Letter pubs.acs.org/JPCL
Electric Field and Strain Effect on Graphene-MoS2 Hybrid Structure: Ab Initio Calculations Xingen Liu and Zhongyao Li* College of Science, University of Shanghai for Science and Technology, Shanghai 200093, P. R. China ABSTRACT: The electronic structures of graphene-MoS2 heterojunction under tension and external electric field were examined on the basis of density-functional theory. The tension of MoS2 changes the hybrid structure from semiconductor to metal. The transition is from the sensitive dependence of the bandgap of MoS2 on the lattice constant. The vertical electric field has little influence on the bandgap of MoS2, while it can also adjust the charge transfer between monolayer MoS2 and graphene. In addition, the Schottky barrier is linearly dependent on the electric field intensity with an effective vacuum spacing of 1.3 Å. It is also discussed in detail that the bandgap of MoS2 dependence on the lattice constant and the S−S spacing.
S
also result in a tunable photoresponsivity.32 Theoretically, the electron mobility of the heterojunction is comparable to graphene.33 Moreover, the bandgap can be changed by adjusting the interfacial distance.33 It provides a new train of thought that the graphene-MoS2 heterojunction can be used to design devices with small bandgap and high carrier mobility. In addition, it was reported that the bandgap of the graphene bilayer can be opened at weak electric gating,8 and the work function and charge transfer of doped graphene can be well adjusted by applying an external electric field.34 External electric field may be also used to adjust the electronic properties of the 2D layered heterojunction. The electronic properties of materials are directly related to various physical and chemical properties and practical applications. In order to further study the potential applications of graphene−MoS2, it is necessary to know more about the possible electronic properties of the heterojunction. In this work, we study the band structures of two kinds of graphene-MoS2 hybrid structures: (5×5)graphene−(4×4)MoS2 and (4×4)graphene−(3×3)MoS2. Graphene is stretched in the first model, while the monolayer MoS2 is stretched in the second model. The stretching of MoS2 would change the hybrid structure from semiconductor to metal due to the charge transfer from graphene to MoS2. Morover, the external electric field can also adjust the charge transfer between graphene and MoS2. Although the bandgap of MoS2 is insensitive to the graphene-MoS2 interaction33 and the vertical electric field, it is greatly dependent on the lattice constant and the S−S spacing. The electronic structures were calculated on the basis of density-functional theory (DFT) at the level of local density
ince the successful invention of isolated graphene in experiments,1 a new materials fieldtwo-dimensional (2D) materialhas received much attention. It is a popular material for manufacturing the miniaturization and integration of electronic devices, such as layered electrodes2,3 and thin film electronic devices.4 Although the most famous 2D material, graphene, has many excellent properties and has been integrated into many different applications, its gapless-semiconductor band structure may be an obvious disadvantage in some cases.5 Band gap is necessary in many application fields, such as light-emitting diode (LED),6 solar battery7 and transistor technology.8 This disadvantage restricts the application of graphene in many areas. The molybdenum disulfide9 is another kind of 2D material. The atomic structure of monolayer MoS2 is two S-layers sandwiching a Mo-layer, and the atoms in layers are hexagonally packed.10 It has good chemical and thermal stability, large specific surface area, and high surface activity.11−14 With unique physical and chemical properties, it has potential application in catalysis, lubrication, and electrochemical lithium storage.15−17 Single-layer MoS2 is a direct bandgap semiconductor, which has very strong luminous intensity.18,19 Moreover, it can be used as a channel material to manufacture an ultralow standby power field effect transistor with high current switch ratio and high electron mobility.17 The layers of different 2D semiconductors can be stacked to form semiconductor heterojunction, and the novel physical phenomena in such heterojunctions have also become a focus of international nanoscience. Currently, the hot research of nanodevices is based on the heterojunction formed by graphene and MoS2, which is a new type of 2D layered heterojunction; the device has a light weight, low power consumption, and flexibility.20−26 Experimentally,27 the growth of MoS2 on graphene will increase the electron transfer rate and improve the electrochemical performance. It has shown very good performance for lithium ion batteries and aerogels.28−31 It can © XXXX American Chemical Society
Received: June 10, 2015 Accepted: August 4, 2015
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DOI: 10.1021/acs.jpclett.5b01233 J. Phys. Chem. Lett. 2015, 6, 3269−3275
Letter
The Journal of Physical Chemistry Letters
the interfacial spacing is about 3.29 Å. The external electric filed is along the z-direction and perpendicular to the graphene plane. The electric filed intensity is from −0.5 V/Å to +0.5 V/ Å. The Γ-centered k-point grids of 9 × 9 × 1 and 21 × 21 × 1 were employed to sample the Brillouin zone for the supercell of graphene-MoS2 heterojunction and for the unit cell of monolayer MoS2 (Figure 1e,f), respectively. The band structure of (5×5)graphene−(4×4)MoS2 heterojunction is shown in Figure 2a. It was reported that the
approximation (LDA).35 Although there may be some limitations within the LDA method,36−38 most of the early DFT results based on LDA about the interface formed between graphene and substrate have been confirmed by experiments.33,39−44 LDA is usually used in the calculations for graphene, MoS 2 , and/or graphene−MoS 2 heterostructure.25,33,45−47 Moreover, it was reported that the DFT with van der Waals (vdW) correction is not more accurate than conventional DFT methods for the graphene-based interface modeling study.25,33,48−55 Therefore, the conventional LDA is used in all our calculations. The projector-augmented wave (PAW) pseudopotentials56 method implemented in the VASP package57,58 were employed to describe the effect of core electrons. The energy cutoff in calculations was set to be 400 eV, and the total energy was converged to better than 10−5eV. The equilibrium structures were obtained through structural relaxation until Hellmann− Feynman forces were less than 0.02 eV/Å. The atomic structure was modeled by a periodic slab geometry, with a vacuum of at least 20 Å between two neighboring slabs. The slab structures are shown in Figure 1. There are two models considered in this
Figure 2. (a−c) The band structure of (5×5)graphene−(4×4)MoS2 heterojunction (M_1) with the external electric field of 0 V/Å (a), −0.3 V/Å (b), and 0.3 V/Å (c), respectively. The Schottky barrier is denoted as φB in panel a. (d−f) The band structure of (4×4)graphene−(3×3)MoS2 heterojunction (M_2) with the external electric field of 0 V/Å (d), −0.3 V/Å (e), and 0.3 V/Å (f), respectively. The Fermi level is set to zero. The Dirac point of graphene (K), the valence band maximum (VBM), and the conduction band minimum (CBM) of MoS2 are marked with a black star, blue square, and circle, respectively. The band gap of MoS2 is denoted as ΔE.
Figure 1. Structures of graphene−MoS2 heterojunction. (a) Side view of the (5×5)graphene−(4×4)MoS2 heterojunction (Model 1, abbreviated as M_1). The red rectangle is the unit cell of MoS2. (b) Side view of the (4×4)graphene−(3×3)MoS2 heterojunction (Model 2, abbreviated as M_2). (c) Top view of the (5×5)graphene− (4×4)MoS2 heterojunction (M_1). (d) Top view of the (4×4)graphene−(3×3)MoS2 heterojunction (M_2). (e) Top view of (1×1)MoS2 as the red rhombus in (c). The lattice constant is denoted as a. (f) Side view of (1×1)MoS2. The S−S layer spacing is denoted as ds.
interlayer orientation would affect the structure and electronic properties of graphene−MoS2 heterostructure.61 However, for the graphene−MoS2 heterostructure studied in this work, the [21̅1̅0] crystallographic directions of the two layers are parallel to one another.61 In this case, the weak graphene−MoS2 interaction has little influence on the band structure of the heterostructure. It is also consistent with the reported results.33 Therefore, the band structure of the heterostructure is simply a combination of the energy bands of individual graphene and MoS2. The weak graphene−MoS2 interaction is not enough to change the morphology of their energy bands. The linear dispersion bands of graphene are in the large bandgap of MoS2. Moreover, the Dirac point of graphene is at the Fermi level (EF = 0), suggesting no charge transfer between graphene and MoS2. The Schottky barrier,22,62 which is the excitation energy of electrons from graphene to MoS2, is also marked as φB in Figure 2a. In the heterojunction with 3.8% strain of graphene, the Schottky barrier φB is about 0.418 eV. At the Dirac point,
work: (5×5)graphene−(4×4)MoS2 and (4×4)graphene− (3×3)MoS2 hybrid structures. In the first model (Figure 1a,c), the length of the superlattice vectors was set to be 12.772 Å. In this case, the lattice constant of MoS2 unit cell was set to be about 3.193 Å,59 and the stretching of the lattice constant of graphene is about 3.8%. At equilibrium, the interfacial spacing, between graphene and MoS2, is about 3.34 Å. In the second model (Figure 1b,d), the length of the superlattice vectors was set to be 9.84 Å. In this case, the lattice constant of the graphene unit cell is set to be about 2.46 Å,60 and the stretching of the lattice constant of MoS2 is about 2.7%. At equilibrium, 3270
DOI: 10.1021/acs.jpclett.5b01233 J. Phys. Chem. Lett. 2015, 6, 3269−3275
Letter
The Journal of Physical Chemistry Letters
less than −0.4 V/Å, the Dirac point of graphene would be above the Fermi level for the (5×5)graphene−(4×4)MoS2 heterojunction; meanwhile, the CBM of MoS2 would be below the Fermi level. Therefore, the heterojunction changes from semiconductor to metal under the electric field. Similarly, the (4×4)graphene−(3×3)MoS2 heterojunction can also be changed from semiconductor to metal when the electric filed intensity is less than 0.2 V/Å. In order to realize the semiconductor-metal transition, both the magnitude and the direction of electric field are different for the two heterojunctions. The difference is from the difference of Schottky barrier induced by stretching. As shown in Figure 3b,c, the Schottky barrier22 in the semiconductor heterojunctions can be fitted as
there is a tiny splitting, which is about 5 meV, due to the weak graphene−MoS2 interaction.33 The band structure of the graphene−MoS2 heterojunction can be changed by the stretching of MoS2. As a comparison, the band structure of (4×4)graphene−(3×3)MoS2 heterojunction is shown in Figure 2d. The bottom of the conduction band of MoS2 is below the Fermi level, while the Dirac point of graphene is above the Fermi level. This suggests that electrons transfer from graphene to MoS2. Therefore, semiconductor−metal transition can be realized by the stretching of MoS2 in the heterojunction. Moreover, the Schottky barrier and the charge transfer can be controlled by external electric field as shown in Figure 2. Figure 3a shows the sketch map of a graphene−MoS2 heterojunction in an external electric field. The positive electric
φB = φ0 + eEd
(1)
where E is the electric field intensity, and d is the effective vacuum spacing between graphene and MoS2. In the (5×5)graphene−(4×4)MoS2 heterojunction, φ0 = 0.418 eV and d = 1.26 Å; while φ0 = −0.311 eV and d = 1.29 Å in the (4×4)graphene−(3×3)MoS2 heterojunction. Considering the interfacial spacing between graphene and MoS2 D ∼ 3.3 Å, the S atomic radius rs ∼ 1.04 Å and the C atomic radius rc ∼ 0.77 Å, the effective vacuum spacing should be close to (D − rs − rc) ≃1.5 Å. Our fitting result, d∼ 1.3 Å, is in good agreement with the estimated value (1.5 Å). Although the effective vacuum spacing is insensitive to the stretching of graphene or MoS2, the constant φ0 in eq 1 can be greatly changed by stretching. It directly leads to the dependence of the Schottky barrier on stretching. The work function,34 which can be measured in experiment, is also discussed. It is linear with the applied electric field.34 Note that positive electric field is from graphene to MoS2 in our models. Both the work functions of graphene surface and MoS2 surface can be fitted as ϕW = ϕ0 + γeE, where ϕ0 is the work function for the heterostructure without electric field, and γ is a coefficient that is negative for graphene surface and positive for MoS2 surface. In the (5×5)graphene−(4×4)MoS2 heterojunction, ϕ0 is about 4.891 eV; the coefficient γ is about −3.943 and 5.375 Å for graphene and the MoS2 surface, respectively. As for the (4×4)graphene−(3×3)MoS2 heterojunction, ϕ0 = 4.816 eV; γ = −4.805 Å for the graphene surface and γ = 4.058 Å for the MoS2 surface. The bandgap of MoS2, which is the energy difference between the CBM and VBM of MoS2, is marked as ΔE in Figure 3b,c. Although the electric field can be used to adjust the Schottky barrier, the work function and the charge transfer between graphene and MoS2, it has little influence on the bandgap of MoS 2 . In the (5×5)graphene−(4×4)MoS 2 heterojunction (Figure 3b), the bandgap ΔE ≈ 1.42 eV; while it is about 0.8 eV in the (4×4)graphene−(3×3)MoS2 heterojunction (Figure 3c) due to the stretching of MoS2. Since molybdenum disulfide has high mechanical flexibility,63 stretching may be an effective measure to adjust the band structure of MoS2 and the electronic properties of graphene− MoS2 heterojunction in practice. In our graphene-MoS2 models, the bandgap of MoS2 is almost unchanged by graphene. The analysis of the bandgap of MoS2 was carried out in MoS2 monolayer. In order to further analyze the influence of strain on the bandgap of monolayer MoS2, we constructed the MoS2 unit cell as shown in Figures 1(e) and 1(f). The lattice constant is denoted as a, and the S−S layer spacing is denoted as ds. Since the nature of the energy
Figure 3. (a) Sketch map of graphene-MoS2 heterojunction in external electric field. The interfacial spacing and the effective vacuum spacing, between MoS2 and graphene, are denoted as D (∼3.3 Å) and d (∼1.3 Å), respectively. (b) The energy of the Dirac point of graphene K, the VBM, and the CBM of MoS2 in (5×5)graphene−(4×4)MoS2 heterojunction (M_1) under electric field. (c) The energy of K, VBM and CBM in (4×4)graphene−(3×3)MoS2 heterojunction (M_2) under electric field. The Fermi level is set to be zero. The Schottky barrier is denoted as φB. It can be fitted by φB = φ0 + eEd, where φ0 = 0.418 eV and d = 1.26 Å in panel b, while φ0 = −0.311 eV and d = 1.29 Å in panel c.
field intensity, which is along the z-direction, would enlarge the Schottky barrier and prevent the charge transfer from graphene to MoS2. The interfacial spacing and the effective vacuum spacing, between graphene and MoS2, are marked as D (∼3.3 Å)33 and d (∼1.3 Å) in Figure 3a, respectively. The interfacial spacing can be obtained by the structural relaxation, while the effective vacuum spacing is from the linear fitting of the Schottky barrier dependence on electric field, which will be discussed in the following. Under the electric field, the energy of the Dirac point of graphene (K), the valence band maximum (VBM), and the conduction band minimum (CBM) of MoS2 are shown in Figure 3b for the (5×5)graphene−(4×4)MoS2 heterojunction and in Figure 3c for the (4×4)graphene− (3×3)MoS2 heterojunction. When the electric field intensity is 3271
DOI: 10.1021/acs.jpclett.5b01233 J. Phys. Chem. Lett. 2015, 6, 3269−3275
Letter
The Journal of Physical Chemistry Letters
Therefore, the equilibrium S−S spacing should have the following dependence on the lattice constant:
bandgap would be changed from direct to indirect for an applied tensile strain,64,65 both the direct and indirect bandgaps are considered in the following. With the lattice constant of 3.193 Å, the equilibrium S−S spacing deq s = 3.064 Å, the direct bandgap at K point66,67 ΔEK = 1.594 eV and the ΓK indirect bandgap65,67 ΔE = 1.426 eV. Figure 4a shows the indirect bandgaps with different lattice constants and S−S layer spacing. When the lattice constant a is
⎡ ⎛ a − a 0 ⎞2 ⎤ ds0 − dseq a − a0 = c0 + c ⎢λ1′ − λ 2′⎜ ⎟⎥ ⎢⎣ ds0 a0 ⎝ a0 ⎠ ⎥⎦
(4)
where c0 and c are constants. The fitted values show that c0 = 2.96 × 10−5 and c = 0.064. Since c0 ≪ 1, the formula can be simplified as ⎡ ⎛ a − a 0 ⎞2 ⎤ ds0 − dseq a − a0 ⎢ = c λ1′ − λ 2′⎜ ⎟⎥ ⎢⎣ ds0 a0 ⎝ a0 ⎠ ⎥⎦
(5)
Take eq 5 into eq 3, the ΓK indirect bandgap at equilibrium, ⎡ ⎛ a − a 0 ⎞2 ⎤ a − a0 ΔE eq = ⎢1 − 17.7 × + 55.73 × ⎜ ⎟ ⎥ΔE0 ⎢⎣ a0 ⎝ a0 ⎠ ⎥⎦ (6)
It can also be equally expressed in the equilibrium S−S spacing: ⎡ d − dseq ⎤ ΔE eq = ⎢1 − 23.11 × s0 ⎥ΔE0 ds0 ⎦ ⎣
(7)
Similarly, the linear relationship in Figure 4b suggests the direct bandgap at the K point can be fitted by the fitting formula: ⎛ a − a 0 ⎞2 ΔE K0 − ΔE K a − a0 d − ds = λ 0 + λ1 − λ 2⎜ ⎟ + η s0 ΔE K0 a0 ds0 ⎝ a0 ⎠ (8)
Figure 4. (a) The ΓK indirect bandgap of MoS2 (ΔE). (b) The direct bandgap of MoS2 at the K point (ΔEK). The bandgaps at equilibrium S−S spacing (deq s ) are marked in green hexagon. (c) The p-component of the VBM and the CBM of MoS2. (d) The d-component of the VBM and the CBM of MoS2. In the unit cell of MoS2 (Figure 1e,f), the lattice constant is denoted as a, the constant a0 = 3.193 Å, and the S−S spacing is denoted as ds.
where ΔEK0 = 1.594 eV. The fitted values show that λ0 = −0.003, λ1 = 5.68, λ2 = 17.88, and η = 1.62. Since |λ0| ≪ 1, the direct bandgap at the K point ΔEK can be simplified as ⎡ ⎤ ⎛ a − a 0 ⎞2 a − a0 d − ds ⎥ ΔE K = ⎢1 − λ1 + λ 2⎜ ΔE K0 ⎟ − η s0 ⎢⎣ a0 ds0 ⎥⎦ ⎝ a0 ⎠ (9)
At equilibrium, considering the S−S spacing dependence on the lattice constant, eq 5, it can be further simplified as
fixed, the indirect bandgap ΔE is linearly dependent on the S−S spacing ds. Based on this phenomenon, the indirect bandgap can be fitted by the fitting formula:
⎡ ⎛ a − a 0 ⎞2 ⎤ a − a0 ΔE Keq = ⎢1 − 6.92 × + 21.79 × ⎜ ⎟ ⎥Δ ⎢⎣ a0 ⎝ a0 ⎠ ⎥⎦
⎛ a − a 0 ⎞2 ΔE0 − ΔE a − a0 d − ds = λ 0′ + λ1′ − λ 2′⎜ ⎟ + η′ s0 ΔE0 a0 ds0 ⎝ a0 ⎠
E K0
(2)
where a0 = 3.193 Å, ds0 = 3.064 Å, and ΔE0 = 1.426 eV. The fitted values show that λ′0 = −0.006, λ′1 = 11.97, λ′2 = 37.69, and η′ = 7.48. Since the constant |λ0′ | ≪ 1, it can be neglected. Therefore, the ΓK indirect bandgap ΔE can be simplified as
(10)
Comparing eq 10 with eq 6, the direct and indirect bandgaps at equilibrium have a simply linear relationship: ΔE Keq = 0.44 × ΔE eq + 0.97 eV
(11)
The above equations are in excellent agreement with our firstprinciples calculations. The lower bound of the bandgap for which the single-layer MoS2 remains as a direct bandgap semiconductor is about 1.72 eV, which is about 1.68 eV in ref 65. It was also reported that single-layer MoS2 turns into metal at a biaxial tensile strain of 9% in refs 64 and 65. Note that the lattice constant of unstrained MoS2 is set to be 3.16 Å in refs 64 and 65, while it is 3.193 Å (a0) in this work. The indirect bandgap from eq 6 would be negative, suggesting single-layer MoS2 turns into metal when 7.4% < (a − a0)/a0 < 24.4% (3.428 Å < a < 3.972 Å). Moreover, the direct bandgap from eq 10 is positive, and it would be larger than the indirect bandgap when −1.1% < (a − a0)/a0 < 32.9% (3.157 Å < a < 4.244 Å).
⎡ ⎤ ⎛ a − a 0 ⎞2 a − a0 d − ds ⎥ ⎢ ΔE0 + λ 2′⎜ ΔE = 1 − λ1′ ⎟ − η′ s0 ⎢⎣ a0 ds0 ⎥⎦ ⎝ a0 ⎠ (3)
Although the quadratic component [(a − a0)/a0]2 ≪ (a − a0)/ a0 for a small tensile strain (
