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Tunable Electronic and Magnetic Properties in BxNyCz Nanohybrids: Effect of Domain Segregation Arun K Manna† and Swapan K Pati*,‡ †
Theoretical Sciences Unit and ‡New Chemistry Unit, Jawaharlal Nehru Centre For Advanced Scientific Research, Jakkur Campus, Bangalore 560064, India
bS Supporting Information ABSTRACT: Motivated by recent experimental realization of the hybrid nanostructures of graphene and hexagonal boron nitride (h-BN) sheet, we have investigated the modification in the electronic structure as well as structural and magnetic properties of two-dimensional sheets with BxNy and graphitic Cz nanodomains, with various shapes and sizes using ab initio density functional theory. We find that embedding of domainsegregated BxNy or Cz nanodomains of different shapes and sizes in graphene or h-BN sheet platform, respectively, is energetically less costly and thermodynamically favorable to synthesize under suitable experimental conditions. Among the various nanodomains, the hexagonal-shaped BxNy and Cz nanodomains patched with graphene and h-BN sheet, respectively, are found to be stabler compared to others. Moreover, both the shape and size of the embedded BxNy (Cz) nanodomains have significant effects in regulating the graphene (h-BN sheet) electronic structure. Interestingly, we find that the presence of triangular-shaped BxNy nanodomain in graphene results in tunable semiconducting, metallic, and half-metallic electronic state depending on nanodomain geometries and its concentrations. Our study clearly shows a variety of electronic states, suggesting potential routes for band-gap engineering of these hybrid BxNyCz nanomaterials for advanced device applications.
’ INTRODUCTION Nanocarbons, like graphene, carbon nanotube, fullerene, and their derivatives, have been of potential research interest in recent years for their novel low-dimensional intriguing structural, electronic and magnetic properties.110 Because of its versatile and unique properties, graphene, a strictly two-dimensional (2D) monolayer of carbon atoms tightly packed into a honeycomb lattice,11,12 has become an ideal candidate for application in the next generation of electronic devices.2,1316 Interestingly, it is a strictly zero-band-gap semiconductor, also known as semimetal, possessing linear dispersive bands at the Fermi level forming a perfect Dirac cone.11 Contrastingly, its boronnitrogen analogue, 2D hexagonal BN (h-BN) sheet, is a large-band-gap insulator with flat bands.1720,34,35 A controlled way of transition from insulators through semiconductors to conductors, among all nanostructured materials, 2D graphene, and h-BN sheet with completely contrasting electronic and magnetic properties, would be of practical interest in nanoscience and nanotechnology. Electronic as well as magnetic properties of low-dimensional materials are mainly governed by their size, geometrical shape, and the carrier types and concentrations. The massless Dirac Fermions present in graphene results in very high carrier mobilities arising from complete delocalization of π electrons, whereas the carriers mobility of h-BN sheet is very poor due to charge-transfer-induced electron localization on B and N atoms. r 2011 American Chemical Society
Moreover, it has been shown that electron or hole mobility can be controlled by tuning external electric field in graphene-based field effect devices.2 Furthermore, the utilization of spin components in graphene-based electronic devices depends on the extent of spin polarization.2124 In this respect, half-metallic materials are potentially demanding that show zero band gap for electrons with one spin orientation and insulating or semiconducting band gap for the other, resulting in a completely spinpolarized current.2528 In fact, appropriate controlling and/or tuning of the electronic and magnetic properties of graphene has numerous applications in fabrication of advanced electronic devices. However, the precise control of carrier type and concentration has been achieved only recently, by electrochemical doping29 and through chemical modifications.30,31 In fact, the molecular doping-induced charge transfer offers a leading approach in tuning of carrier types and its concentrations without invoking significant structural changes in graphene.3033,36,37 In addition, the replacement of graphene C atoms by B or N atoms would result in a desired and tunable carrier type and density. Only recently, the B- and N-substituted nanocarbons, known as BCN analogue, have been realized experimentally,3845 and have been extensively studied by theoretical exploration of their novel Received: March 8, 2011 Revised: April 20, 2011 Published: May 05, 2011 10842
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The Journal of Physical Chemistry C properties.40,4657 Note that the BCN analogue of graphene so far studied mainly consists of irregular distribution of B and N atoms, which results in greater energy cost, and a few studies involve only domain-wise phase segregation.39,41,47,48,58 More recently, an innovative experimental realization of domainsegregated BCN analogue of graphene has materialized in which one region is rich with graphene C while another one is enriched with BxNy nanodomains.59,60 This BCN hybrids are considered as hybridized boron nitride and graphene domains. More interestingly, the band-gap nanoengineering in graphene as well as in h-BN sheet is of potentially demanding and more desirable achievements in fabricating advanced devices. There have been several attempts to fulfill this goal in the literature. Along these lines, the realization of energy band gap in graphene by defects engineering, introducing lattice strain, and by the presence of external dopant as well as chemical functionalizations have been explored both theoretically and experimentally.6165 Moreover, the breaking of A-B sublattice symmetry in graphene by local structural distortion can result in band-gap opening. This has been achieved by surface adsorption of various organic molecules and with nanoparticle adsorbates.32,63 In fact, it has been shown that a tunable band gap can be realized in graphene by the controlled adsorption of water molecules.66 Additionally, the presence of nanoholes in graphene, known as nanoporous graphene or graphene antidots,6772 has also been shown to be effective in semiconductor applications with tunable band gaps varying with nanohole shapes and sizes. The presence of nanoholes in graphene creates a potential barrier for its carriers mobility, giving rise to the band-gap opening. However, most often, the presence of nanoholes in graphene does not provide a suitable structural framework for realistic applications, and therefore this remain a challenging issue to be achieved practically. In contrast, one can build a nanohybrid by filling these nanopores of graphene with suitable semiconducting or insulating nanodomain materials that have a similar sp2-hybridized hexagonal lattice architecture as present in graphene. This can be accomplished by utilizing nanodomains of h-BN with varying shapes and sizes. In fact, nanopatching of graphene, a zero-band-gap material, with its h-BN analogue, a large-band-gap insulator, can produce hybrid (BxNyCz) nanomaterials with tunable band-gap values. Interestingly, this has recently been demonstrated by chemical vapor deposition technique by Ajayan and coworkers.59 The experimental achievements in synthesizing domain-segregated BxNyCz nanohybrids motivate us to pursue the present study in detail, which holds good promise for nextgeneration device applications. In the present study, we have performed a detailed, systematic, and comprehensive analysis of the changes in structural as well as electronic and magnetic properties of BxNy (with variation in x and y integer values) modified 2D graphene and graphitic Cz modified 2D h-BN sheet using first-principles density functional theory (DFT) calculations. Here, we consider a mixture of three elements packed into a 2D honeycomb lattice. Since boron is a Lewis acid, it has strong affinity for nitrogen, resulting in strong BN bonds. In fact, the bonding energy of CC and BN bonds is comparatively higher than that of other hetero bonds (CB and CN) present in the ternary system. Consequently, the hybrid systems will be domain-segregated into two different regions, one with graphene C-rich domain and other with BxNyenriched domain, to gain thermodynamic stability. We have considered a few representative regular-shaped BxNy and Cz nanodomains with varying sizes patched with graphene and
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Figure 1. Schematic diagram of various BxNy nanodomains present in graphene: (a) Ra-BxNy, (b) Rb-BxNy, (c) H-BxNy, (d) Ta-BxNy, and (e) Tb-BxNy nanodomains.
h-BN sheet, respectively. We have considered a hexagonal (H-BxNy), two rhombus (Ra-BxNy and Rb-BxNy), and two triangular (Ta-BxNy and Tb-BxNy) shaped nanodomains in graphene with varying sizes. All BxNy nanodomains under study are shown in Figure 1. Our results show that all the nanohybrids are thermodynamically feasible to synthesize and have intermediate structural stability between that of pristine graphene and h-BN sheet. We find that a variety of electronic and magnetic properties can emerge as a result of BxNy nanodomain substitution in graphene, depending on their shapes and sizes. We also find that it is possible to engineer the band gap of these nanohybrids by simply varying the domain sizes. Interestingly, we find that patching T-BxNy nanodomains of varying shapes and sizes with graphene results in non-spin-polarized metallic and semiconducting as well as spin-polarized metallic and halfmetallic electronic ground states with full control over its spin components. Furthermore, the nanopatching of various-shaped Cz domains with h-BN sheet results in tunable electronic states. In fact, our study offers the potential for designing advanced electronic and magnetic devices.
’ COMPUTATIONAL DETAILS The first-principles calculations are carried out by the linear combination of atomic orbital density-functional theory (DFT) methods implemented in the SIESTA package.73 The generalized gradient approximation (GGA) in the PerdewBurke Ernzerhof (PBE) form74 and double ζ polarized (DZP) basis set are chosen for the spin-polarized DFT calculations. The interaction between ionic cores and valence electrons is described by norm-conserving pseudopotentials75 in the fully nonlocal KleinmanBylander form.76 The pseudopotentials are constructed from 3, 4, and 5 valence electrons for the B, C and N atoms, respectively. A reasonable mesh cutoff of 400 Ry for the grid integration is utilized to represent the charge density. For full relaxation of all systems, we have sampled the Brilliouin zone by 5 5 1 k-points using the MonkhorstPack scheme, whereas for electronic properties calculations, the Brilliouin zone is sampled by 10 10 1 k-points. We have also performed the geometry optimization for a BxNyCz nanohybrid considering 7 7 1 k-points and found that there is a very small (less than millielectronvolt order) change in total energy. Thus, we restrict ourselves for geometry optimization with 5 5 1 k-points for all studied systems. The optimal atomic positions are determined until the magnitude of the forces acting on all atoms is less than 0.04 eV 3 Å1. GGA approximation takes into account the 10843
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Table 1. Cohesive Energy, Formation Energy, and Band Gap for BxNy-Substituted Graphene Systems Ecoh (eV/atom)
Ef (eV/atom)
Eg (eV)
Ra-B8N8
8.50
0.04
0.29
Ra-B15N15 Ra-B24N24
8.38 8.24
0.06 0.08
0.48 0.76
Ra-B35N35
8.08
0.10
0.80
Rb-B4N4
8.54
0.05
0.19
Rb-B9N9
8.47
0.06
0.32
Rb-B16N16
8.35
0.08
0.39
Rb-B25N25
8.21
0.10
0.48
Rb-B36N36
8.05
0.11
0.85
H-B3N3
8.58
0.03
0.12
H-B12N12
8.43
0.05
0.38
H-B27N27
8.20
0.08
0.62
Ta-B7N6
8.52
0.06
0.00
Ta-B6N7
8.51
0.05
0.00
Ta-B12N10 Ta-B10N12
8.45 8.43
0.09 0.08
0.00 0.00
Ta-B25N21
8.26
0.15
0.00
Ta-B21N25
8.22
0.13
0.00
Tb-B6N3
8.55
0.09
Tb-B3N6
8.52
0.08
Tb-B10N6
8.49
0.12
Tb-B6N10 Tb-B15N10
8.45 8.41
0.10 0.15
Tb-B10N15
8.37
0.13
Tb-B28N21
8.23
0.21
Tb-B21N28
8.16
0.18
Tb-B36N28
8.11
0.24
Tb-B28N36
8.03
0.22
nanodomains
semilocal exchange correlations, which have significant impact on low-dimensional spin systems like graphene and carbon nanotubes. Periodic boundary conditions and a supercell approximation are used to model different shapes and sizes of BxNy nanodomains patched with 2D graphene. The 8 8 supercell (19.7 19.7 20 Å) containing 128 atoms of graphene is used for the electronic structure calculations. The vacuum separation of 20 Å between two layers is found to be sufficient to ensure energy convergence. Within the calculation methods, the estimated lattice constants of graphene and h-BN sheet are 2.48 and 2.51 Å, respectively, which correspond to CC and BN bond lengths of 1.43 and 1.45 Å, respectively. These values are close to the experimental values (2.46 Å for graphene and 2.50 Å for h-BN sheet) found at low temperature.77
’ RESULTS AND DISCUSSION First we focus on the relative thermodynamic stability of these modified graphene nanohybrids as a function of the embedded BxNy domain shapes and sizes. In fact, the thermodynamic stability of these modified hybrids strongly relies on the geometry of the nanodomains and their concentrations. The structural
stability and thermodynamic feasibility of a nanohybrid depend on the extent of cohesive and formation energy, respectively. Thus, we calculate the cohesive energy (Ecoh) of all the nanohybrids using eq 1. We also have calculated the formation energy (Ef) following a zero temperature approach customarily used to determine the relative energy cost of the hybrid BxNyCz mixtures compared to their pristine analogues.7882 Note that, within this approach, the formation energies of the pristine graphene and pristine h-BN sheet are equal to zero, and thereby provides us a reference frame for comparing with other nanohybrids: Ecoh ¼ ½Etot Ef ¼ ½Etot
∑i Ni Ei =N
∑i ni μi =N
ði ¼ C, B, NÞ
ði ¼ CC, BN, C, B, NÞ
ð1Þ ð2Þ
where Ecoh and Ef are the cohesive and formation energy per atom of the ground state of BxNy-modified graphene nanohybrid, respectively, while Etot and Ei represent total energies of a nanohybrid and of individual elements present within the same supercell, respectively. Ni and ni are the number of ith species present in BxNyCz for Ecoh and Ef energy calculation, respectively, while N is the total number of atoms present in a supercell (i.e., N = 128). μi is the suitable chemical potential of the ith species. Additionally, depending on the atomic reservoir employed in synthesizing BxNyCz nanohybrids, we can have either a nitrogen- or a boron-rich environment. The chemical potential for C, CC, and BN can be obtained straightforwardly from the corresponding infinite sheet calculation. However, to obtain μB and μN, we use the following thermodynamic constraint: μBN = μB þ μN. Consequently, μB is obtained for a boron-rich environment by considering μN to be R-phase of solid nitrogen (μN = 270.22 eV). Similarly, μN is obtained for a nitrogenrich environment by considering μB to be metallic R-B phase (μB = 77.23 eV). The details of this approach can be found elsewhere.7882 As is well-known, the higher the cohesive and formation energy, the higher the structural stability and the greater the thermodynamic feasibility of nanohybrid formation. In fact, as shown in Table 1, we find that all the BxNy-substituted graphene hybrids have intermediate cohesive energy between that of pristine graphene (8.65 eV/atom) and h-BN sheet (7.79 eV/atom). Consequently, it should have in-between structural stability. However, with increasing concentration of embedded BxNy nanodomains belonging to specific-shaped nanodomains, the cohesive energy decreases and tends to attain the value of pristine h-BN sheet. Moreover, for the nonstoichiometric hybrids where there is a difference between the number of B and N atoms (e.g., T-BxNy substituted graphene hybrids), we find more negative Ecoh for B-rich BxNyCz in comparison to the N-rich one. This can be understood as follows. For B-rich nanohybrids, B, being a strong Lewis acid, induces charge-transfer-driven extra cohesivity between the graphitic border C atoms and B atoms from the substituted BxNy domains, and hence results in relatively larger Ecoh compared to N-rich nanodomains. Furthermore, as shown in Table 1, the relative formation energy slightly decreases (i.e., more positive values) with increasing size of BxNy nanodomains present in graphene irrespective of their shapes. This is because of the greater interfacial energy cost arising from the larger perimeter of embedded nanodomains as we move toward bigger nanodomain sizes. Interestingly, we find that the extent of Ef is smaller for R-BxNy (Figure 1a, b), H-BxNy 10844
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Figure 2. Electronic band structures of (a) pristine graphene and (b) Ra-B8N8, (c) Rb-B9N9, and (d) H-B27N27 substituted graphene nanohybrids. The energy is scaled with respect to the Fermi energy (EF).
(Figure 1c), and Ta-BxNy (Figure 1d) patched graphene compared to other nanopatching. This can be understood as follows. For a ternary alloy containing three elemental species C, B, and N in a 2D honeycomb lattice, the systems always try to maximize the number of CC and BN bonds and, correspondingly, try to avoid the bonds between C and B as well as between C and N to gain the thermodynamic stability arising from the minimized interfacial energy. Consequently, the more regular-shaped BxNyhybridized graphene systems would have more thermodynamic stability compared to any other nanohybrids. In fact, among all regular-shaped BxNy-substituted graphene, the above three systems have smaller interfacial energy and show relatively smaller extent of formation energy (i.e., less positive Ef values). Moreover, we find relatively less Ef for H-BxNy-substituted graphene because of the smaller interfacial energy arising due to their smaller perimeter. This is also expected as the system has a stable six-member borazine unit in place of the stable benzene ring. Interestingly, we find that the N-terminated BxNy-patched graphene nanohybrids have greater extent of Ef in comparison to the presence of B-terminated BxNy nanodomains. This also can be accounted as follows. For the BxNyCz hybrids consisting of B-terminated nanodomains, there is an extra energy cost arising from the interfacial charge transfer between B and C atoms in comparison to the presence of N-terminated nanodomains in graphene. This is well consistent with the results reported in earlier studies, showing the preference for forming the N-terminated edge structures.81 Note that the relative difference in Ef is very small for various BxNyCz nanohybrids. However, we believe that all the BxNy -substituted graphene systems proposed in the present study would be thermodynamically feasible to synthesize under suitable experimental growth conditions, as has already been demonstrated.59 A summary of the results for the optimized structures for all nanohybrids is provided in Table 1. To understand the effect of various -shaped BxNy nanodomains within graphene on electronic structure, we plot band diagrams in Figure 2. We first focus on nanohybrids that are isoelectronic (i.e., possessing the same number of electrons) with their parental compounds, namely, Ra-BxNy, Rb-BxNy, and H-BxNy nanodomains. The grapheneR-BxNy/H-BxNy hybrids can be considered as a 2D mixture of C, B, and N, where some of the CC bonds are substituted by BN bonds. In both cases, the number of B and N atoms present in the domains are exactly equal, and thereby no extra charge carriers are imposed into the systems. As can be seen from Figure 2a, the graphene band structure shows a perfect Dirac cone picture, which arises due to the meeting of valence band maxima and conduction band minima at the Brillouin zone high symmetric K-point. Interestingly, the Fermi level lies exactly in between valence and
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conduction bands, leading to a zero-band-gap semiconductor, also known as semimetallic graphene. Also, as can be seen from Figure 2bd, the graphene nanohybrids containing Ra-B8N8, RbB9N9, and H-B12N12 domains show semiconducting band gaps with gap value varying with the BxNy concentrations (see Table 1). In fact, the band gap increases with increasing nanodomain concentrations in accordance with the experimental findings.59 This can be understood as we move to a hybrid system with higher insulating domain concentration where the intrinsic carriers feel a large potential barrier for its ballistic transport as observed in pure graphene.83 The similar trend in band-gap variation with BxNy nanodomain concentrations for these three different-shaped BxNy nanodomains present in graphene lead us to conjecture that the band-gap variation is not shape-dependent but rather depends solely on the size or concentration of the BxNy nanodomains. We also find that the band structures around the Dirac point are significantly affected by the BxNy substitution in graphene. The linear dispersion of bands at K-point in graphene slowly disappears with increasing BxNy concentrations, and almost localized flat bands characteristic of pure h-BN sheet appear at higher concentrations of BxNy nanodomains (see Figure 2). However, the Fermi level is placed exactly in between the valence and conduction bands as there are no predominating charge carriers (either electrons or holes) in these hybrid systems. These systems can be considered as nanohybrids where the CC pairs are replaced by their isoelectronic analogue BN pairs, thereby inducing no extra charge carriers. Interestingly, as shown in Figure 2, the valence and conduction bands are symmetric with respect to the Fermi energy due to the electron hole symmetry. For pure 2D graphene, spin-polarized DOS vanishes exactly at Fermi level due to the presence of massless Dirac fermions, and thereby there is no net spin polarization in the system. The calculated DOS together with its projections on individual species (pDOS) for various grapheneBxNy nanohybrids clearly show that the accessible electronic states near the Fermi energy mainly arise from the border C atoms (C atoms that are bonded to B and N atoms) and to some extent C atoms of bulk graphene. With the increase in BxNy concentration, the contributions from the B and N atoms become significant along with the C contributions. Furthermore, the extent of contribution to the valence and conduction band energy states are greater from B and N atoms, respectively. Interestingly, we also find that all the systems are stable in nonmagnetic ground states. An extensive analysis of band structure and DOS predicts the carrier spin symmetries for all the systems resulting in a nonmagnetic ground electronic state where all sites bear zero spin moment. We now focus on the changes in electronic and magnetic properties of graphene hybridized with triangular-shaped (T-BxNy) nanodomains. Depending on the triangular geometry, the domain can be classified in two categories, namely, Ta-BxNy and Tb-BxNy (see Figure 1d,e). In each category, there exist two possibilities of edge termination of the embedded nanodomains. The edge can be terminated by either B or N atoms, and depending on the termination, the system might have excess holes or electrons, respectively. Consequently, the patching of T-BxNy nanodomains with graphene results in intrinsically either hole- or electron-doped systems. In Figure 3, we present the electronic band structures of Ta-BxNy-substituted graphene with increasing nanodomain sizes for both B- and N-terminated nanodomains in the top and bottom panels, respectively. We find that all grapheneTa-BxNy hybrids are stabilized in metallic 10845
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Figure 3. Electronic band structures of Ta-BxNy-substituted graphene nanohybrids with varying domain sizes. The pairs (a, d), (b, e), and (c, f) are the complementary nanodomains patched with graphene systems. The energy is scaled with respect to the Fermi energy (EF).
Figure 4. Electronic band structures of Tb-BxNy-substituted graphene nanohybrids with varying substituent concentrations. The pairs (a, f), (b, g), (c, h), (d, i), and (e, j) are the complementary nanodomains present in graphene systems. The energy is scaled with respect to the Fermi energy (EF).
ground states. The metallicity arises due to the presence of midgap states in between valence and conduction bands aligning with the Fermi level. These midgap states originate because of the imbalance in A-B sublattice present in modified graphene. The number of such midgap states is equal to the difference in the sublattice imbalance.84 The existence of these midgap states at or near the Fermi energy leads to various exotic electronic ground states. Interestingly, we find one, two, and four midgap states, according to the difference between the number of B and N atoms present in nanodomains with increasing sizes (see Figure 3). We also analyze the wave functions at different high symmetric k-points in detail to understand microscopically the origin of such states. From an analysis of wave functions, we find that the propensity of the atomic orbitals contribution to these midgap state wave functions do mainly come from the border graphene C atoms, in particular the pz orbitals of carbon atoms. The one-electron wave functions of a representative Ta-B12N10 nanodomain-patched graphene hybrid near the Fermi energy at two high symmetric k-points are shown in Figure 2 in Supporting Information, rationalizing the above conjecture. Increasing sizes of Ta-BxNy domains give rise to a significant contribution from the pz orbitals of both B and N atoms. Furthermore, an analysis of electronic DOS as well as pDOS reveal that the major contribution to the electronic conducting states at the Fermi level arises from graphene C atoms with small contribution from B and N atoms. The presence of spin symmetry between the majority and minority spin channels induces zero spin-polarization for systems with smaller BxNy. Interestingly, we also find that the valence and conduction bands in band diagrams (see Figure 3) of the electron-rich systems (Ta-BxNy with x < y) are changed to an inverted structure for hole-rich systems (Ta-BxNy with x > y). This is because of the presence of electronhole symmetry between these complementary nanohybrids. We now consider a pair of nanodomains making the system isoelectronic [for example, if we consider the pair Ta-B12N10 (Figure 3b) and Ta-B10N12 (Figure 3e) having equal numbers of holes and electrons, respectively] to study the effect on changing the electronic structure. Although the individual nanodomains hybridized with graphene show perfectly metallic electronic ground states, the pair of complementary nanodomains simultaneously hybridized with graphene possessing no extra charge
carriers gives rise to a semiconducting electronic structure. Note that the supercell containing complementary nanodomains patched with graphene does not have any imbalance in A-B sublattice and hence does not provide any midgap states at Fermi energy for metallicity. Here the situation is exactly similar to the case of Ra-BxNy nanodomain hybridized with graphene, as discussed earlier. To analyze the effect of Tb-BxNy nanodomain sizes on electronic structure, we have considered a few representative Tb-BxNy nanodomains with increasing size in graphene supercell. The (x, y) pairs include (6, 3), (10, 6), (15, 10), (28, 21), and (36, 28) for B-terminated nanodomains, and in the case of N-termination the pairs include (3, 6), (6, 10), (10, 15), (21, 28), and (28, 36) for various sizes of nanodomains. In Figure 4, we plot the electronic band diagrams for B- (upper panel) and N-terminated (lower panel) nanodomains patched with graphene. Interestingly, we find that the nanohybrids can have tunable electronic ground states, metallic T semiconducting T half-metallic, by simply varying the sizes of embedded nanodomains. Note that all these systems have midgap electronic states in between valence and conduction bands arising due to the imbalance in A-B sublattice as mentioned above. As shown in Figure 4, we find that the complementary pair Tb-B6N3 and Tb-B3N6 (Figure 4a,f) hybridizing with graphene shows a perfectly conducting ground state as one of the midgap states crosses the Fermi energy, whereas the hybridization of Tb-B10N6 and Tb-B6N10 (Figure 4b,g) nanodomains with graphene leads to a semiconducting band structure as none of these midgap states cross the Fermi level. Interestingly, with increasing Tb-BxNy domain sizes, we also find a metallic and a half-metallic band structure; i.e., one of the spin channel has semiconducting band gap whereas other spin channel is available for electronic conduction. From an analysis of wave functions (see bottom two panels in Figure 2 in Supporting Information), we find that the midgap states near the Fermi energy mainly originate from 2pz orbitals of C atoms directly bonded to the B and N atoms (i.e., border C atoms). However, with increasing nanodomain sizes, the contribution arising from 2pz orbitals of B and N atoms become more significant. For a better understanding of individual species contributions to the total DOS at and near the Fermi energy, we plot the DOS 10846
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Table 2. Cohesive Energy, Formation Energy, and Band Gap for Cz Nanodomain-Substituted h-BN Systemsa
a
nanodomains
Ecoh (eV/atom)
Ef (eV/atom)
Eg (eV)
R-C32
7.92
0.08
0.42
H-C54 Ta-C22
8.07 7.87
0.08 0.08
1.67 1.21 (2.45)
Tb-C25
7.84
0.14
1.43 (2.72)
Eg values shown in parentheses are for minority spin channel.
Figure 5. Electronic total density of states (DOS) and projected density of states (pDOS) of (a) Tb-B36N28 and (b) Tb-B28N36 substituted graphene nanohybrids with their spin density (v-spinV-spin) distribution. The energy is scaled with respect to the Fermi energy (EF).
together with pDOS in top panel of Figure 5 for the representative nanodomains Tb-B36N28 and Tb-B28N36 patched graphene, respectively. It is clear from Figure 5 that the former hybrid is a metal whereas the latter stabilizes as a half-metal. As also can be seen from Figure 5 a,b, the DOS at and near the Fermi energy mainly comes from border C atoms with lesser contribution from B and N atoms. Moreover, a significant contribution from B and N atoms arises for larger domain sizes with greater contribution from B and N atoms for the B- and N-terminated nanodomains, respectively. Here, we should point out that the nanohybrids consisting of Tb-B36N28 and Tb-B28N36 nanodomains exhibit significant structural overlap between the adjacent nanodomains in the supercell and can be considered as a patchwork of triangular h-BN and graphitic nanodomains. However, the calculated energy cost for these nanohybrids is within ∼46 kcal/mol with respect to their pristine analogues, thereby showing the possibilities for their experimental realization under suitable growth conditions. Furthermore, asymmetry in band dispersion (see Figure 4) for two different spin channels near the Fermi level causes a difference in occupation number for two spin channels and hence leads to the magnetic ground states. Also the presence of midgap electronic states with partial occupancy gives rise to the net magnetic moment in these nanohybrids. Note that the grapheneTb-B6N3/Tb-B10N6 nanohybrids as well as their N-terminated counteranalogue show nonmagnetic ground states, as bands for both majority and minority spin channels are symmetrically dispersed with respect to the Fermi level. However, we find magnetic states for larger Tb-BxNy domain sizes patched with graphene that contain a greater number of either electrons or holes. More interestingly, we find that the intrinsic magnetic moments do mainly originate from the graphene border C atoms directly bonded to the B and N atoms (see bottom panel in Figure 5) and can be accounted for the redistribution of charges among KohnSham orbitals induced by the interfacial charge transfer between C and B as well as between C and N atoms, as expected from their electronegativity differences together with Lewis acid character of B atoms.
Figure 6. Electronic density of states (DOS) of (a) R-C32, (b) H-C54, (c) Ta-C22, and (d) Tb-C25 substituted h-BN nanohybrids. The energy is scaled with respect to the Fermi energy (EF).
Similar to the hybridization of graphene with various BxNy nanodomains, we can also have hybrid 2D nanostructures where graphitic Cz domains are present in an insulating single-layer h-BN sheet under suitable experimental growth conditions. Here the situation is like a h-BN antidot with its nanopores filled by graphene Cz domains. Considering this, we too have also performed the electronic structure calculations for variousshaped Cz nanodomain-substituted h-BN sheet to explore their effects in modulating h-BN sheet properties. We consider R-C32, H-C54, Ta-C22, and Tb-C25 Cz nanodomain-patched h-BN sheet as the representative systems. A schematic figure of h-BN sheet containing all Cz nanodomains under study is shown in Figure 1 in Supporting Information. We find that, similar to BxNy nanodomain-patched graphene hybrids, the nanopatching of various Cz domains with h-BN sheet leads to thermodynamically stable structures with comparable formation energy and intermediate cohesive energy (see Table 2) in between that of pristine graphene and h-BN sheet. We also find that all nanohybrids stabilize in nonmagnetic electronic states except for the triangular-shaped Cz nanodomains, which stabilize in a magnetic ground state irrespective of domain sizes. Moreover, the magnetic moment arises mainly from the border C atoms of the substituted graphitic nanodomains. Interestingly, we find the presence of mainly localized electronic states in between valence and conduction bands for these nanohybrids (see Figure 6), originating mainly from the substituted Cz nanodomains with lesser contribution from the border B and N atoms and thus providing a potential route for band-gap engineering in semiconductor applications. Furthermore, the shifting of the Fermi level toward valence or conduction bands by introducing holes or 10847
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Figure 7. Electronic density of states (DOS) of (a) H-B27N27, (b) Ta-B12N10, and (c) Tb-B28N36 substituted graphene nanohybrids. The energy is scaled with respect to the Fermi energy (EF).
electrons, respectively, can lead to a magnetic half-metallic ground state for triangular-shaped Cz-patched h-BN sheet, opening huge possibilities for spintronic device applications. To verify the consistency of observed semiconducting, metallic, and half-metallic behaviors of various BxNy nanodomainsubstituted graphenes, we have also performed the calculations within an extended plane augmented wave85 basis set as implemented in the DFT code Vienna ab initio simulation package (VASP).86 In Figure 7, we plot the total DOS for H-B27N27 (Figure 7a), Ta-B12N10 (Figure 7b), and Tb-B28N36 (Figure 7c) nanodomain-patched graphene systems. Interestingly, we find qualitatively similar observations, that is, semiconducting, metallic, and half -metallic electronic structure, respectively, for these nanodomain-patched graphenes as found with localized basis sets using SIESTA, highlighting the robustness of our predicted results.
’ CONCLUSIONS In the present study, we have shown that the patching of semiconducting and/or insulating BxNy (Cz) nanodomains of various regular shapes and sizes with single-layer graphene (h-BN sheet) can significantly change the electronic and magnetic properties by modulating the carrier type and concentration, using first-principles density functional theory. Our results show that all BxNy (Cz) nanodomain-substituted graphene (h-BN sheet) nanohybrids are energetically less costly in comparison to irregular BxNyCz hybrids, and have intermediate structural stability in between that of pristine graphene and h-BN sheet. We find that the hybridization of BxNy (Cz) nanodomains with graphene (h-BN sheet) opens up a tunable band gap for electronic device integration. We find that the geometrical shape of BxNy (Cz) nanodomains has a significant impact in modulating graphene (h-BN sheet) electronic and magnetic properties. Interestingly, the triangular BxNy (Cz) embedded graphene (h-BN sheet) is either an electron-doped or a hole-doped system depending on the excess of B or N content in the embedded nanodomain, whereas all other BxNy (Cz) substituted graphene (h-BN sheet) hybrids are isoelectronic analogues of the parent graphene (h-BN sheet) without any excess of carrier type. Our findings show that all the studied BxNy (Cz) substituted graphene (h-BN sheet) systems exhibit nonmagnetic semiconducting band structures except for the
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triangular-shaped BxNy-substituted graphene, which stabilizes in either nonmagnetic or magnetic ground states depending on the triangular nanodomain geometries and sizes, with finite magnetic moments for the latter. However, we find a magnetic semiconducting state that is tunable to a half-metallic state by injecting either electrons or holes for the triangular-shaped Cz nanodomain-patched h-BN sheet. We also find that the finite magnetic moment of these magnetic nanohybrids mainly arises from the border C atoms due to charge redistribution induced by the charge-transfer effects. This also can be accounted for by the presence of partially occupied spin-asymmetric midgap states in between valence and conduction bands originating due to the imbalance between A-B sublattice. Interestingly, we find that all Ta-BxNy-substituted graphene nanohybrids exhibit conducting ground states because of the presence of midgap states that cross the Fermi level. We also find nonmagnetic metallic as well as nonmagnetic semiconducting states for smaller Tb-BxNy domain size and spin-polarized metallic and half-metallic ground states with full control over its spin components for larger nanodomain size with B- and N-termination, respectively. This opens up huge possibilities for spintronic device applications in these reduced dimensions. The present study should pave the way for production and utilization of various BxNy (Cz) substituted graphene (h-BN sheet) nanohybrids as band-gap tunable systems for a wide range of electronic and spintronic device applications. Moreover, given the recent progress on synthesizing phase-separated BxNyCz nanohybrids, we believe that the possibility presented here may become part of the experimental development in the field of boroncarbonnitrogen-based nanoelectronics.
’ ASSOCIATED CONTENT
bS
Supporting Information. Two figures, showing various Cz nanodomains patched with h-BN sheet and KohnSham one-electron wave functions for representative systems. This material is available free of charge via the Internet at http://pubs. acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail
[email protected].
’ ACKNOWLEDGMENT A.K.M. acknowledges CSIR, Government of India, for a research fellowship, and S.K.P. acknowledges CSIR and DST, Government of India. for research funding. ’ REFERENCES (1) Dresselhaus, G.; Dresselhaus, M. S.; Eklund, P. C. Science of Fullerenes and Carbon Nanotubes: Their Properties and Applications; Academic: New York, 1996. (2) Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Zhang, Y.; Dubonos, S. V.; Grigorieva, I. V.; Firsov, A. A. Electric field effect in atomically thin carbon films. Science 2004, 306, 666–669. (3) Zhang, Y.; Tan, Y. -W.; Stormer, H. L.; Kim, P. Experimental observation of the quantum Hall effect and Berry’s phase in graphene. Nature 2005, 438, 201–204. (4) Zhang, Y.; Brar, V. W.; Girit, C.; Zettl, A.; Crommie, A. F. Origin of spatial charge inhomogeneity in graphene. Nat. Phys. 2009, 5, 722–726. 10848
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