Electronic Structures of Porous Graphene, BN, and BC2N Sheets with

ARTICLE pubs.acs.org/JPCC

Electronic Structures of Porous Graphene, BN, and BC2N Sheets with One- and Two-Hydrogen Passivations from First Principles Yi Ding,*,† Yanli Wang,*,‡ Siqi Shi,‡ and Weihua Tang‡ † ‡

Department of Physics, Hangzhou Normal University, Hangzhou, Zhejiang 310036, People’s Republic of China Department of Physics, Center for Optoelectronics Materials and Devices, Zhejiang Sci-Tech University, Xiasha College Park, Hangzhou, Zhejiang 310018, People’s Republic of China ABSTRACT: Using first-principles calculations, we investigate the structural and electronic properties of monolayer porous graphene (C), BN, and BC2N sheets. All the porous C, BN, and BC2N sheets with one-hydrogen passivation exhibit directband-gap semiconducting behaviors. The porous BN sheet has a larger band gap than the porous C one, whereas the porous BC2N sheets have variable band gaps depending on the atomic arrangements of B, C, and N atoms. The stablest conformation of porous BC2N sheets is composed of C and BN hexagons, whereas with two-hydrogen passivation, it becomes the structure containing continuous BN and interrupted C zigzag lines. Furthermore, due to the sp3 hybridization of the edge atoms, the two-hydrogen passivation induces the changes of band gaps as well as direct-to-indirect band-gap transitions in all the porous sheets. We also find that it is more possible to form the porous C and BC2N structures in experiments than the porous BN ones. Our studies demonstrate that the porous C, BN, and BC2N sheets have semiconducting behaviors with practical band engineering by different hydrogen passivations.

’ INTRODUCTION Carbon-based nanostructures have attracted lots of interest in condensed matter physics and material sciences due to their novel mechanical, optical, and electronic properties.1-3 Among these nanostructures, graphene, the two-dimensional (2D) monolayer of carbon sheet, becomes one exciting topic in the recent research.4-8 Many unconventional electronic properties of graphene, such as ultrahigh carrier mobilities, near ballistic transport at room temperature, room-temperature quantum Hall effect, and tunable energy gaps, make it a promising material for future nanoelectronics and nanodevices.4-10 Graphene is fabricated by the micromechanical cleavage technique from the layered graphite initially.4 Later, serval high-yield productions of graphene are reported by the chemical methods, such as epitaxial growth on SiC surfaces, chemical vapor deposition on metal surfaces, and reduction of graphite oxide.11-13 The perfect graphene sheet is a semimetal with a zero band gap, for which the size and edge effects have great impacts on its electronic structure.6,8 The corresponding graphene nanoribbons (GNRs) are predicted to be semiconductors with direct energy band gaps theoretically.9 Through the temperature-dependent conductance measurements, experimenters have confirmed the semiconducting behaviors of GNRs and found that the band gaps are inversely proportional to the ribbon widths.10 Taking advantage of these size and edge effects, the electronic properties of GNRs are tuned by edge functionalizations and edge substitutions.14-19 The 2D hexagonal BN sheet has a analogous structure to graphene. In experiments, the BN sheet has been successfully fabricated by the micromechanical cleavage technique,20 the r 2011 American Chemical Society

chemical-solution-derived method,21 and controlled energetic electron beam irradiation through a sputtering process.22,23 The BN sheet is a semiconductor with a large indirect energy gap.24,25 The corresponding BN nanoribbons (BNNRs) are also semiconductors with one-hydrogen-passivated edges.26-28 The band gaps of BNNRs could be tuned by different edge passivations.29-32 The zigzag BNNRs present half-metallic behaviors when the boron edge is one-hydrogen-passivated, whereas the nitride edge is bare.29 Under a hydrogen-rich environment, the zigzag BNNRs with two-hydrogen-terminated edges become ferromagnetic metals.32 Moreover, the electronic and magnetic properties of the BNNRs could be modulated by applying an extra transversal electric field.27,28 The bare zigzag BNNRs can undergo a metallic-semiconducting-half-metallic transition under the increasing electric field.33 Additionally, doping C atoms to the BN systems could lead to spontaneous magnetization.34,35 The hybrid C/BN nanostructures exhibit quite interesting electronic and magnetic properties, which could present the half-metallic characteristics even without applying extra electric field.36-39 For the ordered B-C-N crystals, the graphite-like BC2N materials have been fabricated by the high-pressure/high-temperature synthesis method.40,41 Theoretical calculations predict that the monolayer graphene-like BC2N sheet is a direct-band-gap semiconductor.42-44 The band gap is enlarged when the BC2N sheet is fully hydrogenated.45 For the BC2N nanoribbons with Received: October 28, 2010 Revised: February 5, 2011 Published: March 04, 2011 5334

dx.doi.org/10.1021/jp110336r | J. Phys. Chem. C 2011, 115, 5334–5343

The Journal of Physical Chemistry C

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Figure 1. Structures, band structures, and DOSs of (a, c, e) the porous C sheet and (b, d, f) the porous BN sheet. The solid lines in (a) and (b) denote the unit cells of the porous structures. The partial charge densities of (g) the VBM and (h) the CBM for the porous C sheet. The isosurface is 0.002 e/Å3. The Fermi levels are indicated by the dotted lines in (c) and (d), and the vacuum level is set to be 0 eV.

armchair edges, magnetism could be produced due to the localization of acceptor or donor levels from edge atoms.46 Besides numerous experimental and theoretical studies on the nanosheets, nanotubes, nanoribbons, and nanoflakes, great efforts have been devoted to explore other types of nanostructures. Recently, a highly regular BN nanomesh with hexagonal pores has been formed by high-temperature decomposition of borazine (HBNH)3 on a Rh(111) surface.47 The graphene nanomeshes with a high-density array of nanoscale holes have also been prepared by the block copolymer lithography approach.48 The nanomesh structure transforms the graphene sheet from a semimetal into a semiconductor with a tunable band gap.48,49 In addition, triangular nanoholes with zigzag edges could produce magnetism in both the graphene and the BN sheets.50,51 Recently, a 2D porous

graphene framework with single-atom wide pores and subnanometer periodicity has been fabricated by the coupling of welldesigned molecular building blocks on the Ag surface.52 A similar porous polyphenylene framework has also been synthesized.53 Theoretical calculations find that, unlike the pristine graphene, such a porous structure presents a typical semiconducting behavior with a wide band gap.54-56 Moreover, theoretical calculations have revealed that porous graphene is a promising hydrogen storage material54 and exhibits remarkably high selectivity for small molecule separations, such as H2 and He.55,57 In this paper, we perform a systematic investigation on this porous C structure and its BN and BC2N analogues by first-principles calculations. Both the one-hydrogen passivation for sp2 hybridization and the two-hydrogen passivation for sp3 hybridization are considered. 5335

dx.doi.org/10.1021/jp110336r |J. Phys. Chem. C 2011, 115, 5334–5343


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Table 1. Calculated Lattice Constants, a; Bond Lengths, d; Cohesive Energies, Ec; Band Gaps, Eg; Formation Energies, Ef; and the Values of the CBM, VBM, Fermi Level (Efermi), and Work Function (WF) for the One-Hydrogen-Passivated Porous C, BN, and BC2N Sheets a

dC-C

dB-N

dC-B

dC-N

dC-H

dB-H

dN-H

Ec

Eg

Ef

CBM

VBM

Efermi

WF

(Å)

(Å)

(Å)

(Å)

(Å)

(Å)

(Å)

(Å)

(eV/atom)

(eV)

(meV/atom)

(eV)

(eV)

(eV)

(eV)

-7.68

2.35

41

-3.59

-5.94

-4.77

4.77

1.21

1.02

-7.33

4.27

91

-2.29

-6.56

-4.42

4.42

C

7.44

BN

7.54

1.39/1.48

1.09 1.42/1.47

BN-L

7.55/7.51

1.39/1.48

1.43/1.51

1.49

1.34

1.09

1.19

1.02

-7.35

0.94

63

-3.96

-4.90

-4.43

4.43

C-L C-BN

7.41/7.53 7.65

1.40/1.44 1.39

1.43/1.45 1.42

1.52 1.56

1.36

1.09/1.11 1.10

1.21

1.03 1.02

-7.38 -7.49

1.26 3.52

36 -70

-3.74 -3.01

-5.00 -6.53

-4.37 -4.77

4.37 4.77

C-NB

7.41

1.39

1.43

1.44

1.08

1.19

-7.36

2.81

57

-2.99

-5.80

-4.31

4.31

The structural and electronic properties of porous C, BN, and BC2N sheets with different hydrogen passivations are obtained in detail.

’ METHODS The first-principles calculations are performed by the VASP code.58,59 The total energies and electronic structures are calculated within density functional theory using a plane-wave basis set and projector-augmented wave pseudopotentials. For the exchange and correlation (XC) functional, the local density approximation (LDA) is adopted. The plane-wave cutoff energy is set to be 550 eV. Supercells are used to simulate the isolated sheets, and the distance between sheets is larger than 12 Å in order to avoid interlayer interactions. The Monkhorst-Pack scheme is used to sample the Brillouin zone on a 15 15 1 k-mesh grid. The optimizations of the lattice constants and the atom coordinates are made by minimizing the total energies. All the sheets are fully relaxed until the force on each atom is less than 10-2 eV/Å and the total energy changes are less than 10-4 eV. ’ RESULTS AND DISCUSSION Porous C and BN Sheets. Figure 1a presents the optimized structure of the porous C sheet, which resembles the pristine graphene sheet with periodically missing C hexagons. Similar to the GNRs, each carbon atom at the hole edge is passivated by one hydrogen atom. The hydrogen and carbon atoms are in the same plane, which indicates the sp2-hybridized bonding of C atoms. Following the conventions of porous graphene,55 there are two types of carbon atoms in the porous C sheet: the C1 and C2 atoms bonding with and without hydrogen atoms. The corresponding C1-C2 bonds are in the C hexagons only, whereas the C2-C2 bonds link the different hexagons. The calculated structural parameters are listed in Table 1. We obtained the lattice constant value of 7.45 Å, which agrees well with the experimental measurements (7.4 Å)52 and the previous calculations by Du et al. (7.45 Å)54 and Li et al. (7.455 Å).55 The lengths of the C1-C2 and C2-C2 bonds are 1.39 and 1.48 Å, respectively, and the length of the C1-H bond is 1.09 Å. These calculated values are also in good accordance with the previous study.55 The band structure and density of states (DOSs) of the porous C sheet are shown in Figure 1c,e. Unlike the semimetallic property of graphene, the porous C sheet is a semiconductor with a direct band gap. The band gap is 2.35 eV at the K point, which agrees well with the previous LDA calculation of 2.34 eV.54 The partial DOS analysis in Figure 1e shows that the occupied and

unoccupied states near the Fermi level are contributed by the p orbitals of the C atoms mainly. The band gap is opened between the π- and π*-character bands from the C atoms. A peak of the H s orbital locates about 3 eV below the Fermi level, which corresponds to C-H σ bonding states in the valence bands. According to the facts of graphene nanomeshes,48,60 the bandgap formation in the porous C sheet can be attributed to the quantum confinement of the carbon hexagonal area between the neighboring holes. The band-gap values, Eg, of the graphene nanomeshes scale inversely with the carbon sectional widths, w (defined as the smallest edge-to-edge distance between two neighboring holes), which is expressed as Eg = R/w, with R = 0.95 nm 3 eV.60 For the porous C sheet, the w is 0.427 nm and the band gap is estimated to be 2.22 eV. This value is very close to our LDA result of 2.35 eV. It should be noticed that the DFT Kohn-Sham approach within the LDA XC functional, in general, underestimates the band gaps of materials. An accurate firstprinciples calculation of band gaps requires a quasi-particle approach or hybrid XC functional calculations.54 However, the basic physics discovered here has not been changed. Similar to the porous C sheet, the porous BN sheet can be viewed as the BN sheet with periodical BN hexagonal vacancies, as shown in Figure 1b. In the unit cell of the porous BN sheet, two BN hexagons are joined together via a B-N bond. Similar to the porous C sheet, two types of boron (nitride) atoms exist in the sheet: the B1 (N1) atom bonds with one hydrogen atom and two nitride (boron) atoms, and the B2 (N2) atom bonds with three nitride (boron) atoms. There are also two types of B-N bond lengths existing in the porous BN sheet. The length of the B1-N2 and B2-N1 bonds in the BN hexagons is 1.42 Å, and the length of the B2-N2 bond between the BN hexagons increases to 1.47 Å. The calculated B1-H and N1-H bond lengths are 1.21 and 1.02 Å, respectively, which are almost identical to those of a free borazine molecule.61 The porous BN sheet is a direct-band-gap semiconductor, as shown in Figure 1d. Our LDA calculations determine that the band-gap value at the K point is 4.27 eV, which is larger than that of the porous C sheet. The large band gaps of BN systems are attributed to the strong ionicity of B-N bonds.24,27 Like the pristine BN sheet and BNNRs, in the porous BN sheet, the top valence bands come mainly from the p orbitals of the N atoms, whereas the bottom conduction bands come from the p orbitals of B atoms. The peak of the H s orbital locates at about EF - 1.5 eV in the valence bands, as shown in Figure 1f. The holes slightly affect the electronic structures, which causes the porous BN sheet to have a smaller gap than that (4.53 eV) of the pristine BN one. Previous tight-binding calculations within the simple H€uckel 5336



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Figure 2. Four conformations of the porous BC2N sheets.

approximation have shown that the bands in the K-M range for the porous C sheet are completely flat.56 Such zero dispersions originate from the zero HOMO-HOMO and LUMO-LUMO interactions between the nodal points.56 Our first-principles calculations show that the partial charge densities (the band decomposed charge densities of |ψnk|2 at the special k point for the nth band, which is equivalent to the square of the frontier Bloch functions in the H€uckel approximation) of the porous C sheet also display the nodal character, as shown in Figure 1. However, we obtain nonzero band widths. For the porous C sheet, the widths of the top valence band and the bottom conduction band are 0.15 and 0.39 eV, respectively. For the porous BN sheet, those bands near the Fermi level are flatter, which are only 0.05 and 0.22 eV, respectively. Previous studies have shown that, for the graphene and relative carbon nanostructures, the tight-binding methods with the nearest-neighbor interactions agree with the first-principles calculations only in a limited range of wave vectors, and interactions up to the thirdnearest neighbors are needed to reproduce the first-principles results.62 When more distant neighbors are included, the interactions between the nodal points are no longer zero, which will lead to a nonzero dispersion. Thus, these flat frontier bands obtained from the first-principles calculations deviate from the zero band widths of the tight-binding results for the porous sheets. Porous BC2N Sheets. Next, we discuss the structural and electronic properties of the porous BC2N sheets. Using the same unit cell as those of the porous C and BN sheets, four conformations of porous BC2N sheets are considered as the ordered C/BN hybrid structures. As shown in Figure 2, for the BN-L and C-L conformations, each hexagon is composed of mixed C, B, and N atoms. In the BN-L conformation, there are BN zigzag lines crossing the porous structure, while the C zigzag lines are interrupted by holes. For the C-L conformation, it contains the continuous C zigzag lines and interrupted BN ones. For the C-BN and C-NB conformations, both contain a C hexagon and a BN hexagon in the unit cell. In the C-BN conformation, the hexagons

are connected via the C-B bonds, whereas in the C-NB conformation, they are via the C-N bonds. The calculated structural parameters of these four BC2N sheets are listed in Table 1. Due to the symmetry breaking by the formation of BN (C) zigzag lines, two in-plane lattice constants are not equivalent in the BN-L (C-L) conformation, as shown in Table 1. In the C-BN and C-NB conformations, the two lattice constants are still equivalent. The lengths of C-C, B-N, and X-H (X = B, N, C) bonds are nearly the same as those in the porous C and BN sheets. However, the existence of long C-B bonds elongates the lattice, whereas the short C-N bonds decrease the lattice a little. Thus, the C-BN conformation has the longest lattice constant and the C-NB conformation has the shortest one. The stabilities of these porous BC2N sheets are compared by the cohesive energies, Ec, which are calculated as the difference between the energies of the porous sheets and the sum of the corresponding isolated atom energies. The cohesive energy Ec represents the energy required to decompose the sheets into isolated atoms. It is Ec = Eporous - nBEB atom - nNEN atom - nCEC atom - nHEH atom, where EB atom, EN atom, EC atom, and EH atom are the isolated atom energies of the B, N, C, and H elements. These cohesive energies can be used to compare with the experimental results, which are obtained by measuring the latent heat of sublimation at various low temperatures and extrapolating to zero Kelvin.63 Table 1 shows that the C-BN conformation has the lowest cohesive energy among the four conformations. It is 0.11 eV/atom lower than the C-L conformation, 0.13 eV/atom lower than the C-NB conformation, and 0.14 eV/atom lower than the BN-L conformation. For the pristine BC2N sheet, previous studies show that the most stable structure has the maximum number of C-C and B-N bonds.42,64,65 It is also applicable for the porous BC2N sheets. The BN-L conformation has five C-C bonds and six B-N bonds, and the C-L conformation has six C-C bonds and five B-N bonds in the unit cell. The C-BN and C-NB conformations have the maximal six C-C and six B-N bonds. Considering that the C-B and N-H 5337



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Figure 3. (a) The band structure and (b) the DOS for the C-BN conformation of the porous BC2N sheet. The partial charge densities of (c) the VBM and (d) the CBM for the C-BN conformation. The isosurface is 0.002 e/Å3, and the Fermi level is indicated by the dotted line in (a). The vacuum level is set to be 0 eV.

bonds are more favorable than the C-N and B-H ones, the C-BN conformation is more stable than the C-NB one. Thus, different from the pristine BC2N sheet, which is composed of alternating C and BN zigzag lines,42 the most stable porous BC2N sheet is composed of C and BN hexagons as the C-BN conformation. The structural stabilities also relate to the absolute values of the Fermi levels. The more negative value of the Fermi level corresponds to the larger work function, which means stronger bound electrons and a higher stability for the normal surfaces. As shown in Table 1, the C-BN conformation is the stablest structure among the four porous BC2N conformations, which also has the largest work function of 4.77 eV. Similar to the porous C and BN sheets, these porous BC2N sheets are direct-band-gap semiconductors. For the porous BC2N sheets, we find that the band gaps are sensitive to the atomic arrangements of B, C, and N atoms. The C-BN and C-NB conformations have larger band gaps than that of the pristine BC2N sheet (about 1.6 eV),42,45 whereas the C-L and BN-L conformations have smaller ones. As listed in Table 1, the gap values Eg follow the order of C-BN (3.52 eV) > C-NB (2.81 eV) > C-L (1.26 eV) > BN-L (0.94 eV). As the most stable structure, the C-BN conformation has the largest band gap, as shown in Figure 3, which is even larger than that of the porous C sheet. The partial DOS analysis indicates that the top valence bands are contributed by the p orbitals of C and N atoms only, whereas the bottom conduction bands are from the p orbitals of B, C, and N atoms. The H s orbitals overlap with the p orbitals from the B, C, and N atoms at around EF - 3 eV in the valence bands. The partial charge density isosurfaces in Figure 3c,d are consistent with the partial DOS analysis. The valence band maximum (VBM) is composed of the pz orbitals of the N atoms and the π-bonding orbitals between the C1 and C2 atoms. The conduction band minimum (CBM) is composed of the pz orbitals of the

C1 and N1 atoms and the π-antibonding orbitals between the C2 and B2 atoms. It is different from the pristine BC2N sheet, in which both the VBM and the CBM are composed of the p orbitals of C atoms.44 Two-Hydrogen-Passivated Sheets. For the pristine C, BN, and BC2N sheets, the electronic properties can be tuned by the adsorption of hydrogen atoms.25,45,66-69 The full hydrogenation can transform the sp2-hybridized semimetallic graphene to the sp3-hybridized semiconducting graphane.66,67 The hydrogenation also increases the band gap of the pristine BC2N sheet,45 but decreases the band gap of the pristine BN sheet.25,68 Here, we consider the porous structures with each atom at the hole edge bonding with two hydrogen atoms. To distinguish with sp2hybridized ones, those two-hydrogen-passivated porous sheets are denoted by adding -2H after their names. For the porous C-2H sheet, the C1 atoms become sp3-hybridized bondings, whereas the C2 atoms remain sp2 ones. The carbon atoms are still in the same plane, whereas the hydrogen atoms distribute symmetrically at both sides of the porous C-2H sheet. Similar structural features are also obtained for the porous BN-2H and BC2N-2H sheets. Because of the sp2-sp3 transformation, the bond lengths in the hexagons are elongated and weakened, which leads to the bigger lattice constants, as shown in Table 2. However, through the charge differences in Figure 4, it can be seen that the bonds between the hexagons are shortened and strengthened. Thus, the stabilities of porous BC2N sheets are not depending on the total number of C-C and B-N bonds but are determined by those between two hexagons and the bonds with H atoms. Among the four conformations of porous BC2N-2H sheets, the stablest one becomes the BN-L-2H conformation. In the BN-L-2H and C-L-2H conformations, there are C-C and B-N bonds existing between the hexagons. However, there are eight C-H bonds in the unit cell of the BN-L-2H conformation, 5338



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Table 2. Calculated Lattice Constants, a; Bond Lengths, d; Cohesive Energies, Ec; Band Gaps, Eg; Formation Energies, Ef; and the Values of the CBM, VBM, Fermi Level (Efermi), and Work Function (WF) for the Two-Hydrogen-Passivated Porous C, BN, and BC2N Sheets a

dC-C

dB-N

dC-B

dC-N

dC-H

dB-H

dN-H

Ec

Eg

Ef

CBM

VBM

Efermi

WF

(Å)

(Å)

(Å)

(Å)

(Å)

(Å)

(Å)

(Å)

(eV/atom)

(eV)

(meV/atom)

(eV)

(eV)

(eV)

(eV)

-6.65

3.14

-35

-1.67

-4.81

-3.24

3.24

1.26

1.06

-6.21

2.78

179

-1.89

-4.67

-3.28

3.28

C-2H

7.45

BN-2H

7.51

1.49/1.35

1.12 1.52/1.34

BN-L-2H

7.57/7.52

1.49/1.35

1.54/1.38

1.55

1.44

1.12

1.24

1.04

-6.42

2.58

-17

-1.99

-4.57

-3.28

3.28

C-L-2H C-BN-2H

7.51/7.49 7.73

1.50/1.34 1.50

1.52/1.34 1.53

1.58 1.42

1.46

1.12 1.13

1.26

1.06 1.04

-6.33 -6.31

2.93 1.08

71 86

-2.03 -2.31

-4.96 -3.39

-3.50 -2.85

3.50 2.85

C-NB-2H

7.35

1.47

1.52

1.30

1.12

1.24

-6.40

3.45

-5

-2.61

-6.06

-4.34

4.34

Figure 4. Charge differences of the one-hydrogen-passivated porous (a) C sheet, (c) BN sheet, and (e) C-BN conformation of BC2N sheets and the two-hydrogen-passivated porous (b) C sheet, (d) BN sheet, and (f) BN-L conformation of BC2N sheets. The charge difference is defined as ΔF = Fsheet - Fatom, which is obtained by subtracting the charge density of atoms from those of the porous sheets.

whereas only four, six, and six C-H bonds exist for the C-L-2H, C-BN-2H, and C-NB-2H conformations, respectively. Because the C-H bonds are stronger than the B-H and N-H ones, the BN-L-2H conformation becomes the most favorable porous BC2N-2H sheet. Previous studies show that, when a dipole is formed in the surface, it will decrease the work function and lead to the stable surface with a low work function.70,71 In the twohydrogen passivations, the hydrogen atoms are located out of the porous sheet, which forms local dipoles to lower the work function. Thus, as shown in Table 2, the work functions of

porous C-2H and BN-2H sheets are decreased from the onehydrogen passivations significantly. The stablest BC2N-2H sheet is the C-BN conformation, which also has a medium value of work function among the four conformations. Figure 5 displays the band structures and the DOSs of the porous C-2H and BN-2H sheets and the stablest conformation of the BC2N-2H sheet. We find that these porous sheets exhibit semiconducting behaviors with indirect band gaps, which is different from the direct band-gap nature of their one-hydrogen-passivated porous sheets and the hydrogenated pristine 5339



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Figure 5. Band structures and the DOSs of the two-hydrogen-passivated porous (a, b) C sheet, (c, d) BN sheet, and (e, f) BN-L conformation of the BC2N sheet. The Fermi levels are indicated by the dotted lines in (a), (c), and (e), and the vacuum level is set to be 0 eV.

sheets.45 Comparing to the one-hydrogen-passivated porous sheets, the hydrogenation raises the band gap of the porous C-2H sheet, whereas it lowers that of the porous BN-2H one. The band gap (3.14 eV) of the porous C-2H sheet becomes larger than that (2.78 eV) of the porous BN-2H sheet. For the porous BC2N-2H sheets, the indirect band gaps follow the order of C-NB-2H (3.45 eV) > C-L-2H (2.93 eV) > BN-L-2H (2.58 eV) > C-BN-2H (1.08 eV). The hydrogenation decreases the band gap of the C-BN-2H conformation, whereas it increases those of other conformations. Through the electronic structures in Figure 5 and the partial charge densities of the VBM and CBM in Figure 6, we can see two characteristics of sp3 hybridizations from one-hydrogenpassivated porous sheets. (i) The top valence bands have the contributions from the H s orbitals, which is due to the lifting of the σ bonding states with edge atoms. For the porous C-2H sheet, the VBM at the M point contains the C1-H σ bonding states. For the porous BN-2H sheet, the VBM at the K point also contains the B1-H σ bonding states. (ii) The bottom conduction bands exhibit a nearly free electron (NFE)-like character. The NFE-like character of the CBM state has been reported in the graphane sheet.72 In the porous C-2H and BN-2H sheets, the NFE states form zero-dimensional distributions, which delocalizes

above and below the porous sheets. For the porous C-2H sheet, the NFE states form hexagonal regions in the holes. In the porous BN-2H sheets, the NFE states have the triangular shapes around the BN hexagons. Because of the NFE-like character, the CBM moves to the Γ point and the direct-to-indirect band-gap transitions occurs in the two-hydrogen-passivated porous sheets. Stabilities of the Porous Sheets. Finally, we discuss the stabilities of the porous structures relative to pristine 2D sheets. The formation energy, Ef, is defined as Ef ¼ Eporous - nB μB - nN μN - nC μC - nH μH Here, Eporous is the total energy of the porous sheet. nB, nN, nC, and nH are the numbers of B, N, C, and H atoms, and μB, μN, μC, and μH are the corresponding chemical potentials of them. We adopt μH = EH2/2, where EH2 is the total energy of a H2 molecule. For the porous C and BN sheets, μC = Egraphene and μB þ μN = EBN. For the porous BC2N sheets, it requires μB þ μN þ 2μC = EBC2N. Egraphene, EBN, and EBC2N are the total energies of pristine 2D graphene, BN, and BC2N sheets, respectively. The calculated Ef values for each one- and two-hydrogen-passivated porous sheets are listed in Table 1 and Table 2. The synthesized porous C sheet is 41 meV/atom higher than the graphene sheet, 5340



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Figure 6. Partial charge densities of the VBM and the CBM for the two-hydrogen-passivated porous (a, b) C sheet and (c, d) BN sheet. The isosurface is 0.002 e/Å3.

and the porous BN sheet is 91 meV/atom higher than the pristine BN sheet. However, among the porous BC2N sheets, owing to its large cohesive energy value, the C-BN conformation becomes 70 meV/atom lower than the pristine BC2N sheet. The two-hydrogen passivation will help to stabilize the porous C-2H and the BC2N-2H sheets. For the edge C atoms, the sp3-hybridized bonding with H atoms reduces the formation energies of the porous structures. The porous C-2H sheets and the BN-L-2H and C-NB-2H conformations of porous BC2N-2H sheets have lower formation energies than the pristine ones. For the BN system, the porous BN-2H sheet has a higher formation energy than that of the one-hydrogen-passivated situation, which is up to 179 meV/atom. Thus, it is more possible to synthesize the porous C and BC2N structures in the experiments. Those sheets, which have lower formation energies than the pristine ones, are all wide-band-gap semiconductors, as shown in Tables 1 and 2. The C-BN conformation of the porous BC2N sheet has a direct LDA gap value of 3.52 eV, and the porous C-2H sheets and the BN-L-2H and C-NB-2H conformations of porous BC2N-2H sheets have indirect LDA gap values of 3.14, 2.58, and 3.45 eV, respectively. Considering that those gaps are around 2.5-3.5 eV, the porous C and BC2N sheets can be used as wide-band-gap semiconducting and insulating materials for nanoelectronics and nanodevices. For the application as an effective field-effect transistor, it requires a certain band gap opening in the nanostructures, for which the pristine graphene is unsatisfied. Bai et al. have found that the graphene nanomesh, prepared by block copolymer lithography, can open a gap due to periodic nanoholes. This graphene nanomesh could make upfield-effect transistors and perform better than the individual graphene nanoribbon devices.48 Porous C, BN,

and BC2N sheets have spontaneous nanoholes, which have a uniform size in the whole sheets to open a fixed band gap. Besides, the values of band gaps and work functions can be tuned by edge passivations, which enables those porous structures to be promising nanomaterials for potential semiconducting applications. Bieri et al. have reported that, through surface-assisted coupling of molecular building blocks, two-dimensional porous sheets can be well-fabricated.52 A specifically designed molecular precursor is the first step for the synthesis of porous structures. Borazine is isoelectronic and isostructural with benzene, which may replace some C6 rings of the molecular building block to form B-C-N compounds. Through depositing borazine on the Rh(111) surface, a regular BN nanomesh can be formed by the self-assembly method.73,74 For the production of the porous C sheet, the difference of Cu(111), Au(111), and Ag(111) surfaces affects the final morphology significantly.75 Thus, for the synthesis of porous C, BN, and BC2N sheets, finding a suitable metal surface and fabricating specifically designed molecular building blocks are the two key points for the experiments.

’ CONCLUSION In summary, we investigate the structural and electronic properties of the porous C, BN, and BC2N sheets by firstprinciples calculations. With one-hydrogen passivation, all the porous sheets are direct-band-gap semiconductors. Because of the quantum confinement, a band gap of 2.35 eV is opened in the porous C sheet. For the porous BN sheet, a large direct band gap of 4.27 eV is formed. In the porous BC2N sheets, the gap values are between 0.94 and 3.52 eV depending on the atomic 5341


The Journal of Physical Chemistry C arrangements. The stablest structure is the C-BN conformation for the porous BC2N sheets, which is composed of alternating C and BN hexagons. When the porous sheets are two-hydrogenpassivated, the most favorable structure becomes the BN-L-2H conformation with BN zigzag lines in it. Because of the sp3 hybridization, all the two-hydrogen-passivated porous sheets become indirect-band-gap semiconductors. The band gap increases for the porous C-2H sheet, whereas it decreases for the porous BN-2H sheet. For the porous BC2N sheets, the band gap decreases for the C-BN-2H conformation, whereas it increases for other structures. We also find that the C-BN conformation of the BC2N sheet, the porous C-2H sheets, and the BN-L-2H and C-NB-2H conformations of porous BC2N-2H sheets have negative formation energies, and it is possible to form them in experiments. Because of the rich electronic properties with different hydrogen passivations, the porous C, BN, and BC2N sheets have potential applications in nanoelectrics and nanodevices.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected] (Y.D.), wangyanli-04 @tsinghua.org.cn (Y.W.).

’ ACKNOWLEDGMENT Parts of the calculations were performed in the Beijing Computing Center (BCC) of China. The authors acknowledge the support from the Science Foundation of Zhejiang Sci-Tech University (ZSTU) (Grant No. 0913847-Y), Hangzhou Normal University (HZNU), and BCC. Y.D. would like to thank Dr. Baoxing Li, Dr. Chao Cao, and HZNU College of Science HPC Center for help. ’ REFERENCES (1) Baughman, R. H.; Zakhidov, A. A.; de Heer, W. A. Science 2002, 297, 787. (2) Wu, Y. H.; Yu, T.; Shen, Z. X. J. Appl. Phys. 2010, 108, 071301. (3) Avouris, P.; Chen, Z.; Perebeinos, V. Nat. Nanotechnol. 2007, 2, 605. (4) 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. (5) Geim, A. K.; Novoselov, K. S. Nat. Mater. 2007, 6, 183. (6) Castro Neto, A. H.; Guinea, F.; Peres, N. M. R.; Novoselov, K. S.; Geim, A. K. Rev. Mod. Phys. 2009, 81, 109. (7) Geim, A. K. Science 2009, 324, 1530. (8) Son, Y. W.; Cohen, M. L.; Louie, S. G. Nature 2006, 444, 347. (9) Son, Y. W.; Cohen, M. L.; Louie, S. G. Phys. Rev. Lett. 2006, 97, 216803. (10) Han, M. Y.; Oezyilmaz, B.; Zhang, Y.; Kim, P. Phys. Rev. Lett. 2007, 98, 206805. (11) Rao, C. N. R.; Sood, A. K.; Subrahmanyam, K. S.; Govindaraj, A. Angew. Chem., Int. Ed. 2009, 48, 7752. (12) Park, S.; Ruoff, R. S. Nat. Nanotechnol. 2009, 4, 217. (13) Shivaraman, S.; Barton, R. A.; Yu, X.; Alden, J.; Herman, L.; Chandrashekhar, M.; Park, J.; McEuen, P. L.; Parpia, J. M.; Craighead, H. G.; Spencer, M. G. Nano Lett. 2009, 9, 3100. (14) Dutta, S.; Pati, S. K. J. Phys. Chem. B 2008, 112, 1333. (15) Li, Y.; Zhou, Z.; P., S.; Chen, Z. ACS Nano 2009, 3, 1952. (16) Wu, M.; Wu, X.; Zeng, X. C. J. Phys. Chem. C 2010, 114, 3937. (17) Zheng, X. H.; Wang, X. L.; Abtew, T. A.; Zeng, Z. J. Phys. Chem. C 2010, 114, 4190. (18) Uthaisar, C.; Barone, V.; Peralta, J. E. J. Appl. Phys. 2009, 106, 113715.

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Electronic Structures of Porous Graphene, BN, and BC2N Sheets with

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