Tunable Electronic Properties of Arsenene and Transition-Metal

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Tunable Electronic Properties of Arsenene and Transition-Metal Dichalcogenides Heterostructures: A First Principles Calculation Mingming Dong, Cheng He, and Wenxue Zhang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b05650 • Publication Date (Web): 20 Sep 2017 Downloaded from http://pubs.acs.org on September 24, 2017

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The Journal of Physical Chemistry

Tunable electronic properties of arsenene and transition-metal dichalcogenides heterostructures: A first principles calculation M. M. Dong1, C. He1∗, W. X. Zhang2* 1

State Key Laboratory for Mechanical Behavior of Materials, School of Materials

Science and Engineering, Xi’an Jiaotong University, Xi’an 710049, China 2

School of Materials Science and Engineering, Chang’an University, Xi’an 710064,

China Abstract The structural and electronic properties of arsenene and monolayer transition-metal

dichalcogenides

(β-As/MX2)

heterostructures

have

been

systematically investigated by density functional theory. It is found that all of β-As/MX2 heterostructures with little lattice mismatch possess considerable band gaps. Their electronic properties can be effectively tuned via (biaxial or uniaxial) strain and electric field, but the variation trends are different. The band gaps of the β-As/MX2 heterostructures decrease linearly as the strain arises, while there is a Stark effect of the band gap under suitable electric field due to the spontaneous electric polarization in the heterostructures. Meanwhile, a series change of the semiconductor types of the β-As/MX2 heterostructures could also be obtained by the strain and electric field. These diverse electronic properties may provide a potential application in nanodevices based on arsenene and transition-metal dichalcogenides.

*

Corresponding Authors: C. He ([email protected]), or W. X. Zhang ([email protected]) 1

ACS Paragon Plus Environment


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Introduction In recent years, two-dimensional (2D) materials show excellent electronic, optical and mechanical properties that make them potentially useful in information and energy devices. Besides the intensely studied graphene,1,2 hexagonal boron nitride (h-BN),3,4 MoS2,5,6 silicone,7 phosphorene8-11 and arsenene12-14 have also attracted great attentions in their potential application in nanodevices. Tuning 2D materials’ band gaps ranging from insulator to metal based on their layer thickness can be employed

in

broadband

photonic

device

applications.15

The

monolayer

transition-metal dichalcogenides (TMDs) are widely investigated due to this purpose. The bulk TMDs have indirect band gaps, whereas the monolayer TMDs have direct band gaps, resulting in a significant change in its photoelectric properties. TMDs, with the general form MX2, where M is a transition metal from groups IV-X and X is a chalcogen, have extraordinary mechanical, thermal, optical, electronic and chemical properties.16 Su et al. have investigated the electronic structures of 2D TMDs nanosheets under different out-of-plane pressure, and found that the band gaps of all the nanosheets decrease with the increasing of pressure.17 It is reported that the monolayer or few-layer MoS2 could exhibit an excellent on/off ratio and room-temperature

mobility.18

You

et

al.

have

found

that

the

black

phosphorene/monolayer transition-metal dichalcogenides heterostructures can be applied in p-n diode and logical devices.19 Very recently, arsenene, which is single-atom-thick layer of gray arsenic, has been proposed as an new member of group-V nanosheets.20,21 Arsenene and 2


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antimonene have a larger band gap than most other 2D materials. At the same time, each atom of them follows eight electrons coordination, and self-adjusting forms a highly stable wavy 2D structure. These electronic structural features indicate that arsenene and antimonene have potential applications in blue light detectors, LEDs, lasers and even can be used as flexible sensors.21 α-As (puckered honeycomb structure analogous to black phosphorene) and β-As (buckled honeycomb structure analogous to blue phosphorous10 and known as gray arsenene) keep their structural similarities with monolayer arsenene allotropes.22 β-As due to its high stability is being studied the most. Interestingly, it was reported that free-standing arsenene and antimonene experience an intriguing indirect-to-direct band gap transition under biaxial strain effect.23 Yan et al. gave a detailed investigation on the electronic structure and carrier mobility of arsenene nanosheet and nanoribbon.24 In addition, Tang et al. investigated the structures and electronic properties of fully-halogenated arsenenes and they revealed the presence of Dirac cone in fully-halogenated arsenene compounds.25 At present, the experimental study on arsenene has also been carried out, Tsai et al synthesized arsenene phase by using InAs (001) substrates and estimated the band gap of multilayer arsenene.26 Although monolayer nanosheet materials have unique electronic and optical properties, it is difficult to achieve certain applications directly. Heterostructure formed by stacking different semiconductors together has always been an important way to regulate the electronic properties of materials, and be applied in nanoelectronic devices with excellent properties of both materials.23 There are many theoretical and 3



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experimental studies on the heterostructures of MX2. For example, graphene absorbed on a MoS2 substrate has attracted extensive experimental and theoretical attention.27 The electronic structure of 2D black phosphorene /monolayer MX2 (M = Mo, W; X = S, Se, Te) van der Waals heterostructures have been calculated by the first-principles method.11,19 So far, vdW heterostructures combined with monolayer MX2 and other 2D materials show a wide variety of semiconducting characteristics. Meanwhile, for arsenene, the graphene/arsenene heterostructure has been reported that the vertical electric field can not only control the Schottky barrier height but also the Schottky contacts (n-type and p-type) and Ohmic contacts (n-type) at the interface.21 But a systematically theoretical understanding of effect of strain and electric field on the electronic structures of β-As/MX2 heterostructures is unclear up to now. In this contribution, we report the atomic structures of 2D vdW heterostructures combined with the monolayer β-As and MX2 (M = Mo, W; X = S, Se) by density functional theory. Then, we tune the electronic properties of the heterostructure with strain (ɛ) and external electric field (Eext). These studies might provide us with a deep understanding of the β-As/MX2 heterostructures, which is promising for fabricating high-performance arsenene-based nanodevices in the future. Theoretical approach The first-principle DFT calculations are carried out by using the DMol3 code.28 The generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof scheme (PBE)29 is utilized for the exchange-correlation potential to optimize geometrical structures and calculate properties of β-As/MX2 heterostructures. 4


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Moreover, double numerical atomic orbital plus polarization (DNP) is chosen as the basis set, with the global orbital cutoff 4.4 Å. The Brillouin zone is sampled by 5 × 5 × 1 k-points for all structures in the geometry optimization (electronic) calculations. The convergence tolerance of energy, maximum force, and maximum displacement were set as 1.0 × 10-5 Ha, 0.002 Ha/Å and 0.005 Å, respectively (1 Ha = 27.2114 eV). In geometric optimization, the positions of all atoms in a supercell are fully relaxed while the shape and the volume of the supercell are fixed. The vacuum spacing between neighboring supercells is set to be 20 Å to avoid artificial interactions. The charge density difference is calculated by CASTEP code in this work.30 Meanwhile, it is worth noting that there still exists some discrepancy between theory and experiment in predicting numerically accurate values of band gaps for heterostructure, partly due to the choices in the exchange–correlation functional and the inclusion of many-body effects.2 Binding energy (Eb) can be used to assess the structural stability of the heterostructure system. The formula for the binding energy is that:

Eb = Eheterostructure − EMX 2 − E Arsenene

(1),

where E heterostructure , EMX 2 and E Arsenene are respectively the energy of heterostructure system, MX2 and β-As with the similar lattice parameters. According to this definition, the negative value of Eb means the stable binding of heterostructure system, and a smaller value indicates a more energetically favorable heterostructure system. The effective mass of the material is closely related to the carrier mobility of the material, which is calculated according to the following formula: 5



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(

1 1 ∂2E )i j = 2 ，i , j = x, y , z m* h ∂ki ∂k j

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(2).

From Eq. 2, we can obtain the effective mass of electron (or hole) by the second derivative of the top of valence band (or the bottom of conduction band) for the wave vector; although m* is a second-order tensor with nine components, we can take it as a scalar. Three directions (x, y, z) are calculated when we calculate energy band. Thus, the Eq. 2 could be simplified as:

1 1 ∂ 2 E (k ) = 2 m * h ∂k 2

(3).

Results and discussion (1) The atomic structures and electronic properties of the β-As/MX2 heterostructures In this work, β-As/MX2 heterostructures are stacked by monolayer β-As and MX2 nanosheets MX2 (M = Mo, W and X = S, Se). As usual, the heterostructure is formed easily when the lattice mismatch is small. After geometric optimization, the calculated lattice parameters of the monolayers of MoS2, WS2, MoSe2, WSe2 and β-As are 3.165 Å, 3.150 Å, 3.210 Å, 3.20 Å and 3.607 Å, respectively. The detailed parameters are shown in Table 1. And the calculated band gaps of the monolayer MoS2, WS2, MoSe2, WSe2 and β-As are 1.792 eV, 1.986 eV, 1.420 eV, 1.542 eV and 1.632 eV, respectively, which all agree well with previous studies.14,19,31-33 The monolayer MX2 show direct band gaps where both the conduction band minimum (CBM) and valence band maximum (VBM) are located at K point, while the monolayer β-As has an indirect band gap where VBM is located at Γ point, CBM is 6


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located at K point. The formula of the lattice mismatch is:

γ=

Where the

aMX 2

,

aβ − As

aMX 2 − aβ − As aMX 2

(4)

are respectively the lattice parameter of MX2 and β-As.

In order to simulate the β-As/MX2 heterostructures, we choose MX2 as a substrate to match with β-As, the β-As/MX2 heterostructures are composed of 2×2 primitive MX2 cells (8 X and 4 M atoms) and √3 × √3 β-As primitive cells (6 As atoms). The heterostructure mismatches of β-As with monolayer MoS2, WS2, MoSe2, WSe2 are 1.3%, 0.8%, 2.6% and 2.3%, respectively. Illustrations of top and side views of the β-As/MX2 heterostructures are shown in Fig. 1. To evaluate the structural stability of the β-As/MX2 heterostructures, we have calculated the relationship between the binding energy, band gap and interlayer distance d of heterostructures, which are shown in Fig. 2. According to the definition, a system with smaller Eb value is more favorable. According to Fig. 2, it can be found that when the interlayer distances of β-As and MoS2, WS2, MoSe2, WSe2 heterostructures are 4.043 Å, 4.076 Å, 4.291 Å, 4.208 Å, respectively, the heterostructures are the most stable. We also calculated the phonons of the β-As/MX2 heterostructures, according to the results it can be seen that the heterostructures were no imaginary frequency, indicating that the heterostructure can exist stably. The phonons agree well with the binding energy results. Meanwhile, the band gaps of β-As with MoS2, WS2, MoSe2, WSe2 heterostructures are 1.333 eV, 1.502 eV, 1.272 eV, 1.190 eV, respectively. At the same time we calculated the band gap obtained within the HSE06, the results are 2.070 eV, 2.271 eV, 1.857 eV, 1.697 eV, respectively, 7



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as shown in Fig. 3. It can be found that the HSE06 type calculation only increases the band gap of the heterostructure, does not change the band structure. The results of β-As/MX2 heterostructure are agreement well with the previous study.34 It is worth mentioning that there is an opposite trend for the band gap and binding energy as a function of d of β-As/MS2 (including β-As/MoS2 and β-As/WS2) heterostructures. While for β-As/MSe2 (including β-As/MoSe2 and β-As/WSe2) heterostructures, the band gaps are linear growth with the increasing of d. Considering the effect of periodic lattice, the smaller the carrier effective mass is, the higher the carrier mobility will be when other conditions are constant. We choose the carrier effective mass as a measurement of the carrier mobility. According to the results as shown in Table 2, it is concluded that all of the β-As/MX2 heterostructures maintain high carrier mobilities. So the interlayer distance 4.043 Å, 4.076 Å, 4.291 Å, 4.208 Å of β-As/MX2 heterostructures are chosen as the objects to study the structural and electronic properties of the heterostructures with strain (ɛ) and external electric field (Eext). In order to further verify the stability of heterostructures, we have calculated the phonons spectrums of the β-As/MS2 heterostructures for example. It can be seen that β-As/MS2 heterostructures were no imaginary frequency, indicating that the heterostructures can exist stably. The phonons agree well with the binding energy results, and the phonons spectrums results have been added to the Supplementary Information, as shown in Figure S1. The band structures and density of states of the β-As/MX2 heterostructures are shown in Fig. 4. It can be found obviously that the β-As/MS2 heterostructures have 8


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indirect band gaps, where CBM is located in the K point and mainly contributed by MS2, VBM is located in the Gamma (Γ) point and mainly contributed by β-As. The β-As/MSe2 heterostructures show direct band gaps, where CBM, VBM are both located in the K point. It is worth noting that the monolayer β-As have little contribution to the CBM and VBM, and the electronic states near the Fermi level are mainly contributed by MSe2 for the β-As/MSe2 heterostructures. To gain further insight of electronic properties, the orbital diagrams of β-As/MX2 heterostructures are calculated as shown in Fig. 5. According to the occupancy situation of the Highest Occupied Molecular Orbital (HOMO) and the Lowest Unoccupied Molecular Orbital (LUMO), heterostructures could be divided into two categories: type-I vdW heterostructures (HOMO and LUMO are located in the same material of heterostructures) and type-II vdW heterostructures (HOMO and LUMO are located in different materials of heterostructures).34 Compared with the type-I heterostructures, the basic characteristics of type-II heterostructures are the separation of electrons and holes in the vicinity of the interface and localization in the self-consistent quantum well. Due to the overlap of the wave functions near the interface, the radiation lifetime is prolonged and the exciton binding energy is reduced. Moreover, Light and electric field strongly affect the characteristics of type-II heterostructures and thus type-II heterostructures exhibit unusual carrier kinetics and complex properties, which affect their electrical, optical and photoelectric properties. As shown in Fig. 5, β-As/MS2 belong to the type-II, which the HOMO and LUMO are located in the monolayer β-As and MS2, respectively. While for β-As/MSe2 9



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heterostructures, the HOMO and LUMO are located in the monolayer MSe2, belonging to type-I and indicating that the energy bands near the Fermi level of the heterostructures are mainly contributed by MSe2 nanosheet. These orbital results can also are consistent well with the above band structures and density of states of the β-As/MX2 heterostructures results.

(2) The effect of Eext and ɛ on the band gaps of β-As/MX2 heterostructures Applying external Eext and ɛ have been known as the effective methods to control electronic, transport, and optical properties of semiconductors for decades.35-37 It has been reported that the electronic properties of heterostructures are modulated notably by weak interlayer interactions, so we discuss the regulation of band gaps by Eext and ɛ on the β-As/MX2 heterostructures.7 The direction of Eext from the monolayer β-As to MX2 is taken as the positive direction. According to the results in Fig. 6 (a), it can be found that as 0 ≤ Eext ≤ 0.416 V/Å, the band gap of β-As/MoS2 decreases from 1.333 eV to 0 eV. The band gap firstly increases slightly to 1.438 eV when Eext = -0.104 V/Å and then decreases to zero, indicating a giant Stark effect. The same phenomenon occurs for β-As/WS2. The band gap decreases from 1.502 eV to 0 eV when 0 ≤ Eext ≤ 0.416 V/Å, while the band gap firstly increases to 1.574 eV when Eext = -0.104 V/Å and then decreases to zero with the increasing of negative Eext. Interestingly, the change trend of the band gaps of β-As/MSe2 heterostructures as a function of Eext are opposite with the β-As/MS2 heterostructures. The band gaps of the β-As/MoSe2 and β-As/WSe2 heterostructures enhance slightly to 1.393 eV and 1.496 eV, respectively, when Eext = 0.104 V/Å and then decrease until to zero, while the band gaps reduce 10


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from 1.272 eV and 1.190 eV continuously to zero when the negative Eext up to -0.52V/Å. The influences of positive and negative Eext on band gaps are different due to the spontaneous electric polarization in the heterostructures. The spontaneous electric polarization may originate from the electronegativity difference between X and As.34 Owing to the electronegativity difference, the electrons and holes in the heterobilayer are localized separately around the As and X atoms, respectively. It also can be proved by the Mulliken charge analysis, which is shown in Table 2. The electrons accumulate around the monolayer β-As, while the holes accumulate around the monolayer MX2. Meanwhile, the electrons around the β-As nanosheet are richer than the holes around the MS2 for β-As/MS2 heterostructures. While for the β-As/MSe2 heterostructures, the electrons around the β-As are less. This is the reason why the change trend of the band gaps of β-As/MSe2 heterostructures as a function of Eext are opposite with the β-As/MS2 heterostructures. For clearly understanding the effect of ɛ on the electronic structure of the heterostructures, we have applied a biaxial or uniaxial ɛ on the β-As/MX2 heterostructures as shown in Fig. 6 (b) and Fig. 7. We define the tensile ɛ as positive values, while compressive ɛ as negative. Positive and negative values only represent the ɛ type. The applied method of strain is following Zhang’s previous reports for the atomically thin arsenene and antimonene.38 It can be clearly found that the band gaps of β-As/MX2 heterostructures decrease with the increasing of ɛ regardless tensile or compressive. And the biaxial ɛ that the heterostructures could withstand are basically the same strain from -10% to +15%. For uniaxial ɛ, the band gaps of β-As/MX2 11



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heterostructures also continuously reduce to zero with the increasing of ɛ. In addition, the band gaps of the heterostructures with X- strain and Y- strain are basically the same, indicating that the heterostructures are highly symmetrical and stable. Meanwhile, according to the orbital diagram of the heterostructures under biaxial ɛ as shown in Fig. 8, for β-As/MoS2 heterostructure, the orbital positions are not changed as biaxial ɛ = 5%, but the LUMO are moved to monolayer β-As when ɛ = -5%. While for β-As/WS2 heterostructure as biaxial ɛ = ±5%, the HOMO are not changed and the LUMO are moved to monolayer β-As. The orbital positions of β-As/MSe2 heterostructures are not changed as biaxial ɛ = ±5%, which are not shown in Fig. 8. So it can be concluded that ɛ could not only effect the band gaps but also the orbital distribution of β-As/MX2 heterostructures.

(3) The effect of biaxial ɛ and Eext on the band edges of heterostructures In order to unravel more information about the bonding mechanism, it is worthwhile to investigate the band structures and the band edges of heterostructures under various Eext and ɛ. Meanwhile, the effect of biaxial ɛ on the band structure of materials is more significant than uniaxial ɛ. Hence, in Fig. 9, the band edges EC and EV under biaxial ɛ are investigated, where EC and EV are the energy of CBM and VBM of heterostructures, respectively. Without biaxial ɛ and Eext, EV (EC) of β-As, MoS2, WS2, MoSe2, and WSe2 heterostructures are -0.645 (0.688) eV, -0.754 (0.748) eV, -0.618 (0.654) eV, and -0.556 (0.634) eV, respectively, where EV and EC have a good symmetry around the Fermi level. This excellent symmetry may facilitate the regulation of the band gaps and the recombination of the electron-hole pairs and then 12


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enhance the carrier mobility of the heterostructures. Moreover, after applying Eext or biaxial ɛ, EC decrease while EV increase, the CBM and VBM will approach to Fermi level and thus decrease the band gap. Since the effect of Eext on the four kinds of heterostructures’s band gaps have similar variation trends, we choose β-As/MoSe2 heterostructure as a specific example and present the detailed analysis in Fig 10. When Eext > 0 V/ Å, the β-As/MoSe2 heterostructure has an indirect band gap, where the VBM is located at Γ point and the CBM is located at K point; when Eext < 0 V/ Å, the heterostructure is a direct band gap semiconductor, where the VBM and CBM are both located at K point. As discussed before, the β-As/MS2 heterostructures have indirect band gaps (VBM at Γ point, CBM at K point), and the heterostructures of β-As/MSe2 have direct band gaps (both VBM and CBM are located at K point). Thus, the positive Eext only changes the band gap values of β-As/MS2 heterostructures and don’t change the semiconductor band gap types. While for the β-As/MSe2 heterostructures, the positive Eext induces a direct to indirect transition at the same time. Under the negative Eext, the situations are just opposite. The β-As/MS2 heterostructures undergo the direct to indirect transition with the negative Eext. The reason may be due to the spontaneous electrification of the atoms in the heterostructures, resulting in a spontaneous internal electric field (Eint). In addition, the directions of the spontaneous Eint of β-As/MS2 and β-As/MSe2 are opposite. The effect of biaxial ɛ on the band structures of β-As/MoSe2 heterostructure are also investigated. With the application of biaxial ɛ, the band gaps of β-As/MS2 13



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decrease gradually with the dropping of the CBM, but the semiconductor band gap types do not changed, which are still indirect band gap semiconductors. However, the band gaps for β-As/MSe2 heterostructures are different. Because the semiconductor band gap types of β-As/MSe2 heterostructures under biaxial ɛ are basically the same, we also take the band structure of β-As/MoSe2 heterostructure as an example, as shown in Fig. 11. Without ɛ, the β-As/MoSe2 heterostructure has a direct band gap. When ε changes from -3% to +1%, the band gap of the β-As/MoSe2 heterostructure is reduced, but heterostructure is still the direct band gap semiconductor. When -9% > ɛ > -3%, the VBM of heterostructure will shift to Γ point, which turn the β-As/MoSe2 heterostructure into an indirect semiconductor. When the ɛ increases from +3% to +7%, the heterostructure is still the direct band gap semiconductor, but the CBM and VBM are both transferred to the Γ point. When +15% > ɛ > +7%, the VBM will move from Γ point to the middle Γ-K points, meanwhile the CBM will move from point Γ to point K. Finally, the heterostructures of β-As/MoSe2 and β-As/WSe2 are converted to metal when the ɛ ≥ -9% or ɛ ≥+15%. Therefore, the band gaps of β-As/MSe2 heterostructures are gradually reduced with the increasing of ɛ, and the semiconductor types also have a series of changes. For a clearer representation, we have given the direct to indirect band gap transition with the variation of biaxial strain of β-As/MSe2 heterostructures in Fig. 12.

Conclusion In summary, we have investigated the effect of strain and electric field on structural and electronic properties of β-As/MX2 heterostructures by density 14


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functional theory. The calculated band structures indicate that their electronic properties can be effectively tuned via (biaxial or uniaxial) ɛ and Eext. The β-As/MS2 heterostructures have indirect band gaps, while β-As/MSe2 heterostructures have direct band gaps without ɛ and Eext. The change trend of the band gaps of β-As/MSe2 heterostructures as a function of Eext is opposite with the β-As/MS2 heterostructures due to the spontaneous electric polarization in the heterostructures. Furthermore, for all of the β-As/MX2 heterostructures, they will eventually transit from semiconductor to metal with the applying ɛ or Eext. Our results indicate that the substrate types, ɛ and Eext significantly affect the electronic properties of heterostructures, which provide useful information on the potential application in photoelectric devices based on arsenene and monolayer transition-metal dichalcogenides.

Acknowledgments. The authors acknowledge supports by National Natural Science Foundation of China (NSFC, Grant Nos. 51471124 and 51301020), China Postdoctoral Science Foundation (No. 2015M582585), the special fund for basic scientific research of central colleges of Chang’an University (No. 310831162002) and the Fundamental Research Funds for the Central Universities (No. xjj2016018).

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Table 1 Summary of the structural and electronic properties of MoS2, WS2, MoSe2, WSe2 and β-As. a and Eg mean the lattice parameters and the band gap value of each monolayer. The numbers 1 and 2 are represented our calculation results and the results in the references 14 and 19. β-As

MoS2

WS2

MoSe2

WSe2

a1 (Å)

3.607

3.165

3.15

3.21

3.2

a2 (Å) 14,19

3.677

3.169

3.153

3.289

3.282

Eg1 (eV)

1.632

1.792

1.986

1.42

1.542

Eg2 (eV) 14,19

1.635

1.69

1.81

1.45

1.54

Table 2 Summary of the electronic properties of different heterostructures. Q (e) and m represented the atom Mulliken charges and the carrier effective mass. d/i refers to direct or indirect band gap of semiconductor. Eg is the energy band gap. β-As/MoS2

β-As/WS2

β-As/MoSe2

β-As/WSe2

1.333

1.502

1.272

1.190

i

i

d

d

Qβ-As (e)

0.03

0.023

0.004

0.006

QMX2 (e)

-0.028

-0.023

-0.005

-0.01

mh (m0)

-0.32693

-0.34494

-0.52464

-0.34883

me (m0)

0.3868

0.37687

0.47233

0.48868

Eg (eV) d/i

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Captions Figure 1 Top (left) and side (right) views of the β-As/MX2 heterostructures. Purple represents As atoms, yellow represents X atom, and blue represents M atom. (M = Mo, W and X = S, Se).

Figure 2 The binding energy and band gaps of the β-As/MX2 heterostructures as a function of interlayer distance. (a) β-As/MoS2; (b) β-As/WS2; (c) β-As/MoSe2; (d) β-As/WSe2.

Figure 3 The band structures of the β-As/MX2 heterostructures by the HSE06 method. (a) β-As/MoS2;(b) β-As/WS2; (c) β-As/MoSe2; (d) β-As/WSe2.

Figure 4 The band structures and density of states of the β-As/MX2 heterostructures. (a) β-As/MoS2; (b) β-As/WS2; (c) β-As/MoSe2; (d) β-As/WSe2.

Figure 5 The HOMO and LUMO results of the β-As/MX2 heterostructures. (a) β-As/MoS2; (b) β-As/WS2; (c) β-As/MoSe2; (d) β-As/WSe2. Blue and yellow denote positive and negative wave function contours in charge densities, respectively, and the isosurface values are ±0.06 e/Å3.

Figure 6 The band gaps of the β-As/MX2 heterostructures as a function of electric field (a) and biaxial strain (b).

Figure 7 The band gaps of the β-As/MX2 heterostructures as a function of uniaxial strain. (a) β-As/MS2 heterostructures; (b) β-As/MSe2 heterostructures.

Figure 8 The HOMO and LUMO results of β-As/MoS2 (a, b) and β-As/WS2 (c, d) heterostructures as a function of biaxial strain. The isosurface values are ±0.06 e/Å3.

Figure 9 The energy of the valence band maximum (EV) and conduction band 21



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minmum (EC) of β-As/MX2 heterostructures as a function of electric field and biaxial strain. (a) and (c) β-As/MoS2 and β-As/WS2 heterostructures; (b) and (d) β-As/MoSe2 and β-As/WSe2 heterostructures.

Figure 10 The band gap of the β-As/MoSe2 heterostructure as a function of electric field (Eext).

Figure 11 The band gap of the β-As/MoSe2 heterostructure as a function of biaxial strain (ɛ).

Figure 12 The band gaps of the β-As/MSe2 heterostructures as a function of biaxial strain. Seven strain zones are identified based on its distinct band structures. d/i refers to direct or indirect band gap of semiconductor, m refers to metal.

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Figure 1

23



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Figure 2

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Figure 3

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Figure 4

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Figure 5

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Figure 6

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Figure 7

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Figure 8

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Figure 9

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Figure 10

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Figure 11

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Figure 12

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396x198mm (96 x 96 DPI)


Tunable Electronic Properties of Arsenene and Transition-Metal

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