WSe2 heterostructure by introducing vacancy: First principles calculations

Physica E 116 (2020) 113729

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Physica E: Low-dimensional Systems and Nanostructures journal homepage: http://www.elsevier.com/locate/physe

Tuning optical properties of Graphene/WSe2 heterostructure by introducing vacancy: First principles calculations B. Qiu a, X.W. Zhao a, G.C. Hu a, W.W. Yue a, b, X.B. Yuan a, *, J.F. Ren a, b, ** a

School of Physics and Electronics, Shandong Normal University, Jinan, 250014, China Shandong Provincial Engineering and Technical Center of Light Manipulations & Institute of Materials and Clean Energy, Shandong Normal University, Jinan, 250014, China

b

A R T I C L E I N F O

A B S T R A C T

Keywords: Graphene/WSe2 heterostructure Optical properties Electronic structure Vacancy

The effects of W and Se vacancies on the electronic structure and optical properties in Graphene/WSe2 heter­ ostructure (GW) are studied based on the density functional theory. It is found that both the formation of the heterostructures and the introduction of the W or Se vacancies have great impactions on the electronic structure of WSe2. Additionally, after W or Se vacancies are introduced in GW, the optical properties are greatly red-shifted and the values of the optical parameters become larger than those of the pure GW. In particular, the effects of the W vacancy is greater than that of the Se vacancy. These theoretical results indicate that the introduction of vacancies does tune the electronic structure and the optical properties of the GW heterostructures, which provide a useful guidance for the design of novel optical nanodevices based on two dimensional heterostructures.

1. Introduction Atomically thin two-dimensional (2D) materials, such as graphene, silicene and tinene, offer a variety of intriguing properties for funda­ mental studies and applications [1–3]. Among them, transition metal dichalcogenides (TMDs) have good thermal stability, excellent me­ chanical strength and high electrical conductivity, etc. [4–6]. These unique material properties made TMDs a widespread concern recently. TMDs have potential applications in the fields of electronics and opto­ electronics [7], such as the fabrication of tunnel field effect transistors (FETs), p-n diodes, and photovoltaic electronics and so on [8–11]. While among the semiconducting TMDs in the 2D phase, WSe2 have been extensively investigated due to their highly enhanced quantum effi­ ciency and excellent transistor performance [12]. WSe2 has indirect-to-direct bandgap transition from bulk (~1.2 eV) to monolayer (~1.8 eV) and high p-type mobility up to 500 cm2/V-s at room tem­ perature [12–14]. There are a lot of methods to adjust the properties of WSe2, such as doping atoms or introducing holes and so on. For example, G. Bai et al. offered a general experimental method to prepare wafer-scale lanthanide doped TMDs, and they also widely modulated the luminescence of atomically layered TMDs by introducing lanthanide

ions [15]. S. Ahmedet et al. explored the Co doping effects in WSe2 [16]. X. Chia et al. adjusted the electrocatalytic properties of WSe2 by doping Ta, V, Nb, etc. [17] The introduction of holes into WSe2 can also produce unexpected gains in the valley effect [18]. Due to the fast electron-hole recombination rate, the energy con­ version efficiency of monolayer TMDs observed in the experiments is poor. To improve their electronic and optical properties, van der Waals heterostructures (vdWHs) made by stacking layered TMDs are devel­ oped [19–22]. It is well known that combining together different ma­ terials rarely leads to a simple arithmetic sum of their properties, but giving rise to novel and unexpected behaviors. If two different two-dimensional materials are putted together, they will be combined by van der Waals forces, this double or multi-layer structure becomes a vdWHs. Surprising physical properties can be obtained and vdWHs have been widely studied based on their rich functional properties beyond the two-dimensional materials themselves [23–26]. Graphene has many features, such as good chemical resistance, high stability, and large specific surface area and so on, which make it promising as a substrate for improving TMDs. The graphene-based heterostructures have broad prospects. For example, recent studies reported that MoS2/graphene dots have significant catalytic activity in oxygen evolution reaction

* Corresponding author. ** Corresponding author. Shandong Provincial Engineering and Technical Center of Light Manipulations & Institute of Materials and Clean Energy, Shandong Normal University, Jinan, 250014, China. E-mail addresses: [email protected] (X.B. Yuan), [email protected] (J.F. Ren). https://doi.org/10.1016/j.physe.2019.113729 Received 1 July 2019; Received in revised form 12 September 2019; Accepted 13 September 2019 Available online 14 September 2019 1386-9477/© 2019 Elsevier B.V. All rights reserved.

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Physica E: Low-dimensional Systems and Nanostructures 116 (2020) 113729

[27]. Ni(OH)2/graphene [28] and SnO2/graphene [29] heterostructures has also been studied. These all indicate that the prospects of graphene-based heterostructure are broad. On the other hand, the het­ erostructure constructed by graphene and WSe2 (GW) also attracted research interests in recent years. For example, M. Sun et al. found that the introduction of Se and W vacancies did cause significant improve­ ment of the electronic properties of GW heterostructure, the electronic properties can also be further modulated by changing interlayer coupling or by applying a vertical electric field [18]. A. Gao et al. studied the electrical transport properties including gate-tunable rectification inversion and polarity inversion in atomically thin GW heterostructures [30]. In 2018, B. Yang et al. combined experiments and theories to discuss the factors affecting the interlayer distance in GW hetero­ structures [31]. G. W. Burg et al. reported the experimental observations of strongly enhanced tunneling between graphene bilayers through a WSe2 barrier when the graphene bilayers are populated with carriers of opposite polarity and equal density [32]. Obviously, GW heterostructures have received much attention especially for their electronic properties, however, their optical prop­ erties need to be studied further. Based on the bright prospects of ap­ plications of graphene and the direct bandgap electronic structure of WSe2, we form the GW heterostructures with W or Se vacancies, which are called GW-Vse (GW with one Se vacancy), GW-Vw (GW with one W vacancy) and GW-Vse-double (GW with two Se vacancies), respectively. The optical properties changes induced by the vacancies are investigated in detail. This article is mainly divided into the following four parts. The first part is the introduction, the second part is the computational model and method, the third part is the analysis and discussion of the results,

and the fourth part is the conclusion. 2. Computational model and method In this paper, all calculations are performed by using the VASP (Vienna ab-initio Simulation Package) [33,34]. When constructing the model, an appropriately sized vacuum layer is used to reduce the interaction of the structure in the vertical direction. In our calculation, the vacuum layer is set to 20 Å. The interactions between ions and electrons are described by the projector-augmented-wave (PAW) method [35,36]. In this paper, we mainly discuss the optical properties when vacancies are introduced in GW structure, and we do not focus on the exact values of the band gaps or the large exciton effect in 2D ma­ terials, so we use the Perdew-Burke-Ernzerhof (PBE) functional with generalized gradient approximation (GGA) to describe the electron ex­ change and correlation [37–41]. The cutoff energy is set to 500. Meanwhile, the convergence precision of each interatomic force and EDIFF were less than 0.02 and 1 � 10 5, respectively. K-points are set to 7*7*1. The DFT-D2 method of Grimme is considered for the van der Waals interactions in all simulations [42]. The calculated lattice constants of monolayer WSe2 and pure gra­ phene are 3.16 Å and 2.47 Å, respectively. For lattice matching, the super cells of WSe2 and graphene we used to build GW heterostructure are 3*3*1 and 4*4*1, respectively, so the lattice mismatch ratio of the system is about 0.67%. The formed structure is shown in Fig. 1(a). The calculated distances between graphene and WSe2 are 3.429 Å, 3.426 Å, 3.410 Å, and 3.433 Å for GW, GW-Vse, GW-Vw, GW-Vse-double, respectively. The unit-cell WSe2 is a direct bandgap semiconductor,

Fig. 1. (a) Top and side views of GW vdWHs and the hexagonal Brillouin zone. Wherein, the green and the red circles represent the Se and W vacancy positions. Brown, gray and green atoms represent C, W and Se atoms, respectively. (b) The planar averaged charge densities of the systems. The insets are the top and side views of the differential charge density distributions of GW-Vw, the blue means loss electrons and the yellow means gain electrons. 2

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and the valence band maximum (VBM) and the conduction band mini­ mum (CBM) are located at the K point. Due to the band folding of the 3*3 supercell, the VBM and CBM are folded to the G point, and the band gap is 1.54 eV, as shown in Fig. 2 (a), these data are consistent with the previous theoretical simulations and experimental results [43–46]. Optical properties can be derived from the dielectric constant for­ mula. The composite dielectric constant formula is ε(ω) ¼ ε1(ω)þ iε2(ω), in which ε1(ω) is the real part of the dielectric constant and ε2(ω) means the imaginary part of the complex permittivity. The formula of ε1(ω) is Z ∞ αβ ’ ’ 2 ε2 ðω Þω ε1 ðωÞ ¼ 1 þ p dω’ : (1) π 0 ω’2 ω2 þ iη

�pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi �2 � ε ðωÞ þ iε ðωÞ 1� � � 1 2 RðωÞ ¼ �pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi � ; � ε1 ðωÞ þ iε2 ðωÞ 1� LðωÞ ¼

4π2 e2 1X 2ωk δð2ck lim Ω q→0 q2 c;v;k � � � < uck þ eβq �uvk >* : �

Before studying the influence of vacancies on the optical properties of GW heterostructures, we first explored the electronic and optical properties of the GW itself. The top and side views of the GW hetero­ structure are shown in Fig. 1(a). The green circle indicates the location of the two different Se vacancy types, one for Se vacancy (GW-Vse) is away from the graphene layer, and the other for the case with two Se vacancies (GW-Vse-double). We have compared two kinds of GW-Vse, i. e., the Se vacancy is away from or near the graphene layer, respectively. We can found that properties of electronic and optical are almost identical, so we choose a more stable type in which the Se vacancies is away from the graphene layer. The red circle indicates the W vacancy. In the upper right corner of Fig. 1(a) we also show the Brillouin zone of the heterostructure. In Fig. 1 (b) we plotted the xy-averaged differential charge densities of the systems. It can be seen that there are differences of the charge transfer between GW and GW with vacancies. The intro­ duction of W or Se vacancies will result in a change of the charge transfer. The charge transfers in GW-Vw and GW-Vse systems are greater than that in GW, however, the charge transfer in GW-Vse-double is

� � � �

(2)

From the above two formulas, the other relevant optical parameters can be further calculated. 8 pffiffiffiffiffiffi < �1 2ω � 2 αðωÞ ¼ ε ðωÞ þ ε22 ðωÞ 2 c : 1

912 = ε1 ðωÞ ; ;

(3)

1

2 1 8 9 ; = pffiffi < 2 1 2 ½ε1 ðωÞ þ ε22 ðωÞ�2 þ ε1 ðωÞ : ;

(4)

2

2

GW C W Se

0

-1

-2

GW C W Se

1

Energy(eV)

Energy(eV)

1

0

-1

G

M

K

G

-2

PDOS

G

M

K

(a)

PDOS

2

1

GW C W Se

1

Energy(eV)

0

-1

-2

G

(b)

2

Energy(eV)

nðωÞ ¼

(6)

3. Results and discussion

ωÞ� < uck þ eaq �uvk >

2vk

ε2 ðωÞ : ε21 ðωÞ þ ε22 ðωÞ

where a(ω) represents the absorption coefficient, n(ω) represents refractive index, R(ω) represents reflectance, and L(ω) represents energy loss spectrum, respectively.

And the formula of ε2(ω) is as follows:

ε2 ðωÞ ¼

(5)

GW C W Se

0

-1

G

M

K

G

-2

PDOS

(c)

G

M

K

G

PDOS

(d)

Fig. 2. The band structures and PDOS of (a) GW, (b) GW-Vse, (c) GW-Vw and (d) GW-Vse-double. The Fermi level is set to zero. 3

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Physica E: Low-dimensional Systems and Nanostructures 116 (2020) 113729

30

15

GW GW-Vse GW-Vw GW-Vse-double

24 20 2

16 12

10

8

5 0

WSe2

28

GW GW-Vse GW-Vw GW-Vse-double

20 1

32

WSe2

25

4

0

1

2

3

4

Energy(eV)

0

5

(a)

0

1

2

3

Energy(eV)

4

5

(b)

Fig. 3. (a) The real part of the dielectric constant ε1(ω), (b) the imaginary part of the dielectric constant ε2(ω). The black, red, orange, green, blue line represent WSe2, GW, GW-Vse, GW-Vw, and GW-Vse-double systems, respectively. 0.8

WSe2

1.0

WSe2

5

0.6

GW GW-Vse GW-Vw GW-Vse-double

GW GW-Vse GW-Vw GW-Vse-double

0.4 0.2

4

0.0 0

1 2 3 4 Energy(eV)

5

n( )

( ) /106

1.5

3

0.5 2 0.0

0

5

10

15

20

25

Energy(eV)

1

30

WSe2

4

5

GW GW-Vse GW-Vw GW-Vse-double

0.3 0.2 0.1 0

0.2

0.3 1 2 3 4 Energy(eV)

5

0.2 0.1

0.1 0.0

3

WSe2

0.4

0.4

L( )

R( )

0.3

2

(b)

0.5

GW GW-Vse GW-Vw GW-Vse-double

0.4

1

Energy(eV)

(a) 0.5

0

0

5

10

15

20

Energy(eV)

(c)

25

0.0

30

0

1

2

3

Energy(eV)

4

5

(d)

Fig. 4. (a) Absorption coefficient a(ω), (b) the refractive index n(ω), (c) the reflectance R(ω), and (d) the energy loss spectrum L(ω). The black, red, orange, green, blue lines represent WSe2, GW, GW-Vse, GW-Vw, and GW-Vse-double systems, respectively.

smaller than that in GW. Next, we discuss the band structure and the partial density of states (PDOS) after the GW are formed and the vacancies are introduced, as shown in Fig. 2. Energy band coupling between the graphene and the WSe2 will make the electronic structure of the WSe2 change after the GW heterostructure is formed. Also, compared with the GW heterostructure, W or Se vacancy has significant effects on the energy band and the PDOS. Three impurity levels appeared both in GW-Vse and GW-Vsedouble system, as shown in Fig. 2 (b) and (d). When W vacancy is introduced, the impurity levels pass through the Fermi level, as shown in Fig. 2 (c), which indicating the exhibition of metallic behavior. The electronic structures of WSe2 change significantly both from the for­ mation of the heterostructure and the introduction of the vacancies, so it

is meaningful to study their effects on the optical properties. For the optical properties of these systems, we calculate them in the parallel and vertical directions based on the anisotropic of GW. It is found that the changes of the optical properties caused by the formation of heterostructures and the introduction of vacancies are not obvious in the vertical direction, so only the optical properties in the parallel di­ rection are discussed. The ε1(ω) is the real part of the ε(ω) and represents the energy storage term of the material. The displacement polarization inside the material has a huge impact on ε1(ω). We can see from Fig. 3(a) that ε1(ω) changes significantly after the heterostructure is formed, and the values in each energy range are increased, also a little red shift oc­ curs. The peak of WSe2 appears around 1.5 eV, while the peak of GW appears at 0.8 eV. Moreover, the peak sizes of the two systems are also 4

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Physica E: Low-dimensional Systems and Nanostructures 116 (2020) 113729

significantly different, WSe2 is about 5, and GW is about 8. After va­ cancies are introduced, it is found that the change of ε1(ω) at the low energy region is obvious, and the images after 5eV are basically coin­ cident, so we focus on the low energy zones. The introduction of va­ cancies will bring different degrees of red shift and different peak increase, and effects of the W vacancies (GW-Vw system) is most obvious. After the introduction of the W vacancy, the first peak changes to bigger than 30, and it is only 10 both for GW-Vse and GW-Vse-double system. All these peak values are higher than those of the pure GW. As shown in Fig. 3 (b), for the imaginary part of the dielectric constant ε2(ω), it is found that the threshold of ε2(ω) for WSe2 has a value at about 1.5eV, and it becomes 0eV after the formation of the heterostructure. The ε2(ω) value of the heterostructure is higher than that of WSe2 over the entire energy region. Comparing the positions of the first peak, there is also obvious red shift after the formation of the heterostructure and the introduction of the vacancies. The red shift and peak change caused by the introduction of W vacancies are greater than the effects of introducing Se vacancies. In general, building of the heterostructures or introducing of the W or Se vacancies in GW will lead to changes of the ε(ω), red-shift appears and the values of ε(ω) become larger than that in WSe2. Fig. 4 (a) shows the absorption coefficient a(ω). The loss or gain of the absorption coefficient of the material is closely related to ε2(ω). After the heterostructure is formed, less energy can be used to excite photo­ electrons to generate absorption, which is also consistent with the ε2(ω). As the energy increases, we see that the value a(ω) of the GW hetero­ structure is still higher than that of WSe2. In particular, when the energy is higher than 20 eV, the pure WSe2 no longer absorb, however, the GW heterostructure still has a high a(ω) until the energy is increased to 23 eV. This shows that the formation of the heterostructure does have a significant effect on the absorption spectrum of the system. When the vacancies are introduced, the absorption coefficient of the system un­ dergoes a significant red shift, especially in GW-Vw system. GW-Vw can absorb near 0 eV, however, WSe2, GW, GW-Vse, and GW-Vse-double absorb at around 0.6 eV, indicating that in the infrared region, the introduction of the W vacancy has a significant improvement effect of the absorption coefficient. In the visible range of 2.4 eV (corresponding to 517 nm) and after 2.9 eV (corresponding to 428 nm), the GW heter­ ostructure with vacancies have a more obvious absorption. According to Equation (4), it is found that the refractive index n(ω) is essentially related to the ε1(ω) and ε2(ω). In general, the refractive index image and the real part of the dielectric constant image discussed in Fig. 4 (a), are almost identical, including the overall trend and the peak positions, and the only difference is the size of the peak. The influence of ε1(ω) on n(ω) plays a major role, and this conclusion can be obtained by comparing the trends of Figs. 3(a) and 4(b). Formation of the hetero­ structure has great influence on the refractive index n(ω), especially in 0–5eV. After the heterostructure is formed, the values of the n(ω) at the infrared, visible light and part of the ultraviolet light regions are significantly improved. The n(ω) curve undergoes a significant red shift when vacancies, especially a W vacancy is introduced. Fig. 4(c) is the reflectance R(ω) of the system. In most cases, the R(ω) of the GW heterostructure is higher than that of the WSe2 system, especially at the low energy region. When the energy is greater than 20eV, the WSe2 system is almost no longer reflected, and at the same time, the GW has almost no R(ω) value after 25eV. Red shift and peak increase of R(ω) appear when the vacancies are introduced, especially in the low energy region. Compared with the GW, GW-Vw has the most obvious redshift and its first peak has the biggest value of 0.6, so W vacancy has the most obvious effect in GW heterostructure. The energy loss spectrum L(ω) is shown in Fig. 4(d). It is found that L (ω) in GW has a significant red shift compared with that in WSe2. The starting position has a value from 0.8 eV of WSe2 to 0.5 eV of GW. The change of their peak values is not obvious. In the low energy area which we are interested in, it is found that the first peak of the L(ω) in pure GW heterostructure is around 2eV with a value of 0.06. The peak of L(ω)

shifts to the left when Se vacancies are introduced, which means redshift appears. However, the peak value does not change much. For GW-Vw system, the first peak is located around 0.5eV, so the redshift in this case is the biggest one, and the peak value reaches to 0.14, which means that W vacancy has the most important impaction on the energy loss spectrum. 4. Conclusion In this article, we focus on the effects of W or Se vacancies on the electronic structure and optical properties of GW heterostructures under first-principles calculations. We have found that the formation of het­ erostructures, the optical properties will be significantly improved, and this improvement is mainly for parallel optical parameters, however, the change in the vertical direction is less obvious. The optical properties of the GW system will change significantly and different degrees of red shift appears when W or Se vacancies are introduced. It is found that the effects of the W vacancy is greater than that of the Se vacancies. The construction of the GW heterostructure and the introduction of the W or Se vacancies will all improve the optical properties compared with the single-layer WSe2, which provide an effective strategy to tune perfor­ mance of two dimensional optical nanodevices. Funding This work was supported by the National Natural Science Foundation of China (Grant Nos. 11674197 and 11974215) and the Natural Science Foundation of Shandong Province (Grant Nos. ZR2018MA042). Acknowledgments B.Q. did the calculations and wrote the paper, X.Z. collected the references, G.H. prepared the figures, W.Y. and X.Y. analyzed the data, J. R. generated the research idea. All authors read and approved the final manuscript. References [1] B. Cai, S. Zhang, Z. Hu, Y. Hu, Y. Zou, H. Zeng, Tinene: a two-dimensional Dirac material with a 72 meV band gap, Phys. Chem. Chem. Phys. 17 (2015) 12634–12638. [2] W. Wei, T. Jacob, Strong many-body effects in silicene-based structures, Phys. Rev. B 88 (2013), 045203. [3] C. Mattevi, H. Kim, M. Chhowalla, A review of chemical vapour deposition of graphene on copper, J. Mater. Chem. 21 (2011) 3324–3334. [4] X. Duan, C. Wang, J.C. Shaw, R. Cheng, Y. Chen, H. Li, X. Wu, Y. Tang, Q. Zhang, A. Pan, J. Jiang, R. Yu, Y. Huang, X. Duan, Lateral epitaxial growth of twodimensional layered semiconductor heterojunctions, Nat. Nanotechnol. 9 (2014) 1024–1030. [5] Z. Yin, H. Li, H. Li, L. Jiang, Y. Shi, Y. Sun, G. Lu, Q. Zhang, X. Chen, H. Zhang, Single-Layer MoS2 Phototransistors, ACS Nano 6 (2012) 74–80. [6] C. Tan, Z. Lai, H. Zhang, Ultrathin two-dimensional multinary layered metal chalcogenide nanomaterials, Adv. Mater. 29 (2017), 1701392. [7] Q.H. Wang, K. Kalantar-Zadeh, A. Kis, J.N. Coleman, M.S. Strano, Electronics and optoelectronics of two-dimensional transition metal dichalcogenides, Nat. Nanotechnol. 7 (2012) 699–712. [8] W. Liu, J. Kang, D. Sarkar, Y. Khatami, D. Jena, K. Banerjee, Role of metal contacts in designing high-performance monolayer n-type WSe2 field effect transistors, Nano Lett. 13 (2013) 1983–1990. [9] W.H. Baugher, H.O.H. Churchill, Y. Yang, P. Jarillo-Herrero, Optoelectronic devices based on electrically tunable p-n diodes in a monolayer dichalcogenide, Nat. Nanotechnol. 9 (2014) 262–267. [10] A. Pospischil, M.M. Furchi, T. Mueller, Solar-energy conversion and light emission in an atomic monolayer p-n diode, Nat. Nanotechnol. 9 (2014) 257–261. [11] H. Fang, S. Chuang, T.C. Chang, K. Takei, T. Takahashi, A. Javey, Highperformance single layered WSe2 p-FETs with chemically doped contacts, Nano Lett. 12 (2012) 3788–3792. [12] R. Addou, R.M. Wallace, Surface analysis of WSe2 crystals: spatial and electronic variability, ACS Appl. Mater. Interfaces 8 (2016) 26400–26406. [13] M.P. Deshpande, G.K. Solanki, M.K. Agarwal, Optical band gap in tungsten diselenide single crystals intercalated by indium, Mater. Lett. 43 (2000) 66–72. [14] V. Podzorov, M.E. Gershenson, C. Kloc, R. Zeis, E. Bucher, High-mobility fieldeffect transistors based on transition metal dichalcogenides, Appl. Phys. Lett. 84 (2004) 3301–3303.

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