT calculations showed that the band gap values in such two-dimensional heterostructures are mainly governed by the distance between BN clusters. 22 We examined these results by performing band structure calculations for two different periodic structures of BN rings embedded into graphene, shown in the lower panels in Figure 6. According to our calculations two-dimensional array of BN rings closely packed within an infinite graphene sheet is a heterostructure with the band gap as large as 1.03 eV (Figure 6a). When the BN clusters are arranged in a periodic structure with twice larger distance between them the corresponding band gap is reduced to the value of 0.27 eV, as depicted in Figure 6b. The band gaps of true antodot lattices formed from the structures in lower panels of Figure 6 upon removal of the BN domains and saturation of all broken C-N and C-B bonds with H atoms are 0.55 and 1.80 eV, respectively. Thus, the calculations clearly show that changing the spacing between BN rings or creating holes in graphene sheet by removing BN domains are possible routes for tuning the band gap in graphene based materials by more than 1.50 eV. Our tests demonstrate that the same trends in the band gap values occur for other BN clusters in Figure 2. Small graphene clusters in h-BN monolayer are another class of in-plane heterostructures which could form when the flux of C atoms is considerable smaller that the flux of B and N species. The graphene clusters are examples of quantum dots with the electronic and optical properties profoundly dependent on their sizes. The total density of states (DOS) of the smallest and largest



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Figure 6: (color online) The band structure plots (upper panels) and the corresponding atomic structures of the BN rings in graphene (lower panels). graphene clusters investigated in this work are presented in Figure 7a and Figure 7b. The highest occupied and lowest unoccupied orbitals correspond to the states localized on C atoms. A large band gap of 3.6 eV has been calculated for a hexagon of C atoms in h-BN monolayer. For a cluster with 24 C atoms (Figure 3t) the band gap value decreases by 1.4 eV. The band gap values in the corresponding free graphene clusters with six and 24 C atoms are 5.08 eV and 2.87, respectively. The difference in the band gaps of free graphene nanoflakes and those embedded in the h-BN is governed by the same microscopic mechanisms as in the zigzag GNRs. The charge distribution at the boundaries between graphene and BN domains is qualitatively the same as at their ideal zigzag or armchair interfaces, as shown in Figure S1c and S1d in the Supporting Information. Larger graphene quantum dots in h-BN, with the radius in a range from 9 Å to 17 Å, were recently in-


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3

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1 0

Eg = 2.2 eV

Eg = 3.6 eV

-1 -2 -3

total DOS (arb. units)

Figure 7: (color online) The density of states (DOS) plots of a) carbon ring (Figure 3a) and b) graphene cluster in Figure 3t, embedded into h-BN monolayer. The calculated values for the corresponding band gaps Eg are also shown. vestigated by Huang and Chelikowsky. 41 The calculated trends for graphene clusters in h-BN are fully in line with the results produced for free graphene nanoflakes, 42,43 where was found that the band gap size decreases with an increase in the size of the nanoflakes.

3.3 Reactivity of in-plane heterostructures In this subsection we describe reactivity of the graphene/h-BN heterostructures, using atomic hydrogen as a probe. The H binding at an ideal graphene sheet has been extensively studied in the past. 44–48 Due to differences in used methodologies and computational setups, the calculated binding energies of a single H atom on graphene vary in range from 0.6 to 0.8 eV. We calculated the value of 0.75 eV, in a good agreement with results from the literature. According to recent reports the enhanced electron density at the edges gives rise to stronger H binding at the polycyclic aromatic hydrocarbons compared to an ideal graphene sheet. 49,50 The DFT studies of H adsorption on 17 ACS Paragon Plus Environment


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defect-free h-BN layer indicate a weak adsorption on B sites, with the binding energy smaller than 0.05 eV. 51,52 The H adsorption on the N site is very unfavorable with the negative binding energy of -0.57 eV. 51 Our calculations confirm these findings - we calculated the binding energies of -0.01 eV and -0.81 eV, for H chemisorption at B and N sites, respectively. Since our test calculations for various in-plane heterostructures considered in this work demonstrate a strong preference for H adsorption on C compared to B or N sites, in the following we will consider only H binding on-top of carbon atoms. Table 4: The binding energies of a single H atom adsorbed at graphene, h−BN layer and selected graphene/h−BN in-plane heterostructures. The H adsorption sites are labeled in Figure 8 and Figure 9. structure

adsorption H binding site energy (eV) graphene 0.75 h-BN on-top B -0.01 on-top N -0.81 armchar I 1.03 interface II 0.86 zz − A III 2.31 interface IV 2.10 graphene ring V 0.67 (Figure 3a) VI 0.56 graphene cluster VII 0.97 in Figure 3t VIII 0.80

3.3.1 Ideal interfaces between graphene and h-BN We examined H adsorption at C atoms in the vicinity of the armchair and zz − A interfaces between graphene and h-BN, identified as two interfaces with the lowest formation energies. According to our calculations the H binding energies on-top of C atoms near armchair interface are higher than at the infinite graphene sheet (see Table 4). The strongest binding of 1.03 eV is found for H adatoms in the adsorption site labeled with I in the right panel of Figure 8a. The H adsorption at zz-A interfaces is however considerably stronger, with the binding energies 2.31 and 2.10 eV in the


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adsorption sites III and IV, respectively (Figure 8b). To rationalize the marked difference in the H binding at these two interfaces we inspected electronic properties of the relevant C atoms. In the left panels of Figure 8a and Figure 8b we plotted DOS projected on the 2p orbitals of four C atoms labeled by I to IV, prior to the H adsorption. The plots show high DOSs near the Fermi level at the sites III and IV which give rise to their high reactivity. The DOSs projected on 2p orbitals of C atoms in the vicinity of the armchair interfaces are without any pronounced peaks close to the Fermi level.

a)

b)

C-2p projected DOS (1/eV/atom)

We also calculating H binding energies at free GNRs to compare their reactivity and the reactivity


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-6 1.0

-4

energy (eV) 0 -2

a)

2

4

EF

0.5 0.0 1.0

I

b)

EF

II

0.5 0.0 -6

-6 1.0

-4

-4

-2 0 energy (eV) energy (eV) 0 -2

a)

2

4

2

4

EF

0.5 0.0 1.0

III

b)

EF

0.5 0.0 -6

IV -4

-2 0 energy(eV)

2

4

Figure 8: (color online) The DOS projected on the 2p orbitals of C atoms near a) armchair and b) zz − A graphene/h-BN interface. The orbitals are centered on C atoms marked with arrows in the panels on the right. The atoms are colored according the same color scheme as in Figure 1. of GNRs embedded in the h-BN. The calculated binding energy at the edge of free zigzag GNR 19 ACS Paragon Plus Environment


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is as high as 2.78 eV, by ∼0.5 eV larger than at the most reactive site of the zigzag graphene/hBN interface. Similar increase in the H binding is also accounted for free armchair GNRs (Table S1 in the Supporting Information). General trend that the edges of GNRs embedded in the h-BN are less reactive than those of free GNRs can be attributed to the hybridization of the C-2p and the 2p states of nearby N or B atoms, which obviously does not occur in free GNRs. Since the hybridization gives rise to a partial delocalization of the electronic states, the DOSs projected on the 2p orbitals of the C atoms at the edges of free GNRs is higher than for the corresponding atoms near the graphene/h-BN interface, which results in the higher reactivity.

3.3.2 Small graphene clusters in h-BN The study of reactivity of small graphene clusters embedded into h-BN is restricted to the ring structure (Figure 3a) and the cluster in Figure 3t, which represent the smallest and the largest graphene clusters investigated in this work. The calculated H binding energies at the adsorption sites V-VIII in Figure 9a and Figure 9b indicate lower reactivity of the carbon ring compared to both an infinite graphene sheet and the graphene cluster in Figure 3t. The comparison of the calculated binding energies and the local electronic properties of the corresponding adsorption sites suggests that the H binding energies decrease when the value of the band gaps of graphene clusters is increased. This finding can be rationalized based on a simple two-level interaction between H-1s and C-2p states. Prior to the interaction with carbon the H-1s states were positioned close to the Fermi level. Since their hybridization with the C-2p states decreases with an increase in the energy mismatch between interacting orbitals, the H interaction with graphene quantum dots weakens when the band gap in graphene nanostructures is widened (see Figure 9). The trend that H binding at free graphenic structures is stronger than at those embedded in the h-BN also holds for graphene quantum dots (Table S1 in the Supporting Information).


a)

b)


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-6 2.0

0.0 -6

-4


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-6 2.0

-4

-4

energy (eV) 0 -2

2

4

EF

V

1.0 0.0 2.0

EF

1.0

VI -2 0 energy (eV) energy (eV) 0 -2

2

4

2

4

EF

1.0

VII

0.0 2.0

EF

1.0 0.0 -6

VIII -4

-2 0 energy (eV)

2

4

Figure 9: (color online) The DOS projected on the 2p orbitals of C atoms from a) graphene ring (Figure 3a) and b) graphene cluster in Figure 3t. The orbitals are centered on C atoms marked with arrows in the panels on the right. The atoms are colored according the same color scheme as in Figure 1.

4 Conclusions We carried out an extensive set of DFT calculations to examine structural and electronic properties, together with the reactivity of in-plane heterostructures of graphene and h-BN. The study included their armchair and zigzag interfaces as well as small domains of one two-dimensional crystal embedded into an infinite layer of another one. The formation energies of the heterostructures calculated using DFT are well reproduced by a simple bond model which can be also used to predict the stability of the structures with the graphene or h-BN domain sizes well beyond the grasp of DFT calculations. The electronic properties of a graphene layer doped with BN islands share 21 ACS Paragon Plus Environment


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similarity to those of graphene antidots lattices, and hence these heterostuctures could be utilized for band gap engineering of graphene. On the other hand, the h-BN layer doped with graphene is an example of the two-dimensional structure of graphene quantum dots. Their electronic and optical properties can be controlled by controlling the size of embedded graphene clusters. Our calculations show that controlled adjustment of the C/BN ratio during synthesis of two-dimensional grahene/h-BN heterostructures is a promising route towards designing graphene based materials with tunable electronic band gaps. In addition to this we demonstrated that the reactivity of the in-plane heterostructures of graphene and h-BN is governed by their electronic properties in the vicinity of the Fermi level. A marked increase in the reactivity of the C atoms at zigzag interfaces is driven by the edge states which exclusively occur on these types of the interfaces. Free graphenic structures are found to be more reactive than the ones embedded in the h-BN sheet since graphene coupling to the h-BN gives rise to a partial delocalization of the electronic states at graphene edges.

5 Acknowledgments This work has been supported by the Serbian Ministry of Education and Science under Grant No. 171033.

Supporting Information Available The calculated Bader charges of the selected graphene/h-BN heterostructures are presented in Figure S1. The binding energies of H atoms adsorbed at the edges of graphene clusters and graphene nanoribbons are listed in Table S1.

This material is available free of charge via the Internet at

http://pubs.acs.org.

References (1) Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Katsnelson, M. I.; Grigorieva, I. V.; Dubonos, S. V.; Firsov, A. A. Two-dimensional Gas of Massless Dirac Fermions in 22 ACS Paragon Plus Environment

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I 0.75 eV

II

2.31 eV

H binding energies at the middle (I) and at the edge(II) C sites and the corresponding local DOS.


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Atomic Structure, Electronic Properties, and Reactivity of In-Plane

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