Much attentionhas been paid to two-dimensional (2D) materials owing to their distinctive performances such as extraordinary electronic, optical, mechanical, chemical and thermal properties, recently.^[1–5] The excellent 2D materials are expected to be an alternativeto the next-generation optoelectronic and nano-electronic devices. The first 2D material that has aroused great interest is graphene. Graphene, a carbon monolayer material hybridized by sp² orbits, has been widely investigated due to its remarkable properties.^[2,6–8] However, the gapless nature of monolayer graphene has restricted its applications. Recently, a bland new class of 2D material, such as the transition metal dichalcogenides (TMDCs), provides a new research field.^[9,10] The WS₂ is a member of the most studied TMDCs. The bulk WS₂ is a layered material with the neighboring layers held by weak van der Waals (vdW) force. Unlike gapless graphene, the bulk WS₂ is a semiconductor with an indirect band gapof 1.4 eV. However it can be tailored into a direct band gap (2.1 eV) material when exfoliated into a monolayer state. The monolayer WS₂ is sandwiched structure comprised of a tungsten layer and two sulphur layers. The monolayer WS₂, with a relatively small band gap, can be used as a barrier material in increasing the ON/OFF ratio of the field effect transistors (FETs). Excellent performances have been found in the heterostructure consisting of the layered WS₂ and graphene.^[11,12] At present the heterostructures held by the vdW interaction open a hot research field. The heterostructures are vertical stacks of 2D layers of dissimilar materials. In the heterostructures held by vdW interaction, some intrinsic electronic properties of the individual materials can be preserved, at the same time some particularly advantageous properties can be created.^[13–16] Experimental and theoretical investigation show that the heterostructures such as graphene/MoS₂,^[13,17] graphene/hexagonal boron nitride,^[18–23] graphene/silicone,^[24,25] and graphene/phosphorene^[16,26,27] are novel materials with wide application prospects due to their light weight, low power consumption and flexibility. The improvement of the electron transfer rate and the electrochemical performance can be achieved by the growth of WS₂ on graphene.^[11] The applications of the WS₂/graphene heterojunction (WGH)is mainly restricted by its electronic properties. The direct band gap and suitable energy barrier, which are beneficial for electronic transmission and photoelectric switch, are expected. The electronic properties of the ultrathin WS₂ in the WGH are seldom discussed theoretically. In the article, we focus on tuning the electronic properties of the WGH based on the density-functional theory calculation.

Strain engineering has been identified as one of the best possible strategies to tune the energy band of single layer material.^[27–31] For example, the Peelaers and Van de Walle’s work^[32] showed that the band gap reduction of the crystal structure of MoS₂ under uniaxial compressive strain was induced by the conduction band minimum (CBM) and valence band maximization (VBM) moving toward each other, further the direct band can turn into an indirect band by applying strain. Recently, Liu et al.^[31] has predicted the contacted properties (n-Schotty or p-Schotty) of heterostructure can be tuned by the biaxial strain, at the same time the Schotty height can be controlled by strain. The application of strain is an effective and experimental method for band engineering of the 2D materials, which can sustain much larger strains than the bulk crystals, and practical strain experiments have shown the results consistent with theoretical predictions.^[32,33] Ganatra and Zhang have pointed that the electronic properties of few layers MoS₂ can be tailored for specific application.^[34] Therefore, we expect to tune the electronic properties(band type and n-Schotty barrier height) of the WGH by different strains.

In the present work, the electronic properties of the WGH are investigated by first principles calculations. The calculated results show that due to the weak vdW force between the graphene and the monolayer WS₂, the monolayer WS₂ of the equilibrium WGH is characterized by an indirect band gap, which is different from the free monolayer WS₂. The schottky barrier height of the WGH at the equilibrium structure is 0.13 eV (lower than the conventional MoS₂/metal), the low schottky barrier is beneficial to electronic transport. In addition, we will use in-plane strains to modulate the electronic properties of the WGH, and we find that the schottky barrier height (SBH) of the single layer WS₂ in the WGH can be reduced into zero when applying compressive strains. Particularly the direct band gap of the monolayer WS₂ in the WGH can be attained when applying tensile strains. Our studies may provide some instrumental guidance in designing and fabricating the nano-devices held by vdW force for FETs.

All the work is done by Vienna Ab-initio Simulation Package (VASP),^[35–38] based on the density-functional theory, with the projected augmented wave (PAW) method implemented. The exchange–correlation functional is described by the generalized gradient approximation (GGA) of the Perdew–Burke–Ernzerhof (PBE) functional.^[39–41] A general drawback of all common GGA functions is that they cannot describe the long-range electron correlations that are responsible for vdW forces. To overcome the drawback, the van der Waals density functional 2 (vdW + DF2) proposed by Grimme,^[42–44] which describes the long-range vdW interactions well, is included in our calculations. The calculations are performed with Brillouin zone (BZ) sampled by 5× 5 × 1 Monkhorst–Pack k-point mesh, and the wave function of single electron in the effective field is expanded by plane-waves with the energy cutoff at 550 eV. During the ionic relaxation, the shape and size of the super cell are fixed and the atoms are allowed to be fully relaxed. The stopping criterion for the ionic relaxation is that the Hellmann–Feynman force on each atom is below 0.01 eV/Å. For the electronic optimization, the convergence criterion of energy is set to be 10⁻⁴ eV.

The calculated lattice parameters of the monolayer WS₂ and graphene are 3.16 Å and 2.46 Å, respectively, which are reasonable.^[11] The WGH is build by the graphene as a substrate matched with the WS₂. The unit cell of our model is composed of 2 × 2 unit cells of WS₂ and 3 × 3 unit cells of graphene along with rotating 19. For the hybrid structure, the lattice mismatch is near 3%, which can be tolerated. In order to avoid the interactions between the adjacent slabs, a vacuum space of 15 Å is added along the z direction. The diagrammatic geometric configuration of WGH is depicted in Figs. 1(a) and 1(b).

Fig. 1.

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	Fig. 1. (color online) Side (a) and top (b) view of the WS2/graphene heterojunction. The C, W, and S atoms are shown as blue, green, and red balls, respectively. (c) Evolution of the total energy as a function of displacement d of the WS2 layer relative to graphene.

For the WS₂ layer combining with graphene layer by vdW interaction, the vertical interlayer distance (marked by d in Fig. 1(a)) is crucial to eliminate the spurious interactions. In order to obtain the right vertical interlayer distance of the WS₂ layer with respect to the graphene one, the WS₂-graphene configuration is fully relaxed, with the shape and lattice parameter fixed firstly. Then the configuration is re-optimized by different interlayer distance, with the atom position along the z direction remaining unchanged. The binding energy (eV/cell) between the layer of WS₂ and graphene one is calculated as a function of d according to

At first, the equilibrium interfacial distance is acquired by fitting the bind energy versus the interlayer distance (d) of the WGH, and we find that the value is 3.57 Å. According to the long interfacial distance value, we can infer that the interfacial interaction should be very weak. To verify it, the reduced binding energy () per carbon atom between the WS₂ monolayer and the graphene at the equilibrium vertical interlayer distance is calculated from , where the is the binding energy of the WGH at the equilibrium vertical interlayer distance and is the number of carbon atoms in the unit cell. The calculated binding energy per C atom is −22.7 meV, which agrees well with the result of the heterostructure contacted by the vdW force.^[26] According to the equilibrium interfacial distance and negligible reduced binding energy, it can be concluded that the electronic coupling in the WGH is very weak. The above results ensure the PBE functional corrected by vdW + DF2 feasibility.

Then, the electronic properties of the WGH at the equilibrium distance are studied. Figure 2(a) shows the electronic band structures of the WGH at the equilibrium interfacial distance, and the contributions from the WS₂ monolayer and graphene sheet are denoted by the blue and red line, respectively. We find that the WS₂ part in the WGH is a semiconductor with an indirect band gap of about 1.22 eV, which is different from the free WS₂ (direct band gap about 2.1 eV). This can be explained as follows. The free single-layer WS₂ is a semiconductor with the direct band gap (2.1 eV), while the bulk WS₂ held by vdW interaction is a semiconductor with an indirect-band gap of 1.4 eV. The monolayer WS₂ connected by the graphene sheet will result in the transformation from the direct band of pristine WS₂ sheet to the indirect band and the reduction of band gap. At the same time it is found that the intrinsic electronic properties of the graphene (the gapless nature and linear dispersion relationship around the Fermi level)^[45] are retained.

Fig. 2.

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Fig. 2. (color online) (a) Electronic band structures of WS2/graphene heterostructure at the equilibrium distance. The blue and red line denote the contributions from WS2 monolayers and graphene, respectively. The Fermi level is set to be zero and marked by green dotted lines. (b) Schematic diagram of the Gr/WS2 interface contact. The n-type (p-type) Schottky barrier height is the energy difference between the CBM (VBM) and the Fermi level.

The WS₂-graphene configuration is a representative of metal-semiconductor contact heterojunction. The performance of the WGH is dependent extremely on the electronic property of the WS₂ sheet. The Fermi level (FL) of the composite lies in the band gap region of WS₂, resulting in the formation of a schottky barrier at the interface, which is a crucial parameter for the contact. For the rectifying contact, the relative alignment of the semiconductor VBM or CBM to the FL of the combined system is the heterostructure intrinsic property, which is defined as schottky energy barrier. As shown in Fig. 2(b), The n-type Schottky barrier () means that the Fermi level is located above the midgap (CBM + VBM)/2, which is an energy barrier for electronic transmission. On the contrary, the p-type Schottky barrier means that the Fermi level is located down the midgap, which is a barrier for hole transport. The n-type (p-type) Schottky barrier height (SBH) is the energy difference between FL and CBM (VBM). Figure 2(a) shows that the monolayer WS₂ is an n-type semiconductor with the SBH about 0.13 eV, which is lower than the conventional metal/MoS₂ contact (0.5 eV ∼ 1 eV).^[46–51]

Due to the lattice mismatch between the parent structures, applying strain is a simple and effective method to module the electronic properties of the WGH. To show the influence of strains on the electronic properties of the WGH, the electronic properties under different in-plane biaxial strains is discussed. The in-plane biaxial strain ε (shown in Fig. 1(b)), which denotes that the strain is applied along the x direction and y direction at the same time, can be defined as follows: , where and a are the in-plane lattice constants of the unstrained and strained WGH, respectively. The ε with positive/negative value means compressive/tensile strain. The band structures of the WGH under different in-plane biaxial strains are shown in Fig. 3. The in-plane strain applied varies from −6% to 6%inlength steps of 2%. The blue and red line represent the contributions from WS₂ monolayer and graphene sheet, respectively. It is shown that the Dirac point of graphene always lies at the FL under different strains, which means that the intrinsic electronic properties of the graphene are still kept. From the energy band plots shown in Figs. 3(a)–3(c), with the strain varying from 2% to 6%, the indirect band characters of the WS₂ part in the WGH is reserved because the CBM is located at K point and VBM is located at point. However as shown in Figs. 3(d)–3(f), with the strain varying from −2% to −6%, both the CBM and VBM of the monolayer WS₂ are located at K point, which indicates that the monolayer WS₂ in the WGH is characterized by a direct band gap when applying an tensile strain. Therefore, the band of the single WS₂ in the WGH can be tuned effectively by applying different strains.

Fig. 3.

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	Fig. 3. (color online) Band structures of the WS2/graphene heterostructure under different strains. Blue and red denote the contributions from WS2 monolayers and graphene, respectively. Panels (a)–(g) show the strains of 2%, 4%, 6%, −2%, −4%, and −6%, respectively. The Fermi level is set to be zero and denoted by green dotted line.

In order to study SBHs of the WGH under different strains, the magnitudes of CBM and VBM of the monolayer WS₂ are shown in Table 1. The results show that n-type SBHs of the WGH under the compressive strains of 2%, 4%, and 6% are 0 eV, −0.03 eV, and −0.06 eV, respectively and n-type SBHs under tensile strains of −2%, −4%, and −6% are 0.27 eV, 0.42 eV, and 0,23 eV, respectively. The change of SBHs in the WGHis induced by the FL shifting under the in-plane biaxial strain.^[26,27] The compressive strains induce the FL of the WGH to move up, even to pass through the CBM, while the tensile strain causes the FL to move down, resulting in the SBHs increasing. Although the magnitude of SBHis nearly zero under compressive strain, the WS₂ part in heterostructures keeps an indirect band gap, which is the disadvantage to electronic transport. However the WS₂ part of the WGH under tensile strain keeps the direct band gap, and the SBH is still low. Hence, the tensile strain is beneficial to the enhancing of optoelectronic conversion efficiency and electronic transmission due to the direction band gap and low SBH.

Table 1.

Table 1.

Table 1. Calculated values of CBM (SBH), VBM, band gaps under strains from −6% to 6%. The “D” and “I” represent direct band gap and indirect band gap, respectively. To show the structural properties, the values of interlayer distance (d) under different strains are also listed here. . Stress/% d/Å CBM/eV VBM/eV gap/eV Type −6 3.46 0.23 −1.62 1.85 D −4 3.46 0.42 −1.54 1.96 D −2 3.47 0.27 −1.46 1.73 D 0 3.57 0.13 −1.09 1.22 I 2 3.61 0 −0.77 0.77 I 4 3.66 −0.03 −0.45 0.42 I 6 3.83 −0.06 −0.20 0.14 I

Table 1. Calculated values of CBM (SBH), VBM, band gaps under strains from −6% to 6%. The “D” and “I” represent direct band gap and indirect band gap, respectively. To show the structural properties, the values of interlayer distance (d) under different strains are also listed here. .

In order to apperceive the conversion of electronic properties in WGH from microcosmic prospect, the charge densities of the CBM and the VBM of the WGH are shown in Figs. 4(a)–4(f). The charge densities of the CBM and the VBM under the strains of 0%, 6%, and −6% are shown in panels (a) and (d), (b) and (e), (c) and (f), respectively. The results reveal that the electronic states near the CBM and the VBM are mainly from the contribution of W atoms. It is clear that the CBM is completely dominated by the d_z2 orbits of W atoms under different strains. However, the VBM exhibits strong in-plane orbital characters (d_xy and with negligible contribution from the d_z2 orbit in the WGH. Therefore, the band gap characters of the WGH are mainly determined by orbits of W atoms, which is consistent with previous theoretical study.^[42] Further, a comparison among Figs. 4(a)–4(c) shows that the S atoms and W atoms present hybridization in the WGH under −6% strain, which is different from under the 0% or 6% strain. It can be inferred that the hybridization induces the formation of direct band gap.

Fig. 4.

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	Fig. 4. (color online) Electric charge densities of CBM and VBM calculated from the WS2/graphene heterostructure under strains of ((a) and (d)) 0%, ((b) and (e)) 6% and ((c) and (d)) −6%, respectively.

To further sustain our speculation, the local density of states (DOS)of W atoms and S atoms under the strains of 0%, 6%, and −6% in the WGH are shown in Fig. 5. In Fig. 5(a), we find that the orbital characteristics above FL are occupied by S- orbits under 0% strain and the orbital characteristics below FL are occupied by S- orbits. To study the integral electronic properties, we show the total DOS and local DOS of total W atoms, total S atoms and total C atoms of the balanced WGH in Fig. 5(b). We find that the orbits of W atoms, S atoms and C atoms are hardly hybrid with each other. In Fig. 5(c), we find that the orbital characteristics near FL are determined by W- orbits under 0% strain, which is consistent with the charge densities shown in Fig. 4(a). When exerting the strain of 6% on the WGH, the orbital characteristics are basically consistent with those of the 0% configuration as shown in Fig. 5(d). However from Fig. 5(e), we find that the orbits of W-d_z2 and S-p_z present hybridization above fermi level, which is in accordance with the charge densities in Fig. 4(c). Further as shown in Fig. 5(f), we find that the S atoms hybridize not only with W-, but also with W- and W-d_xy. Therefore, it can be inferred that the direct band character of the WS₂ partly kept in the WGH under the tensile strain originates from the hybridization between the S atoms orbits and the W-, W-, and W- orbits.

Fig. 5.

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	Fig. 5. (color online) Local densities of states of W atoms and S atoms under the strains of ((a)–(c)) 0%, (d) 6%, and ((e) and (f)) −6% in the WS2-graphene heterostructure, respectively.

The structural and electronic properties of the WGH under different strains are investigated based on the density functional calculations. It is found that the monolayer WS₂ of the equilibrium WGH is characterized by indirect band gap and the electronic structure of graphene is unperturbed significantly due to the weak vdW interaction. The SBH of the equilibrium WGH is lower than the conventional metal/MoS₂ contact. The indirect band gap of WS₂ is kept in the heterojunction under compressive strain. While applying in-plane tensile strains, we find that the direct band gap of the free monolayer WS₂ is recovered, which is because S atoms orbits hybridize with the W-, W-, and W-d_xy orbits from the electron structure calculation. Our calculation results show that the direct band gap and low SBH of the WGH are acquired by applying tensile strains, which is favorable for electronic transmission. This may provide an instrumental technology for fabricating the WS₂-based field effect transistors.