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A B–C–N hybrid porous sheet: an efficient metal-free visible-light absorption material† Ruifeng Lu,‡*ab Feng Li,‡a Juan Salafranca,cd Erjun Kan,ab Chuanyun Xiaoab and Kaiming Deng*ab The polyphenylene network, known as porous graphene, is one of the most important and widely studied two-dimensional materials. As a potential candidate for photocatalysis and photovoltaic energy generation, its application has been limited by the low photocatalytic activity in the visible-light region. State-of-the-art hybrid density functional theory investigations are presented to show that an analogous B–C–N porous sheet outperforms the pristine polyphenylene network with significantly enhanced visible-light absorption. Compared with porous graphene, the calculated energy gap of the B–C–N hybrid crystal shrinks to 2.7 eV and the optical absorption peak remarkably shifts to the visible light region.
Received 19th November 2013, Accepted 9th January 2014 DOI: 10.1039/c3cp54879a
The redox potentials of water splitting are well positioned in the middle of the band gap. Hybridizations among B_p, N_p and C_p orbitals are responsible for these findings. Valence and conduction band calculations indicate that the electrons and holes can be effectively separated, reducing charge recombination and improving the photoconversion efficiency. Moreover, the band gap and optical properties of the B–C–N
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hybrid porous sheet can be further finely engineered by external strain.
1. Introduction Enormous efforts have been made to develop new technologies to provide clean and safe energy. Nowadays, photovoltaic cells are considered as reliable power generators which can directly convert light energy into electricity without any intermediate chemical or mechanical procedures. Also, hydrogen energy has been regarded as another ideal alternative energy source, which can be produced from water dissociation by means of a catalyst and solar energy. Despite the wide-ranging prospects of photovoltaic cells and hydrogen energy, the efficiencies of photovoltaic energy conversion and photogeneration of various materials are limited by several factors.1,2 Among them, the efficiency of the visible-light absorption is the determining factor. Current photovoltaic and photocatalytic materials cannot respond to the entire spectrum of sunlight, and about a
Department of Applied Physics, Nanjing University of Science and Technology, Nanjing 210094, China. E-mail: [email protected] b Key Laboratory of Soft Chemistry and Functional Materials, Ministry of Education, Nanjing University of Science and Technology, Nanjing 210094, China. E-mail: [email protected] c Departamento de Fı´sica Aplicada III, Universidad Complutense de Madrid, Madrid 28040, Spain d Material Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA † Electronic supplementary information (ESI) available: The definition of formation energy and optimized geometric coordinates of the BN-PG isomers. See DOI: 10.1039/c3cp54879a ‡ These authors contributed equally to this work.
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45% of the solar light is in the visible short-wave part.3 Therefore, the major issue in delivering future photovoltaic and photocatalytic technologies is to enhance the light absorption of available materials in the visible region of the solar spectrum. Graphene has been proposed to be a solar absorber because of its high electrical conduction and the large surface-tovolume ratio.4–9 Because of its gapless band structure, however, graphene cannot be directly utilized.10,11 Optical absorption is mainly governed by the band gap of materials, so it is important to achieve an appropriate band gap. Many strategies have been proposed to explore the gap-opening issue of graphene, including molecular adsorption,12,13 being tailored into nanoribbons,14–16 defects,17,18 and graphene–substrate hybrid structures,19 etc. Besides the band structure, the intrinsic charge distributions of photoinduced electrons and holes play a key role in the photoconversion efficiency. To our knowledge, very few single layer structures (graphitic carbon nitride,20 two-dimensional covalent organic frameworks,21 and semihydrogenated BN sheets22) satisfy these two fundamental requirements. Recently, a two-dimensional polyphenylene network, also known as porous graphene (PG),23,24 has been synthesized and demonstrated to possess semi-conductor characteristics with a gapped band structure. Based on PG structure, multifunctional properties have been widely studied, including applications for hydrogen purification,25,26 hydrogen storage,27–29 atmospheric filtering,30 and isotopic He31 or H2 separation,32 etc. Density functional theory (DFT) calculations show that the direct band gap of PG (about 2.3 eV in local density approximation (LDA)25 and 2.48 eV
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in generalized gradient approximation (GGA)27) lies in the visible-light region. However, the standard DFT calculations generally underestimate the band gaps of materials. The energy gap of PG from more accurate first-principles calculations using the Heyd–Scuseria–Ernzerhof (HSE06) hybrid functional is found to be in the ultraviolet region (3.2 eV),27 which is still large for applications necessitating significant visible-light absorption. Thus, the question is how to enhance the visible-light absorption of PG. It is well known that the introduction of B or/and N atoms can modify the electronic properties of carbon nanostructures.33–38 In this work, by performing high accuracy first-principles calculations, we found that PG modified by B and N atoms (BN-PG) has a narrower fundamental energy gap of 2.7 eV with the HSE06 functional. In comparison with PG, the optical absorption of the BN-PG is significantly improved with the absorption peak red-shifted to the visible-light spectrum. Additionally, the electrons in the conduction band and holes in the valence band of BN-PG are observed to be effectively separated. Finally, we also suggest that the gap of the BN-PG can be further tuned by external strains with red shift or blue shift in the visible-light region.
2. Computational methods DFT calculations within the LDA and GGA systematically underestimate the band gap of the insulator and the semiconductor by about 30–40%; thus all calculations were performed using the HSE06 hybrid functional39–41 as implemented in Vienna Ab-initio Simulation Package.42,43 In HSE06, electron exchange energy includes the short part of the exact exchange energy and correlation energy, and long range exchange is described by PBE exchange and correlation.44–47 The optimizations of the lattice constants and the atom coordinates were carried out by minimizing the total energies. Cutoff energy of 550 eV is good enough for numerical convergence using 7 7 1 Monkhorst– Pack k-mesh grids. About 28 000 plane waves were used to describe the valence and semi-core states. All structures were fully relaxed until the force on each atom is less than 10 3 eV Å 1 and the total energy changes are less than 10 5 eV. Self-consistent calculations were performed with a convergence criterion of 10 6 eV for energy. For the partial density of state (PDOS) calculations, 15 15 1 k-point grids were employed while for the optical spectra 17 17 1 k-mesh grids were used to calculate the imaginary dielectric functions.48,49 The absolute Fermi level is defined as Efermi = eF Evac, in which eF is the calculated Fermi energy and Evac is the vacuum potential by averaging the LOCPOT file along the specified plane from VASP. The work function can be obtained from the absolute value of Efermi.
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Fig. 1 Geometric and band structures with respect to the vacuum potential of (a) PG and (b) BN-PG calculated from the HSE06 functional. The position of the reduction level for H+ to H2 is indicated by the dashed blue line and the oxidation potential of H2O to O2 is indicated by a red dashed line. The vacuum level is set to 0 eV.
two types of carbon atoms in PG: C atoms bonded to H atoms and to C atoms, labeled as C1 and C2. The optimized C1–C2 and C2–C2 bond lengths are 1.40 and 1.50 Å, and the C1–H bond length is 1.086 Å, which agree well with the reported theoretical results of 1.39, 1.48 Å and 1.09 Å, respectively.33 For the analogous two-dimensional structures, previous work has investigated the band engineering of BN and BC2N sheets,33 however, we have also studied these reported binary and ternary atomic layers from DFT calculations, finding that the visiblelight absorption and charge separation of these structures are dissatisfactory for photovoltaic and photocatalytic applications. Therefore, more extra configurations of the BN-PGs are considered in this work (Fig. S1 in the ESI†), and all the B and N atoms at the pore edge are passivated by H atoms. Fig. 1b presents the most favorable structure of the BN-PG, with the total energy of the unit cell lower than the other three isomers by at least 1.5 eV. In this most stable BN-PG configuration, all atoms are in the same plane indicating an sp2-hybridized bonding character. The calculated values of Fermi energies and vacuum potentials directly from VASP are, respectively, eF = 4.54 eV and Evac = 1.11 eV for PG, and eF = 2.21 eV and Evac = 1.87 eV for BN-PG. Compared with PG, the C–C bond length connecting two hexagons in BN-PG is reduced from 1.50 to 1.40 Å, while the lattice constant of BN-PG is slightly enlarged from 7.52 to 7.55 Å (Table 1). This is a combined result of the long B–C bond and the short C–N bond, which are calculated to be 1.53 and 1.37 Å, respectively. The positive value of formation energy (Ef, see the definition in ESI†) in Table 1 implies that the reaction for elemental B and N substitutions of C in the Table 1 Lattice constants, energy gaps, formation energies, and absolute Fermi levels of PG and BN-PG
3. Results and discussion PG
Fig. 1a presents the optimized structure of the PG sheets in which each carbon atom at the pore edge is passivated by the H atom. Due to the different chemical environments, there are
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BN-PG a
a0 (Å)
Eg (eV)
Ef (meV per atom)
7.52 7.45a, 7.44b 7.55
3.20 2.34a, 2.35b 2.70
40.2 41b 22.4
LDA results from ref. 27.
b
Efermi (eV) 5.65 4.77b 4.08
LDA results from ref. 33.
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aromatic ring is endothermic, and the ordered B–C–N hybrid porous sheet can be constructed from the relatively lower Ef value of BN-PG than that of PG, however, it should be carefully conducted under nonequilibrium conditions determined by the real kinetics.50,51 The band structures of the PG and BN-PG were calculated from the HSE06 hybrid functional and are also shown in Fig. 1. We found that the minimum gap of PG is placed at the K point of the Brillouin zone, and a clear direct energy gap of 3.20 eV can be observed, which agrees very well with previous prediction from the same functional. It is about 0.8 eV larger than 2.41 eV from our GGA calculations with the PBE functional and the reported LDA results of 2.34 eV27 and 2.35 eV.33 The tightbinding method studies claimed that the nearest-neighbor interaction is limited to obtain accurate band structures for the graphene and the relative carbon nanostructures.52 A hybrid functional like HSE06 can predict the conduction band better than GGA and LDA, giving a more accurate value. From the band dispersion of BN-PG, the minimum direct energy gap is at the M point, and the top valence band together with the bottom conduction band in the K–M range is flatter than PG. The band gap of BN-PG is 2.70 eV, smaller than that of PG by 0.5 eV. This value is just located in the visible light region from 1.61 to 3.10 eV (400–770 nm). In addition to the magnitude of the bandgap, the absolute values of the valence and conduction bands with respect to the reduction and oxidation levels are also important. The accurate values for the reduction level of hydrogen and the oxidation level of H2O are used, which are 4.4 eV and 5.67 eV, respectively. Fig. 1b shows that the reduction level for H+ is well located inside the gap. This indicates that the reduction process is energetically favored. The oxidation level is located slightly above the top of the valence band, which could transfer holes, but with low driving force. Then, we calculated the charge density of the valence band maximum (VBM) and the conductive band minimum (CBM) to check if the electrons and holes are effectively separated. Similar to other graphene nanomeshes, the formation of a band gap in BN-PG can be attributed to the quantum confinement of the hexagonal area between the neighboring aromatic rings.53 In order to explore more details of the electronic structures, the PDOSs are displayed in Fig. 2a. The VBM and CBM of PG are contributed, respectively, by the p and p* states, and both incorporate the C_pz orbitals. A peak of the H_s orbital located at about 5.0 eV corresponds to the C–H valence bond. For BN-PG, we found that the VBM is mostly dominated by the p orbitals of the C and N atoms, a smaller portion from the B_p orbitals, whereas the CBM comes chiefly from the p orbitals of the C and B atoms, partially from the N_p orbitals. Besides, the overlaps between B_p and C_p at around 3.3, 3.8, 5.0, 5.8 eV and the overlaps at around 2.2 and 3.6 eV between N_p and C_p indicate the strong B–C and N–C valence bonding, respectively. Therefore, the hybridizations among C, B, and N atoms significantly affect the electronic structures of BN-PG, reducing the energy gap into the range of visible light. Moreover, charge density plots of the VBM and CBM for PG and BN-PG are shown in Fig. 2b and c. We can clearly see that
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Fig. 2 (a) PDOSs of PG and BN-PG. The Fermi level is located at 0 eV (dotted line). Charge density of the valence band maximum (VBM) and the conductive band minimum (CBM) for PG (b) and BN-PG (c), respectively. The isosurfaces are 0.004 e Å 1.
the charge densities of both VBM and CBM in PG are distributed around the carbon rings with typical C–C conjugation. For BN-PG, the electrons and holes are spatially separated. The charge density of CBM is mainly located at the B–C rings, whereas the VBM almost comes from the C–N rings. These results are well consistent with the above PDOS analyses. Photoexcitation consequently leads to a spatial charge separation between the electron in the conduction band and the hole in the valence band. This suggests that the nitrogen–carbon rings would be the preferred oxidation sites for H2O to form O2, whereas the boron–carbon rings provide the reduction sites for H+ to H2. Thus, the efficient charge separation in BN-PG implies that it is a good candidate for improving photocatalytic activity by reducing charge recombination. To address the relationship between optical properties and electronic structures, we accurately calculated imaginary dielectric functions using the HSE06 hybrid functional of PG and BN-PG and are presented in Fig. 3. The main peak of the PG is at 293 nm (corresponding photon energy of 4.23 eV), and the dominant absorption wavelength is less than 350 nm, exhibiting a clear ultraviolet absorption. Since most of the solar energy comes from the visible-light region, to enhance the photoelectric conversion efficiency, the absorption peak of photovoltaic cells and photocatalytic materials should be located within the range of visible light from 400 to 770 nm. Thus, the weak visible-light activity of the pristine PG is not suitable for a solar absorber. Surprisingly, the calculated imaginary dielectric function of the BN-PG has an optical absorption peak at 433 nm (2.86 eV), red-shifting obviously by 140 nm. The shaded area in Fig. 3 represents the overlapping with the visible light, which indicates
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Fig. 5 Calculated imaginary dielectric functions of the strained BN-PG versus energy. The negative and positive values of Z stand for the (a) compression and (b) elongation, respectively.
Fig. 3 Calculated imaginary dielectric functions versus wavelength for PG and BN-PG. The shaded area stands for the visible light region.
that the optical absorption of BN-PG in the visible region of the solar spectrum is greatly enhanced compared to the PG. This could be understood by the fact that the B–C and C–N couplings have modified the orbital projections of the bands, as shown in Fig. 2. Therefore, the B and N atoms play crucial roles in the optical properties of BN-PG. To be applied in real systems, BN-PG should be grown on the flexible substrate, and the lattice constant mismatch would inevitably result in a strain effect.54,55 Plenty of experimental and theoretical studies have shown that the band gaps of twodimensional sheets are tunable by strain.56–58 In this scenario, it is desirable to examine the effect of strain on the band gap of the BN-PG, which would also affect the optical properties. The biaxial strain can be represented by Z = (a a0)/a0, where a0 is the optimized lattice constant, and a is the lattice length along the strain direction. Negative and positive values of Z stand for compression and elongation, respectively. The band gaps of strained PG and BN-PG as a function of Z are presented in Fig. 4. Within the whole strain range from 5% to 5%, the gap of BN-PG decreases almost linearly from 2.82 to 2.51 eV as Z increases. It should be noted that the calculated energy gaps of both PG and BN-PG from GGA are smaller than those from the hybrid functional HSE06 by about 0.8 eV. The gap of both PG and BN-PG can be continuously tuned by external strain, nevertheless, the tunable trend of BN-PG is totally different from that of PG that exhibits a monotonous increase upon increasing the applied strain.
From the above mentioned band engineering, we predict that the visible light absorption of the strained BN-PG could be further subtly controlled as well. Because the computational demands of optical property calculations using the HSE06 are prohibitively high, unlike Fig. 3, we provide the imaginary dielectric functions of the BN-PG under compression and elongation within GGA in Fig. 5 to avoid very expensive computations, and we believe that the optical engineering here is qualitatively meaningful for the potential applications. In contrast to the unstrained BN-PG, we found that the main optical absorption peak of BN-PG is blueshifted by 44 nm upon compression, while red-shifted by 67 nm upon elongation. Fig. 3 and 5 clearly show that the optical properties of the BN-PG could achieve better visible light absorption by just being stretched by a substrate, which could be more practically realized than the compressive stress.
4. Conclusion In summary, we have performed high accuracy first-principles calculations to investigate the electronic and optical properties of B and N modified porous graphene. The calculated energy gap of BN-PG is narrower than that of pristine PG by 0.50 eV. The optical calculations confirm the fascinating optical properties of the B–C–N hybrid porous sheet that the main absorption peak shifts to the visible light region at 433 nm. Our findings indicate that the BN-PG has visible-light absorption characteristics more suitable for photovoltaic and photocatalytic applications compared to pure PG. Moreover, the band gap shows a linear decreasing relationship with increasing strain and the optical properties of the BN-PG can be further adjusted by external strains. The physical insights from our calculations thus unveil a useful strategy to seek two-dimensional photovoltaic and photocatalytic materials.
Acknowledgements
Fig. 4 Band gaps of (a) PG and (b) BN-PG as a function of strain Z.
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This work was supported by NSF of China Grant No. 11174150 and 21373113, Jiangsu Creative Foundation CXLX11_0243 for PhD candidates, Jiangsu Province Science Foundation for Youths with Grant No. BK2012394, and the Special Foundation for PhD Programs of the Ministry of Education of China with Grant No. 20113219110032. JS was supported by the Juan de la Cierva program JCI-2011-09428, and ERC starting Investigator Award, grant #239739 STEMOX.
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A B–C–N hybrid porous sheet: an efficient metal-free visible-light absorption material† Ruifeng Lu,‡*ab Feng Li,‡a Juan Salafranca,cd Erjun Kan,ab Chuanyun Xiaoab and Kaiming Deng*ab The polyphenylene network, known as porous graphene, is one of the most important and widely studied two-dimensional materials. As a potential candidate for photocatalysis and photovoltaic energy generation, its application has been limited by the low photocatalytic activity in the visible-light region. State-of-the-art hybrid density functional theory investigations are presented to show that an analogous B–C–N porous sheet outperforms the pristine polyphenylene network with significantly enhanced visible-light absorption. Compared with porous graphene, the calculated energy gap of the B–C–N hybrid crystal shrinks to 2.7 eV and the optical absorption peak remarkably shifts to the visible light region.
Received 19th November 2013, Accepted 9th January 2014 DOI: 10.1039/c3cp54879a
The redox potentials of water splitting are well positioned in the middle of the band gap. Hybridizations among B_p, N_p and C_p orbitals are responsible for these findings. Valence and conduction band calculations indicate that the electrons and holes can be effectively separated, reducing charge recombination and improving the photoconversion efficiency. Moreover, the band gap and optical properties of the B–C–N
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hybrid porous sheet can be further finely engineered by external strain.
1. Introduction Enormous efforts have been made to develop new technologies to provide clean and safe energy. Nowadays, photovoltaic cells are considered as reliable power generators which can directly convert light energy into electricity without any intermediate chemical or mechanical procedures. Also, hydrogen energy has been regarded as another ideal alternative energy source, which can be produced from water dissociation by means of a catalyst and solar energy. Despite the wide-ranging prospects of photovoltaic cells and hydrogen energy, the efficiencies of photovoltaic energy conversion and photogeneration of various materials are limited by several factors.1,2 Among them, the efficiency of the visible-light absorption is the determining factor. Current photovoltaic and photocatalytic materials cannot respond to the entire spectrum of sunlight, and about a
Department of Applied Physics, Nanjing University of Science and Technology, Nanjing 210094, China. E-mail: [email protected] b Key Laboratory of Soft Chemistry and Functional Materials, Ministry of Education, Nanjing University of Science and Technology, Nanjing 210094, China. E-mail: [email protected] c Departamento de Fı´sica Aplicada III, Universidad Complutense de Madrid, Madrid 28040, Spain d Material Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA † Electronic supplementary information (ESI) available: The definition of formation energy and optimized geometric coordinates of the BN-PG isomers. See DOI: 10.1039/c3cp54879a ‡ These authors contributed equally to this work.
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45% of the solar light is in the visible short-wave part.3 Therefore, the major issue in delivering future photovoltaic and photocatalytic technologies is to enhance the light absorption of available materials in the visible region of the solar spectrum. Graphene has been proposed to be a solar absorber because of its high electrical conduction and the large surface-tovolume ratio.4–9 Because of its gapless band structure, however, graphene cannot be directly utilized.10,11 Optical absorption is mainly governed by the band gap of materials, so it is important to achieve an appropriate band gap. Many strategies have been proposed to explore the gap-opening issue of graphene, including molecular adsorption,12,13 being tailored into nanoribbons,14–16 defects,17,18 and graphene–substrate hybrid structures,19 etc. Besides the band structure, the intrinsic charge distributions of photoinduced electrons and holes play a key role in the photoconversion efficiency. To our knowledge, very few single layer structures (graphitic carbon nitride,20 two-dimensional covalent organic frameworks,21 and semihydrogenated BN sheets22) satisfy these two fundamental requirements. Recently, a two-dimensional polyphenylene network, also known as porous graphene (PG),23,24 has been synthesized and demonstrated to possess semi-conductor characteristics with a gapped band structure. Based on PG structure, multifunctional properties have been widely studied, including applications for hydrogen purification,25,26 hydrogen storage,27–29 atmospheric filtering,30 and isotopic He31 or H2 separation,32 etc. Density functional theory (DFT) calculations show that the direct band gap of PG (about 2.3 eV in local density approximation (LDA)25 and 2.48 eV
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in generalized gradient approximation (GGA)27) lies in the visible-light region. However, the standard DFT calculations generally underestimate the band gaps of materials. The energy gap of PG from more accurate first-principles calculations using the Heyd–Scuseria–Ernzerhof (HSE06) hybrid functional is found to be in the ultraviolet region (3.2 eV),27 which is still large for applications necessitating significant visible-light absorption. Thus, the question is how to enhance the visible-light absorption of PG. It is well known that the introduction of B or/and N atoms can modify the electronic properties of carbon nanostructures.33–38 In this work, by performing high accuracy first-principles calculations, we found that PG modified by B and N atoms (BN-PG) has a narrower fundamental energy gap of 2.7 eV with the HSE06 functional. In comparison with PG, the optical absorption of the BN-PG is significantly improved with the absorption peak red-shifted to the visible-light spectrum. Additionally, the electrons in the conduction band and holes in the valence band of BN-PG are observed to be effectively separated. Finally, we also suggest that the gap of the BN-PG can be further tuned by external strains with red shift or blue shift in the visible-light region.
2. Computational methods DFT calculations within the LDA and GGA systematically underestimate the band gap of the insulator and the semiconductor by about 30–40%; thus all calculations were performed using the HSE06 hybrid functional39–41 as implemented in Vienna Ab-initio Simulation Package.42,43 In HSE06, electron exchange energy includes the short part of the exact exchange energy and correlation energy, and long range exchange is described by PBE exchange and correlation.44–47 The optimizations of the lattice constants and the atom coordinates were carried out by minimizing the total energies. Cutoff energy of 550 eV is good enough for numerical convergence using 7 7 1 Monkhorst– Pack k-mesh grids. About 28 000 plane waves were used to describe the valence and semi-core states. All structures were fully relaxed until the force on each atom is less than 10 3 eV Å 1 and the total energy changes are less than 10 5 eV. Self-consistent calculations were performed with a convergence criterion of 10 6 eV for energy. For the partial density of state (PDOS) calculations, 15 15 1 k-point grids were employed while for the optical spectra 17 17 1 k-mesh grids were used to calculate the imaginary dielectric functions.48,49 The absolute Fermi level is defined as Efermi = eF Evac, in which eF is the calculated Fermi energy and Evac is the vacuum potential by averaging the LOCPOT file along the specified plane from VASP. The work function can be obtained from the absolute value of Efermi.
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Fig. 1 Geometric and band structures with respect to the vacuum potential of (a) PG and (b) BN-PG calculated from the HSE06 functional. The position of the reduction level for H+ to H2 is indicated by the dashed blue line and the oxidation potential of H2O to O2 is indicated by a red dashed line. The vacuum level is set to 0 eV.
two types of carbon atoms in PG: C atoms bonded to H atoms and to C atoms, labeled as C1 and C2. The optimized C1–C2 and C2–C2 bond lengths are 1.40 and 1.50 Å, and the C1–H bond length is 1.086 Å, which agree well with the reported theoretical results of 1.39, 1.48 Å and 1.09 Å, respectively.33 For the analogous two-dimensional structures, previous work has investigated the band engineering of BN and BC2N sheets,33 however, we have also studied these reported binary and ternary atomic layers from DFT calculations, finding that the visiblelight absorption and charge separation of these structures are dissatisfactory for photovoltaic and photocatalytic applications. Therefore, more extra configurations of the BN-PGs are considered in this work (Fig. S1 in the ESI†), and all the B and N atoms at the pore edge are passivated by H atoms. Fig. 1b presents the most favorable structure of the BN-PG, with the total energy of the unit cell lower than the other three isomers by at least 1.5 eV. In this most stable BN-PG configuration, all atoms are in the same plane indicating an sp2-hybridized bonding character. The calculated values of Fermi energies and vacuum potentials directly from VASP are, respectively, eF = 4.54 eV and Evac = 1.11 eV for PG, and eF = 2.21 eV and Evac = 1.87 eV for BN-PG. Compared with PG, the C–C bond length connecting two hexagons in BN-PG is reduced from 1.50 to 1.40 Å, while the lattice constant of BN-PG is slightly enlarged from 7.52 to 7.55 Å (Table 1). This is a combined result of the long B–C bond and the short C–N bond, which are calculated to be 1.53 and 1.37 Å, respectively. The positive value of formation energy (Ef, see the definition in ESI†) in Table 1 implies that the reaction for elemental B and N substitutions of C in the Table 1 Lattice constants, energy gaps, formation energies, and absolute Fermi levels of PG and BN-PG
3. Results and discussion PG
Fig. 1a presents the optimized structure of the PG sheets in which each carbon atom at the pore edge is passivated by the H atom. Due to the different chemical environments, there are
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BN-PG a
a0 (Å)
Eg (eV)
Ef (meV per atom)
7.52 7.45a, 7.44b 7.55
3.20 2.34a, 2.35b 2.70
40.2 41b 22.4
LDA results from ref. 27.
b
Efermi (eV) 5.65 4.77b 4.08
LDA results from ref. 33.
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aromatic ring is endothermic, and the ordered B–C–N hybrid porous sheet can be constructed from the relatively lower Ef value of BN-PG than that of PG, however, it should be carefully conducted under nonequilibrium conditions determined by the real kinetics.50,51 The band structures of the PG and BN-PG were calculated from the HSE06 hybrid functional and are also shown in Fig. 1. We found that the minimum gap of PG is placed at the K point of the Brillouin zone, and a clear direct energy gap of 3.20 eV can be observed, which agrees very well with previous prediction from the same functional. It is about 0.8 eV larger than 2.41 eV from our GGA calculations with the PBE functional and the reported LDA results of 2.34 eV27 and 2.35 eV.33 The tightbinding method studies claimed that the nearest-neighbor interaction is limited to obtain accurate band structures for the graphene and the relative carbon nanostructures.52 A hybrid functional like HSE06 can predict the conduction band better than GGA and LDA, giving a more accurate value. From the band dispersion of BN-PG, the minimum direct energy gap is at the M point, and the top valence band together with the bottom conduction band in the K–M range is flatter than PG. The band gap of BN-PG is 2.70 eV, smaller than that of PG by 0.5 eV. This value is just located in the visible light region from 1.61 to 3.10 eV (400–770 nm). In addition to the magnitude of the bandgap, the absolute values of the valence and conduction bands with respect to the reduction and oxidation levels are also important. The accurate values for the reduction level of hydrogen and the oxidation level of H2O are used, which are 4.4 eV and 5.67 eV, respectively. Fig. 1b shows that the reduction level for H+ is well located inside the gap. This indicates that the reduction process is energetically favored. The oxidation level is located slightly above the top of the valence band, which could transfer holes, but with low driving force. Then, we calculated the charge density of the valence band maximum (VBM) and the conductive band minimum (CBM) to check if the electrons and holes are effectively separated. Similar to other graphene nanomeshes, the formation of a band gap in BN-PG can be attributed to the quantum confinement of the hexagonal area between the neighboring aromatic rings.53 In order to explore more details of the electronic structures, the PDOSs are displayed in Fig. 2a. The VBM and CBM of PG are contributed, respectively, by the p and p* states, and both incorporate the C_pz orbitals. A peak of the H_s orbital located at about 5.0 eV corresponds to the C–H valence bond. For BN-PG, we found that the VBM is mostly dominated by the p orbitals of the C and N atoms, a smaller portion from the B_p orbitals, whereas the CBM comes chiefly from the p orbitals of the C and B atoms, partially from the N_p orbitals. Besides, the overlaps between B_p and C_p at around 3.3, 3.8, 5.0, 5.8 eV and the overlaps at around 2.2 and 3.6 eV between N_p and C_p indicate the strong B–C and N–C valence bonding, respectively. Therefore, the hybridizations among C, B, and N atoms significantly affect the electronic structures of BN-PG, reducing the energy gap into the range of visible light. Moreover, charge density plots of the VBM and CBM for PG and BN-PG are shown in Fig. 2b and c. We can clearly see that
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Fig. 2 (a) PDOSs of PG and BN-PG. The Fermi level is located at 0 eV (dotted line). Charge density of the valence band maximum (VBM) and the conductive band minimum (CBM) for PG (b) and BN-PG (c), respectively. The isosurfaces are 0.004 e Å 1.
the charge densities of both VBM and CBM in PG are distributed around the carbon rings with typical C–C conjugation. For BN-PG, the electrons and holes are spatially separated. The charge density of CBM is mainly located at the B–C rings, whereas the VBM almost comes from the C–N rings. These results are well consistent with the above PDOS analyses. Photoexcitation consequently leads to a spatial charge separation between the electron in the conduction band and the hole in the valence band. This suggests that the nitrogen–carbon rings would be the preferred oxidation sites for H2O to form O2, whereas the boron–carbon rings provide the reduction sites for H+ to H2. Thus, the efficient charge separation in BN-PG implies that it is a good candidate for improving photocatalytic activity by reducing charge recombination. To address the relationship between optical properties and electronic structures, we accurately calculated imaginary dielectric functions using the HSE06 hybrid functional of PG and BN-PG and are presented in Fig. 3. The main peak of the PG is at 293 nm (corresponding photon energy of 4.23 eV), and the dominant absorption wavelength is less than 350 nm, exhibiting a clear ultraviolet absorption. Since most of the solar energy comes from the visible-light region, to enhance the photoelectric conversion efficiency, the absorption peak of photovoltaic cells and photocatalytic materials should be located within the range of visible light from 400 to 770 nm. Thus, the weak visible-light activity of the pristine PG is not suitable for a solar absorber. Surprisingly, the calculated imaginary dielectric function of the BN-PG has an optical absorption peak at 433 nm (2.86 eV), red-shifting obviously by 140 nm. The shaded area in Fig. 3 represents the overlapping with the visible light, which indicates
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Fig. 5 Calculated imaginary dielectric functions of the strained BN-PG versus energy. The negative and positive values of Z stand for the (a) compression and (b) elongation, respectively.
Fig. 3 Calculated imaginary dielectric functions versus wavelength for PG and BN-PG. The shaded area stands for the visible light region.
that the optical absorption of BN-PG in the visible region of the solar spectrum is greatly enhanced compared to the PG. This could be understood by the fact that the B–C and C–N couplings have modified the orbital projections of the bands, as shown in Fig. 2. Therefore, the B and N atoms play crucial roles in the optical properties of BN-PG. To be applied in real systems, BN-PG should be grown on the flexible substrate, and the lattice constant mismatch would inevitably result in a strain effect.54,55 Plenty of experimental and theoretical studies have shown that the band gaps of twodimensional sheets are tunable by strain.56–58 In this scenario, it is desirable to examine the effect of strain on the band gap of the BN-PG, which would also affect the optical properties. The biaxial strain can be represented by Z = (a a0)/a0, where a0 is the optimized lattice constant, and a is the lattice length along the strain direction. Negative and positive values of Z stand for compression and elongation, respectively. The band gaps of strained PG and BN-PG as a function of Z are presented in Fig. 4. Within the whole strain range from 5% to 5%, the gap of BN-PG decreases almost linearly from 2.82 to 2.51 eV as Z increases. It should be noted that the calculated energy gaps of both PG and BN-PG from GGA are smaller than those from the hybrid functional HSE06 by about 0.8 eV. The gap of both PG and BN-PG can be continuously tuned by external strain, nevertheless, the tunable trend of BN-PG is totally different from that of PG that exhibits a monotonous increase upon increasing the applied strain.
From the above mentioned band engineering, we predict that the visible light absorption of the strained BN-PG could be further subtly controlled as well. Because the computational demands of optical property calculations using the HSE06 are prohibitively high, unlike Fig. 3, we provide the imaginary dielectric functions of the BN-PG under compression and elongation within GGA in Fig. 5 to avoid very expensive computations, and we believe that the optical engineering here is qualitatively meaningful for the potential applications. In contrast to the unstrained BN-PG, we found that the main optical absorption peak of BN-PG is blueshifted by 44 nm upon compression, while red-shifted by 67 nm upon elongation. Fig. 3 and 5 clearly show that the optical properties of the BN-PG could achieve better visible light absorption by just being stretched by a substrate, which could be more practically realized than the compressive stress.
4. Conclusion In summary, we have performed high accuracy first-principles calculations to investigate the electronic and optical properties of B and N modified porous graphene. The calculated energy gap of BN-PG is narrower than that of pristine PG by 0.50 eV. The optical calculations confirm the fascinating optical properties of the B–C–N hybrid porous sheet that the main absorption peak shifts to the visible light region at 433 nm. Our findings indicate that the BN-PG has visible-light absorption characteristics more suitable for photovoltaic and photocatalytic applications compared to pure PG. Moreover, the band gap shows a linear decreasing relationship with increasing strain and the optical properties of the BN-PG can be further adjusted by external strains. The physical insights from our calculations thus unveil a useful strategy to seek two-dimensional photovoltaic and photocatalytic materials.
Acknowledgements
Fig. 4 Band gaps of (a) PG and (b) BN-PG as a function of strain Z.
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This work was supported by NSF of China Grant No. 11174150 and 21373113, Jiangsu Creative Foundation CXLX11_0243 for PhD candidates, Jiangsu Province Science Foundation for Youths with Grant No. BK2012394, and the Special Foundation for PhD Programs of the Ministry of Education of China with Grant No. 20113219110032. JS was supported by the Juan de la Cierva program JCI-2011-09428, and ERC starting Investigator Award, grant #239739 STEMOX.
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