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Strain and Electric Field Tunable Band Alignments in van der Waals WSe-Graphene Heterojunctions 2

Zhi Gen Yu, Yong-Wei Zhang, and Boris I. Yakobson J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b07418 • Publication Date (Web): 14 Sep 2016 Downloaded from http://pubs.acs.org on September 20, 2016

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The Journal of Physical Chemistry

Strain and Electric Field Tunable Band Alignments in van der Waals WSe2-Graphene Heterojunctions Zhi Gen Yu,† Yong-Wei Zhang,†,* and Boris I. Yakobson§,** †Institute of High Performance Computing, Singapore 138632, Singapore §Department of Mechanical Engineering and Materials Science. Rice University, Houston, Texas 77005, United States

∗ To

whom correspondence should be addressed. E-mail: [email protected]; Tel: +65 6419-1478

∗* To

whom correspondence should be addressed. E-mail:

[email protected]; Tel: +1 (713) 348-3572

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Abstract We study the band alignments and band structures of van der Waals WSe2-graphene heterojunctions by varying out-of-plane external electric field and in-plane mechanical strain using density-functional calculations. We find that the electronic properties of WSe2-graphene heterojunctions are insensitive to the change of the mechanical strain, showing strong robustness. However, the external electrical field intensity is able to significantly change the band alignments of WSe2-graphene heterojunctions, while a constant band gap value of WSe2 in the heterojunctions is nearly maintained. We further show that the highest hole concentration injected by the external electric field is estimated as high as 6.42×1012 cm-2, while the highest electron density is about 2.99×1012 cm-2. These findings suggest that the WSe2-graphene heterojunctions are a promising structure instrumental for electronic device applications.


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INTRODUCTION A heterojunction is the interface that is formed between two layers of dissimlar solid-state materials. It is the most commonly used structure for engineering the electronic energy bands

in

solid

state

device

applications,

such

as

lasers,

solar

cells

and

field-effect-transistors et al.1 For a heterojunction, its electronic properties are crucially dependent on the alignment of the energy bands at the interface. In general, the procedure for theoretically predicting band alignments in heterojunctions based on conventional materials has been well established.2-5

It has been predicted, however, that Si-based

electronics will reach their physical limit soon,6 therefore, a great deal of effort has already been devoted to looking for new materials and thus new heterojunctions. For nanoscale materials, the band energies are dependent on material size due to the quantum size effects, which thus provides an effective route for band offset engineering in nanoscale heterostructures.

Graphene and other 2D materials, which are considered as the next generation electronic materials, have recently attracted massive interest owing to their unique structures, fascinating electronic properties and novel potential applications in nanoelectronics and optoelectronic devices.7-9 For example, graphene is a promising material for electrode and also active layer, and has been successfully intergraded into all graphene-based transistor.10 It is also an excellent channel material, which has been employed in graphene field-effect transistors (GFETs) fully encapsulated in hexagonal boron nitride (h-BN).11 Besides these interesting applications, graphene was also used for fabricating flexible GFETs electronics on flexible substrates.12,13 Unlike gapless



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graphene, the monolayer semiconducting transition-metal dichalcogenides (TMDs) in general possess a direct band gap in the range of 1.6−2.0 eV, a relatively high charge carrier mobility and a robust mechanical stability, thus promising for applications in nanoelectronics and optoelectronics.14-16 In fact, TMDs-based transistors were already demonstrated.14,17-28

It is well-known that 2D materials can have very different electronic properties in comparison with their 3D counterparts due to the quantum confinement effect. Hence, it is expected that the band alignments or the band offsets in 2D materials are drastically different from those in their bulk counterparts. Indeed, this expectation was confirmed by the fact that the band offsets for the heterostructures composing of monolayer and few-layer TMDs are distinctively different.29 Since band alignments between two layer materials in heterojunctions are crucial to the performance of electronic devices, an accurate band alignment between two different 2D materials is highly desirable in the design of a full 2D-material based heterojunction. It should be noted that the band alignments between bulk molybdenum and tungsten dichalcogenides, MX2 (M=Mo and W; X=S and Se), have been systematically explored.30 However, the electric field and the strain effect were not considered in those previous theoretical studies. In addition, external electric field was found to have a remarkable effect on the band alignment in bulk heterojunctions31-33 , the electronic properties of bilayer TMDs34,35 and the heterojunction of black phosphorus and MoS2.36,37 Hence, it is expected that a similar effect may also exist in other 2D-materials-based heterojunctions. In order to develop robust, high performance 2D-material-based electronic devices, an in-depth understanding


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on the electric field and strain effect on the band alignments of 2D heterojunction is critically important.

We note that some interesting measurements on the alignment of WSe2 -graphene (in short, WSe2-G) heterojunctions, such as the graphene neutrality point and the conduction and valence band edges of WSe2, have been recently performed.38 Undoubtedly, these experimental measurements provide a great opportunity and a valuable comparative base for systematically examining the band alignment and electronic structures of WSe2-G heterojunctions. Therefore, in this work, we will conduct a comprehensive study of the effects of electric field and mechanical strain on the band alignments, and band structures of WSe2-G heterojunctions using density functional theory (DFT) calculations. We find that the electronic properties of WSe2-G heterojunctions are robust against the change in mechanical strain. The external field, however, is able to effectively tune the band alignments. Meanwhile, it does not exert any significant change to the band gap of WSe2. We also show that high electron/hole concentrations can be achieved by the injection driven by the external electric field. Our work suggests that the WSe2-graphene heterojunctions are a promising structure instrumental for novel device applications.

RESULTS AND DISCUSSION In this study, we use the state-of-the-art first-principles calculations to systematically investigate the electric field-dependent electronic properties of WSe2-G heterojunctions. In general, mechanical strains can be introduced either intentionally or unintentionally, for example, due to the lattice mismatch between WSe2 and graphene. Thus, we



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comprehensively consider the strain effect on the electronic properties of the heterojunctions. First, we calculated the unitcell lattice constants of monolayer WSe2 and monolayer graphene by setting a large interlayer spacing of c=25 Å. The optimized lattice constants of monolayer WSe2 and monolayer graphene are 3.316 Å and 2.469 Å, respectively. The optimized lattice constants are in good agreement with experimental values of 3.282 Å (bulk) 39 for WSe2 and 2.452 Å for graphene.40 In the calculations of the heterostructures, we expand the WSe2 unitcell to a 3×3 supercell and the graphene unitcell to a 4×4 supercell using the optimized lattice constants for reducing the internal strain resulted by the lattice mismatch. In this setting, the lattice constant of the expanded WSe2 supercell is 9.948 Å, which is slight larger than that of the expanded graphene lattice, 9.876 Å. Both supercells are used to build a vertical heterojunction (containing 18 Se and 9 W or 32 C atoms). In order to comprehensively examine the strain effects on the electronic properties of the heterojunction, we consider the following three types of heterojunctions. HS-1: WSe2 is placed on top of graphene and the lattice constant of WSe2 is compressed to the lattice constant of graphene. Therefore, the graphene is in strain-free state; while WSe2 is under the biaxial compressive strain of -0.72%. HS-2: The average value (a=9.912 Å) of the lattice constants of graphene and WSe2 is considered. Therefore, WSe2 is under the biaxial compressive strain of -0.36% and graphene is under the biaxial tensile strain of 0.36%. HS-3: Graphene is placed on top of monolayer WSe2 and the lattice constant of graphene (a=9.876 Å) is stretched to the lattice constant of WSe2 (a=9.948 Å). Therefore, WSe2 is in strain-free state and graphene is under the biaxial tensile strain of 0.72%.


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It was shown that TMDs bilayers have five possible stacking structures.34,35 To examine the stacking stability of the WSe2-G heterojunctions, we consider a representative case of the WSe2-G heterojunctions, HS-1. We consider six possible stacking configurations according to the symmetry of the WSe2-G heterojunction, which are shown in Figure S1. It should be noted that we only consider the translation between graphene and WSe2 along x, y and diagonal directions. In order to find the most stable stacking configuration, we calculate the stacking formation energy ∆E, which is defined as ∆ = ( ) − ( + ), where, , , and ( ) is the energy of monolayer graphene, monolayer WSe2 and the WSe2–G heterojunction, respectively. It should be noted that the energy of monolayer graphene is calculated based on the lattice constant of HS-1. The calculated stacking formation energies with the consideration of van der Waals (vdW) correction are shown in Figure S2. It is seen that the stacking configuration of ST1 is the most stable one, with a stacking formation energy of -1.72 eV per unit or -29 meV/atom. This low stacking formation energy indicates that their interaction is in the range of van der Walls force, which confirms that WSe2 and graphene form a van der Waals heterojunction. In the following, we will solely use the ST1 configuration to study the electric field and strain effects unless stated otherwise.



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Figure 1. Atomic structures of ST1 WSe2-G heterojunction. (a) Top view of ST1 atomic configuration. (b) Side view of ST1 atomic configuration. (c) Schematic diagram of ST1 under the external electric field and its positive direction is defined as along the red arrow direction. C, W and Se atoms are denoted using small black, big black and green balls, respectively.

The atomic configuration of the ST1 WSe2-G heterojunction is shown in Figure 1(a) and 1(b). In this stacking configuration, graphene sits on the top surface of WSe2 along the diagonal direction with the highest degree of symmetry. In order to explore the electric field effect on the electronic properties of the heterojunction, we apply the external electric field varying from -0.45 to 0.45 V/Å. The positive electric field intensity is defined as along the red arrow, that is, from WSe2 to graphene as shown in Figure 1(c). In order to explore the strain effect on the electronic properties of the WSe2-G heterojunctions without considering external electric field, we also examine the changes in the band gap for monolayer WSe2 both before and after forming WSe2-G


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heterojunctions under three different strain states. It should be noted that for HS-1 and HS-2, a compressive strain of -0.72% and -0.36% is applied to WSe2, respectively; while no strain is applied to WSe2 for HS-3. In order to distinguish the effect on the band gap of WSe2 arising from strain, we also calculate the band structures of monolayer WSe2 and graphene under the strain of -0.72%, -0.36% and zero, respectively. The calculated band structure of HS-1, HS-2 and HS-3 using Fermi level as the alignment reference is shown in Figure 2(a), 2(b) and 2(c), respectively. It is worth noting that we have used the Fermi level as a common reference to plot the band structures of monolayer graphene, monolayer WSe2 and WSe2-G heterojunction in one figure to find the change of band gap in WSe2 without (isolated monolayer) and with graphene (forming WSe2-G heterojunction) under different strain states.

It is seen that the band structures of the WSe2-G

heterojunctions are nearly composed of energy bands of the individual WSe2 and graphene. This is not surprising since the weak WSe2-G interaction is insufficient to modify the characteristics of the band structures of the heterojunctions and thus should have nearly negligible effect on the band structure of the heterojunctions. For these three heterojunctions, the Dirac point of graphene locates at K point and pins to the Fermi level. The calculated band gap of WSe2 is 1.66 eV, 1.62 eV and 1.57 eV for HS-1, HS-2 and HS-3 heterojunctions, respectively. The calculated band gap of isolated monolayer WSe2 is 1.63 eV, 1.59 eV, and 1.54 eV under the strain of -0.72%, -0.36% and 0, respectively. The difference in the band gap of WSe2 between with and without graphene under the same strain is only 0.03 eV, signifying that both graphene and strain have only very weak influence on the band gap of WSe2. Note that our calculated monolayer WSe2 band gap of 1.54 eV is close to the experimentally reported value of ∼1.65 eV.41 It is well-known that plain DTF calculation normally underestimates the band 9 Environment ACS Paragon Plus


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gap.

We note that a recent study showed that the band gap of MoS2 was found to be

reduced to ∼1.47 eV in graphene-MoS2 hybrid structure.42 In another experimental study, however, it was shown that a band gap narrowing of MoS2 by 0.1 eV was observed.43 It is also seen that our calculated band structures of individual graphene and graphene in the WSe2-G heterojunction are almost identical, indicating that the tensile strain of 0.72% has very weak effect on the band structure of graphene, as well as the position of the Dirac point. These results are consistent with the previously reported ones that the gapless Dirac spectrum is robust against small and moderate deformations.44 From the viewpoint of the band gap change, clearly, the WSe2-G heterojunctions are more advantageous than graphene-MoS2 ones in terms of fabricating robust electronic devices.

Figure 2. The calculated band structures of WSe2-G heterojunctions, individual monolayer WSe2 and graphene. (a) HS-1 Heterostructure based on HS-1. (b) HS-2 heterostructure. (c) HS-3 heterostructure. The Fermi level is used as the common reference for the band alignment.


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Figure 3. The band structures of HS-1 heterostructure with and without SOC under the external electric field intensities of -0.45 V/Å (a), 0 V/Å (b) and 0.45 V/Å (c). (d–f) The band structures of HS-2 heterostructure with and without SOC under the external electric field intensities of -0.45 V/Å (d), 0 V/Å (e) and 0.45 V/Å (f). The band structures of HS-3 heterostructure with and without SOC under the external electric field intensities of -0.45 V/Å (g), 0 V/Å (h) and 0.45 V/Å (i). The horizontal dashed line denotes the Fermi level. The red lines represent the PBE+SOC band structures and the black lines represent the PBE band structures, respectively.

It was reported that the spin-orbital coupling (SOC) has a strong effect on band structure calculations, and its resulting valence band spin-splitting for WSe2 can be as large as 0.4 eV.45 As a benchmark, we also calculated the band structures of monolayer graphene and WSe2. The calculated results are shown in Fig. S3. It is seen that the SOC has a very week effect on the band structure of monolayer graphene since the band



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structures of monolayer graphene with and without SOC are nearly identical. However, the SOC has a strong effect on the band structure of monolayer WSe2, especially on the valence band. Our calculations show that although the conduction band spin-splitting is only 0.036, the valence band spin-splitting is 0.461 eV. Note that the latter is consistent with the reported value of 0.4 eV.45 The large valence band spin-splitting in WSe2 also results in a marked change in band gap. The calculated band gap of monolayer WSe2 is 1.54 eV without SOC, but it decreases to 1.28 eV with SOC. A previous study showed that the band gap of bilayer graphene can be widely tuned by a perpendicularly applied external electric field and further increase in the electric field is able to turn the bilayer graphene gapless again.46 Then, an interesting question arises: Can the band gap and band alignment of the WSe2-G heterojunctions be tuned by applying an external electric field? To answer this question, we explore the electronic properties of the WSe2-G ST1 heterojunction with three different strain levels. The band structures of WSe2-G heterojunctions under the three specific electric field intensities are shown in Figure 3, in which the top, middle and bottom panels show the calculated band structures of HS-1, HS-2 and HS-3 under the external electric field intensities of -0.45 V/Å, 0 V/Å, and 0.45 V/Å, respectively. The red lines represent the band structure with considering SOC and the black lines represent the band structures without considering SOC, respectively. (More results on the calculated band structures of HS-1, HS-2 and HS-3 heterojunctions at different electric field intensities are shown in Figures S4, S5 and S6, respectively). Based on our calculation results, it can be seen that the strain within the range considered has a very weak effect on the electronic properties of the heterojunctions. As


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shown in Figure 3(b), we denote the band gap of WSe2 as ∆E in the ST1 heterojunctions, which is defined as the energy difference between the conduction band minimum (CBM) and the valence band maximum (VBM) contributed from WSe2 at Γ point. Therefore, ∆E or ∆E shows the energy difference between CBM and the Dirac point or VBM and the Dirac point of graphene. If we consider that electrons are injected from graphene to WSe2, the corresponding energy ∆E can be considered as the Schottky barrier. Due to the concern over the effect of SOC on the band structure calculations, one may anticipate that the SOC may also affect the band alignments in the three types of heterojunctions.

However, we find that the SOC has a very weak effect on

the band alignments, especially under external electrical fields. Since the three types of heterojunctions show a similar behavior, here, we only discuss the band alignments obtained from PEB and PEB+SOC for the case of HS-1 heterojunction. Without external electrical field, as shown in Figure 3(b), the value of ∆E of WSe2 is 1.66 eV without SOC and 1.34 eV with SOC, which are slightly higher than those of isolated WSe2 (that is, 1.63 eV using PBE and 1.28 eV using PBE+SOC). We find that the increase in the band gap of WSe2 is largely due to the tensile strain of -7.2% in monolayer WSe2 in HS-1 heterojunction. For the strain-free state, the values of ∆E and ∆E are reduced from 0.97 eV (PBE) to 0.82 eV (PBE+SOC) and from 0.69 eV (PBE) to 0.52 eV (PBE+SOC), respectively. Under the negative electrical filed intensity of -0.45 V/ Å, as shown in Figure 3(a), the values of ∆E and ∆E are reduced from 1.65 eV (PBE) to 1.51 eV(PBE+SOC) and from 0.26 eV (PBE) to 0.15 eV(PBE+SOC), respectively; while under the positive electrical field intensity of

0.45 V/ Å, as shown in Figure 3(c), the

value of ∆E is nearly unchanged and ∆E is reduced from 1.67 eV (PBE) to 1.35 eV



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(PBE+SOC). Based on our above calculations, we can see that the SOC does not cause any significant changes in the band alignments of WSe2-G heterojunctions. Therefore, we mainly focus on the band alignments without SOC in our study. The calculated electrical field-dependent band alignments in WSe2-G heterojunctions are shown in Figures S4–S6. Based on our calculation results as shown in Figures S4–S6, for HS-1 heterojunction, the position of the Dirac point from graphene is pinned at K point and the Fermi level when the external electric field intensity varies between -0.3 and 0.35 V/Å, regardless of the applied strain value. For a negative electric field, it drives the Dirac point below the Fermi level when the electric field intensity is more than -0.35 V/Å. Meanwhile, a negative electric field pushes the VBM of WSe2 up to the Fermi level. For a positive electric field, the Dirac point moves up beyond the Fermi level when the electric field intensity is more than 0.40 V/Å. Meanwhile, a positive electric field drives the CMB of WSe2 down towards the Fermi level, thus reducing the Schottky barrier between graphene and WSe2. For the band gap of WSe2, ∆E , it can be seen that the effect from the external electric field is very weak. In addition, WSe2 in WSe2-G heterojunction also retains the nature of direct band structure at Γ point. Hence, graphene can be considered as an effective protective material for preserving the value and nature of WSe2 band gap.


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Figure 4. Variations of the energy at the graphene Dirac point K and the VBM and CMB of WSe2 with the applied electric field intensity for HS-1 (a), HS-2 (b) and HS-3 (c), respectively. The Schottky barrier is considered the same as ∆E . EC (EV) is the energy of CBM (VBM) and ED is the energy of the Dirac point of graphene.

The variations of the energy level at the Dirac point of graphene, the CBM and VBM of WSe2 with the applied external electric field intensity for HS-1, HS-2 and HS-3 heterostructures are shown in Figure 4. It can be seen that the VBM EV and CBM EC have nearly a linear relationship with the external electric field intensity, and the band gaps of WSe2 in three cases are almost unchanged. The average band gap of WSe2 changes from 1.66 eV to 1.57 eV when the field intensity E varies from -0.35 V/Å to 0.45 V/Å. For comparison, the calculated band gap of isolated monolayer WSe2 is 1.63 eV, 1.59 eV, and



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1.54 eV corresponding to the lattice constant of HS-1, HS-2 and HS-3, respectively. Hence, the presence of graphene only slightly increases the band gap of the WSe2 in the heterostructures. For all three types of heterojunctions, when the positive electric field intensity is higher than 0.4 V/Å, the bottom of the conduction band of WSe2 is below the Fermi level, while the Dirac point of graphene is above the Fermi level. When the negative electric field intensity is higher than -0.3 V/Å, the top of the valence band of WSe2 is pinned at the Fermi level, while the Dirac point of graphene is below the Fermi level. Therefore, a semiconductor-to-metal transition can be achieved by applying a relatively high external electric field.

In order to explore the charge transfer between graphene and WSe2 in the ST1 heterojunction, we further calculate the Schottky barrier as a function of the external electric field intensity, and the results are shown in Figure 5, in which the open symbols denote the Schottky barriers in the three types of heterojunctions. It can be seen that the Schottky barriers in HS-1 (denoted as open squares G-ϕc), HS-2 (denoted as open circles A-ϕc) and HS-3 (denoted as open triangles W-ϕc) are nearly identical, which further confirms that the strain has very weak effect on the band alignments and electronic properties of WSe2-G heterojunction. It can be also seen that the Schottky barrier is negative when the external electric field is higher than 0.4 V/Å. As a consequence, electrons from graphene would be injected into WSe2 without any barrier, signifying that WSe2 possesses a metallic conductivity, and thus realizing a semiconductor-to-metal transition. Our simulation results suggest that the range of the electric field applied to the WSe2-G heterojunction should be confined within -0.3 V/Å≤E≤ 0.4 V/Å. Otherwise, a


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dielectric breakdown of the WSe2-G heterojunctions may occur, leading to their malfunction.

Figure 5. The electric field intensity-dependent band alignments, as well as the Schottky barrier in the WSe2-G heterojunctions. Here, G-ϕc, A-ϕc and W-ϕc are the Schottky barriers in HS-1, HS-2 and HS-3, respectively.

According to Figure 5, the Schottky barrier ϕc in a heterojunction can be approximately expressed as: ϕ = ϕ +

(1),

where ϕ is a constant and E is the external electric field intensity, and d is the effective vacuum spacing between WSe2 and graphene as shown in Figure 1(c). Using a linear fit to our calculated results as shown in Figure 5, we obtain the values of ϕ are 0.95 eV, 0.92



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eV and 0.89 eV for HS-1, HS-2 and HS-3 heterojunctions, respectively, and the effective vacuum spacing d is ∼2.21 Å for all the three cases. Based on our calculation results, we can see that the effective vacuum spacing between WSe2 and graphene is independent of the strain and applied external electric field intensity, while the constant ϕ as well as the Schottky barrier can be weakly adjusted by stretching graphene and/or applying the external electric field.

The energy difference between the bottom of the conduction band (the top of the valence band) of WSe2 and the Dirac point of graphene is defined as the band offset of the conduction band ∆E (the band offset of the valence band ∆E). From Figure 5, it can be seen that the strain has very weak effect on the band alignments, and the band alignments in the three heterojunctions are nearly identical. In contrast, the external electric field has strong effect on the band alignments of WSe2-G heterojunctions. We find that ∆E is nearly inversely proportional to the external electric field intensity. For HS-1 heterostructure, ∆E is 0.98 eV when E=0 V/Å, increases to 1.61 eV when E=−0.30 V/Å and then deceases to 0.29 eV when E=0.30 V/Å. Since the external electric field has very weak on the band gap of WSe2, therefore, ∆E is nearly proportional to the external electric field intensity. For HS-1, ∆E is 0.68 eV when E=0 V/Å, decreases to 0.05 eV when E=−0.30 V/Å and then increases to 1.37 eV when E=0.30 V/Å. Hence, the electric field intensity-dependent ∆E and ∆E are linked by the nearly constant band gap of the heterojunctions.


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Figure 6. The charge transfer between graphene and WSe2 under the varying electric field intensity in the heterojunctions of HS-1 (a), HS-2 (b) and HS-3 (c). The squares and triangles denote the net charge transfer from graphene in units of eV and the corresponding carrier concentration in units of cm-2, respectively. The red lines indicate that the WSe2 gains electrons while the black lines indicate that the WSe2 loses electrons or gains holes.

In order to explore the charge transfer between WSe2 and graphene under the varying electric field intensity, we use Bader method47 to explore the charge transfer between graphene and WSe2 under the external electric field and the calculation results are shown in Figure 6, in which the red line segments represent the electron gain while the black line segments represent the electron loss (hole gain) of WSe2. It can be seen that WSe2 gains electrons from the graphene under a negative electric field; while the WSe2 donates electrons to the graphene under a positive electric field. By comparing with our



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simulation results of HS-1 shown in Figure 6(a), HS-2 shown in Figure 6(b) and HS-3 shown in Figure 6(c), we can see that the three types of heterojunctions are nearly identical, which again confirms that the strain effect on the electronic properties of WSe2-G heterojunctions is very weak. From our calculation results for HS-1 heterojunction as shown in Figure 6, we can see that ∼0.013e are transferred to graphene from WSe2, which results in a p-type conductivity with a hole concentration of 1.52×1012 cm-2 in WSe2 without any external electric field. With increasing the external electric field intensity, more electrons are transferred to graphene, and the number of electrons transferred from WSe2 to graphene is nearly a linear function with the external electric field intensity. For E=0.45 V/Å, ∼0.055e leave from WSe2 to graphene, resulting in a hole concentration of 6.42×1012 cm-2 in WSe2. Under the negative electric field condition, electrons are transferred from graphene to WSe2, resulting in an n-type conductivity. For HS-1 heterojunction, it can be seen that ∼0.034e are injected into WSe2 from graphene when E=−0.2 V/Å, and the electron transfer increases to 0.026e when E=−0.45 V/Å. Meanwhile, the corresponding n-type carrier concentration is increased to 2.99×1012 cm-2 from 3.97×1011 cm-2. It should be noted that WSe2 would like to donate electrons even though the applied electric field is only -0.1 V/Å, and the total electron transfer is 0.053e, 0.051e and 0.048e per unitcell for HS-1, HS-2 and HS-3 heterostructure, respectively. From Figure 6, it is seen that the injected hole concentration is higher than the electron concentration under the same absolute value of electric field intensity for all the three types of heterojunctions. The predicted hole concentration is 6.42×1012 cm-2 when E=0.45 V/Å, while the predicted electron concentration is 2.99×1012 cm-2 when E=−0.45 V/Å for HS-1 heterojunction. The


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same trend can also be found for HS-2 and HS-3 heterojunctions as well. The corresponding hole concentration is 6.42×1012 cm-2 (6.52×1012 cm-2) and electron concentration is 3.03×1012 cm-2 (3.10×1012 cm-2) for HS-2 (HS-3) heterojunction.

It is interesting to point out that self-compensation between the external electric field and the carrier concentration exists in the WSe2-G heterojunctions. Based on our calculation results as shown in Figure 6, the WSe2 as an n-type layer in FET devices needs a negative electric field to inject electrons and the electron density increases with increasing the electric field intensity. However, we find that a positive electric field reduces the Schottky barrier, while a negative electric field intensity increases the Schottky barrier. The same is also true for WSe2 used as a p-type layer in FET devices. This self-compensation results in the presence of the saturation regime in FET devices. Hence, our simulation results clearly show that WSe2 is a promising p-type active layer material for FET devices, which explains the previous experimental observation that field-effect transistors that used WSe2 as a p-type active layer showed excellent electronic properties.24,48

CONCLUSIONS We have performed a systematic theoretical study on the effects of electric field and mechanical strain on the band structures and band alignments of WSe2-G heterojunctions. We show that the strain has nearly no effect on the electronic properties of the heterojunctions. On the contrary, external electric field has strong effect on the band alignment, but it has very weak effect on the band gap of WSe2 in the heterojunctions. We further obtained the values of band alignment and band gap of WSe2 in the 21 Environment ACS Paragon Plus


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heterojunctions under the varying electric field intensity. In addition, the charge transfer between graphene and WSe2 and the charge concentration in WSe2 layer are also analyzed. The findings obtained in this study may provide interesting guidelines for designing high performance WSe2-G heterojunctions and FET devices.

ASSOCIATED CONTENT Supporting Information Available Description of the atomic models of WSe2-G heterojunctions and formation energies, the band structures of HS-1, HS-2 and HS-3 under the varying electric field intensity, and first-principle calculation method.

This material is available free of charge via the

Internet at http://pubs.acs.org/.

AUTHOR INFORMATION Author Contributions ZGY carried out the DFT calculations. All authors performed data analysis and manuscript writing.

Conflict of interest The authors declare no competing financial interest.

ACKNOWLEDGEMENT This research was sponsored by the Agency for Science, Technology and Research (A*STAR) with a grant number of 152-70-00017 and computational resource was provided by A*STAR Computational Resource Centre, Singapore (A*CRC).

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