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Graphene/g-C3N4 bilayer: considerable band gap opening and effective band structure engineering Xinru Li, Ying Dai,* Yandong Ma, Shenghao Han and Baibiao Huang The layered graphene/g-C3N4 composites show high conductivity, electrocatalytic performance and visible light response and have potential applications in microelectronic devices and photocatalytic technology. In the present work, the stacking patterns and the correlations between electronic structures and related properties of graphene/g-C3N4 bilayers are investigated systematically by means of first-principles calculations. Our results indicate that the band gap of graphene/g-C3N4 bilayers can be up to 108.5 meV, which is large enough for the gap opening at room temperature. The calculated
Received 30th October 2013, Accepted 24th December 2013
charge density difference unravels that the charge redistribution drives the interlayer charge transfer
DOI: 10.1039/c3cp54592j
the band gap of graphene/g-C3N4 bilayers effectively. Our research demonstrates that graphene on
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g-C3N4 with a tunable band gap and high carrier mobility may provide a novel way for fabricating high-performance graphene-based nanodevices.
from graphene to g-C3N4. Interestingly, the investigation also shows that external electric field can tune
I. Introduction Graphene, due to its intriguing electronic properties as well as its high carrier mobility, has grabbed enormous attention since its experimental realization in 2004.1–4 Unfortunately, the lack of a finite band gap implies that the current can never be turned off completely, which is a formidable hurdle to the use of graphene in logic and high speed switching devices. So a considerable energy gap must be opened for graphene’s practical application in microelectronic devices. Various methods have been proposed to introduce a band gap into graphene, such as patterning graphene into nanoribbons,5–8 chemical functionalization with O, H, and halogen atoms,9–15 and uniaxial strain.16–18 However, despite these intensive research efforts, experimental realization of such schemes still remains a significant challenge. As an alternative approach, heterostructures of graphene materials provide a straightforward way for tuning the electronic properties of graphene. Examples include SiO2, SiC, diamond, MoS2 and BN.19–23 Despite these achievements, the search for ideal substrates is still underway.24 Very recently, C3N4 has attracted considerable attention because of its promising application in electronic devices.25,26 It can exist in several allotropes, of which graphitic carbon nitride (g-C3N4) is considered to be the most stable one under ambient conditions.27,28 g-C3N4 has a two-dimensional structure, as shown in Fig. 1. Such a synthesized metal-free polymer semiconductor is chemically and thermally stable and does School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, People’s Republic of China. E-mail: [email protected]
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not rely on complicated device manufacturing.29 Recently, the layered graphene/g-C3N4 composites were synthesized with improved conductivity and electrocatalytic performance.30 Subsequently, the use of graphene/g-C3N4 composites for hydrogen production via photocatalytic water splitting was studied,31 and the visible light response enhancement of the hybrid graphene/g-C3N4 complex was reported.32 In spite of its importance, the band gap engineering relative to different stacking patterns of the graphene/g-C3N4 bilayer has not been explored systematically so far. On the other hand, it is noted that external electric field (E-field) can efficiently tune the electronic properties of layered materials.33–35 For example, a recent experiment indicated that the transport properties of trilayered graphene can be tuned by the perpendicular electric field, although it would be the only response to rather large fields.33 Theoretical calculations revealed that external electric field can effectively modulate the energy gap of the graphene/fluorographene bilayer, and correspondingly cause a semiconductor–metal transition.40 So, we wonder if the related properties of graphene/g-C3N4 heterostructures can be modulated by the E-field, which may provide a new approach for tuning the electronic devices to meet different environments and demands. In the present work, we systematically explore the electronic behaviors of graphene/g-C3N4 bilayers with different stacking patterns by means of vdW-corrected density functional theory calculations. It is revealed that a considerable band gap would be induced by interlayer interactions. What’s more, the charge density difference reveals that the interlayer charge transfers from graphene to g-C3N4. Most interestingly, all the band gaps
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Fig. 1
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Optimized geometric structures of g-C3N4 (a) and the graphene monolayer (b). Calculated band structures of g-C3N4 (c) and graphene (d).
with different stacking patterns increase monotonically with decreasing external electric field perpendicular to the bilayer, and the much smaller external electric field can tune the band gaps significantly. Our work is expected to provide an effective way to tune the electronic properties of layered graphenerelated nanoelectronic devices.
II. Computational methods Our calculations on the graphene/g-C3N4 bilayer are performed using density functional theory with the generalized gradient approximation (GGA) in the parametrization of Perdew–Burke– Ernzerhof (PBE) by using the plane-wave basis Vienna Ab initio Simulation Package (VASP) code.36,37 Due to the absence of strong bonding interactions between the graphene and g-C3N4, the weak van der Waals interactions are expected to be important. Since the standard PBE functional cannot describe the weak interactions well, we adopted a damped vdW correction (PBE-D2) proposed by Grimme.38 This method is a hybrid semiempirical solution that introduces damped atom-pairwise dispersion correction of the form C6R6 in the DFT formalism. For all calculations, including geometric optimization and electronic structural calculations, the cutoff kinetic energies for plane waves is set as 450 eV, which is sufficiently large because all results are converged at this value. And the convergence tolerance of force on each atom during structure relaxation is less than 0.02 eV Å1. The convergence criterion for energy is chosen as 104 eV. The 2D Brillouin zone is sampled by 9 9 1 k-points within the Monkhorst–Pack scheme for structural optimization and by 11 11 1 k-points for electronic structural calculations.43 In geometric optimization, the positions of all atoms in a supercell are fully relaxed while the shape and the volume of the supercell are fixed. A vacuum slab of 20 Å is set along the direction normal to the interface, which is large enough to avoid the interaction between periodic images after examination of other larger values.
III. Results and discussion The graphene/g-C3N4 heterostructure is modeled by using a supercell, which contains one g-C3N4 monolayer and one
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graphene monolayer. The lattice parameters of related graphene and g-C3N4 are 2.44 and 7.06 Å, respectively. The lattice parameter of g-C3N4 is about three times larger than graphene, thus, we impose a commensurability of 7.06 Å between g-C3N4 and the graphene monolayer, which means a 1 1 supercell g-C3N4 (Fig. 1a) and a 3 3 supercell graphene (Fig. 1b) are employed. The hybrid structures above can be taken as the minimum size because of the smallest commensurability. To simulate the hybrid graphene/g-C3N4 composite, a 3 3 graphene supercell is used to match the 1 1 g-C3N4 supercell with a small 3.5% strain in the graphene monolayer. The artificial strain introduced to match the lattice parameters does not affect the main conclusions. Actually, such a negligible effect of the small lattice mismatch on the electronic structure has been well demonstrated and reported in the recent calculations for the similar graphene-based hybrid structures.19–21 The corresponding band structure of g-C3N4 and the 3 3 graphene supercell are also depicted in Fig. 1c and d. It should be noted that for g-C3N4, the valence band maximum (VBM) locates at G points while the conduction band minimum (CBM) locates at M points, thus resulting in a semiconductor with an indirect band gap of 1.02 eV, in good agreement with previous studies.39 On the other hand, the Dirac cone at the K point in the unit cell of graphene maps onto the G point in the 3 3 supercell. In order to explore the interaction between graphene and g-C3N4, four representational stacking patterns are discussed: (1) pattern I, part of C atoms of graphene are placed above N atoms of the g-C3N4 surface while others are placed above the hollow of g-C3N4, as shown in Fig. 2a; (2) pattern II, part of C atoms of graphene are placed above C atoms of the g-C3N4 surface, as shown in Fig. 2b; (3) pattern III, part of C atoms of graphene are placed right above N and C atoms of g-C3N4, as shown in Fig. 2c; (4) pattern IV, part of C atoms of graphene are placed on the bridge sites of the g-C3N4 surface, as shown in Fig. 2d. The four typical packing patterns are chosen according to the hollow, the bridge, and the top configurations between the two layers. However, other random configurations are also examined and discarded because of their larger total energies and worse thermodynamic stability. For all the cases, graphene maintains an almost plane and hexagonal honeycomb network, and the interlayer distances are listed in Table 1. To evaluate
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Fig. 2 Top (upper) and side (bottom) views of optimized structures of the graphene/g-C3N4 bilayer in four stacking patterns. White, gray and blue balls represent C atoms on graphene and C and N atoms on the g-C3N4 monolayer, respectively.
the structural stability of the four stacking patterns, the binding energies are calculated as Eb = Egraphene + Eg-C3N4 Egraphene/g-C3N4 where Egraphene/g-C3N4 is the total energy of the graphene/g-C3N4 bilayer, Egraphene is the energy of the corresponding graphene sheet, and Eg-C3N4 is the energy of the corresponding g-C3N4. It shows in Table 1 that pattern I is more favorable in energy than other stacking patterns and its interlayer distance is 2.89 Å. Besides, we have tested the interlayer distance of stacking pattern I without considering any long-range dispersion correction, the distance of the interlayer is 3.1 Å and the results show that the vdW interactions play an important role in accurately describing the geometry of the graphene and the g-C3N4 monolayers. Notice that the graphene retains its plane structure and the interlayer distance is much larger than the sum of covalent radii of C and N atoms, which means that the C atoms of graphene and the C/N atoms of g-C3N4 are beyond the bonding range. Now a question arises as to whether the electronic structures of graphene can be affected by g-C3N4 monolayers. Taking the energetically favorable pattern (pattern I) as an example, we examine the electronic properties of the graphene/ g-C3N4 heterostructure. The corresponding results are plotted in Fig. 3. For graphene/g-C3N4 composites, the linear band structure is disrupted compared with that of the pristine graphene as in Fig. 1(d), leading to a metal–semiconductor transition. In detail, as plotted in Fig. 3a, graphene/g-C3N4 heterostructure is a direct semiconductor with VBM and CBM both located at the G point. To explore the electronic structure
Table 1 Calculated interlayer distances (Å) and binding energies (eV) of four different stacking patterns
Stacking patterns
I
II
III
IV
Interlayer distance (Å) Binding energy (eV)
2.89 3.41
2.98 3.12
3.05 2.97
2.91 3.31
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Fig. 3 (a) Band structures and (b) total and partial DOSs of the graphene/ g-C3N4 bilayer. The Fermi level is assigned at 0 eV.
variations induced by the interface, the total and partial density of states of graphene/g-C3N4 bilayers are depicted in Fig. 3b. The results show that only a little weight of the g-C3N4 states contributes to the states near the Fermi level. Thus, the energy states near the Fermi level mainly consist of carbon 2p orbitals of graphene. It is important to note that the high carrier mobility may be easily maintained, though the band gap can be opened by the interactions between graphene and g-C3N4. Since the energy difference between different stacking patterns is insignificant (0.44 eV or less), the band structures of the other three stacking patterns are also investigated. As a result, all the other patterns of graphene/g-C3N4 bilayers present a similar band structure as pattern I, and the band gaps are 41.5, 108.5 and 35.2 meV, respectively. These band gaps are significantly larger than kBT (26 meV) at room temperature. The information above demonstrates that the band gaps can be well maintained at room temperature, which may have a wide range of applications in practice. Since the absence of a finite band gap without degrading the electronic properties of the graphene is a significant obstacle in the construction of graphene-based switching devices, our results here strongly suggest that graphene/g-C3N4 could have enormous potential to overcome the aforementioned challenges. In order to unravel more information about the bonding mechanism, it is worthwhile to investigate charge density difference, Dr = rgraphene/g-C3N4 rgraphene rg-C3N4, constructed by subtracting the electronic charge of graphene/g-C3N4 from that of the corresponding isolated graphene and the g-C3N4 monolayer, where rgraphene/g-C3N4, rgraphene, and rg-C3N4 are the charge densities of the graphene/g-C3N4 heterobilayer, isolated graphene and the g-C3N4 monolayer. Plots of charge density difference for graphene/g-C3N4 of pattern I clearly show that charge density is redistributed by forming electron-rich and hole-rich regions within the graphene layer. And the redistribution
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drives the interlayer charge transfer from graphene to g-C3N4. It is worth mentioning that other than vertical interactions between graphene and g-C3N4, interactions along lateral orientations are also crucial to promote charge transfer in some similar organic heterojunctions. Moreover, the number of layers can also have an influence on charge redistribution and interface interactions.49 These points are deserved to be investigated further. Intuitive charge density difference of graphene/g-C3N4 confirms that the different chemical environment of two sublattices of graphene is the reason of band gap opening in hybrid structures. Thus, it is expected that the vertical external electric field (E-field) can modulate charge density difference in order to tune the band gap of graphene/g-C3N4.40–42 Very recently, the band gap of dual-gated trilayer graphene was efficiently tuned by the external perpendicular electric field.19 Inspired by these studies, we further examined the effect of E-field on the binding strength and electronic properties of the graphene/g-C3N4 bilayer in pattern I. Two directions of E-field (+z, z) perpendicular to the planes of graphene and g-C3N4 are considered, and the values from 0.6 to 0.6 V Å1 are used. We define the positive direction of the E-field as pointing from g-C3N4 to graphene, as shown in the inset of Fig. 5. The band gaps of the graphene/g-C3N4 bilayer decrease with the E-field along the +z direction increasing. And binding energies indicate that the
Fig. 4 Top and side views of charge density difference of graphene/ g-C3N4 for stacking pattern I. Grey and brown balls represent C and N atoms, respectively. Blue and yellow isosurfaces represent, respectively, charge accumulation and depletion in the space with respect to isolated graphene and g-C3N4. The isovalue chosen to plot the isosurface is 0.001 e Å3.
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interaction between graphene and g-C3N4 can be enhanced by applying appropriate E-field. Moreover, the variation of band gaps with the external electric field for the other three stacking patterns of graphene/g-C3N4 has also been studied. The results show that the band gaps of other stacking patterns all increase monotonically with decreasing external electric field, and the band gaps can be tuned significantly by a much smaller external electric field. The mechanism can be explained by charge redistribution mentioned above in Fig. 4. As the interlayer interaction drives charge to transfer from graphene to g-C3N4, these results indicate that the difference in the chemical environment between two sublattices of graphene can be affected by modulating charge transfer. Applying E-field is an effective way to change the chemical environment and cause charge redistribution, thus, the band gaps can be changed regularly by the appropriate E-field. The investigation above unravels that the band gaps of the graphene/g-C3N4 bilayer will be increased by applying an external field along a specific direction. Moreover, calculations with an E-field of 0.3 and 0.3 V Å1 show that the morphologies of band structures under the external electric field will not change dramatically except for the gap difference, as shown in Fig. 5. This character is good for graphene-based nanodevices to maintain stable properties under different external environments. Considering the current practical applications of graphenerelated nanoelectronics, higher carrier mobility and linear band dispersion are very important aspects. Thus the effective mass of electrons (me*) and holes (mh*) are calculated by fitting parabolic functions to the VBM and CBM of graphene/g-C3N4 2 1 d Ek according to the equation m ¼ h , where k is the dk2 wave vector and Ek is the energy corresponding to the wave vector k. We present the me* and mh* along G - M and G - K directions of pattern I with the external field 0.3, 0, 0.3 V Å1 in Table 2. We can see from Table 2 that all effective masses have an approximately linear relationship with E-fields and band gaps: the effective masses and band gaps decrease with the increase of E-fields along the +z direction. It shows that the band gap opening may block the linear band dispersion to
Fig. 5 (a) Band gaps of the graphene/g-C3N4 bilayer as a function of the E-field. (inset) The directions of the E-field. (b) Calculated band structures of stacking pattern I with the electric field of 0.3 V Å1 and 0.3 V Å1. (Insets) Magnification of the bands at G points near the Fermi levels.
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Table 2 Effective masses of electrons and holes for graphene/g-C3N4 in different external electric fields of 0.3, 0 and 0.3 V Å1, obtained from parabolic fitting to the CBM and VBM along G - M and G - K directions in the reciprocal space
E-field (V Å1)
Band gaps (meV)
Effective mass
G-M
G-K
0.3
143.5
0
106
me* mh* me* mh* me* mh*
0.0205 0.0208 0.0173 0.0174 0.0149 0.0149
0.0214 0.0217 0.0183 0.0184 0.0159 0.0160
0.3
95.6
some extent. Fortunately, the effective masses of electrons and holes at VBM and CBM for the graphene/g-C3N4 heterostructure under appropriate external electric fields are still smaller than the vast majority of graphene-based nanoelectronics.44,45 This indicates that the graphene/g-C3N4 bilayer may have high carrier mobility which have a good application in high speed spintronics. On the other hand, according to this model the dispersion relation near the Fermi level can be described as qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi EðkÞ ¼ D2 þ ðhvF kÞ2 ,46,47 where k is the wave vector relative to the K point, vF is the Fermi velocity, and D is the onsite energy difference between the two sublattices. As for the strict graphene monolayer, the onsite energy of the two sublattices are equivalent, while for the graphene/g-C3N4 bilayer different external environments break the equivalence of the two graphene sublattices, resulting in a nonzero band gap, Eg = 2D, and parabolic dispersion relation near the Dirac point, E(k) E (D + h2vF2k2/2D). Under the p-electron tight-binding approximation of this system, the effective mass of carriers of graphene/g-C3N4 near the G point can be calculated as m* E Eg/2vF2. It can be seen that Fermi velocity vF is larger with m* smaller, which means higher carrier mobility with appropriate Eg in the graphene/g-C3N4 heterostructures. Further calculations show that four patterns of graphene/g-C3N4 heterostructures all have considerable Fermi velocities (very close to that of isolated graphene 1.0 106 m s1).48 Our results regarding applying an E-field reveal that the interlayer effect plays an important role in the graphene/g-C3N4 system and the band gaps can be modulated monotonously by the E-field along a specific direction. Meanwhile, the calculated effective mass and Fermi velocity indicate that appropriate external electric field does not reduce the carrier mobility of graphene/g-C3N4. So, an ideal switching device with the high carrier mobility and certain band gap on graphene/g-C3N4 based nanomaterials can be expected to be achieved.
IV. Conclusion A comprehensive first principles study is performed on the structural and electronic properties of graphene/g-C3N4 bilayers. Four possible stacking patterns have been considered. The calculated band gaps of different stacking patterns are considerably larger than kBT (26 meV) at room temperature, this may overcome one of the main obstacles to using graphene
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as an electronic device, namely, the lack of intrinsic band gap. Furthermore, the band gaps of graphene/g-C3N4 can be tuned regularly under an experimentally achievable E-field. In addition, fitting carrier effective mass and Fermi velocity reveal that the graphene/g-C3N4 heterostructure will have high carrier mobility under appropriate external electric field. The present work may not only provide a fundamental basis for the application of the graphene/g-C3N4 bilayer as a candidate nanomaterial for novel spintronic devices, but also open up an effective way to modulate band gap regularly through an external perpendicular electric field. It is believed that the experimental peers can realize the graphene/g-C3N4 bilayer with small energy gaps very soon and use them in novel integrated functional nanodevices.
Acknowledgements This work is supported by the National Basic Research Program of China (973 program, 2013CB632401), National Natural Science Foundation of China under Grants 21333006, 11174180 and 61176019, the Fund for Doctoral Program of National Education 20120131110066, and the Natural Science Foundation of Shandong Province under Grant number ZR2011AM009.
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Graphene/g-C3N4 bilayer: considerable band gap opening and effective band structure engineering Xinru Li, Ying Dai,* Yandong Ma, Shenghao Han and Baibiao Huang The layered graphene/g-C3N4 composites show high conductivity, electrocatalytic performance and visible light response and have potential applications in microelectronic devices and photocatalytic technology. In the present work, the stacking patterns and the correlations between electronic structures and related properties of graphene/g-C3N4 bilayers are investigated systematically by means of first-principles calculations. Our results indicate that the band gap of graphene/g-C3N4 bilayers can be up to 108.5 meV, which is large enough for the gap opening at room temperature. The calculated
Received 30th October 2013, Accepted 24th December 2013
charge density difference unravels that the charge redistribution drives the interlayer charge transfer
DOI: 10.1039/c3cp54592j
the band gap of graphene/g-C3N4 bilayers effectively. Our research demonstrates that graphene on
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g-C3N4 with a tunable band gap and high carrier mobility may provide a novel way for fabricating high-performance graphene-based nanodevices.
from graphene to g-C3N4. Interestingly, the investigation also shows that external electric field can tune
I. Introduction Graphene, due to its intriguing electronic properties as well as its high carrier mobility, has grabbed enormous attention since its experimental realization in 2004.1–4 Unfortunately, the lack of a finite band gap implies that the current can never be turned off completely, which is a formidable hurdle to the use of graphene in logic and high speed switching devices. So a considerable energy gap must be opened for graphene’s practical application in microelectronic devices. Various methods have been proposed to introduce a band gap into graphene, such as patterning graphene into nanoribbons,5–8 chemical functionalization with O, H, and halogen atoms,9–15 and uniaxial strain.16–18 However, despite these intensive research efforts, experimental realization of such schemes still remains a significant challenge. As an alternative approach, heterostructures of graphene materials provide a straightforward way for tuning the electronic properties of graphene. Examples include SiO2, SiC, diamond, MoS2 and BN.19–23 Despite these achievements, the search for ideal substrates is still underway.24 Very recently, C3N4 has attracted considerable attention because of its promising application in electronic devices.25,26 It can exist in several allotropes, of which graphitic carbon nitride (g-C3N4) is considered to be the most stable one under ambient conditions.27,28 g-C3N4 has a two-dimensional structure, as shown in Fig. 1. Such a synthesized metal-free polymer semiconductor is chemically and thermally stable and does School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, People’s Republic of China. E-mail: [email protected]
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not rely on complicated device manufacturing.29 Recently, the layered graphene/g-C3N4 composites were synthesized with improved conductivity and electrocatalytic performance.30 Subsequently, the use of graphene/g-C3N4 composites for hydrogen production via photocatalytic water splitting was studied,31 and the visible light response enhancement of the hybrid graphene/g-C3N4 complex was reported.32 In spite of its importance, the band gap engineering relative to different stacking patterns of the graphene/g-C3N4 bilayer has not been explored systematically so far. On the other hand, it is noted that external electric field (E-field) can efficiently tune the electronic properties of layered materials.33–35 For example, a recent experiment indicated that the transport properties of trilayered graphene can be tuned by the perpendicular electric field, although it would be the only response to rather large fields.33 Theoretical calculations revealed that external electric field can effectively modulate the energy gap of the graphene/fluorographene bilayer, and correspondingly cause a semiconductor–metal transition.40 So, we wonder if the related properties of graphene/g-C3N4 heterostructures can be modulated by the E-field, which may provide a new approach for tuning the electronic devices to meet different environments and demands. In the present work, we systematically explore the electronic behaviors of graphene/g-C3N4 bilayers with different stacking patterns by means of vdW-corrected density functional theory calculations. It is revealed that a considerable band gap would be induced by interlayer interactions. What’s more, the charge density difference reveals that the interlayer charge transfers from graphene to g-C3N4. Most interestingly, all the band gaps
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Fig. 1
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Optimized geometric structures of g-C3N4 (a) and the graphene monolayer (b). Calculated band structures of g-C3N4 (c) and graphene (d).
with different stacking patterns increase monotonically with decreasing external electric field perpendicular to the bilayer, and the much smaller external electric field can tune the band gaps significantly. Our work is expected to provide an effective way to tune the electronic properties of layered graphenerelated nanoelectronic devices.
II. Computational methods Our calculations on the graphene/g-C3N4 bilayer are performed using density functional theory with the generalized gradient approximation (GGA) in the parametrization of Perdew–Burke– Ernzerhof (PBE) by using the plane-wave basis Vienna Ab initio Simulation Package (VASP) code.36,37 Due to the absence of strong bonding interactions between the graphene and g-C3N4, the weak van der Waals interactions are expected to be important. Since the standard PBE functional cannot describe the weak interactions well, we adopted a damped vdW correction (PBE-D2) proposed by Grimme.38 This method is a hybrid semiempirical solution that introduces damped atom-pairwise dispersion correction of the form C6R6 in the DFT formalism. For all calculations, including geometric optimization and electronic structural calculations, the cutoff kinetic energies for plane waves is set as 450 eV, which is sufficiently large because all results are converged at this value. And the convergence tolerance of force on each atom during structure relaxation is less than 0.02 eV Å1. The convergence criterion for energy is chosen as 104 eV. The 2D Brillouin zone is sampled by 9 9 1 k-points within the Monkhorst–Pack scheme for structural optimization and by 11 11 1 k-points for electronic structural calculations.43 In geometric optimization, the positions of all atoms in a supercell are fully relaxed while the shape and the volume of the supercell are fixed. A vacuum slab of 20 Å is set along the direction normal to the interface, which is large enough to avoid the interaction between periodic images after examination of other larger values.
III. Results and discussion The graphene/g-C3N4 heterostructure is modeled by using a supercell, which contains one g-C3N4 monolayer and one
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graphene monolayer. The lattice parameters of related graphene and g-C3N4 are 2.44 and 7.06 Å, respectively. The lattice parameter of g-C3N4 is about three times larger than graphene, thus, we impose a commensurability of 7.06 Å between g-C3N4 and the graphene monolayer, which means a 1 1 supercell g-C3N4 (Fig. 1a) and a 3 3 supercell graphene (Fig. 1b) are employed. The hybrid structures above can be taken as the minimum size because of the smallest commensurability. To simulate the hybrid graphene/g-C3N4 composite, a 3 3 graphene supercell is used to match the 1 1 g-C3N4 supercell with a small 3.5% strain in the graphene monolayer. The artificial strain introduced to match the lattice parameters does not affect the main conclusions. Actually, such a negligible effect of the small lattice mismatch on the electronic structure has been well demonstrated and reported in the recent calculations for the similar graphene-based hybrid structures.19–21 The corresponding band structure of g-C3N4 and the 3 3 graphene supercell are also depicted in Fig. 1c and d. It should be noted that for g-C3N4, the valence band maximum (VBM) locates at G points while the conduction band minimum (CBM) locates at M points, thus resulting in a semiconductor with an indirect band gap of 1.02 eV, in good agreement with previous studies.39 On the other hand, the Dirac cone at the K point in the unit cell of graphene maps onto the G point in the 3 3 supercell. In order to explore the interaction between graphene and g-C3N4, four representational stacking patterns are discussed: (1) pattern I, part of C atoms of graphene are placed above N atoms of the g-C3N4 surface while others are placed above the hollow of g-C3N4, as shown in Fig. 2a; (2) pattern II, part of C atoms of graphene are placed above C atoms of the g-C3N4 surface, as shown in Fig. 2b; (3) pattern III, part of C atoms of graphene are placed right above N and C atoms of g-C3N4, as shown in Fig. 2c; (4) pattern IV, part of C atoms of graphene are placed on the bridge sites of the g-C3N4 surface, as shown in Fig. 2d. The four typical packing patterns are chosen according to the hollow, the bridge, and the top configurations between the two layers. However, other random configurations are also examined and discarded because of their larger total energies and worse thermodynamic stability. For all the cases, graphene maintains an almost plane and hexagonal honeycomb network, and the interlayer distances are listed in Table 1. To evaluate
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Fig. 2 Top (upper) and side (bottom) views of optimized structures of the graphene/g-C3N4 bilayer in four stacking patterns. White, gray and blue balls represent C atoms on graphene and C and N atoms on the g-C3N4 monolayer, respectively.
the structural stability of the four stacking patterns, the binding energies are calculated as Eb = Egraphene + Eg-C3N4 Egraphene/g-C3N4 where Egraphene/g-C3N4 is the total energy of the graphene/g-C3N4 bilayer, Egraphene is the energy of the corresponding graphene sheet, and Eg-C3N4 is the energy of the corresponding g-C3N4. It shows in Table 1 that pattern I is more favorable in energy than other stacking patterns and its interlayer distance is 2.89 Å. Besides, we have tested the interlayer distance of stacking pattern I without considering any long-range dispersion correction, the distance of the interlayer is 3.1 Å and the results show that the vdW interactions play an important role in accurately describing the geometry of the graphene and the g-C3N4 monolayers. Notice that the graphene retains its plane structure and the interlayer distance is much larger than the sum of covalent radii of C and N atoms, which means that the C atoms of graphene and the C/N atoms of g-C3N4 are beyond the bonding range. Now a question arises as to whether the electronic structures of graphene can be affected by g-C3N4 monolayers. Taking the energetically favorable pattern (pattern I) as an example, we examine the electronic properties of the graphene/ g-C3N4 heterostructure. The corresponding results are plotted in Fig. 3. For graphene/g-C3N4 composites, the linear band structure is disrupted compared with that of the pristine graphene as in Fig. 1(d), leading to a metal–semiconductor transition. In detail, as plotted in Fig. 3a, graphene/g-C3N4 heterostructure is a direct semiconductor with VBM and CBM both located at the G point. To explore the electronic structure
Table 1 Calculated interlayer distances (Å) and binding energies (eV) of four different stacking patterns
Stacking patterns
I
II
III
IV
Interlayer distance (Å) Binding energy (eV)
2.89 3.41
2.98 3.12
3.05 2.97
2.91 3.31
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Fig. 3 (a) Band structures and (b) total and partial DOSs of the graphene/ g-C3N4 bilayer. The Fermi level is assigned at 0 eV.
variations induced by the interface, the total and partial density of states of graphene/g-C3N4 bilayers are depicted in Fig. 3b. The results show that only a little weight of the g-C3N4 states contributes to the states near the Fermi level. Thus, the energy states near the Fermi level mainly consist of carbon 2p orbitals of graphene. It is important to note that the high carrier mobility may be easily maintained, though the band gap can be opened by the interactions between graphene and g-C3N4. Since the energy difference between different stacking patterns is insignificant (0.44 eV or less), the band structures of the other three stacking patterns are also investigated. As a result, all the other patterns of graphene/g-C3N4 bilayers present a similar band structure as pattern I, and the band gaps are 41.5, 108.5 and 35.2 meV, respectively. These band gaps are significantly larger than kBT (26 meV) at room temperature. The information above demonstrates that the band gaps can be well maintained at room temperature, which may have a wide range of applications in practice. Since the absence of a finite band gap without degrading the electronic properties of the graphene is a significant obstacle in the construction of graphene-based switching devices, our results here strongly suggest that graphene/g-C3N4 could have enormous potential to overcome the aforementioned challenges. In order to unravel more information about the bonding mechanism, it is worthwhile to investigate charge density difference, Dr = rgraphene/g-C3N4 rgraphene rg-C3N4, constructed by subtracting the electronic charge of graphene/g-C3N4 from that of the corresponding isolated graphene and the g-C3N4 monolayer, where rgraphene/g-C3N4, rgraphene, and rg-C3N4 are the charge densities of the graphene/g-C3N4 heterobilayer, isolated graphene and the g-C3N4 monolayer. Plots of charge density difference for graphene/g-C3N4 of pattern I clearly show that charge density is redistributed by forming electron-rich and hole-rich regions within the graphene layer. And the redistribution
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drives the interlayer charge transfer from graphene to g-C3N4. It is worth mentioning that other than vertical interactions between graphene and g-C3N4, interactions along lateral orientations are also crucial to promote charge transfer in some similar organic heterojunctions. Moreover, the number of layers can also have an influence on charge redistribution and interface interactions.49 These points are deserved to be investigated further. Intuitive charge density difference of graphene/g-C3N4 confirms that the different chemical environment of two sublattices of graphene is the reason of band gap opening in hybrid structures. Thus, it is expected that the vertical external electric field (E-field) can modulate charge density difference in order to tune the band gap of graphene/g-C3N4.40–42 Very recently, the band gap of dual-gated trilayer graphene was efficiently tuned by the external perpendicular electric field.19 Inspired by these studies, we further examined the effect of E-field on the binding strength and electronic properties of the graphene/g-C3N4 bilayer in pattern I. Two directions of E-field (+z, z) perpendicular to the planes of graphene and g-C3N4 are considered, and the values from 0.6 to 0.6 V Å1 are used. We define the positive direction of the E-field as pointing from g-C3N4 to graphene, as shown in the inset of Fig. 5. The band gaps of the graphene/g-C3N4 bilayer decrease with the E-field along the +z direction increasing. And binding energies indicate that the
Fig. 4 Top and side views of charge density difference of graphene/ g-C3N4 for stacking pattern I. Grey and brown balls represent C and N atoms, respectively. Blue and yellow isosurfaces represent, respectively, charge accumulation and depletion in the space with respect to isolated graphene and g-C3N4. The isovalue chosen to plot the isosurface is 0.001 e Å3.
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interaction between graphene and g-C3N4 can be enhanced by applying appropriate E-field. Moreover, the variation of band gaps with the external electric field for the other three stacking patterns of graphene/g-C3N4 has also been studied. The results show that the band gaps of other stacking patterns all increase monotonically with decreasing external electric field, and the band gaps can be tuned significantly by a much smaller external electric field. The mechanism can be explained by charge redistribution mentioned above in Fig. 4. As the interlayer interaction drives charge to transfer from graphene to g-C3N4, these results indicate that the difference in the chemical environment between two sublattices of graphene can be affected by modulating charge transfer. Applying E-field is an effective way to change the chemical environment and cause charge redistribution, thus, the band gaps can be changed regularly by the appropriate E-field. The investigation above unravels that the band gaps of the graphene/g-C3N4 bilayer will be increased by applying an external field along a specific direction. Moreover, calculations with an E-field of 0.3 and 0.3 V Å1 show that the morphologies of band structures under the external electric field will not change dramatically except for the gap difference, as shown in Fig. 5. This character is good for graphene-based nanodevices to maintain stable properties under different external environments. Considering the current practical applications of graphenerelated nanoelectronics, higher carrier mobility and linear band dispersion are very important aspects. Thus the effective mass of electrons (me*) and holes (mh*) are calculated by fitting parabolic functions to the VBM and CBM of graphene/g-C3N4 2 1 d Ek according to the equation m ¼ h , where k is the dk2 wave vector and Ek is the energy corresponding to the wave vector k. We present the me* and mh* along G - M and G - K directions of pattern I with the external field 0.3, 0, 0.3 V Å1 in Table 2. We can see from Table 2 that all effective masses have an approximately linear relationship with E-fields and band gaps: the effective masses and band gaps decrease with the increase of E-fields along the +z direction. It shows that the band gap opening may block the linear band dispersion to
Fig. 5 (a) Band gaps of the graphene/g-C3N4 bilayer as a function of the E-field. (inset) The directions of the E-field. (b) Calculated band structures of stacking pattern I with the electric field of 0.3 V Å1 and 0.3 V Å1. (Insets) Magnification of the bands at G points near the Fermi levels.
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Table 2 Effective masses of electrons and holes for graphene/g-C3N4 in different external electric fields of 0.3, 0 and 0.3 V Å1, obtained from parabolic fitting to the CBM and VBM along G - M and G - K directions in the reciprocal space
E-field (V Å1)
Band gaps (meV)
Effective mass
G-M
G-K
0.3
143.5
0
106
me* mh* me* mh* me* mh*
0.0205 0.0208 0.0173 0.0174 0.0149 0.0149
0.0214 0.0217 0.0183 0.0184 0.0159 0.0160
0.3
95.6
some extent. Fortunately, the effective masses of electrons and holes at VBM and CBM for the graphene/g-C3N4 heterostructure under appropriate external electric fields are still smaller than the vast majority of graphene-based nanoelectronics.44,45 This indicates that the graphene/g-C3N4 bilayer may have high carrier mobility which have a good application in high speed spintronics. On the other hand, according to this model the dispersion relation near the Fermi level can be described as qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi EðkÞ ¼ D2 þ ðhvF kÞ2 ,46,47 where k is the wave vector relative to the K point, vF is the Fermi velocity, and D is the onsite energy difference between the two sublattices. As for the strict graphene monolayer, the onsite energy of the two sublattices are equivalent, while for the graphene/g-C3N4 bilayer different external environments break the equivalence of the two graphene sublattices, resulting in a nonzero band gap, Eg = 2D, and parabolic dispersion relation near the Dirac point, E(k) E (D + h2vF2k2/2D). Under the p-electron tight-binding approximation of this system, the effective mass of carriers of graphene/g-C3N4 near the G point can be calculated as m* E Eg/2vF2. It can be seen that Fermi velocity vF is larger with m* smaller, which means higher carrier mobility with appropriate Eg in the graphene/g-C3N4 heterostructures. Further calculations show that four patterns of graphene/g-C3N4 heterostructures all have considerable Fermi velocities (very close to that of isolated graphene 1.0 106 m s1).48 Our results regarding applying an E-field reveal that the interlayer effect plays an important role in the graphene/g-C3N4 system and the band gaps can be modulated monotonously by the E-field along a specific direction. Meanwhile, the calculated effective mass and Fermi velocity indicate that appropriate external electric field does not reduce the carrier mobility of graphene/g-C3N4. So, an ideal switching device with the high carrier mobility and certain band gap on graphene/g-C3N4 based nanomaterials can be expected to be achieved.
IV. Conclusion A comprehensive first principles study is performed on the structural and electronic properties of graphene/g-C3N4 bilayers. Four possible stacking patterns have been considered. The calculated band gaps of different stacking patterns are considerably larger than kBT (26 meV) at room temperature, this may overcome one of the main obstacles to using graphene
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as an electronic device, namely, the lack of intrinsic band gap. Furthermore, the band gaps of graphene/g-C3N4 can be tuned regularly under an experimentally achievable E-field. In addition, fitting carrier effective mass and Fermi velocity reveal that the graphene/g-C3N4 heterostructure will have high carrier mobility under appropriate external electric field. The present work may not only provide a fundamental basis for the application of the graphene/g-C3N4 bilayer as a candidate nanomaterial for novel spintronic devices, but also open up an effective way to modulate band gap regularly through an external perpendicular electric field. It is believed that the experimental peers can realize the graphene/g-C3N4 bilayer with small energy gaps very soon and use them in novel integrated functional nanodevices.
Acknowledgements This work is supported by the National Basic Research Program of China (973 program, 2013CB632401), National Natural Science Foundation of China under Grants 21333006, 11174180 and 61176019, the Fund for Doctoral Program of National Education 20120131110066, and the Natural Science Foundation of Shandong Province under Grant number ZR2011AM009.
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