English

• 0.   Introduction

  As a low-cost, high-stable, nontoxic and visiblelight-responsive photocatalyst, graphitic carbon nitride (g-C₃N₄) has a multifunctional application in photocatalytic hydrogen evolution^[1-3], CO₂ reduction^[4-5] and photo-catalytic degradation of pollutants^[6-7]. In order to further enhance the photocatalytic performance of g-C₃N₄, bulk g-C₃N₄ is usually cut into nano-sized g-C₃N₄, such as g-C₃N₄ nanosheets^{[3, 8-11]} and g-C₃N₄ nanoribbons (g-C₃N₄ NRs)^[12-13], which possesses favorable photocatalytic activity because of the larger specific surface area with abundant active sites and short diffusion distance of photogenerated charge carriers.

  Due to the quantum size effect, the properties of g-C₃N₄ NRs are considerably different from those of g-C₃N₄ nanosheets. In experiments, Wang et al. have successfully synthesized the Mn-doped g-C₃N₄ NR catalyst by a two-step calcination method^[13]. Zhao et al. have fabricated g-C₃N₄ NR on graphene sheets by using a simple one-step hydrothermal method^[12]. However, litttle attention is paid to theoretical research on the armchair nanoribbons (AC-g-C₃N₄NRs) or zigzag g-C₃N₄ nanoribbons (ZZ-g-C₃N₄NRs) which can be obtained by cutting nanosheets along specific directions, and thus the electronic and optical properties of these above two g-C₃N₄ NRs as function of widths are not clear. Exposure of these properties will help the design and fabrication of g-C₃N₄ NRs-based electronic and optical devices in experiment.

  In this work, the rest of the paper is organized as follows: the computational method and models of AC-g-C₃N₄NRs and ZZ-g-C₃N₄NRs with the width of 7 (i.e. the number of the atom chains) are given in Section 2. The binding energies, band gaps, band structure, partial charge density, partial density of states and optical properties of g-C₃N₄ NRs are analyzed and the conclusions are drawn in the last section.

  1.   Computational method and models

  The computation of electronic and optical properties was performed within the framework of the density functional theory (DFT) implemented in the Vienna ab-initio Simulation Package (VASP)^[14-18]. The electronionic core interactions were treated by the projected augmented wave (PAW) potentials^[19]. The Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional^[20] within the generalized-gradient approximation (GGA) was used in order to yield the correct ground-state structure of the systems. An efficient Broyden/Pulay mixing scheme^[21-22] was used for the mixing of the charge density. The cut-off energy of the plane waves was 500 eV. The energies and the forces on each ion were converged to less than 10^-5 eV·atom^-1 and 0.1 eV·nm^-1, respectively. The Gaussian smearing broadening was chosen as 0.05 eV. The Brillouin zones were sampled by 1×1×11 and 1×1×25 K-point meshes according to Monkhorst-Pack scheme^[23] for calculations of electronic structures and optical properties, respectively. The number of energy bands was increased to 300 when the optical properties were computed. The absorption coefficient and reflectivity can be derived from the computational dielectric function. Compared with the experiment value 2.7 eV, the computed band gap of bulk g-C₃N₄ was 1.28 eV and the difference in band gap was 1.42 eV. The same conclusion is also drawn by Wu et al^[24]. However, the PBE computations can still reveal the variation tendency of the electronic structures and optical properties.

  The width of AC-g-C₃N₄NR (or ZZ-g-C₃N₄NRs) was classified by the number of the atom chains N_A (or N_Z) across the ribbon width and denoted as N_A-AC-g-C₃N₄NR (or N_Z-ZZ-g-C₃N₄NR). In the present work, we focus our attention on the structures of AC-g-C₃N₄NR and ZZ-g-C₃N₄NRs with the width N_A or N_Z=4~10. As examples, geometry structures of 7-AC-g-C₃N₄NR and 7-ZZ-g-C₃N₄NR are shown in Fig. 1a and 1b, respectively. g-C₃N₄NRs periodically extend along the z direction. To avoid the interactions between the neighboring ribbons, g-C₃N₄NRs were separated from each other by the vacuum region with 1.6 nm in both edge-to-edge (i.e. x direction) and layer-to-layer (i.e. y direction).

  Figure 1

  

  Figure 1.  Geometry structures of monolayer g-C₃N₄NRs with H termination: (a) 7-AC-g-C₃N₄NR; (b) 7-ZZ-g-C₃N₄NR

  A periodic unit cell is presented between the two red solid lines; Green straight line or zigzag curve shows atom chain; Total number of the atom chains across AC-g-C₃N₄NRs and ZZ-g-C₃N₄NRs width is also described by N_A and N_Z, respectively; Gray, blue and white balls represent the C, N and H atoms, respectively

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  2.   Results and discussion

  2.1   Binding energies and band gaps

  The binding energies E_b are usually adopted to investigate the binding strength between H atoms and g-C₃N₄NRs. E_b was computed according to E_b=(E_passivated-E_bare -nE_H)/n, where n is the number of H atoms, E_passivated and E_bare refer to the total energy of g-C₃N₄NR with H termination and g-C₃N₄NR without H termination, respectively. EH is the half of the total energy of a H₂ molecule at 0 K and 0 GPa and was computed by equation E_H =1/2E_H2. The evolution of the binding energies of AC -and ZZ-g-C₃N₄NRs as a function of the width N_A or N_Z is shown in Fig. 2a. It can be seen that the binding energies of these fourteen g-C₃N₄NRs are all negative values, indicating that the edge H atoms can exist stably. The black curve and red curve represent that the binding energy of the AC-g-C₃N₄NR has a small fluctuation, whereas that of ZZ-g-C₃N₄NR has a large fluctuation with the increasing number of atom chains. In addition, the smaller binding energies of ZZ-g-C₃N₄NRs with the width N_Z =4, 6, 8, 10 indicate that H atoms are preferred to adsorb on the edges of these systems. Fig. 2b displays the evolution of the band gaps of AC-and ZZ-g -C₃N₄NRs as a function of the width N_A or N_Z. It can be seen from Fig. 2b that the band gaps of the remaining eleven semiconductor g-C₃N₄NRs present a small fluctuation except for ZZ-g-C₃N₄NR with N_Z=5, 7, 9 which are metallic systems with no band gaps. Table 1 shows the molar ratio (ε) of C and N atoms of the AC-and ZZ-g-C₃N₄NRs. Table 1 and Fig. 2 indicate that the binding energies and band gaps of AC-g-C₃N₄NRs have no obvious change rule, while ZZ-g-C₃N₄NRs have the smaller binding energies and the larger band gaps when the ε of C and N atoms is 3/4.

  Figure 2

  

  Figure 2.  Evolution of the binding energies (a) and band gaps (b) of AC-g-C₃N₄NRs and ZZ-g-C₃N₄NRs as a function of the width N_A or N_Z

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  Table 1

  

  Table 1.  ε of C and N atoms of AC-g-C₃N₄NRs and ZZ-g-C₃N₄NRs

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  System	ε		System	ε
  4-AC-g-C3N4NR	3/4		4-ZZ-g-C3N4NR	3/4
  5-AC-g-C3N4NR	7/10		5-ZZ-g-C3N4NR	7/10
  6-AC-g-C3N4NR	3/4		6-ZZ-g-C3N4NR	3/4
  7-AC-g-C3N4NR	5/7		7-ZZ-g-C3N4NR	5/7
  8-AC-g-C3N4NR	3/4		8-ZZ-g-C3N4NR	3/4
  9-AC-g-C3N4NR	13/18		9-ZZ-g-C3N4NR	13/18
  10-AC-g-C3N4NR	3/4		10-ZZ-g-C3N4NR	3/4

  In the following sections, the aforementioned stable semiconductor AC-g-C₃N₄NRs with the width N_A =4, 7, 10 and semiconductor ZZ-g-C₃N₄NRs with the width N_Z=4, 10 will be taken as examples for further investigating the electronic and optical properties of g-C₃N₄NRs.

  2.2   Band structure, partial charge density and partial density of states

  Fig. 3 shows band structures of AC-g-C₃N₄NRs with (a) N_A=4, (b) N_A=7, (c) N_A=10 and ZZ-g-C₃N₄NRs with (d) N_Z=4, (e) N_Z=10. Fig. 3a and 3d reflect that AC-g-C₃N₄NR and ZZ-g-C₃N₄NR with N_A or N_Z=4 are both indirect band gap semiconductors because of the valence band maximum (VBM) and the conduction band minimum (CBM) locating at different points of K-space, whereas Fig. 3b, 3c and 3e are all the direct band gap systems due to the VBM and CBM located at Γ point of K-space.

  Figure 3

  

  Figure 3.  Band structures of AC-g-C₃N₄NRs with (a) N_A=4, (b) N_A=7, (c) N_A=10 and ZZ-g-C₃N₄NRs with (d) N_Z=4, (e) N_Z=10

  Red and green bands denote the top valence band and the bottom conduction band, respectively; Blue circles shown on the red and green bands indicate the VBM and CBM, respectively; Fermi level (E_F) was set to 0 eV, and it is the energy level at which the Fermi-Dirac distribution function of an assembly of fermions is equal to one-half

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  In order to intuitively recognize compositions of the VBMs and CBMs, Fig. 4 shows partial charge densities for VBMs and CBMs of AC-g-C₃N₄NRs with (a) N_A= 4, (b) N_A=7, (c) N_A=10 and ZZ-g-C₃N₄NRs with (d) N_Z= 4, (e) N_Z=10. It can be seen that the VBMs of AC-g-C₃N₄NRs (the red isosurface in Fig. 4a~4c are mainly distributed on most of N atoms, whereas the VBMs of ZZ-g-C₃N₄NRs (the red isosurface in Fig. 4d and 4e are contributed by the N atoms near the CH edge. Moreover, these charge distributions contributing to VBMs are all within the g-C₃N₄ plane. However, the CBMs of AC-g-C₃N₄NRs (the green isosurface in Fig. 4a~4c) mainly belong to C and N atoms near the one edge or two edges of AC-g-C₃N₄NRs, while CBMs of ZZ-g-C₃N₄NRs (the green isosurface in Fig. 4d and 4e) mainly belong to C and N atoms near the NH edge of ZZ-g-C₃N₄NRs. Interestingly, these charge distributions are perpendicular to the g-C₃N₄ plane.

  Figure 4

  

  Figure 4.  Partial charge densities for VBMs (red isosurface) and CBMs (green isosurface) of AC-g-C₃N₄NRs with (a) N_A=4, (b) N_A=7, (c) N_A=10 and ZZ-g-C₃N₄NRs with (d) N_Z=4, (e) N_Z=10

  Isosurface level was set as 4 e·nm^-3

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  Furthermore, we computed the partial density of states of AC-g-C₃N₄NRs with (a) N_A=4, (b) N_A=7, (c) N_A =10 and ZZ-g-C₃N₄NRs with (d) N_Z=4, (e) N_Z=10. As shown in Fig. 5, the VBMs of AC-and ZZ-g-C₃N₄NRs are composed of the 2p states of N atoms, while the CBMs are mainly contributed by the 2p states of C and N atoms of the systems. In terms of element compositions, this is in good agreement with the above analysis of the partial charge densities.

  Figure 5

  

  Figure 5.  Partial density of states of AC-g-C₃N₄NRs with (a) N_A=4, (b) N_A=7, (c) N_A=10 and ZZ-g-C₃N₄NRs with (d) N_Z=4, (e) N_Z=10

  E_F=0 eV

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  2.3   Optical properties

  In the present work, for comparison, the optical properties of g-C₃N₄NRs, bulk g-C₃N₄ and the armchair graphene nanoribbons (AC-GNRs) are characterized by absorption coefficient (α), reflectivity (R) and energy loss (L), which are defined as follows^[25-26]:

  $ \begin{array}{*{20}{l}} {\alpha = {2^{1/2}}\omega {{\left[ {{{\left( {\varepsilon _1^2 + \varepsilon _2^2} \right)}^{1/2}}-{\varepsilon _1}} \right]}^{1/2}}}\\ {R = {{\left[ {{{\left( {{\varepsilon _1} + {\rm{j}}{\varepsilon _2}} \right)}^{1/2}}-1} \right]}^2}/{{\left[ {{{\left( {{\varepsilon _1} + {\rm{j}}{\varepsilon _2}} \right)}^{1/2}} + 1} \right]}^2}}\\ {L = {\rm{Im}}\left[ {-1/\varepsilon } \right] = {\varepsilon _2}/\left[ {\varepsilon _1^2 + \varepsilon _2^2} \right]} \end{array} $

  Where the real part ε₁ and imaginary part ε₂ of the complex dielectric function ε = ε₁+jε₂ can be obtained based on the computational electronic states, and ω is the circular frequency.

  Fig. 6 shows the computed optical absorption coefficients of (a) AC-g-C₃N₄NRs with N_A=4, 7, 10, (b) ZZ-g -C₃N₄NRs with N_Z=4, 10, (c) AC-GNRs with N_A=4, 7, 10 and (d) bulk g-C₃N₄ as a function of energy. In the work, ZZ-GNRs are not investigated because the computed band gaps are 0. Seen from the Fig. 6a and 6b, the absorption coefficient of AC-g-C₃N₄NR or ZZ-g-C₃N₄NR increased with the increasing width of the corresponding nanoribbon. In Fig. 6a, these absorption peaks of 4-AC-g-C₃N₄NR, 7-AC-g-C₃N₄NR and 10-AC-g-C₃N₄NR (i. e. the black, red and green absorption peaks) in the low-energy range of 0~5 eV are specifically located at 3.58, 3.84, and 4.31 eV, respectively. Therefore, an obvious blueshift phenomenon can be generated in the low-energy range as the width increase of AC-g-C₃N₄NR. In Fig. 6b, the black and green absorption peaks are respectively located at 4.28 and 4.32 eV in the low energy region, indicating that there is only a very weak blueshift. By contrast, Fig. 6c displays an obvious redshift phenomenon in the low-energy range as the width increase of AC-GNR. Compared with bulk g-C₃N₄ (shown in Fig. 6d), the AC-and ZZ-g-C₃N₄NRs have the smaller absorption coefficient.

  Figure 6

  

  Figure 6.  Computed absorption coefficients of (a) AC-g-C₃N₄NRs with N_A=4, 7, 10, (b) ZZ-g-C₃N₄NRs with N_Z=4, 10, (c) AC-GNRs with N_A=4, 7, 10 and (d) bulk g-C₃N₄

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  Fig. 7 shows the computational reflectivity of (a) AC-g-C₃N₄NRs with N_A=4, 7, 10 and (b) ZZ-g-C₃N₄NRs with N_Z=4, 10, (c) AC-GNRs with N_A=4, 7, 10 and (d) bulk g-C₃N₄ as a function of energy. It also can be seen from Fig. 7a and 7b that the reflectivity is increasing with the increased width increase of AC-or ZZ-g-C₃N₄NR, and the strongest reflectivities of these NRs are all in the low energy range of 2~5 eV. By contrast, AC-GNRs can draw the same conclusion (Fig. 7c). In addition, bulk g-C₃N₄ has a larger reflectivity compared with g-C₃N₄NRs.

  Figure 7

  

  Figure 7.  Computed reflectivity of (a) AC-g-C₃N₄NRs with N_A=4, 7, 10, (b) ZZ-g-C₃N₄NRs with N_Z=4, 10, (c) AC-GNRs with N_A=4, 7, 10 and (d) bulk g-C₃N₄

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  3.   Conclusions

  The electronic and optical properties of g-C₃N₄ nanoribbons have been investigated by using the first-principles calculations. The results are as follows:

  (1) The edge H atoms of AC-and ZZ-g-C₃N₄NRs studied in the present work can exist stably. AC-g-C₃N₄NRs with N_A=4~10 and ZZ-g-C₃N₄NRs with N_Z=4, 6, 8, 10 are semiconductors, whereas ZZ-g-C₃N₄NR with N_Z=5, 7, 9 are metallic systems with no band gaps.

  (2) The VBMs of AC-g-C₃N₄NRs are mainly distributed on most of N atoms, whereas the VBMs of ZZ-g -C₃N₄NRs are contributed by the N atoms near the CH edge. The CBMs of AC-g-C₃N₄NRs mainly belong to C and N atoms near the one edge or two edges of AC-g-C₃N₄NRs, while the CBMs of ZZ-g-C₃N₄NRs mainly belong to C and N atoms near the NH edge of ZZ-g-C₃N₄NRs. The VBMs of AC-and ZZ-g-C₃N₄NRs are composed of the 2p states of N atoms, while the CBMs are mainly contributed by the 2p states of C and N atoms of the systems.

  (3) The absorption coefficient and the reflectivity of AC-g-C₃N₄NR or ZZ-g-C₃N₄NR are increased with the width increase of the corresponding nanoribbon. For the absorption coefficient, an obvious blueshift phenomenon can be generated in the low-energy range as the width increase of AC-g-C₃N₄NR.

  
  Acknowledgements: The authors would like to acknowledge the support from the National Natural Science Foundation of China (Grants No.11705124, 51871158, 11704274).
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• 

  Figure 1  Geometry structures of monolayer g-C₃N₄NRs with H termination: (a) 7-AC-g-C₃N₄NR; (b) 7-ZZ-g-C₃N₄NR

  A periodic unit cell is presented between the two red solid lines; Green straight line or zigzag curve shows atom chain; Total number of the atom chains across AC-g-C₃N₄NRs and ZZ-g-C₃N₄NRs width is also described by N_A and N_Z, respectively; Gray, blue and white balls represent the C, N and H atoms, respectively

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  Figure 2  Evolution of the binding energies (a) and band gaps (b) of AC-g-C₃N₄NRs and ZZ-g-C₃N₄NRs as a function of the width N_A or N_Z

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  Figure 3  Band structures of AC-g-C₃N₄NRs with (a) N_A=4, (b) N_A=7, (c) N_A=10 and ZZ-g-C₃N₄NRs with (d) N_Z=4, (e) N_Z=10

  Red and green bands denote the top valence band and the bottom conduction band, respectively; Blue circles shown on the red and green bands indicate the VBM and CBM, respectively; Fermi level (E_F) was set to 0 eV, and it is the energy level at which the Fermi-Dirac distribution function of an assembly of fermions is equal to one-half

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  Figure 4  Partial charge densities for VBMs (red isosurface) and CBMs (green isosurface) of AC-g-C₃N₄NRs with (a) N_A=4, (b) N_A=7, (c) N_A=10 and ZZ-g-C₃N₄NRs with (d) N_Z=4, (e) N_Z=10

  Isosurface level was set as 4 e·nm^-3

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  Figure 5  Partial density of states of AC-g-C₃N₄NRs with (a) N_A=4, (b) N_A=7, (c) N_A=10 and ZZ-g-C₃N₄NRs with (d) N_Z=4, (e) N_Z=10

  E_F=0 eV

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  Figure 6  Computed absorption coefficients of (a) AC-g-C₃N₄NRs with N_A=4, 7, 10, (b) ZZ-g-C₃N₄NRs with N_Z=4, 10, (c) AC-GNRs with N_A=4, 7, 10 and (d) bulk g-C₃N₄

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  Figure 7  Computed reflectivity of (a) AC-g-C₃N₄NRs with N_A=4, 7, 10, (b) ZZ-g-C₃N₄NRs with N_Z=4, 10, (c) AC-GNRs with N_A=4, 7, 10 and (d) bulk g-C₃N₄

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  Table 1.  ε of C and N atoms of AC-g-C₃N₄NRs and ZZ-g-C₃N₄NRs

  System	ε		System	ε
  4-AC-g-C3N4NR	3/4		4-ZZ-g-C3N4NR	3/4
  5-AC-g-C3N4NR	7/10		5-ZZ-g-C3N4NR	7/10
  6-AC-g-C3N4NR	3/4		6-ZZ-g-C3N4NR	3/4
  7-AC-g-C3N4NR	5/7		7-ZZ-g-C3N4NR	5/7
  8-AC-g-C3N4NR	3/4		8-ZZ-g-C3N4NR	3/4
  9-AC-g-C3N4NR	13/18		9-ZZ-g-C3N4NR	13/18
  10-AC-g-C3N4NR	3/4		10-ZZ-g-C3N4NR	3/4

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•