Band Gap Opening of Graphene by Forming Heterojunctions with the

May 9, 2016 - To solve a challenging issue, i.e., the gap opening of graphene, we designed several heterojunctions of graphene and other two-dimension...
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Band Gap Opening of Graphene by Forming Heterojunctions with the 2D Carbonitrides Nitrogenated Holey Graphene, g‑C3N4, and g‑CN: Electric Field Effect Xiong Cao,† Jun-jie Shi,*,† Min Zhang,‡ Xin-he Jiang,† Hong-xia Zhong,† Pu Huang,† Yi-min Ding,† and Meng Wu† †

State Key Laboratory for Mesoscopic Physics and Department of Physics, Peking University, Beijing 100871, P. R. China College of Physics and Electronic Information, Inner Mongolia Normal University, Hohhot 010022, P. R. China

‡

ABSTRACT: To solve a challenging issue, i.e., the gap opening of graphene, we designed several heterojunctions of graphene and other two-dimensional carbonitride materials with natural holes in their monolayers, namely, nitrogenated holey graphene (NHG), g-C3N4, and g-CN, to destroy graphene’s sublattice symmetry and we investigated their electronic structures by first-principles calculations, in which the external electric field effect was also considered. We found that the heterojunctions, except for that with g-CN, have a direct band gap and that their important band edge states are dominated mainly by their graphene layer. The electric field can open band gaps and reduce the effective mass of electron and hole. The graphene/NHG has a large band gap (186.6 meV) and electron effective mass, which can be reduced from 1.31 to 0.014 m0 by applying an electric field of 0.4 V/Å. The NHG/graphene/NHG has the largest band gap of 250.7 meV among all of the graphene-based heterojunctions. The band gap of g-C3N4/graphene/g-C3N4 can be enlarged from 76.8 to 85.5 meV by applying a perpendicular electric field (0.6 V/Å). Interestingly, the external electric field can also convert the indirect band gap of graphene/g-CN into a direct one of 83.3 meV. Our results are useful for fast graphene-based nano-optoelectronic devices.

1. INTRODUCTION Graphene is a star material with great industrial prospects due to its high carrier mobility (2 × 105 cm2 V−1 s−1) and stable stucture.1−3 It is highly desirable in the next generation of graphene-based nanoelectronic devices, such as field effect transistor and optoelectronic devices.4,5 However, the lack of an energy band gap extremely constrains graphene’s widespread application because the small band gap means a large offcurrent and a low on/off ratio. The essence of the zero band gap of graphene is due to the symmetry between two kinds of nonequivalent carbon atoms. To open the band gap of graphene, it is necessary to break this symmetry. Up to now, many attempts have been made to open the energy band gap of graphene, including cutting two-dimensional (2D) graphene into nanoribbons,6−8 application of a strain on graphene,9−12 hydrogenating graphene with a certain pattern,13,14 and growth of graphene on various substrates.15,16 Notwithstanding the intensive investigations carried out, there is still a great challenge to put these methods into practice. As an alternative way, the graphene-based heterojunctions formed with other 2D materials, such as BN17,18 and gC3N4,19,20 provide a new method for opening graphene’s band gap. The graphene/g-C3N4 has a direct band gap of 57 meV (PAW-GGA-PBE)21 or 70 meV (HSE06)19 with a minor difference of 13 meV, and graphene/BN has a larger band gap of 120 meV.18 However, these band gaps are still not sufficient © XXXX American Chemical Society

for practical device applications. We note that, just a few months ago, Mahmood et al. successfully synthesized nitrogenated holey graphene (NHG),22 a new 2D material, with a substantial direct band gap of 1.96 eV.23 Since one primitive cell of NHG consists of 6 nitrogen and 12 carbon atoms, the NHG is also called C2N. The NHG, a 2D semiconductor with a lattice constant matching that of graphene, can be a potential substitute of the other 2D materials, such as BN and g-C3N4, to form a heterojunction with graphene. It has been known that, if applying an electric field perpendicular to a heterojunction, the interlayer distance and geometric structure of its layers can be altered, and consequently, the band gap and carrier mobility will be modified. Attempts have been made to enlarge the band gap of graphene/g-C3N4 with an electric field, and the band gap increases by about one-half when electric field is added to 0.6 V/Å.20 This fact indicates that the electric field has a remarkable influence on the band gap. With this feature, we can make a trade-off between the band gap and the carrier mobility. By changing the electric field, we can easily increase the band gap with only a slight sacrifice of the carrier mobility, and vise versa. By stacking different 2D monolayers together Received: March 31, 2016 Revised: April 30, 2016

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DOI: 10.1021/acs.jpcc.6b03308 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C and applying an electric field, we can obtain various heterojunctions and effectively modify their electronic structures to have a suitable band gap and carrier effective mass, which is very promising for fast graphene-based optoelectronic nanodevices. Considering that 2D carbonitrides, such as NHG, g-C3N4, and g-CN, have natural holes in their monolayers, we thus build several heterojunctions of graphene and these 2D carbonitrides. The band gap of graphene can be expected to open because its sublattice symmetry is broken owing to the holes of those carbonitrides. We investigate the electronic structures of graphene/NHG, NHG/graphene/NHG, g-C3N4/graphene/gC3N4, and graphene/g-CN heterojunctions because they can be expected to destroy the sublattice symmetry of graphene more remarkably than other combinations, such as graphene/NHG/ graphene and NHG/graphene/graphene. Our calculations show that graphene/NHG, NHG/graphene/NHG, and gC3N4/graphene/g-C3N4 have a direct band gap and their band edges are mainly determined by their graphene layer. The band gap of graphene can be opened up to 250.7 meV by forming a NHG/graphene/NHG heterojunction. The electron effective mass in graphene/NHG can be reduced from 1.31 to 0.014 m0 at an electric field of E = 0.4 V/Å. The band gap of g-C3N4/ graphene/g-C3N4 can be enlarged from 76.8 to 85.5 meV at E = 0.6 V/Å.

dispersions derived from these three functionals do not have any difference in nature, which are qualitatively identical. Quantitatively, there is only a minor difference for the band gap (∼10 meV for graphene/NHG bilayer) using different functionals (see Figure 1). So we can draw the same

2. CALCULATION METHODS In order to determine the geometric and electronic structures of 2D carbonitride/graphene heterojunctions, we perform firstprinciples calculations based on the density functional theory (DFT) using the projector augmented wave (PAW) method and generalized gradient approximation (GGA) with the PBE (PAW-GGA-PBE) functional.24 Computations are made by using the Vienna Ab Initio Simulation Package (VASP) code.25−27 We have optimized all of geometrical structures and chosen the one with the lowest energy because it is stable. The other energetically disfavored conformers are not considered here. In our calculations, the kinetic energy cutoff is set to 500 eV for the plane-wave expansion. The convergence tolerance of energy and force acting on each atom during structure relaxation is chosen as 10−5 eV and 0.01 eV/Å, respectively. The hexagonal Brillouin zone is sampled by 11 × 11 × 1 Monkhorst−Pack28 k-points for structural optimization and 13 × 13 × 1 k-points for calculations of electronic structures. To avoid interaction between two heterojunctions, a vacuum slab of 20 Å is set. Since chemical bonds are absent between two monolayers of a heterojunction, the van der Waals interaction is the only force that combines monolayers together. However, the popular density functional cannot correctly describe the van der Waals interaction. We thus adopt a revised correlation functional named vdW-DF, proposed by Dion et al. and implemented by Klimeš,29 and use the optB88 exchange functional30 as a more accurate substitute for the original Dion’s version known as revPBE.31 For simplicity, the band gap is not revised in the present calculations by using the time-consuming HSE functional because this revision is usually small (∼13 meV) for the graphene/g-C3N4 heterojunction.19,21 Furthermore, considering that the band gap is sensitive to the functional, we further calculate the electronic band structures of 2D carbonitride/graphene heterojunctions using the other two functionals, namely, PP-GGA24 and PAW-GGA-PW91,32 and compare their electronic band structures with results of PAWGGA-PBE functional. We find that the electronic band

Figure 1. Optimized graphene/NHG bilayer with a carbon−carbon bond length of 1.41 Å for graphene and an interlayer distance of 3.23 Å is shown in panels a and b. The calculated electronic band structures are given for (c) PP-GGA, (d) PAW-GGA-PW91, and (e) PAW-GGAPBE functionals. The corresponding density of states (DOS) is shown in panel f for the PAW-GGA-PBE functional. Here brown and gray balls represent C and N atoms, respectively.

conclusions from PAW-GGA-PBE as from PP-GGA and PAW-GGA-PW91. Moreover, the PAW-GGA-PBE functional is the most widely used to calculate the electronic band structures of semiconductors;20,21,23 we thus adopt PAW-GGAPBE functional in our following calculations.

3. RESULTS AND DISCUSSION 3.1. Graphene/NHG Heterojunction. First of all, we choose a supercell of graphene/NHG heterojunction with 24 carbon atoms of graphene and 1 primitive cell of NHG, as shown in Figure 1a,b. Because of strong sp2 hybridization between the carbon and nitrogen atoms, both graphene and B

DOI: 10.1021/acs.jpcc.6b03308 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

Figure 2. Band structure of graphene/NHG heterojunction with an electric field of (a) 0 V/Å, (b) −0.1 V/Å, (c) −0.2 V/Å, (d) −0.3 V/Å, and (e) −0.4 V/Å. Here we define that a positive electric field points upward from graphene to NHG, and a negative electric field points in the opposite direction. The charge density that corresponds to each electric field is given under the corresponding band structure. The upper/lower panel shows the charge density isosurface (ρ = 0.002 e Å−3) of CBM/VBM, dominated by graphene rather than NHG.

NHG display flat 2D structures. Our optimized lattice constants of graphene and NHG are 2.44 and 8.29 Å, respectively, which are in good agreement with the previous calculations.23 To build a model of graphene/NHG heterojunction, we stack monolayers of graphene and NHG with ideal commensurability of 8.45 Å, with only a small strain of 2% in the NHG monolayer. Indeed, the small virtual strain brought in to match the lattice constants of the two monolayers has only minor effect on the electronic structures of the heterojunction. We find that the graphene/NHG heterojunction has a direct band gap, and both the valence band maximum (VBM) and conduction band minimum (CBM) locate at the Γ-point. The band gaps derived from PP-GGA (197.1 meV) and PAWGGA-PW91 (196.8 meV) are slightly larger than that of the PAW-GGA-PBE functional (186.6 meV). The band dispersions are identical qualitatively for the three functionals. We can thus trust the following PAW-GGA-PBE functional calculations. By analyzing the PROCAR file generated by VASP, we know that both CBM and VBM are mainly determined by graphene instead of NHG, indicating that this band gap is the opened zero band gap of graphene. The band gap of the graphene/ NHG heterojunction, although large enough, is still insufficient for fabricating fast semiconductor devices. This is because the conduction band near the CBM is so flat that the electron effective mass is too large, resulting in the low carrier mobility of ther heterojunction. To solve this problem, we apply an external electric field to modify the electronic structure and carrier effective mass. In order to enhance the carrier mobility, we create a balance between the carrier effective mass and the band gap by applying an electric field perpendicular to the heterojunction from NHG to graphene. As we mentioned above, without an electric field, the graphene/NHG heterojunction has a low carrier mobility. In order to enlarge the mobility, we need to restore some properties of graphene, since graphene has the Dirac cone and zero band gap, which means its carrier mobility is extremely high (2 × 105 cm2 V−1 s−1).1 Fortunately, both CBM and VBM are determined by graphene and have little relation to NHG, as we can see from Figure 2 and the PROCAR file. That is to say,

if two monolayers of the heterojunction are kept apart a little more, the influence of NHG on graphene becomes less, and the CBM and VBM of the heterojunction will resemble graphene’s Dirac cone more. Upon increasing electric field from 0 to 0.4 V/Å, we can see from Figure 2 that the band gap of graphene/ NHG heterojunction is reduced from 186.6 to 72.1 meV, and the electron cloud overlap between graphene and NHG becomes smaller. The physical reason is that the interlayer distance of graphene/NHG heterojunction increases from 3.2354 to 3.2413 Å with the electric field. This is because the applied electric field polarizes the wave function of both conduction and valence bands toward the graphene layer (see the charge density panels in Figure 2), which weakens the dispersion interaction between the layers and consequently increases the interlayer distance. We thus know that the electronic structure of graphene/NHG heterojunction sensitively depends on the electric field, and graphene makes a major contribution to the CBM and VBM. Moreover, we can find from Figure 2 that the dispersion of the energy band of graphene/NHG near CBM and VBM gradually approaches the graphene’s linear dispersion when the electric field pointing from NHG to graphene is increased. According to the definition of effective mass, i.e., m* = ℏ2

d2E dk 2

−1

( )

, we can estimate the effective mass of

electron (me*) and hole (mh*) by fitting a parabola to the energy band near CBM and VBM, respectively. Here, E is the energy at the wave vector k. Since effective mass sensitively depends on the direction in reciprocal space, we thus list me* and mh* in both Γ → M and Γ → K directions in Table 1. We can see from Table 1 that the electron effective mass decreases by 2 orders of magnitude if the electric field is increased to 0.1 V/Å, although the band gap is reduced slightly. Upon increasing the electric field further, the effective mass of electron and hole decreases more slowly. This opens up a new way for us to trade off band gap for carrier mobility without destroying the heterojunction’s structure and quality. We thus can find a suitable external electric field to meet requirements for both band gap and mobility in practical graphene-based C

DOI: 10.1021/acs.jpcc.6b03308 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C Table 1. Effective Mass (in units of free-electron mass m0) of Electron and Hole along Γ → M and Γ → K Directions in Graphene/NHG Heterojunction in an External Electric Field, Together with Band Gap Eg and Interlayer Distances electric field (V/Å)

interlayer distance (Å)

Eg (meV)

effective mass (m0)

Γ→M

Γ→K

0.0

3.2354

186.6

−0.1

3.2385

145.6

−0.2

3.2392

115.3

−0.3

3.2408

95.5

−0.4

3.2413

72.3

me* mh* m*e m*h m*e m*h m*e m*h m*e m*h

1.3095 0.0693 0.0552 0.0371 0.0301 0.0255 0.0195 0.0182 0.0141 0.0137

0.9509 0.0694 0.0559 0.0373 0.0307 0.0260 0.0202 0.0189 0.0149 0.0145

device applications. By the way, if inverting the direction of the external electric field, the band gap of graphene/NHG will increase from 186.6 to 211.2 meV at an electric field of 0.1 V/Å, 222.5 meV at 0.2 V/Å, and 227.3 meV at 0.4 V/Å. However, the carrier effective mass will also increase. Hence it is not a good idea to increase the band gap of graphene/NHG using this method because the carrier effective mass is also enlarged at the same time. 3.2. NHG/Graphene/NHG Heterojunction. Let us now consider a NHG/graphene/NHG heterojunction as shown in Figure 3a,b. Our calculations (see Figure 3) show that, compared with graphene/NHG, NHG/graphene/NHG has a much larger band gap of 250.7 meV and a similar effective mass of electron and hole. Both CBM and VBM, especially for CBM, are determined by the graphene monolayer in NHG/graphene/ NHG. The large band gap of NHG/graphene/NHG is due to the obvious destruction of the sublattice symmetry of graphene by the two NHG monolayers. It is worthwhile to note that the mobility of NHG/graphene/NHG cannot be easily increased by applying an electric field. This is because for a given electric field perpendicular to NHG/graphene/NHG, for one graphene/NHG bilayer, the electric field is downward, and for the other, it is upward. According to our analysis of Figure 2, we know that the variation tendency of the two bands belonging to the two graphene/NHG bilayers is opposite. Hence, neither CBM nor VBM can become sharp and the carrier mobility cannot be increased by the electric field. 3.3. The g-C3N4/Graphene/g-C3N4 Heterojunction. The electronic structure and optical response of graphene/g-C3N4 heterojunction have been investigated previously.19,21 It has been found that the common PAW-GGA-PBE calculation gives a band gap of 57 meV approximately,21 which is in good agreement with our calculation of 56 meV. Here, we extend the graphene/g-C3N4 to the next level by stacking one more layer of g-C3N4 on it, i.e., g-C3N4/graphene/g-C3N4 heterojunction. Our calculations show that it has a direct band gap of 76.8 meV (please refer to Figure 4), which is 20 meV larger than that of graphene/g-C3N4. Moreover, both CBM and VBM are sharp and determined by the graphene layer in g-C3N4/graphene/gC3N4. Table 2 indicates that the effective mass of electron and hole is small and insensitive to the electric field. The carrier mobility is thus considerable, which makes it feasible to trade off mobility for larger band gap. By applying electric field, the band gap can reach at least 85 meV without sacrifice the mobility too much (see Table 2). We find that if the electric

Figure 3. Optimized NHG/graphene/NHG heterojunction with the carbon−carbon bond length of 1.41 Å for graphene and the interlayer distance of 3.23 Å is shown in parts a and b. The calculated electronic band structure is given in part c and the corresponding density of states is shown in part d. The inset of part c shows that it has a direct energy band gap of Eg = 250.7 meV. Parts e and f show the charge density isosurface (ρ = 0.002 e Å−3) of CBM and VBM, respectively. The CBM is dominated by graphene rather than NHG.

field exceeds 0.7 V/Å, the band gap will transform into an indirect one, and the new CBM locates at the K-point. 3.4. Graphene/g-CN Heterojunction. We further study the electronic structure of graphene/g-CN heterojunction and the influence of the electric field on the size of the band gap and carrier effective mass (see Figures 5 and 6). We find that graphene/g-CN has an indirect band gap of 68 meV with VBM located at the Γ-point and CBM at the K-point. By applying a small external electric field (∼0.05 V/Å), we can not only modify the size of band gap but also turn the indirect band gap into a direct one of 83.3 meV at the Γ-point. If increasing the electric field further, the energy difference between the original and the new CBM becomes larger. Figure 5 shows that, without the electric field, the electron effective mass is much larger than that of hole because the conduction band near the CBM at the K-point is a weak dispersion. The electron effective mass can be remarkably reduced at a weak external electric field, for example, 0.05 V/Å, and consequently, the carrier mobility can be greatly improved. Hence, the electric field is a useful tool to modify the electronic structure of graphene/g-CN heterojunction, making both VBM and the new CBM at the Γ-point determined mainly by the graphene layer in graphene/g-CN. D

DOI: 10.1021/acs.jpcc.6b03308 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

Figure 5. Optimized graphene/g-CN bilayer with an interlayer distance of 3.22 Å is shown in parts a and b. The calculated electronic band structure is given in part c and the corresponding density of states is shown in part d. It has an indirect energy band gap of Eg = 68 meV from Γ (VBM) to K (CBM) points. Panels e and f show the charge density isosurface (ρ = 0.002 e Å−3) of the Γ-point in the conduction band and VBM, respectively. By applying a small electric field, the Γ-point in the conduction band can become the new CBM (see Figure 6). Both the Γ-point in the conduction band and VBM are determined by graphene, sandwiched between two g-CN layers.

Figure 4. Optimized g-C3N4/graphene/g-C3N4 heterojunction with the carbon−carbon bond length of 1.41 Å for graphene and the interlayer distance of 3.16 Å is shown in parts a and b. The calculated electronic band structure is given in part c and the corresponding density of states is shown in part d. The inset of part c shows it has a direct energy band gap of Eg = 76.8 meV. Panels e and f show the charge density isosurface (ρ = 0.002 e Å−3) of CBM and VBM, respectively. Both CBM and VBM are dominated by graphene, which is sandwiched between two g-C3N4 layers.

Table 2. Effective Mass (in Unit of Free-Electron Mass m0) of Electron and Hole along Γ → M and Γ → K Directions in g-C3N4/Graphene/g-C3N4 Heterojunction in an External Electric Field, Together with the Direct Band Gap Eg electric field (V/Å)

Eg (meV)

effective mass (m0)

Γ→M

Γ→K

0.0

76.8

0.2

78.1

0.4

81.2

0.6

85.5

me* mh* m*e m*h m*e m*h m*e m*h

0.0132 0.0131 0.0133 0.0133 0.0138 0.0137 0.0144 0.0142

0.0140 0.0142 0.0141 0.0143 0.0145 0.0147 0.0151 0.0152

Figure 6. Band structure of graphene/g-CN heterojunction with an external electric field of (a) −0.05 V/Å and (b) −0.1 V/Å. The minus sign means that the electric field is pointing from g-CN to the graphene layer. Even if the applied electric field is only 0.05 V/Å, the indirect band gap of the graphene/g-CN heterojunction becomes a direct one (83.3 meV).

4. CONCLUSIONS In conclusion, we investigated a challenging problem, i.e., the gap opening of graphene, by destroying its sublattice symmetry with the aid of heterojunctions formed with 2D carbonitride materials with natural holes in their monolayers, such as NHG, g-C3N4, and g-CN, by means of first-principles calculations with the PAW-GGA-PBE functional, in which the external electric field effect is also included. The band structures, density of

states, and charge density are calculated and the effective masses of electron and hole at CBM and VBM are obtained by E

DOI: 10.1021/acs.jpcc.6b03308 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C fitting a parabola to the energy band edges. We find that graphene/NHG, NHG/graphene/NHG, and g-C3N4/graphene/g-C3N4 have a direct band gap at the Γ-point, and both CBM and VBM are determined mainly by the graphene layer included in these heterojunctions. The electric field can effectively modify their electronic structures and carrier effective mass. For graphene/NHG, the electron effective mass at CBM can be reduced from 1.31 to 0.014 m0 when the electric field is added to 0.4 V/Å, with the band gap decreasing from 186.6 to 72.3 meV. Typically, with an external electric field of 0.1 V/Å, the effective mass of electron drops considerably to 0.0552 m0, and meanwhile, the band gap still maintains a large value of 145.6 meV. The NHG/graphene/ NHG has a large band gap of 250.7 meV, and its effective mass of electron and hole cannot be reduced by the electric field. For g-C3N4/graphene/g-C3N4, it has a band gap of 76.8 meV, which is 20 meV larger than that of graphene/g-C3N4 bilayer, and can ultimately reach 85.5 meV at an external electric field of 0.6 V/Å before becoming an indirect one, without sacrificing its carrier mobility too much. Its effective mass of electron and hole is small and insensitive to the electric field. Moreover, we find that, for graphene/g-CN, the indirect band gap of 68 meV from the Γ-point (VBM) to the K-point (CBM) can be transformed into a direct band gap of 83.3 meV at the Γ-point with only a small electric field of 0.05 V/Å. The electron effective mass can be remarkably reduced with a weak external electric field, in which both CBM and VBM are determined mainly by the graphene layer in graphene/g-CN. We believe that, by utilizing an external electric field, we can effectively alter the electronic structures of heterojunctions composed of graphene and 2D carbonitride materials and precisely design the band gap and carrier mobility to make heterojunctions appropriate for fabrication of some graphene-based nanooptoelectronic devices with high speed and a low off-current.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +86-10-62757594. Fax: +8610-62751615. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors gratefully acknowledge the financial support from the Ministry of Science and Technology of China (No. 2012CB619304) and the National Natural Science Foundation of China (11474012, 11364030 and 11404013). We used computational resource of the “Explorer 100” cluster system of Tsinghua National Laboratory for Information Science and Technology.

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