Interpolation of Atomically Thin Hexagonal Boron Nitride and

Apr 29, 2011 - Theoretical study of electronic and tribological properties of h-BNC 2 /graphene ... effects in graphene, hexagonal boron nitride and h...
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Interpolation of Atomically Thin Hexagonal Boron Nitride and Graphene: Electronic Structure and Thermodynamic Stability in Terms of All-Carbon Conjugated Paths and Aromatic Hexagons Jun Zhu,†,‡ Sumanta Bhandary,§ Biplab Sanyal,*,§ and Henrik Ottosson*,† †

Department of Biochemistry and Organic Chemistry, Box 576, Uppsala University, 751 23 Uppsala, Sweden Department of Chemistry and Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China § Department of Physics and Astronomy, Box 516, Uppsala University, 751 20 Uppsala, Sweden ‡

bS Supporting Information ABSTRACT: Two-dimensional hexagonal composite materials (BN)n(C2)m (n, m = 1, 2, ...), which all are isoelectronic with graphene and hexagonal boron nitride (h-BN), have been studied by density functional theory (DFT) with a focus on the relative energies of different material isomers and their band gaps. The well-established chemical concepts of conjugation and aromaticity were exploited to deduce a rationale for identifying the thermodynamically most stable isomer of the specific composites studied. We find that (BN)n(C2)m materials will not adopt structures in which the B, C, and N atoms are finely dispersed in the 2D sheet. Instead, the C atoms and C C bonds, which provide for improved conjugation when compared to B N bonds, gather and form all-carbon hexagons and paths; that is, the (BN)n(C2)m materials prefer nanostructured distributions. Importantly, there are several isomers of similarly low relative energy for each (BN)n(C2)m composite type, but the band gaps for these nearly isoenergetic isomers differ by up to 1.0 eV. This feature in the band gap variation of the most stable few isomers is found for each of the four composites studied and at two different DFT levels. Consequently, the formation of a distinct (BN)n(C2)m material isomer with a precise (small) band gap will likely be nontrivial. Therefore, one likely has to invoke nonstandard preparation techniques that exploit nanopatterned h-BN or graphene with voids that can be filled with the complementary all-carbon or boron nitride segments.

’ INTRODUCTION Since the successful formation of graphene in 2004 by Geim and co-workers,1,2 the field of atomically thin materials has literarily exploded as exemplified by recent reports on the formation of the hexagonal boron nitride (h-BN) by Meyer et al.,3 the graphene nanomesh by Bai et al.,4 the polyphenylene networks of Bieri et al.,5 and the graphdiyne by Li et al.6 Such two-dimensional (2D) materials will doubtlessly find many applications in the decades to come. Our focus herein is on hexagonal 2D-composites of graphene and h-BN, the former being a semimetal with zero band gap and the latter being a wide band gap material (Eg = 5.971 eV).7 At first glance, one may assume that a continuum of (BN)n(C2)m materials covering every band gap in the range 0 < Eg < 6.0 eV can be formed by combining suitable portions n and m of h-BN and graphene, respectively. Yet is this the case? Also, is there a rationale for which isomer of a particular h-BN:graphene 2D-composite is the most stable and most likely to form under thermodynamically controlled processes? If so, what are the geometric and electronic structures of the isomers that are the most preferred? r 2011 American Chemical Society

The semimetallic character of graphene with a zero band gap limits its application for efficient field-effect transistors, and hence there is a perpetual interest to find low band gap 2D materials.8 Also, such low band gap materials are particularly desirable for photovoltaics applications as they will absorb solar irradiation in a broad wavelength window;9 for example, a material with a band gap of 0.8 eV can theoretically harvest as much as 75% of the incoming solar irradiation. A few h-BN:graphene 2D composites have earlier been reported, and theoretical analyses reveal a semiconducting behavior.10 14 Rao and co-workers prepared a BCN material, that is, the 2:1 h-BN:graphene composite, and found that it exhibits higher electrical resistivity than graphene, but weaker magnetic features.13 It also showed a high propensity for CO2 adsorption. Six isomers with different arrangements of B and N atoms in the hexagonal lattices were examined computationally, and it was Received: February 19, 2011 Published: April 29, 2011 10264

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Scheme 1

Figure 1. The two isomers of the BCN and BC2N 2D-materials that earlier have been postulated to be the most stable ones (refs 13 and 10, respectively).

concluded that an isomer with NB3 and BN3 local motifs is the energetically most favorable one (Figure 1).13 This BCN isomer was calculated to have a band gap of about 1.8 eV using the PBE GGA (Perdew Becke Ernzerhof generalized gradient approximation) functional. Recently, Ajayan and co-workers reported on the synthesis and characterization of large-area hexagonal BCN materials and found through high-resolution transmission electron microscopy (TEM) that separate h-BN and graphene domains are formed.14 It was concluded that the experimentally observed structure should be a nonequilibrium-grown structure, and that the material morphology could be controlled by factors such as growth temperature, deposition rate, and the effect of the substrate. Apart from these two recent studies, Liu et al. earlier examined three possible atomic arrangements of the 1:1 h-BN:graphene composite (BC2N) at the DFT LDA (density functional theory local density approximation) level and found that, among the material isomers investigated, the BC2N isomer shown in Figure 1 maximizes the chemical bond strength within the material as it allows for the highest number of C C and B N π-bonds, giving it the lowest total energy.10 On the basis of DFT energies, Yuge studied the stability of BCN by the cluster expansion method and Monte Carlo simulations. A tendency of phase separation between BN and C was indicated. It was also shown that lattice vibrations significantly increased the solubility limit.15 Although there is a tendency for phase separation, Lam et al. very recently revealed on the basis of DFT calculations that the activation energy for phase separation is as high as 1.63 eV/atom, clearly indicating that this transformation is efficiently hindered at room temperature.16 They also concluded that the band gap of evenly distributed Cx(BN)y materials can be adjusted by controlling the carbon concentration, making the material useful for electronics applications. Graphene and h-BN are hexagonal arrays with the molecular analogues being benzene (C6H6) and borazine (B3N3H6), respectively. Benzene is the prototype for a molecule extensively stabilized by aromaticity, and chemical reactions in which it is formed are generally highly exothermic. Borazine is isoelectronic with benzene and has been termed ”inorganic benzene”, but it only exhibits onethird of the aromatic stabilization of benzene,17 22 a fact that is useful for deriving a rationale for the relative thermodynamic stabilities of various isomeric (BN)n(C2)m composite materials. A combination of graphene and BN in several compositions could yield interesting electronic properties, and the concept of aromaticity could be

exploited to analyze the relative stability of the structures, similar to how aromaticity is regularly used to explain molecular structure and stability.23 Here, we report on a density functional theory investigation in which the n:m mixing ratio of h-BN and graphene is set to 2:1, 1:1, 2:3, and 1:3 with an objective to identify the most important (BN)n(C2)m materials with a relatively high carbon content exhibiting small band gaps. Several issues are addressed that should assist both for an improved understanding of how these materials are best tailored and to help reduce the problems that likely will be encountered in future synthesis of a specific (BN)n(C2)m composite with a well-defined geometric and electronic structure.

’ RESULTS AND DISCUSSION Our first working hypothesis is that there should be a preference for (BN)n(C2)m materials to form as many all-C hexagons, benzene rings, as possible. If this is the case, how are these all-C hexagons optimally arranged in the (BN)n(C2)m material? We examine material isomers in which the hexagons are surrounded by B and N atoms as well as isomers in which the all-C hexagons are connected to form carbon paths. Our second hypothesis is that the all-C hexagons, which are linked together, allow for π-conjugated pathways that give these material isomers a high relative stability. In this context, we also examine the band gap variations and relate these to the structural features. We impose the structural constraint that our materials cannot contain hexagons that are described by zwitterionic and biradical resonance structures (Scheme 1) as such structures will increase the reactivity of the material. Zwitterionic and biradical resonance structures are enforced into the material when B and N atoms in a hexagon are placed at positions 1 and 3 relative to each other as this implies two all-C segments, each with an odd number of π-electrons, in the hexagons. Thus, a pair of B and N atoms must be placed in either 1- and 2- or in 1- and 4-positions, so that one can form a resonance structure with the π-electrons at neighboring C-atoms confined to local C C π-bonds. As a second materials constraint, we do not allow any B B and N N bonds as these lead to a lower total number of π-bonds and, consequently, a higher relative energy of such a material isomer. We search the thermodynamically most favorable isomers as these will be the ones that should form at elevated temperatures. These conditions are fulfilled with, for example, chemical vapor deposition (CVD), a technique that has been applied to yield large-scale graphene.24 Noteworthy, the two recently reported syntheses of hexagonal (BN)n(C2)m 2D-materials were both carried out at elevated temperatures of 600 1000 C.13,14 We optimized the structures of the (BN)n(C2)m materials with both PBE25 and Heyd Scuseria Ernzerhof (HSE)26 density functionals by using Quantum Espresso27 and Gaussian 0928,29 packages, 10265

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Figure 2. Valence bond representations and qualitative molecular orbital diagrams displaying, for isomer I, a zwitterionic (donor acceptor) resonance structure and the opening of the HOMO LUMO gap (ΔεHL) due to interaction between para-positioned atoms/groups, and for isomer II the reduction of the HOMO LUMO gap.

respectively. Whereas functionals based on the local spin density approximation (LSDA) and generalized gradient approximation (GGA) tend to underestimate band gaps due to self-interaction errors, hybrid functionals such as HSE are better able to reproduce experimentally measured band gaps and lattice constants with high accuracy.30 However, we also report PBE data to allow for comparisons of our computed (BN)n(C2)m material properties with the large number of existing computational data of other 2D-materials. To estimate the degree of aromaticity of the all-C hexagons, we exploit the harmonic oscillator model of aromaticity (HOMA) of Krygowski and co-workers, an aromaticity index based on bond lengths.31 An ideal aromatic compound (benzene) has a HOMA value of 1.0, whereas a nonaromatic compound has a value close to zero, and antiaromatic systems of low stability have negative values. Among the various isomers of a particular (BN)n(C2)m composition, the isomers I and II herein have the all-C hexagons arranged linearly into poly(para-phenylene) (PPP) paths, that is, the thinnest possible graphene nanoribbon with edges of armchair configuration. Of these two isomers, isomer I has two B-ring-N para-arrangements around each all-C hexagon, that is, B and N atoms placed as substituents at the 1- and 4-positions of the ring enabling for donor acceptor (D A) interactions (Figure 2). Isomer II, on the other hand, has one B-ring-B and one N-ring-N para-arrangement around each all-C hexagon, a connectivity that does not permit D A interaction across the ring, even though D A interactions will take place between adjacent B and N atoms as substituents at positions 1 and 2 of the ring, as well as at positions 4 and 5. Local D A interactions around an all-C hexagon should increase the HOMO LUMO gap ΔεHL (cf., band gap) (Figure 2), whereas the B-ring-B and N-ring-N para-arrangements will lead to lowered ΔεHL. In support of this qualitative argumentation, we find that when hydrogen terminated, the two isomeric diamino-diboryl substituted benzenes of Figure 2 in their planar conformations have ΔεHL of 4.10 (isomer I) and 1.86 eV (isomer II), respectively, at the HSE/6-311G(d) level. The 1:1 h-BN:Graphene 2D-Composite. We investigated the largest number of isomers (six) for the 1:1 mix of h-BN and graphene, that is, BC2N (Figure 3). Among these isomers, two have the all-C hexagons connected into PPP paths (BC2N-I and BC2N-II), one has the all-C hexagons arranged in linear arrays as

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in polyacenes (BC2N-III), one has disconnected all-C hexagons (BC2N-IV), and two lack all-C hexagons (BC2N-V and BC2NVI). Of the last two, BC2N-VI has polyacetylene paths, whereas BC2N-V has only isolated C C bonds. Even though a large number of other isomers also exist, with this selection we can deduce the importance of aromaticity and conjugation. Among our six isomers, the first three are particularly stable and nearly isoenergetic at both PBE and HSE levels (relative energies per formula unit (f.u.) differ by at most 0.15 eV (PBE) and 0.07 eV (HSE)). The calculated HOMA values of BC2N-I and BC2N-II (0.842 and 0.888, respectively) reveal that their all-C hexagons are aromatic and benzene-like. Although the C N bond lengths are the same in BC2N-I and BC2N-II (1.405 and 1.406 Å, respectively), the C B bonds differ by 0.02 Å (1.502 and 1.520 Å, respectively), revealing some D A interaction in BC2N-I that leads to a slightly lowered HOMA value. The HOMA value of the all-C hexagons in BC2N-III is lower (0.614), but this material is stabilized by the two adjacent conjugated polyacetylene paths rather than by aromaticity. The C C bond lengths in the two polyacetylene paths (the outer polyacene C C bonds) are 1.418 Å, revealing a perfect π-delocalization. The C N bonds of BC2N-III are short (1.380 Å) when compared to those of BC2N-I and BC2N-II, indicating a C N π-bonding, whereas its C B bonds are longer (1.525 Å). Within the all-C hexagons of BC2N-III, the internal C C bonds between the hexagons are slightly shorter than the C C bonds of the outer two polyacetylene paths (1.418 vs 1.440 Å), and this bond length difference is smaller than in polyacene (1.398 and 1.457 Å, respectively). The isomers BC2N-IV and BC2N-VI are nearly isoenergetic with relative energies of 0.42 and 0.34 eV/f.u. at HSE level. The BC2N-IV isomer has isolated all-C hexagons with the strongest aromatic character among the BC2N isomers studied here according to the HOMA value, thus revealing reduced conjugative interaction with the surrounding B and N network. As isomers BC2N-I III are of lower relative energies than BC2N-IV, this reveals that it is more favorable for the all-C hexagons to connect into paths with slightly reduced aromaticity than being isolated with high internal aromaticity. Interestingly, the BC2N-VI, which was earlier suggested by Liu et al. to be the most stable BC2N isomer,10 does not contain any all-C hexagons, yet it is of moderately low relative energy. The reason for its rather low energy is found in the all-C polyacetylene paths that are strongly conjugated as revealed by C C bonds of length 1.418 Å. The least stable isomer, BC2N-V, has isolated C C bonds of rather short length (1.372 Å). The comparison of BC2N-V with BC2N-VI therefore confirms our hypothesis that π-conjugation within all-C paths is a key factor for the higher thermodynamic stability of BC2N-VI. Taken together, the results of the relative energies of the BC2N isomers reveal that (i) π-conjugation within all-carbon paths stabilizes BC2N material isomers, (ii) formation of aromatic all-C hexagons (benzene π-sextets) also stabilizes BC2N material isomers and the stabilization becomes stronger when these π-sextets are connected, and (iii) there is no significant energy difference between the material isomers with arrangements of the B and N atoms around the PPP paths into either B-ring-B/N-ring-N or two B-ring-N paraarrangements (isomers I and II). We will see below that these findings also can be applied to rationalize the thermodynamic stabilities of the isomers of other h-BN:graphene composites. The three isoenergetic isomers, which are lowest in energy, have band gaps in the range 1.6 2.6 eV with HSE, and in the range 0.7 1.7 eV with PBE. Noteworthy, the band gap of BC2NI is 0.5 0.7 eV larger than that of BC2N-II, with the only structural difference being the arrangement of the B and N atoms 10266

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Figure 3. The six material isomers of the BC2N composite investigated herein. Relative energies (eV/formula unit) and band gaps given in parentheses (eV) calculated at HSE (normal print) and PBE (italic) levels. The isomer with the lowest energy at HSE level is chosen as reference for the relative energy. The HOMA values for all-C hexagons are given at HSE level. The unit cells are denoted with dashed lines.

around the PPP paths. This band gap difference is in line with the observation above that diamino-diboryl benzene isomer I has a ΔεHL, which is larger by 2.24 eV than that of isomer II (Figure 2). As already remarked, the geometry of BC2N-I indicates that zwitterionic resonance structures, as a result of donor acceptor interactions between para-positioned B and N atoms, play a role because the B C bond lengths are shorter in BC2N-I than in BC2NII (1.502 vs 1.520 Å, respectively). It should, however, be noted that both BC2N-I and BC2N-II have larger band gaps than an isolated PPP band in the planar conformation (0.74 eV at HSE/6-311G(d) level), suggesting that in both isomers D A interactions between B and N atoms at adjacent ortho-positions (i.e., 1,2- and 4,5-positions) around the all-C hexagon raise the band gaps. With regard to BC2NIII, it is not surprising that this isomer has the smallest band gap as it contains an all-C polyacene path, that is, the thinnest possible graphene nanoribbons with edges of zigzag configuration. With flanking N and B atoms as donors and acceptors, this gap will naturally open (cf., Figure 2). At this point, a note should be given to the HSE functional. Polyacene has recently been estimated to have an optical band gap of 1.18 ( 0.06 eV extrapolated from the lowest transitions in the UV vis absorption spectra of oligomers up until nonacene.32 With regard to computed results, an estimated CCSD(T)/cc-pV¥Z singlet triplet energy splitting of polyacene of 0.17 eV was obtained from an extrapolation using the corresponding energy splittings obtained through a focal point analysis of shorter oligoacenes.33 Calculations using many-body Green’s function approach within the GW approximation have provided a gap of 1.5 eV for hydrogen endcapped thin zigzag graphene nanoribbons.34 Although states that are not observed in the UV vis spectra of the oligomers could exist below the lowest optically active state and the optical band gap extrapolated from the experiments is not directly comparable with the computed band gap as being a difference between orbital energies, usage of HSE/6-311G(d) clearly leads to a too small gap for polyacene as an Eg of merely 0.03 eV was calculated. Thus, despite that HSE provides greatly improved band gaps for a range of 3D materials,30 it may still not be an optimal functional for 2D materials with small band gaps. As the same trends are observed with HSE and PBE, one can conclude that the trends provided by the

Figure 4. The band structure (left) and the projected density of states (right) of BC2N-III isomer at PBE level.

calculations are correct, although the correct band gaps in general likely are slightly larger than the ones calculated, also with the HSE functional. We also analyzed the band structure and the density of states (DOS) of the three lowest isomers at PBE level. For BC2N-III, the sharp peaks at HOMO and LUMO in the DOS appear due to the presence of more or less dispersionless flat bands (Figure 4), and in the projected DOS (pDOS) we observe mainly pz(C) contributions in the electronic structure near the band gap. Small contributions from B in HOMO and from N in LUMO are present, indicating a weak π-type bonding with C as the contributions mainly come from pz orbitals. A rather broad feature in the DOS comprised of contributions from all three atom types is seen in the energy range 2 8 eV below HOMO. Regarding the pDOS for all three low-energy BC2N isomers (Figure 5), BC2N-I and BC2N-II have no sharp peak at HOMO or LUMO as in the case for BC2N-III. Moreover, for BC2N-I and -II, almost no contributions from B and N are seen in HOMO and LUMO, respectively. The 2:1 h-BN:Graphene 2D-Composite. We also examined BCN, the 2D-composite that was recently synthesized by Rao and co-workers.13 Three different isomers were considered herein (Figure 6): one with the all-C hexagons connected in 10267

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The Journal of Physical Chemistry C armchair PPP paths (BCN-I), another with the all-C hexagons linked in zigzag polyacene bands (BCN-III), and a third being the previously considered minimum-energy isomer (BCN-IV).13 Here, it should be remarked that we only consider one of the BCN material isomers with PPP paths, the isomer with two B-ring-N para-arrangements (isomer-type I, Figure 2).

Figure 5. The atom-projected densities of states of BC2N-I, BC2N-II, and BC2N-III materials isomers at PBE level.

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Isomers BCN-I and -III are both approximately 0.5 eV/f.u. lower in energy than BCN-IV, revealing the importance of aromaticity and conjugation within and between all-C segments and paths. Moreover, isomer BCN-I is essentially isoenergetic with BCN-III, similar to that found for the corresponding BC2NI and -III isomers above. Examining the structure of BCN-I, we find that the all-C hexagons comply with aromatic benzene rings (HOMA = 0.846), whereas this is not the case in BCN-III (HOMA = 0.557), again resembling the findings for the analogous BC2N isomers. In BCN-I, the C C bonds connecting benzene rings are 1.454 Å, which is slightly shorter than in PPP (1.477 Å). The shorter C C bonds in BCN-I than in PPP are understandable as the C C bonds in the 2D-material are constrained but able to relax freely in PPP. Interestingly, the calculated HSE band gaps for BCN-I and BCN-IV are 2.68 and 2.66 eV, respectively, whereas BCN-III has a significantly lower band gap. Because of the fact that BCN-I and BCN-III are isoenergetic, they should form in equal amount during a high-temperature formation process such as that used by Rao and co-workers.13 It will thus be difficult to estimate the exact electronic properties of such mixed materials, although the BCN composite should be a low band gap material with calculated band gap in the range 1.3 2.7 eV with HSE.

Figure 6. The material isomers of BCN, BC3N, and BC6N composition investigated herein. Relative energies (eV/formula unit) and band gaps in parentheses (eV) calculated at HSE (normal print) and PBE (in italics) levels. The isomer with the lowest energy at HSE level is chosen as reference for the relative energy. The HOMA values for all-C hexagons are given at HSE level. The unit cells are denoted with dashed lines. 10268

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Figure 7. The band structure (left) and the atom-projected density of states (right) of the BCN-III isomer at PBE level.

It should finally be noted that the band structure for BCN-III resembles that of BC2N-III as the pDOS of BCN-III reveals a prominent C contribution along with a small B contribution to HOMO and a prominent C and a weak N contribution to LUMO, similar to that for BC2N-III (Figures 7 and 4, respectively). The broad feature between 2 and 8 eV below HOMO also resembles the DOS of BC2N-III. The electronic properties of h-BN:graphene composites with all-C polyacene segments are therefore dominated by these pathways. The 2:3 and 1:3 h-BN:Graphene 2D-Composites. We also examined (BN)n(C2)m 2D materials with a gradually larger graphene portion, these being BC3N and BC6N, that is, 2:3 and 1:3 mixes of h-BN and graphene (Figure 6). One can expect that a gradually larger graphene portion will lead to a gradually smaller band gap. For both BC3N and BC6N, the isomer-I and isomer-II arrangements lead to essentially isoenergetic material isomers, similar to that found for the two analogous BC2N isomers. Moreover, BC3N-I and BC3N-II, as well as BC6N-II, have connected all-C hexagons that are aromatic according to their HOMA values (above 0.8). Isomer BC6N-I, on the other hand, has a slightly lowered HOMA. Among the BC6N isomers, the two isomers with connected benzene rings (BC6N-I and BC6NII) are significantly lower in energy than the isomer with noninteracting all-C hexagons (BC6N-III), again demonstrating the importance of conjugation between all-C hexagons. With regard to the band gaps of BC3N materials, the isomer with two B-ring-N para-arrangements around the all-C hexagons has a larger band gap (2.14 eV; BC3N-I) than the isomer with a B-ring-B and a N-ring-N arrangement in the para-positions (0.94 eV for BC3N-II). For the BC6N isomers, one can note that BC6N-III with no conjugated all-C hexagons has a larger band gap than the other two isomers. The calculated band gaps within PBE and HSE for all isomers and materials compositions are summarized in Figure 8. As expected, the values of the band gaps obtained from HSE calculations are higher than those obtained from PBE calculations. Despite this quantitative difference, one observes similar trends in the relative stability of various isomers in both types of calculations. Also, a

Figure 8. The band gaps of the (BN)n(C2)m 2D-material isomers investigated herein at (A) HSE and (B) PBE levels plotted against their respective BN concentrations in percent. The relative energies per formula unit are given in parentheses and taken from Figures 3 and 6. The markers and their color correspond to the relative stability order of a certain material isomer, with b, red 9, and green [ being the isomer with the lowest, second lowest, and third lowest energy, respectively.

general decrease of the gap as the increase in carbon content in the hBN:graphene material is seen. It should be noted that the lowest energy isomers for each of the four (BN)n(C2)m composites considered have a spread in the band gap of about 1 eV. A more rigorous and comprehensive combinatorial search is, however, needed for an exact understanding of how materials properties depend on composition. In this context, it should be noted that ab initio computations recently revealed that nanopatterning of graphene and graphane (graphene with H) domains can give rise to similar semiconducting or metallic behavior depending on the formation of armchair and zigzag interfaces, respectively.35 For the (BN)n(C2)m 2D-materials, it becomes clear that the exact placement of the B and N atoms around the all-carbon paths also influences the band gap, even though the relative energy is essentially unaffected by how the flanking B and N atoms are arranged around the all-carbon segment.

’ CONCLUSIONS In summary, our results show that conjugation and aromaticity, two well-established concepts used to explain molecular stability in (organic) chemistry,23 can be used to rationalize the relative thermodynamic stabilities of various (BN)n(C2)m material isomers. We can conclude that a fine distribution of the B, C, and N atoms throughout a 2D-composite is not the best from an energetic point of view, and 10269

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The Journal of Physical Chemistry C this is in line with the finding in the recent study of Ajayan and coworkers in which large graphene and h-BN domains were found.14 Isomers that have all-C hexagons connected into armchair PPP paths as well as into zigzag polyacene paths, that is, the thinnest possible graphene nanoribbons, are nearly isoenergetic and of lowest relative energy among the material isomers considered herein. Formation of even larger all-carbon segments with well-developed conjugated paths could possibly be even more energetically favorable and would be in line with the recent experimental observations. Indeed, the better conjugation and aromaticity within carbon paths and hexagons should be a driving force for the phase separation. In addition to the problem with potential mixtures of various (BN)n(C2)m isomers, we also find large variations in the band gap energies (∼1 eV) among the most stable isomers within each of the four composite categories investigated herein. This pattern is found at both PBE and HSE levels, and it is found for the relative energies of the isomers of all four (BN)n(C2)m components studied herein. Despite that the true band gaps of the materials examined herein likely differ from the calculated ones, they will most presumably display the same large variations for the lowest few composite isomers. We can therefore predict that the formation of a specific isomer of a (BN)n(C2)m composite with specific n:m ratio and a specific (small) band gap will be complicated. Thus, our conclusion is not as optimistic as that of Lam et al. who very recently claimed that the band gaps of evenly distributed (BN)n(C2)m materials could be varied by variation of the carbon concentration of the material.16 Even if the material were to be synthesized by the usage of precursors that provide diatomic C2 and BN segments, the C2 segments will likely prefer to form π-conjugated all-carbon paths and aromatic hexagons also at materials synthesis temperatures that are low. Instead, a very careful experimental design of the interface pattern between graphene and h-BN as well as the relative widths and arrangement (armchair vs zigzag) of the all-carbon regions will become crucial in realizing nanostructured (BN)n(C2)m materials with desired band gaps. The growth of such nanostructured (BN)n(C2)m materials will likely need to exploit an unconventional preparation technique in which a h-BN or a graphene layer is nanopatterned with voids into which the complementary all-carbon or boron nitride segments can be incorporated.

’ COMPUTATIONAL METHODS The first principles density functional theory (DFT)-based Quantum Espresso code27 has been used with plane wave basis and ultrasoft pseudopotentials. The exchange correlation potential has been approximated by the usage of the PBE functional in generalized gradient approximation (GGA).25 We have used Monkhorst Pack k-point sampling in the calculations done by Quantum Espresso code. The k-point meshes are carefully chosen according to the unit cells considered, and convergence of total energies is checked with respect to the k-point sets. We have considered 65 Ry wave function cutoff and 450 Ry charge density cutoff, which are sufficient to take the delocalized character of electron into consideration. A 20 Å separation between the layers in the consecutive unit cells is considered to prevent the interaction between the layers. Structural optimization has been performed for each structure by minimizing the Hellman Feynman force with a tolerance of 0.001 Ry/a.u. with the same energy cutoff. Spin-polarized calculations were performed for all cases. The calculations with the HSE hybrid-DFT

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method were performed with the periodic boundary conditions (PBC)36 code implemented in Gaussian 0928 without any symmetry constraint. For these calculations, we exploited the 6-311G(d) valence triple-ζ basis set of Pople and co-workers29 and the default option by the program for the k-points depending on the cell size.

’ ASSOCIATED CONTENT

bS

Supporting Information. Complete refs 27 and 28 as well as optimal bond lengths and Cartesian coordinates of the various materials isomers. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected] (H.O.), biplab.sanyal@ fysik.uu.se (B.S.).

’ ACKNOWLEDGMENT We are grateful to the Carl Trygger Foundation for the postdoctoral fellowship of J.Z., the Swedish Research Council, and the Uppsala University KoF initiatives on graphene and molecular electronics (U3MEC) for financial support. We also acknowledge the National Supercomputer Center (NSC) in  SweLink€oping, UPPMAX in Uppsala, and HPC2N in Umea, den, for generous allotments of computer time. ’ REFERENCES (1) Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Zhang, Y.; Dubonos, S. V.; Grigorieva, I. V.; Firsov, A. A. Science 2004, 306, 666. (2) (a) Tung, V. C.; Allen, M. J.; Yang, Y.; Kaner, R. B. Nat. Nanotechnol. 2009, 4, 25. (b) Kechedzhi, K.; Horsell, D. W.; Tikhonenko, F. V.; Savchenko, A. K.; Gorbachev, R. V.; Lerner, I. V.; Fal’ko, V. I. Phys. Rev. Lett. 2009, 102, 066801. (c) Elias, D. C.; Nair, R. R.; Mohiuddin, T. M. G.; Morozov, S. V.; Blake, P.; Halsall, M. P.; Ferrari, A. C.; Boukhvalov, D. W.; Katsnelson, M. I.; Geim, A. K.; Novoselov, K. S. Science 2009, 323, 610. (d) Geim, A. K.; Novoselov, K. S. Nat. Mater. 2007, 6, 183. (e) Radovic, L. R.; Bockrath, B. J. Am. Chem. Soc. 2005, 127, 5917. (3) Meyer, J. C.; Chuvilin, A.; Algara-Siller, G.; Biskupek, J.; Kaiser, U. Nano Lett. 2009, 9, 2683. (4) Bai, J.; Zhong, X.; Jiang, S.; Huang, Y.; Duan, X. Nat. Nanotechnol. 2010, 5, 190. (5) Bieri, M.; Treier, M.; Cai, J.; Aït-Mansour, K.; Ruffieux, P.; Gr€oning, O.; Gr€oning, P.; Mastler, M.; Rieger, R.; Feng, X.; M€ullen, K.; Fasel, R. Chem. Commun. 2009, 6919. (6) Li, G.; Li, Y.; Liu, H.; Guo, Y.; Li, Y.; Zhu, D. Chem. Commun. 2010, 3256. (7) Watanabe, K.; Taniguchi, T.; Kanda, H. Nat. Mater. 2004, 3, 404. (8) (a) Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Katsnelson, M. I.; Grigorieva, I. V.; Dubonos, S. V.; Firsov, A. A. Nature 2005, 438, 197. (b) Meric, I.; Han, M. Y.; Young, A. F.; Ozyilmaz, B.; Kim, P.; Shepard, K. L. Nat. Nanotechnol. 2008, 3, 654. (c) Bai, J. W.; Zhong, X.; Jiang, S.; Huang, Y.; Duan, X. F. Nat. Nanotechnol. 2010, 5, 190. (9) Bundgaard, E.; Krebs, F. C. Sol. Energy Mater. Sol. Cells 2007, 91, 954. (10) Liu, A. Y.; Wentzcovitch, R. M.; Cohen, M. L. Phys. Rev. B 1989, 39, 1760. (11) Kawaguchi, M. Adv. Mater. 1997, 9, 615. (12) Panchokarla, L. S.; Subrahmanyam, K. S.; Saha, S. K.; Govindaraj, A.; Krishnamurthy, H. R.; Waghmare, U. V.; Rao, C. N. R. Adv. Mater. 2009, 21, 4726. 10270

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