Article pubs.acs.org/JPCA
Isoelectronic Doping of Graphdiyne with Boron and Nitrogen: Stable Configurations and Band Gap Modification Hongxia Bu,†,‡ Mingwen Zhao,*,† Hongyu Zhang,† Xiaopeng Wang,† Yan Xi,† and Zhenhai Wang† †
School of Physics and State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, China College of Science and Technology, Shandong University of Traditional Chinese Medicine, Jinan 250355, China
‡
ABSTRACT: Graphdiyne, consisting of sp- and sp2-hybridized carbon atoms, is a new member of carbon allotropes which has a natural band gap ∼1.0 eV. Here, we report our first-principles calculations on the stable configurations and electronic structures of graphdiyne doped with boron−nitrogen (BN) units. We show that BN unit prefers to replace the sp-hybridized carbon atoms in the chain at a low doping rate, forming linear BN atomic chains between carbon hexagons. At a high doping rate, BN units replace first the carbon atoms in the hexagons and then those in the chains. A comparison study indicates that these substitution reactions may be easier to occur than those on graphene which composes purely of sp2-hybridized carbon atoms. With the increase of BN component, the band gap increases first gradually and then abruptly, corresponding to the transition between the two substitution motifs. The direct-band gap feature is intact in these BN-doped graphdiyne regardless the doping rate. A simple tight-binding model is proposed to interpret the origin of the band gap opening behaviors. Such wide-range band gap modification in graphdiyne may find applications in nanoscaled electronic devices and solar cells.
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tubes22 and two-dimensional BNC nanosheet23,24 have been synthesized. Graphdiyne is a new layered carbon allotrope, which was first proposed by Haley et al.25 Quite different from graphene, graphdiyne is composed of sp- and sp2-hybridized carbon atoms, i.e., the sp2-hybridized C atoms form hexagons which are joined together by two acetylenic linkages (CCC C), as shown in Figure 1. Varying the number of acetylenic
INTRODUCTION Carbon, the fundamental element for life on earth, never stops to surprise the world with its various allotropes and fantastic physical properties. From fullerene to carbon nanotubes to graphene, these carbon allotropes consisting purely of sp2-like hybridized carbon atoms have drawn worldwide attention in the past two decades.1−3 Almost at the same time, the boron nitride (BN) analogs of these carbon allotropes have been proposed theoretically and synthesized via different methods.4−10 Because of the different electronegativity between boron and nitrogen atoms, most properties of these BN nanostructures differ significantly from their carbon counterparts, e.g., the former always has a wide band gap. Hybrid BCN structures constructed by incorporating B and N atoms into carbon network are interesting materials that are expected to possess tunable properties depending on the ratios of the components.11−18 For example, with the increase of the C ratio, the BN/C biribbons formed by joining two zigzag-edged BN and graphene nanoribbons undergo manifold electronic structure transition from semiconductor to half-metal and to ferromagnetic metal.18 BN quantum dots (QDs) embodied in graphene open a band gap in the semimetallic graphene,19 whereas the triangular-shaped graphene QDs embodied in graphene-like BN monolayer exhibit electron spin polarization, although neither graphene nor BN-graphene is magnetic.20,21 Motivated by the intriguing properties, considerable efforts have been devoted to the realization of BCN nanomaterials. Very recently, one-dimensional BNC heterostructured nano© 2012 American Chemical Society
Figure 1. Atomic structure of a (2 × 2) supercell of graphdiyne single layer. The primitive cell is indicated by the rhombus with dashed lines.
linkages yields a new family of carbon allotropes, e.g., graphyne (CC), etc. First-principles calculations have indicated that these allotropes have a natural band gap,26,27 in contrast to zero band gap graphene. So far, only graphdiyne has been Received: January 4, 2012 Revised: March 15, 2012 Published: March 21, 2012 3934
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was 3 × 3 × 1 according to the Monkhorst-Pack scheme.36 To check the convergence of the k-points sampling, we also adopted a 7 × 7 × 1 k-points mesh to calculate a selected configuration, and found that the total energy difference is less than 0.06 meV. Both lattice vectors and internal coordinates were fully optimized to get the equilibrium structures. The forces on atoms were converged to be less than 0.03 eV/Å, and the total stress tensor was reduced to the order of 0.05 GPa. The primitive cell of a graphdiyne single layer consists of 18 C atoms, as shown in Figure 1. Two-dimensional periodic boundary conditions along the x- and y-direction were applied to the graphdiyne, while a vacuum region of 20 Å was set along the direction perpendicular to the basal plane of graphdiyne (zdirection) to exclude the mirror interactions between adjacent images.
synthesized, although first-principles calculations showed that it is less stable than graphyne.26,28 The great progress in growing graphdiyne was achieved by Li’s group in 2010.29 They successfully synthesized large-area graphdiyne film on copper substrate via a cross-coupling reaction using hexaethynylbenzene. The experimental achievement reignites theoretical interest in the graphdiyne family and their analogs. By use of the GW many-body theory, Lu et al. improve the band gap value of graphdiyne monolayer from 0.44 eV given by localdensity-approximation (LDA) to 1.10 eV.30 The optical absorption spectrum obtained from the Bethe−Salpeter equation (BSE) calculations is in good agreement with the experimental result. The high mobility and high capacity of lithium in multilayered graphyne predicted in our previous work imply the potential applications of graphyne in lithium battery.28 The electronic structures of graphdiyne sheet and nanoribbons have been studied using first-principles calculations.27,31 The work of Shuai et al., indicates that the electron mobility in single graphdiyne sheet can reach 2 × 105 cm2/(V s) at room temperature, while that in graphdiyne nanoribbons is an order of magnitude lower which increases with the increase of ribbon width.27 Zhang et al. calculated the electronic structures and absorption behaviors of the BN analogs of graphyne and its family.32 Their work shows that these BN analogs have wide band gaps (3.803−4.202 eV) and a strong UV absorption. Sun et al. designed an interesting BCN analog of graphyne family, that is, BN hexagons joined together by C chains.33 They predicted that the band gap of the BCN analogs decreases monotonously from 2.65 to 1.14 eV with the increase of C-chain length from n = 2 to n = 12, n being the number of C atoms in a C-chain. This implies a possible way to modulate the band gap of graphyne family. In view of the intriguing properties of BN-doped graphene, isoelectronic doping of graphdiyne with B and N is an interesting issue and worth study. In this contribution, we focus on two basic questions. (1) Which site is preferable for BN doping in graphdiyne? (2) How BN-doping modulates the electronic structures of graphdiyne? To answer these questions, we perform first-principles calculations to investigate the energetically stable configurations and the corresponding electronic structures of BN-doped graphdiyne monolayer. Our numerical results indicate that BN units prefer to replace the sp-hybridized C atoms in the chain rather than the sp2hybridized C atoms in the hexagons at a low doping rate. With the increase of doping rate, the BN substitution for the sp2hybridized C atoms becomes dominant. A comparison study implies that these substitution reactions may be easier to take place than those on graphene. Increasing the BN concentration, the band gap of BN-doped graphdiyne increases first gradually and then abruptly, but the direct-band-gap feature is intact. We also present a tight-binding model to understand the origin of the band gap modulation behaviors.
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RESULTS AND DISCUSSIONS I. Pristine Graphdiyne. We first calculated the equilibrium configuration of pristine graphdiyne single-layer using the above-mentioned method, as shown in Figure 1. The optimized lattice constant is 9.37 Å, in good agreement with the result of previous works.26,30 The averaged C−C bond length in carbon hexagons is 1.41 Å, while the bond lengths along the C-chain are not uniform which are 1.39, 1.22, 1.33, 1.22, and 1.39 Å aligned from one carbon hexagon to adjacent carbon hexagon. These bond lengths correspond to the four types of C−C bonds in graphdiyne: (a) CC bonds joining two adjacent sp2hybridized C atoms around carbon hexagon; (b) CC bonds connecting a sp-hybridized C atom and a sp2-hybridized C atom; (c) CC bonds connecting two sp-hybridized C atoms; and (d) CC bonds connecting two sp-hybridized C atoms. Compared with high-symmetric graphene, the diversity of C−C bonds in graphdiyne offers more freedoms for BN doping. Distinct properties are therefore expectable in this new carbon network. II. Stable Configuration of BN-Doped Graphdiyne. Previous work23,37 has indicated that the B and N atoms incorporated into the carbon network of graphene prefer to occupy adjacent sites. Therefore, we follow the rule that each BN pair replaces two adjacent C atoms of graphdiyne in this work. To evaluate the relative energetic stability of BN-doped graphdiyne with different BN concentrations (represented by the number of BN pairs in per supercell, n), we define formation energy, E(n)form and a differential formation energy ΔE(n) using the formulas E(n)form = [E(n)BN − graphdiyne − Egraphdiyne − 2nμC + nμ BN] /n
(1)
... ΔE(n) = n × E(n)form − (n − 1) × E(n − 1)form
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(2)
...where E(n)BN−graphdiyne and Egraphdiyne are the total energies of BN-doped graphdiyne containing n BN pairs and pristine graphdiyne. μC and μBN are the chemical potentials of C atom in graphene and BN pair in graphene-like BN monolayer. We start to from doping a BN pair in one graphdiyne cell, corresponding to the doping rate of 1:9. When the B and N atoms are placed in adjacent sites, there are six doping configurations, as shown in Figure 2. Our first-principles calculations indicate that the energetically most stable configuration has the BN pair substituting the two carbon atoms in acetylenic linkage (CC) in the chain, as shown
METHODS AND COMPUTATIONAL DETAILS We performed first-principles calculations within densityfunctional theory (DFT) implemented in the CASTEP code.34 The electron−electron interaction was treated by using a generalized gradient approximation (GGA) with the exchange-correlation functional proposed by Perdew, Burke, and Ernzerhof (PBE).35 The interactions between valence electrons and core electrons were represented by ultrasoft pseudopotentials. The energy cutoff of the plane wave basis set was set to 280 eV. The k-points sampling of the Brillouin zone 3935
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structures by the number of BN pair (n) in one supercell and denote them as nBN-graphdiyne. For 2BN-graphdiyne, the substitution of chain atoms generates five isomers, as shown in the second column of Figure 2. Energy calculations indicate that the two BN pairs prefer to reside on the same chain, forming a BNBN bridge between two carbon hexagons. The length of this bridge, 6.62 Å, is slightly longer than that of the CCCC bridge, 6.54 Å, in undoped graphdiyne, which distorts the supercell of the 2BN-graphdiyne. The average length of the CCCC linkages in the 2BN-diyne is also enlarged to 6.57 Å. The formation energy of the 2BN-graphdiyne is reduced to 1.59 eV, compared to that of 1BN-graphdiyne. This implies that the doping BN pairs prefer to aggregate at the chains at low BN concentration, forming BNBN bridges between carbon hexagons. Such behavior differs significantly from those in BN-doped graphene where the BN aggregation takes place at carbon hexagons, forming BN domains.9 We paid more attention to the 3BN-graphdiyne structures, since the three BN pairs can replace a carbon hexagon. We considered eight possible isomers which can be classified to three types, as shown in the third column of Figure 2. Type I has the three BN pairs uniformly distributed at the chains. For type II, a BNBN linkage is formed accompanied by a BNCC bridge in an adjacent chain. A carbon hexagon is replaced by a BN hexagon in type III. Our calculations clearly showed that type II is energetically most favorable. The formation energy of the type-II is higher than that of the 2BN-graphdiyne by about 0.08 eV/BN pair. This suggests that compared with the BNBN linkage, the BNCC linkage in the 3BN-graphdiyne is energetically disadvantageous. Therefore, for the 4BN-graphdiyne isomers, the energetically most favorable structure has two BNBN linkages, as shown in the fourth column of Figure 2, and the formation energy is further reduced to 1.56 eV/BN pair, compared to that of 3BNgraphdiyne. When the BN ratio is further increased to 5BN-graphdiyne, the energetically favorable modify changes. The five BN pairs replace first the six carbon atoms in a carbon hexagon and then the chain carbon atoms, forming BN(BN hexagon) BN, as shown in the fifth column of Figure 2. The BN pairs prefer to align in the same chains to reduce the ratios of BNCC and CBNC. Our calculations indicate that this modify dominates the stable configurations of nBN-graphdiyne for n ≥ 5. Figure 3 gives the formation energies and differential formation energies of the most stable nBN-graphdiyne (n = 1−9). The data of correspondent BN-doped graphene are also plotted for comparison. Notably, the formation energy of nBNgraphdiyne (Figure 3a) decreases with the increase of n, while there are local minima of differential formation energies corresponding to n = 2, 4, and 7, as shown in Figure 3b. For BN-doped graphene, the appearance of each ΔE(n) local minimum is accompanied by the formation of a BN hexagon in carbon network. For the nBN-graphdiyne, however, it corresponds to the formation of a BNBN chain. It is interesting to see that the local minima of nBNgraphdiynes are lower than those of BN-doped graphene, confirming that the BN substitution reactions are energetically preferable in graphdiyne consisting of sp- and sp2-hybridized carbon atoms rather than in graphene with sp2-hybridized carbon atoms. 7BN-graphdiyne which is made up of a BN
Figure 2. The primitive cells of nBN-graphdiynes (n = 1−8) with different isomeric structures. The energetically most favorable isomers are plotted in the front row, whose formation energies (in eV per BN) are listed in the parentheses. The numbers in parentheses from the second row represent formation energies referenced to the most stable isomers.
in the front row of Figure 2. In this configuration, the effects of BN doping on the bond feature of graphdiyne is reduced to minimum. The π-bonds in carbon hexagons and the residual acetylenic linkages in the chains are preserved. The energetic disadvantage of other configurations is related to the breakage of π-bonds or CC bonds induced by BN doping which increases the energy of the systems. Structural optimization shows that the bond lengths of CN, NB, and BC bond in the most stable configuration are 1.32, 1.25, and 1.43 Å, respectively. The length of the NB linkage is 4.00 Å, slightly longer than that of the CC linkage, 3.94 Å. Slight distortion in the graphdiyne lattice is therefore inevitable. The lengths of the two basis vectors are enlarged to 9.41 Å and 9.40 Å, compared to 9.37 Å and 9.37 Å of undoped graphdiyne. It is noteworthy that the positive formation energy of the BN-doped graphdiyne implies that the BN substitution reaction in graphdiyne is endothermic. To evaluate the feasibility of the BN substitution we calculated the formation energy of BNdoped graphene, according to the definition in formula 1. We employed a (3 × 3) graphene supercell doped with a BN pair. This BN-doped graphene has the same stoichiometry as the BN-doped graphdiyne. We found that the formation energy of the BN-doped graphene, 3.64 eV, is higher than that of the BNdoped graphdiyne, 1.89 eV. The codoping of graphene with boron and nitrogen atoms has been achieved experimentally. Therefore, the lower formation energy of BN-doped graphdiyne compared to BN-doped graphene implies the high feasibility of the BN substitution reaction in graphdiyne. We further increase the BN concentration in BN-doped graphdiyne. Hereafter, we classify the BN-doped graphdiyne 3936
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Figure 4a. This band gap is slightly larger than the LDA result, 0.44 eV.30 As we well know, both GGA and LDA functionals always underestimate the band gap values. We also adopted more accurate Heyd-Scuseria-Ernzerhof (HSE) hybrid functional to calculate the band gap of graphdiyne.38,39 We found that the HSE band gap 1.10 eV is in good agreement with the GW band gap.30 Spatial distribution of wave functions corresponding to the valence band maximum (VBM) and conduction band maximum (CBM) indicate that they arise from the π-bindings between the C(2pz) orbitals on the basal plane, as shown in Figure 5a. However, different from the case
Figure 3. The formation energy (a) and the differential formation energy (b) of the most stable nBN-graphdiyne (n = 1−9) as a function of n. The corresponding data of BN-doped grapheme are also plotted for propose of comparison.
hexagon, two BNBN linkages, and one C CCC linkage (as shown in Figure 2) has the lowest value of ΔE(n). Notably, high-symmetric motifs, such as BNhexagons joined by three CCCC linkages33 or carbon hexagons bridged by three BNBN linkages, are energetically disadvantageous from the present calculations. For examples, our present calculations showed that the formation energy of the 3BN-graphdiyne composing of BN hexagons joined by CCCC linkages is higher than that of the most stable isomer by about 0.44 eV/BN. III. Electronic Structures of BN-Doped Graphdiyne. We first studied the electronic band structures of a pristine graphdiyne single layer. Our DFT-GGA calculations gave a direct band gap of about 0.53 eV at the γ point, as shown in
Figure 5. The isosurfaces of the Kohn−Sham states of the VBM and CBM of graphdiyne and the most stable nBN-graphdiynes with n = 2, 4, and 7 at the γ point.
of graphene, the π-bindings are inhomogeneous in graphdiyne, i.e., the π-bindings in the chains differ from those around the
Figure 4. The band structures of (a) pristine graphdiyne; (b) 2BN-graphdiyne; (c) 4BN-graphdiyne; (d) BNdiyne. The Brillouin zone is shown in the inset of (d). The energy at the valence band maximum is set to zero. 3937
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that the band gap of the sp-sp2 hybridized carbon network can be tuned by changing the inhomogeneity of the π-bindings. When BN pairs are incorporated in the sp-sp2 hybridized network, the inhomogeneity of the π-bindings will be increased and the band gap modification is expectable, as shown in parts b−d of Figure 5. Additionally, the ionic-features of the B−N binding localize the electron states and contribute to the band gap modification. We applied the TB Hamiltonian to the BN analog of graphdiyne (BNdiyne) by taking the different on-site energies of B and N atoms into account. We found that the band gap of the BN analog of graphdiyne is much wider than that of graphdiyne. This was also confirmed by the DFT+GGA calculations of the BN analog which show a direct band gap of 4.39 eV at the γ point, as shown in Figure 4d. Therefore, it is not surprising that the band gap of BN-graphdiyne varies in between the values of pristine graphdiyne and BNdiyne as a function of BN ratio. We calculated the band structures of the energetically most stable nBN-graphdiyne for n = 1−8. We found that the direct band gap at the gamma point is preserved, as shown in parts b and c of Figure 4. This suggests that the γ point direct band gap feature is related to the atomic arrangement rather than the atomic species. This was also confirmed by our TB model. We changed randomly the on-site energies and hopping integrals but fixed that atomic arrangement and found that the band gap always appears at the γ point. The direct-band gap feature is crucial for the optoelectronic device applications. The variation of band gap Eg of nBN-graphdiyne with the increase of n exhibits two stages, as shown in Figure 7. For n ≤
carbon hexagons. This is also confirmed by the different bond lengths in these two regions. The natural band gap of graphdiyne may be related to such inhomogeneous π-bindings To verify the origin of the band gap of graphdiyne, we propose a tight-binding (TB) Hamiltonian of the π-electrons of graphdiyne, as follows H=
∑ εici+ci − ∑ i
tij(ci+cj + hc)
where, εi, and ci are the on-site energy, creation, and annihilation operators of an electron at the ith atom, respectively, and hc is the Hermitian conjugate. The parameter tij is hopping integral of an electron between the ith and jth atoms. For simplification, in graphdiyne, we omitted the on-site energy difference of an electron in sp2- and sp-hybridized carbon atoms and considered only the hopping between nearest-neighboring atoms.40 The hopping integrals tij in graphdiyne can be classified into four types, hopping between two adjacent sp2-hybridized C atoms (t1); hopping between adjacent sp- and sp2-hybridized C atoms (t2); hopping between two adjacent sp-hybridized C atoms (t3 and t4), as shown in Figure 6a. Band lines can be obtained by diagonalizing the TB c+i ,
Figure 6. (a) Schematic represent of nearest-hopping model of the πelectrons in graphdiyne. The band lines calculated by using tightbinding model within nearest-hopping approximation with the parameters: (b) t1 = t2 = t3 = t4 = 2.70 eV; (c) t1 = 2.70 eV, t2 = 2.50 eV, t3 = 2.80 eV, t4 = 2.50 eV.
Figure 7. The band gap variation of the most stable nBN-graphdiynes with respect to the number of BN units.
4, Eg changes slightly around ∼1.0 eV. In the stage, BN pairs prefer to substitute the C atoms in the chains. For n ≥ 5, the BN substitution reactions prefer to occur at the hexagons and the Eg increases drastically. Although, DFT+GGA scheme always underestimates the band gap values of the nBNgraphdiyne, the variation trend revealed in these calculations is reasonable. The tunable band gap of nBN-graphdiyne is helpful for the possible applications in nanoscaled devices.
Hamiltonian. We found that if the four types of hopping integrals are set to be identical, a zero band gap accompanied by a linear dispersion appears at the γ point, as shown in Figure 6b. However, our first-principles calculations have shown that the bond lengths corresponding to these four types of hopping are different, which are 1.41, 1.39, 1.22, and 1.33 Å, respectively. Therefore, the hopping integrals are no longer identical. Figure 6c gives the TB band lines near the Fermi level with the parameters t1 = 2.70 eV, t2 = 2.50 eV, t3 = 2.80 eV, t4 = 2.50 eV, respectively. The band gap, 0.53 eV, and the band dispersion given by TB model agree well with the DFT-GGA calculations. The profiles of the bands near the Fermi level (shown in Figure 6c) are also very similar to those obtained from DFT-GGA calculations (shown in Figure 4a). The above results confirmed that the natural band gap of graphdiyne can be attributed to the inhomogeneous π-bindings in sp-sp2 hybridized carbon network. More interestingly, this implies
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CONCLUSIONS In summary, our first-principles calculations of nBN-graphdiyne revealed two types of substitution motifs: the chain-first motif and the hexagon-first motif. At low doping rate with n ≤ 4, the former is dominant, i.e., the BN pairs prefer to substitute the C atoms in the chains, while for n ≥ 5, the BN pairs replace first the C atoms in the hexagons and then the C atoms in the chains (hexagon-first motif). The formation energies of nBNgraphdiyne are lower than those of the BN-doped graphene with the same stoichiometry, implying that the BN substitution 3938
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reactions in graphdiyne may be easier to occur than those on graphene. With the increase of the BN ratio, the band gap increases first gradually and then abruptly, corresponding to the two different substitution motifs. The direct-band gap feature at the γ point is intact. The band gap modification of nBNgraphdiyne can be attributed to the inhomogeneity of the πbindings as well as the electron state localization. The tunable direct band gap of nBN-graphdiyne may find applications in nanoscaled electronic devices and solar cells.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work is supported by the National Basic Research Program of China (Grant No. 2012CB932302), the National Natural Science Foundation of China (Grant No. 10974119), and the Natural Science Fund for Distinguished Young Scholars of Shandong Province (Grant No. JQ201001).
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