Defects and strain engineering the electronic structure and magnetic properties of monolayer WSe2 for 2D spintronic device

Applied Surface Science 497 (2019) 143788

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Defects and strain engineering the electronic structure and magnetic properties of monolayer WSe2 for 2D spintronic device

T

⁎

Jiaxin Ye, Yukai An , Hui Yan, Jiwen Liu Key Laboratory of Display Materials and Photoelectric Devices, Ministry of Education, Tianjin Key Laboratory for Photoelectric Materials and Devices, National Demonstration Center for Experimental Function Materials Education, School of Material Science and Engineering, Tianjin University of Technology, Tianjin 300384, China

A R T I C LE I N FO

A B S T R A C T

Keywords: Structural defects Biaxial strain Electronic structure Magnetism

The electronic structure and magnetic properties of vacancy or antisite defect doped monolayer WSe2 with tensile strain from 0% to 10% were investigated systematically by using first-principles calculations. Among the unstrained defective configurations, including VSe, VSe2, VW, VW2, VWSe3, VWSe6 and SeW, only the VWSe6 complex defects display obvious spin polarization with half-metallicity and induce an amazing spin magnetic moment of 5.94 μB, which originates from the environment-induced W 5d orbital electron delocalization due to the loss of Se atoms. As tensile strain increases, the nonmagnetic VSe, VW and VW2 defective configurations transform to the magnetic state. This transition is due to the relative change of atomic spatial position, leading to further electron delocalization as well as the alteration of bonding effects around the vacancies. It can be predicted that strain can effectively drive the occurrence of spin polarization within the pressure range that the material can withstand through facilitating electron delocalization of W atoms in the defective monolayer WSe2.

1. Introduction Recently, atomically thin two-dimensional (2D) materials have attracted tremendous attention due to their potential applications in field effect transistors, flexible electronic devices, sensors, biocatalysis and so on [1–3]. As the members of 2D family, graphene and transition metal dichalcogenides (TMDs) own strong reciprocal effect among atoms in a plane, but only weak Van der Waals interaction between the layers [4,5]. So far, graphene has been extensively studied due to unique two-dimensional crystalline structure and distinctive physical properties. However, the intrinsic zero band gap and weak spin-orbit coupling limit its applications in the fields of 2D materials. In contrast, TMDs with single-layer stability exhibit extraordinary mechanical, electrical and optical properties, and have become the ideal candidates for the applications of nanoscaled semiconductor devices [6,7]. Tungsten diselenide (WSe2), composed of Se-W-Se sandwich structure in a layer, is a typical layered TMDs [8]. Multilayer WSe2 is an indirect bandgap semiconductor, while monolayer WSe2 is a direct bandgap material with strong spin/valley coupling, accompanied by an extension of forbidden band from 1.0 eV to 1.6–1.7 eV [9,10]. As is well known, there exist a great deal of point defects in CVD grown TMDs due to the highly non-equilibrium growth process. The introducing of defects in TMDs can give rise to the changes in the atom interaction and local electron mobility, and even break the degeneration of some ⁎

atomic orbitals (mainly for d-orbital) [11,12]. Until now, limited reports are available in the monolayer WSe2 with different structural defects. The effect of defects on the electronic structure and magnetic properties is still not clear. The measurements like exerting stress [13–15], element doping [16–20] and substrate environment changing [21–24], have been considered as a magical remote in 2D materials for functional applications, because they can intensify electron-hole excitation and broaden the motion area of some electrons. Element doping is effective to activate the ferromagnetism in some 2D systems, but it also complicates the matters both in experiment and in explanation. Among them, strain can well meet the requirement of regulating band gap and inducing spin polarization without introducing impurity atoms. For examples, monolayer MoS2 has better elasticity than graphene under elastic strain, accompanied with the direct-indirect bandgap transition and semiconductor-metal transition [25]. The monolayer VX2 (X = S, Se) shows an exciting ferromagnetic behavior, and its magnetic coupling increases rapidly with the increase of isotropic strain [26]. Strain can also effectively separate the contributions of interface and valley states into the conductivity of monolayer WTe2, showing an obvious electric field dependence [27]. In addition, strain has made great contributions in inducing Raman activity, improving the performance of double gate field effect transistors (DGFETs) [28], changing the thermal conductivity of materials [29], and causing some shifts in optical spectra [30]. Obviously, strain plays an important role

Corresponding author. E-mail address: [email protected] (Y. An).

https://doi.org/10.1016/j.apsusc.2019.143788 Received 5 April 2019; Received in revised form 22 August 2019; Accepted 23 August 2019 Available online 24 August 2019 0169-4332/ © 2019 Elsevier B.V. All rights reserved.

Applied Surface Science 497 (2019) 143788

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in engineering the electronic structure and magnetic properties of 2D materials by changing the bond length, bond angle as well as the coupling effect of electron-phonon [31,32]. In this letter, a series of vacancy and antisite defects, including VSe, VSe2, VW, VW2, VWSe3, VWSe6 and SeW, are fabricated on the monolayer WSe2. Furthermore, biaxial tensile strain is applied to all the defective monolayer WSe2. We comprehensively investigate the effects of defects and strain on the electronic structure, electron charge distribution and magnetic properties of the defective monolayer WSe2 by density functional theory. The defects and strain can effectively induce and drive the occurrence of spin polarization. These results give an important guidance for further experimental investigations of monolayer WSe2-based magnetic devices.

Table 1 Total energy (ETotal), magnetic moment (μ), formation energy (ΔEf) of the pristine and defective monolayer WSe2 configurations, respectively. System

ETotal (eV)

−345.946 −339.774 −334.048 −327.722 −311.603 −331.120 −313.219 −293.574

Pristine VSe VSe2 VW VW2 SeW VWSe3 VWSe6

△Ef (eV)

μ (μB)

W-rich

Se-rich

– 0.766 1.085 7.416 12.726 9.424 5.699 9.124

– 3.006 5.564 2.935 3.767 2.705 7.939 18.083

0 0 0 0 0 0 0 5.940

2. Computational methods and models

18

Formation Energy (eV)

The Vienna ab-initio simulation package (VASP) was carried out within the spin-polarized density functional theory framework using generalized gradient approximation (GGA) functionals such as PerdewBurke-Enrzerhof (PBE). A vacuum layer of 15 Å was adopted in the direction perpendicular to the monolayer surface to avoid the interactions between periodic slabs. The optimization was self-consistent with all the configurations fully relaxed starting from experimental lattice constants a = b = 3.286 Å and c = 12.980 Å in P63/mmc space group symmetry with the W atoms having a trigonal prismatic coordination with the Se atoms. The position of all the atoms was relaxed until the Hellmann–Feynman force was less than 0.02 eV/Å. A plane-wave energy was expanded with a cutoff energy of 500 eV, and the energy convergence criteria in the self-consistency process was set to 10−5 eV, using Gaussian smearing with a width of 0.05 eV. A 4 × 4 × 1 Monkhorst-Pack k-point mesh was selected in Brillouin zone, containing 16 W atoms and 32 Se atoms. Tensile strain was considered in x0y plane for all the models. The mesh of k space was increased to 9 × 9 × 1 in the band structure and density of state (DOS) calculations.

VWSe6

15 12

VW2

SeW

9

VWSe3

VW 6 3 0

VSe2 VSe -5.2

-4.8

-4.4

-4.0

-3.6

-3.2

Se Chemical Potential (eV)

3. Results and discussion

Fig. 2. The relationship between formation energy and Se chemical potential for the defective monolayer WSe2 configurations.

The optimal lattice parameters are, a0 = b0 = 3.322 Å for the pristine monolayer WSe2, as shown in Fig. 1(a)–(b), which is consistent

Fig. 1. Top views of the optimized structure of the pristine and defective configurations (VSe, VSe2, VW, VW2, SeW, VWSe3 and VWSe6) for the monolayer WSe2. Cyan and orange balls stand for W and Se atoms, respectively. 2

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J. Ye, et al.

(a) Pristine 2

(b) VSe

(c) VSe2

(d) VW

Energy (eV)

1 Eg=1.670 eV

0

-1

-2 F

B

G F

(e) VW2

2

Energy (eV)

g

g

B

G F

(f) SeW

g

B

G F

(g) VWSe3

g

B

G

(h) VWSe6

1

0

-1

-2

F

g

B

GF

g

B

GF

g

B

G F

g

B

G

Fig. 3. Band structure of the pristine and defective monolayer WSe2 configurations, respectively. Fermi energy level is set at Ef = 0 eV.

defective or doped atom, respectively. The chemical potential of the atoms is different in the Se-rich and W-rich situations. In the case of a W atom, μW in W-rich condition stands for its stable energy in the reducing atmosphere, while in Se-rich condition refers to the deviation of its energy from the normal stoichiometric ratio in the atmosphere of extreme oxidation. Total energy and formation energy of monolayer WSe2 with different defective configurations are set out in Table.1. The Se chemical potential dependence of the formation energy for different defective configurations is shown in Fig. 2. It is perceived that the formation energy for the monolayer WSe2 with the cationic vacancies (VW and VW2) as well as the antisite defect (Sew) is low in the Se-rich environment. On the contrary, the formation energy of anionic vacancies (VSe and VSe2) are much lower under the W-rich environment. Besides, the Se vacancy has the lowest formation energy in any extreme environment, suggesting that VSe is the relatively stable defect and

with the previous results [33]. Optimized structures of unstrained defective monolayer WSe2 configurations are shown in Fig. 1(c)–(i), including a selenium vacancy (VSe), two selenium vacancies attached to the same tungsten atom (VSe2), a tungsten vacancy (VW), two tungsten vacancies (VW2), a selenium atom substituting for a tungsten atom (SeW), the vacancy complex of one tungsten atom and three selenium atoms nearby (VWSe3) and the vacancy complex of one tungsten atom and six selenium atoms nearby (VWSe6). To evaluate the stability of 2D materials, the formation energy (Ef) of monolayer WSe2 with different defective configurations is defined as ΔE = E(defect)-E(pristine) + N1·μ(defective atom)-N2·μ(doped atom), where E(defect) and E(pristine) refer to the total energy of the defective and pristine monolayer WSe2 configurations, N1 and N2 are the number of the atoms removed from or inserted into the system, μ(defective atom) (i.e., μW and μSe) and μ(doped atom) are the relevant chemical potential of 3

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DOS (States/eV)

90

90

(a) Pristine

60

60

30

30

30

0

0

0

TDOS W 5d Se 4p

-60 -90 -6 60

60

-30

-30

DOS (States/eV)

90

(b) VSe

-4

-2

-90 2

-6 90

(e) VW2

60

-30

TDOS W 5d Se 4p

-60 -6

-4

-2

0

-4

-2

0

4 60

Energy (eV)

30

30

0

0

-30

-30

TDOS W 5d Se 4p -6

-4

-2

0

-4

-2

4

-90

0

-6

4 60

-4

-2

0

2

4

2

4

(h) VWSe6

30 0 -30

TDOS W 5d Se 4p -6

-4

-2

0

Energy (eV)

Energy (eV)

TDOS W 5d Se 4p

-60 2

(g) VWSe3

-60 2

-30

TDOS W 5d Se 4p -6

90

-90 4

0

-90 2

(f) SeW

-60 2

30

-60

30 0

(d) VW

-30

TDOS W 5d Se 4p

-60

0

60

(c) VSe2

TDOS W 5d Se 4p

-60 -90 2

4

-6

-4

-2

0

Energy (eV)

Fig. 4. TDOS and PDOS of W 5d and Se 4p orbitals of the pristine and defective monolayer WSe2 configurations, respectively. Fermi energy level is set at Ef = 0 eV.

characteristic transitions, namely, the transition of direct-to-indirect band-gap in the VW2, SeW and VWSe6 configurations as well as the nonmagnetic-to-magnetic transition in the VWSe6 configuration. The obvious energy level splitting can be observed near the Ef between the spin-up and spin-down channels, indicating the existence of spin polarization for the VWSe6 configuration, as shown in Fig. 3(h). Especially, the spin-down VB maximum shifts down across the Ef and exhibits metallicity, while the spin-up channel remains semiconducting with a gap of 0.98 eV for the VWSe6 configuration, revealing a good half-metallic character. To further verify the electronic structure and magnetic properties of the pristine and defective monolayer WSe2, the DOS, as a visual result of the band structure, is also plotted in Fig. 4. For the pristine monolayer WSe2, the spin up state is exactly equal to the spin down state, indicating that there does not exist spin polarization. The W 5d states significantly overlap with the Se 4p states in the whole energy range, implying the forming of strong WeSe covalent bonds. In addition, there seems to be pseudogaps for the SeW, VW and VW2 configurations, indicating a certain covalent relationship between the atoms that miss the WeSe bond around the defects. That is, those who constitute the atomic orbital are the contributors of these impurity bands. The VWSe3 and VWSe6 vacancy complexes include one W vacancy and three or six Se vacancies, which can be observed in some systems using Transmission Electron Microscope (TEM). Obviously, the band gap Eg largely decreases and the Ef shifts to the VB with the increase of Se vacancies, implying a higher concentration of holes. For all the defective configurations, only VWSe6 shows the high spin magnetic moments of 5.940μB, with is consistent with the previous theoretical results (6 μB) for the VMoS6 in the MoSe2 monolayer [34]. The DOS curves of other configurations are completely symmetrical without spin polarization, implying a non-magnetic state. The spin density distribution for the VWSe6 defect configuration is shown in Fig. 5. It can be seen that the magnetic moment mainly derives from the W atoms around the vacancies. The adjacent two W atoms form metallic bonds due to short WeW atom distance, but there still exist many unsaturated localized electronic states originating from the loss of Se atoms for the six W atoms around the vacancies. After double axial tensile strain is applied to all the defective

Fig. 5. The spin density distribution of VWSe6 defect configuration. (The isosurface value is 0.003 eV/Å3). Black and green balls stand for W and Se atoms, respectively.

easily spontaneously form under thermodynamic equilibrium conditions. The complex defects, VWSe3 and VWSe6, have very high formation energy in the whole Se chemical potential range among the considered structural defects, which are thermodynamically unfavorable under equilibrium conditions. However, they are possibly induced in some non-equilibrium processes like e-beam lithography. Fig. 3 illustrates the results of unfolded band structure of the pristine and defective monolayer WSe2 configurations at their equilibrium lattice constants. It is obvious that the pristine monolayer WSe2 is a direct bandgap semiconductor with a band gap of 1.670 eV, which is consistent with previous results [10]. Compared with the pristine case, all the defective configurations introduce some impurity bands inside the band gap, resulting in the decrease of band-gap in some degree. The impurity bands are near below the conduction band (CB) minimum for the VSe and VSe2 configurations, indicating the effective n-type doping. In contrast, the acceptor levels for the cation vacancy configurations, namely VW and VW2, are close to the valence band (VB) maximum, showing a p-type character. This is consistent with the anticipation that monolayer WSe2 in W-rich and Se-rich conditions can result in the nand p-type behavior, respectively. Moreover, it is accompanied by two 4

Applied Surface Science 497 (2019) 143788

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(b) VW

1.2

d/d0

1.6

1.3

(a) VSe

d/d0

1.8 1.4 1.2

1.1

1.0

1.0

2

3 2

1

1

0

0 0

1.2

2

4

6

8

0

10

(c) VW2

1.0

3.5 2.8 2.1 1.4 0.7

3

12

d/d0

d/d0

1.1

2

4

6

8

6

8

10

(d) VWSe6 da/da0 db/db0

9

2

6

1

3

0 0

2

4

6

8

10

0

2

4

10

Fig. 6. The dependence of magnetic moments and parameter d/d0 on the strain ε% for the monolayer WSe2 with VSe, VW, VW2 and VWSe6 configurations. Insets are the optimized structures of five defective configurations under the representative strain.

the Se vacancy. The spin density distribution, as shown in Fig. 8(a), also indicates that the magnetic moment of VSe under 10% strain mainly comes from the three W atoms around the Se vacancy. Different from the case of VSe, the electron accumulation in the Se atoms around the W vacancy gradually increases with the increase of strain, as shown in Fig. 7(b), suggesting that there exists electronic delocalization among the W atoms under strain, leading to the formation of dangling bonds of edge atoms. Similarly, it's also an important feature for the VW2 configuration, as shown in Fig. 7(c). Beyond that, the two Se atoms in the middle of VW2, which covalently bond with each other by sharing electrons, become electronegative through covalent bonding with the adjacent W atoms nearby under 8% and 10% strain. It means that the strain gives rise to the change of atomic interaction, together with the formation of the delocalized W 5d electrons around the vacancy. Therefore, the delocalized W atoms and the Se atom with localized unpaired electrons in the VW and VW2 configurations contribute the majority magnetic moment, as shown in Fig. 8(b) and (c). As for the VWSe6 configuration, the neighboring W atoms at the corners of vacancy are metallically bonded with each other until the strain increases to 6%. Correspondingly, da/da0 and db/db0 also almost remain unchanged, as shown in Fig. 6(d), thus, the magnetic moment stably maintains 5.940 μB. When the strain increases to 8%, it is obvious that the metallic bonds between neighboring W atoms become weak, which increases the number of the unpaired 5d electrons of W atoms around the vacancy and leads to a large magnetic moment of 11.702 μB, as shown in Fig. 8(d). As the strain further increases to 10%, da/da0 remarkably increases and db/db0 decreases, resulting that the neighboring W atoms at the corners of vacancy again form stronger WeW metallic bonds. This means that the unsaturated W 5d electrons around the vacancy are paired, corresponding to the large decrease in magnetic moment

configurations, the magnetic moments are also observed in the VSe, VW and VW2 configurations. The strain is given by ε% = (c-c0)/c0, where c0 and c are the unstrained and constrained lattice constants, respectively. Here, a parameter d/d0 is defined to quantify the evolution of the local geometry of structural defects under the strain, where d0 and d are the distances between the two adjacent W atoms before and after stretching, as shown in Fig. 6. It is clear that the VSe configuration remains non-magnetic until the strain is less than 10%. When the strain increases to 10%, the spin polarization is prominent, leading to a transition from non-magnetic to magnetic with a magnetic moment of 2.1 μB. Unlike the case of VSe configuration, the magnetic moment of VW and VW2 configurations gradually increases with the increase of strain. For the VWSe6 configuration, which has exhibited magnetism at 0% strain, its magnetic moment reaches the maximum at 8% strain, then remarkably decreases at 10% strain. The biaxial strain can remarkably change the bond length and bond angle of 2D materials, leading to great changes in electron transfer. In order to further understand the evolution of chemical bond with strain, the cross-sectional views of the (001) plane of the difference charge density for the VSe, VW, VW2 and VWSe6 defect configurations under different strain are shown in Fig. 7(a)–(d). For the VSe configuration, as shown in Fig. 7(a), it is obvious that there exist the electron accumulation among the three W atoms around the Se vacancy, suggesting that the W atoms form WeW metallic bonds each other under 0% strain. As the strain increases, the electron accumulation among the W atoms gradually become weak and complete disappear under 10% strain. This implies that the WeW metallic bonds around the Se vacancy break, which is consistent with the remarkable increase of d/d0 under 10% strain, as shown in Fig. 6(a). The breaking of WeW metallic bonds results in forming the unpaired 5d electrons in these W atoms around

5

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Fig. 7. Cross-sectional view of the (001) plane of the difference charge density of VSe, VW, VW2 and VWSe6 defect configurations under strain. (Red and blue represent the accumulation and loss of charge, i.e., the distribution of W and Se atoms in the red circle and the yellow oval, respectively. The black line is a contour of 0.077 in the range of 0 to 0.2.)

Fig. 8. The maximum spin density distribution for the monolayer WSe2 with the VSe, VW, VW2 and VWSe6 defect configurations. (The isosurface value is 0.003 eV/Å3). Black and green balls are the W and Se atoms, respectively.

clearly observed both in W 5d and Se 4p orbitals, as shown in Fig. 9(a). Similarly, the magnetic interaction could be also explained by p-d orbital hybridization and slight spin splitting for the VW and VW2 configurations under large strain. The degree of spin splitting of W 5d orbital and Se 4p orbital in the VWSe6 configuration is the largest. The wave functions between two adjacent atoms are different. In the process of being stretched, the relative position of atoms would affect the overlap of their wave functions, leading to d-d orbital hybridization and

around VWSe6. The DOS curves for the VSe, VW, VW2 and VWSe6 defect configurations with the maximum magnetic moment are also discussed to visualize the distribution of net magnetic moments, as shown in Fig. 9. For the VSe configuration, the p-d hybridization between Se 4p orbital in the z direction and W 5d orbital in the y0z and x0z planes makes a major contribution on spin-polarization, which is consistent with the results of difference charge density. Moreover, the spin splitting is 6

Applied Surface Science 497 (2019) 143788

J. Ye, et al.

(a) 10% VSe

0

dxy

dyz

dzx

dx -y 2

dz

2

2

25 0

px

-25

W 5d Se 4p

(c) 8% VW

15

-40 -80

W 5d Se 4p

(e) 10% VW2

40 0 -40 -80 80

py

pz

(d) 8% VW

0

0

80

(b) 10% VSe

-25

40

DOS (States/eV)

25

W 5d Se 4p

PDOS (states/eV)

120 80 40 0 -40 -80 -120 80

-15

dxy

dyz

dzx

dx -y 2

dz

2

2

35 0

px

-35

py

pz

(f) 10% VW2

20 0 -20

dxy

dyz

dzx

dx -y 2

2

dz

2

dz

2

25 0 -25 -50 15

W 5d Se 4p

(g) 8% VWSe6

40

py

pz

(h) 8% VWSe6

0

0

-15 15

-40

dxy

dyz

dzx

dx -y 2

2

0

-80

-2

px

px

-15

-1

0

Energy (eV)

1

2

-2

-1

py 0

Energy (eV)

pz 1

2

Fig. 9. TDOS and PDOS of W 5d and Se 4p orbitals for the VSe, VW, VW2 and VWSe6 defect configurations under strain, respectively. Fermi energy level is set at Ef = 0 eV.

metallic bonds steadying.

Acknowledgments

4. Conclusions

This work was supported by Tianjin Natural Science Foundation of China (Grant No. 17JCYBJC17300). References

In general, the spin-polarization induced magnetic moment and the change of electronic structure for the unstrained and strained monolayer WSe2 with vacancy or antisite defects are systematically investigated by using first-principles calculations. It was found that the VSe, VSe2, VW, VW2 and VWSe3 doped monolayer WSe2 systems are nonmagnetic, and only VWSe6 doped systems are magnetic under 0% strain. The VWSe6 complex defects exhibit magnetic half-metallicity and induce a large magnetic moment of 5.940 μB due to the unsaturated 5d electrons of W atoms around the vacancy. After applying biaxial stress, the VSe, VW and VW2 doped monolayer WSe2 systems also exhibit magnetism. The variation of bond length and bond angle of defective monolayer WSe2 under strain leads to the 5d electron delocalization of W atoms around the vacancy and further induces the magnetic moment. These results enrich our understanding of the strained monolayer TMDs and lay a foundation for developing applications exploiting their straindependent spintronics, including the strain detection and transistor switching modulation of logic circuit.

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