MoSSe van der Waals heterostructures by external electric field and strain

MoSSe van der Waals heterostructures by external electric field and strain

Applied Surface Science 497 (2019) 143809 Contents lists available at ScienceDirect Applied Surface Science journal homepage: www.elsevier.com/locat...

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Applied Surface Science 497 (2019) 143809

Contents lists available at ScienceDirect

Applied Surface Science journal homepage: www.elsevier.com/locate/apsusc

Full length article

Tunable electronic structures in BP/MoSSe van der Waals heterostructures by external electric field and strain

T

Diancheng Chen, Xueling Lei , Yanan Wang, Shuying Zhong, Gang Liu, Bo Xu, Chuying Ouyang ⁎

Department of Physics, Laboratory of Computational Materials Physics, Jiangxi Normal University, Nanchang, Jiangxi 330022, China

ARTICLE INFO

ABSTRACT

Keywords: BP/MoSSe heterostructures Electronic structures External electric field Strain First principles calculations

Motivated by the successful preparations and extraordinary properties of blue phosphorus (BP) and Janus MoSSe monolayer, we constructed the van der Waals (vdW) heterostructures composed of BP and Janus MoSSe monolayer denoted by BP-SMoSe and BP-SeMoS, respectively, investigated their electronic structures and the effects of external electric field and strain. We find that the BP-SMoSe vdW heterostructure exhibits type-I band alignment, while the BP-SeMoS vdW heterostructure shows type-II band alignment. Moreover, the bandgap and band alignment of BP-SMoSe and BP-SeMoS vdW heterostructures can be tuned effectively by applying external electric field and strain. The results indicate that these BP/MoSSe vdW heterostructures will have great applications in multi-functional device.

1. Introduction Since the experimental realization of graphene in 2004 [1], many novel physical and chemical properties of graphene have been discovered [2–5]. However, its applications in field-effect transistors (FETs) devices are limited due to its zero bandgap [6]. Therefore, many other 2-dimensional (2D) materials with a nonzero bandgap were explored and discovered such as hexagonal boron nitride (h-BN) [7,8], transition metal dichalcogenides (TMDs) [9,10], and phosphorene (BP) [11,12]. In parallel with the investigation on 2D materials, a new type of 2D materials based on van der Waals (vdW) heterostructures has also been investigated theoretically and experimentally. Breaking the limitation of a single 2D material in the applications of devices, vdW heterostructures, achieved by vertically stacking two different 2D materials via vdW interaction, generally exhibit novel properties than their components. For example, Janus-MoSSe bilayer heterostructure can significantly extend the recombination time of a photoexcited electron and hole [13]. 2D phosphorene/SnS2 (SnSe2) vdW heterostructures can be used to explore the tunnel field-effect transistors [14]. Typically, the vdW heterostructures display three band alignments including straddling type-I [15], staggered type-II [16,17], and broken-gap type-III [14,18] due to the different 2D materials of their building layers and diverse stacking arrangements. Moreover, vdW heterostructures with different type of band alignment have particular applications to different varieties of devices. For instance, the vdW heterostructures with type-I band alignment are promising in electronic applications such as



light-emitting diodes [19,20], quantum-well lasers [21], and high-frequency modulators [22], while the vdW heterostructures with type-II band alignment are suitable for photovoltaics [23,24], optoelectronics [25], and photocatalysis [26], and the vdW heterostructures with typeIII band alignment can be used to understand the current transport and optoelectronic effects such as FETs [27–29]. It has been demonstrated that combining the distinct 2D materials to construct heterostructures can engineer the electronic properties and bring new exciting physical phenomena [30,31]. As a consequence, considerable number of vdW heterostructures have been theoretically reported and experimentally realized for versatile applications [32–41]. Blue phosphorus (BP) has been successfully prepared first in 2016 year [42,43]. Unlike other 2D materials, BP exhibits excellent properties such as in-plane hexagonal structure [44], tunable bandgap and mobility [45], thermoelectric and superconductor materials [46,47], application as an anode material for Li-ion batteries [48], and so on [49–51], thereby drawing enormous interests. Moreover, the BPbased materials have caused a flourish of investigations, especially the BP-based vertical vdW heterostructures have been fabricated and studied [52–59]. For example, the vdW heterostructures formed by BP with graphene-like gallium nitride (g-GaN) [52], graphitic zinc-oxide (g-ZnO) [57] and black phosphorus (BlackP) [53] demonstrate type-II energy band alignment, ensuring that the photogenerated electron-hole pairs spatial separation can be realized. At the interface of these heterostructures, a strong electrostatic electric field has been built, resulting in the photogenerated electrons transfer from the g-GaN, g-ZnO

Corresponding author. E-mail address: [email protected] (X. Lei).

https://doi.org/10.1016/j.apsusc.2019.143809 Received 17 June 2019; Received in revised form 23 August 2019; Accepted 26 August 2019 Available online 27 August 2019 0169-4332/ © 2019 Elsevier B.V. All rights reserved.

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Fig. 1. Band structures of (a) BP and (b) MoSSe monolayer calculated at PBE level. The Fermi level is set as zero. Brillouin zone with high-symmetry points labeled (c), and total energy as a function of the lattice parameter in the BP-SeMoS heterostructure (d). The inset is unit cell.

describe electron-ion interactions [78,79] and the GGA-PBE exchange–correlation functional [80] was used to calculate the electron exchange and correlation energies. The Mo 4p65s14d5, S 3s23p4, Se 4s24p4, and P 3s23p3 electrons were considered as valence electrons. A cutoff energy of 500 eV was applied to wave function. The Monkhorst–Pack scheme [81] with 11 × 11 × 1 k-point grid was used for the integration in the first Brillouin zone. The lattice parameters and ionic positions were fully relaxed until the total energies and forces were less than 10−5 eV and 0.02 eVÅ−1, respectively. To avoid the interactions between the periodic images, a vacuum space of more than 15 Å and 20 Å along the z direction was used for BP and MoSSe monolayer and BP/MoSSe vdW heterostructures, respectively. To eliminate the errors caused by periodic boundary condition, dipole correction was adopted in the present work [82]. The vdW interactions were included in our calculations by the DFT-D2 method of Grimme [83]. All the calculations were performed by non-spin polarized density functional theory. The calculations of density of states (DOS) was smeared by the Gaussian smearing in combination with a SIGMA = 0.05. In addition, the Heyd–Scuseria–Ernzerhof (HSE06) method [84] was used to correct the bandgap values, where a 25% of exact nonlocal Hartree-Fock exchange functional was added to the PBE functional. The atomic charge distribution was analyzed by the Bader charge [85]. For the first-principles molecular dynamics (FPMD) calculations, the 4 × 4 supercells (80 atoms) of the optimized most stable stacking configurations of BP-SMoSe and BP-SeMoS vdW heterostructures were used as the starting geometry, respectively. All FPMD simulations were conducted with the NVT ensemble. A Verlet algorithm was integrated with Newton's equations of motion at a time step of 1 fs for a total simulation time of 6 ps, i.e., 6000 time steps in total. The frequency of the temperature oscillations was controlled by the Nosé mass during the simulations. Additionally, a 1 × 1 × 1 k-point mesh was used at the Γpoint.

and BlackP layer to the BP layer, and thus g-GaN, g-ZnO and BlackP can be used as active layer for BP to facilitate charge injection and enhance the device performance. More recently, a new 2D material of Janus MoSSe has been successfully synthesized though the chemical vapor deposition (CVD) method [60,61]. Because of breaking the out-of-plane structural symmetry, Janus MoSSe has an intrinsic dipole moment perpendicular to the monolayer plane, and thus induces the built-in electric field. Soon after, theoretical predictions show that MoSSe is a direct-bandgap semiconductor, and the bandgap can be tuned by rich modulation methods such as strain [62,63], layer number [64], dipole moment and interlayer distance [65], and transition metal atom adsorption [66]. In addition, studies demonstrate that Janus MoSSe can be used as a photocatalyst for water splitting [62,63] and piezoelectric devices [67]. Following these work, we also performed a first-principles calculation, revealing that Janus MoSSe can be utilized as a potential anode material for high performance Li-ion batteries [68]. Most interestingly, we found that the bilayer MoSSe has a type-II band alignment due to its intrinsic dipole, making it a good candidate for applications in optoelectronics [65]. Moreover, it is interesting that both vertical heterostructures and lateral heterostructures composed of Janus MoSSe and WSSe monolayers have type-II band alignment, enabling the separation of excitons [69]. Therefore, the MoSSe-based heterostructures exhibit interesting physical properties owning to the intrinsic dipole moment in the MoSSe layer [70–75]. Inspired by the aforementioned, we naturally wonder how about the electronic properties of the vdW heterostructures formed by BP and Janus MoSSe monolayer (BP/MoSSe). How to engineer the electronic properties of BP/MoSSe vdW heterostructures? To answer these questions, we investigate the electronic properties of BP/MoSSe vdW heterostructures by means of first-principles calculations, focusing on the structures, electronic properties, and modulations of electronic structure by external electric field and strain. 2. Computational methods All the calculations in this paper were carried out using the VASP code [76,77]. The projected augmented plane-wave (PAW) was used to 2

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3. Results and discussion

heterostructure has the lowest formation energy of −130 meV, and the corresponding configuration is shown in Fig. 2(a), the same as in Fig. S2(c). In Fig. 2(a), the upper P atoms are located on the top of Mo atoms, and the lower P atoms are positioned above the hexagonal center. From Table S2, it is evident that the best stacking configuration of BP-SeMoS heterostructure has the lowest formation energy of −166 meV, and the corresponding configuration is shown in Fig. 2(d), the same as in Fig. S3(a). In Fig. 2(d), the upper and lower P atoms are directly above the Se and Mo atoms, respectively. The interlayer distances of optimal BP-SMoSe and BP-SeMoS heterostructures are 3.13 and 3.17 Å, respectively, which are in good agreement with the interlayer distances of 3.11 Å in SnS2/polyphenylene vdW heterostructure [31], 3.21 Å in g-ZnO/BP vdW heterostructure [57], and 3.252 Å (3.294 Å) in InSe/GeSe (SnS) typical vdW heterostructures [88]. Therefore, both the formation energy and the interlayer distance indicate that BP-SMoSe and BP-SeMoS heterostructures are typical vdW heterostructures with vdW interactions between BP and MoSSe monolayer. Furthermore, the bond distances of PeP, MoeS, and MoeSe are almost the same for different stacking configurations, and are in good agreement with those in single BP monolayer and single MoSSe monolayer reported previously [51,65]. This also demonstrates that the structural and electronic properties of constituted layers will not be greatly affected. On the other hand, for the best configurations of BPSMoSe and BP-SeMoS vdW heterostructures, Tables S1 and S2 show that the dipole moments are 0.11 and −0.24 Debye, respectively, which are analyzed in detail in the Section 3.2. The PBE bandgaps are 0.95 and 0.93 eV, respectively, while the HSE06 bandgaps are 2.26 and 2.45 eV, respectively (see Fig. S4). Although the HSE06 bandgap is 1.31–1.52 eV higher than the PBE bandgaps, the band structures of HSE06 is very similar to those obtained at the PBE level (see Fig. S5). To examine the dynamic stabilities of the most stable stacking configurations of BP-SMoSe and BP-SeMoS vdW heterostructures, we carried out the FPMD simulations. The temperature and total energy fluctuation for BP-SMoSe and BP-SeMoS vdW heterostructures are presented in Fig. 2, respectively. Clearly, the small range of total energy fluctuation indicates that the distortion is negligible and there are no bonds broken after heating the systems at 300 K for 6 ps. These results further demonstrate that the studied systems have good dynamic stability at room temperature. Therefore, the proposed BP-SMoSe and BPSeMoS heterostructures are taken into account in the follow discussions.

3.1. Construction of BP-SMoSe and BP-SeMoS vdW heterostructures Fig. 1(a) and (b) show the energy band structures of BP and MoSSe monolayer as well as their unit cell structures. Fig. 1(c) shows the Brillouin zone of unit cell labeled with high-symmetry k-points. Clearly, BP monolayer possesses an indirect bandgap of 1.91 eV, while MoSSe monolayer shows a direct bandgap of 1.55 eV, which agree well with previous PBE results [44,51,65,69]. It is well known that GGA-PBE underestimates the bandgap of semiconductors, while the advanced HSE06 has a better prediction on the bandgap value. In our HSE06 calculations, the bandgap of relaxed BP and MoSSe monolayer are 2.76 and 2.05 eV, respectively (see Fig. S1), which are in good agreement with those previously reported [45,69,70,86,87]. On the other hand, the lattice constants of BP and MoSSe unit cell are 3.28 and 3.26 Å, respectively, which are consistent with previous theoretical and experimental values [42,43,65]. The lattice mismatch is estimated by 2 | a b| × 100% to be about 0.6% between BP and MoSSe, where a and b a+b are the lattice constants of BP and MoSSe, respectively. Such a small lattice mismatch allows us to construct the heterostructure consisting of BP and MoSSe monolayer using unit cell. Considering the discrepancy in atoms on each side of MoSSe monolayer, there are two types of heterostructures denoted by BP-SMoSe and BP-SeMoS. BP-SMoSe represents the interface of heterostructure is P atom layer and S atom layer, while BP-SeMoS represents the interface of heterostructure is P atom layer and Se atom layer. First of all, the lattice parameter of heterostructure was tested. Fig. 1(d) shows the total energy as a function of the lattice parameter in the BP-SeMoS heterostructure (the corresponding configuration see Fig. S3(a)). It is clear that the best lattice parameter of the BP-SeMoS heterostructure is 3.27 Å. Hereafter, the lattice parameters of constructed BP-SMoSe and BP-SeMoS heterostructures are set to be 3.27 Å. To obtain the optimal stacking pattern between BP and Janus MoSSe, five typical stacking configurations with high symmetry for BPSMoSe and BP-SeMoS heterostructures were respectively checked, as shown in Figs. S2–S3. The stability of these configurations can be evaluated by the formation energy, Eform = Etotal − EBP − EMoSSe, where Etotal, EBP, and EMoSSe represent the total energies of heterostructures, isolated BP monolayer, and isolated MoSSe monolayer, respectively. The calculated formation energies as well as the interlayer distances, dipole moments, bandgaps, and bond lengths of various stacking configurations are listed in Tables S1 and S2, respectively. Clearly, Table S1 shows that the formation energies of five stacking configurations of BPSMoSe heterostructure are −86, −83, −130, −45, and −85 meV, respectively, indicating that the most stable configuration of BP-SMoSe

3.2. Electronic structures of BP-SMoSe and BP-SeMoS vdW heterostructures After confirming the configurations and the stabilities of BP-SMoSe and BP-SeMoS vdW heterostructures, we further examined their

Fig. 2. Configurations of BP-SMoSe (a) and BP-SeMoS vdW heterostructure (d), fluctuation of total energy of BP-SMoSe (b) and BP-SeMoS vdW heterostructure (e), and temperature of BP-SMoSe (c) and BP-SeMoS vdW heterostructure (f) with time obtained from first-principles molecular dynamic simulation at 300 K for 6 ps. 3

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Fig. 3. Total density of states (TDOS) and projected density of states (PDOS) for BP-SMoSe and BP-SeMoS vdW heterostructures, respectively. TDOS, SMoSe, and BP (a), and PDOS of Mo-4d, BP-3p, S-3p, and Se4p orbitals (b) for BP-SMoSe vdW heterostructure. TDOS, SeMoS, and BP (c), and PDOS of Mo-4d, BP-3p, S-3p, and Se-4p orbitals (d) for BP-SeMoS vdW heterostructure. The Fermi level is set to zero.

electronic properties in the following of this paper. Fig. 3 shows the total density of states (TDOS) and the projected density of states (PDOS) for BP-SMoSe and BP-SeMoS vdW heterostructures, respectively. From Fig. 3(a)–(b), it is evident that the TDOS of BP-SMoSe vdW heterostructure is mainly contributed by MoSSe layer near the Fermi level. Moreover, both the valence band maximum (VBM) and the conduction band minimum (CBM) are also originated from MoSSe layer. Furthermore, the PDOS manifests that both the VBM and the CBM are contributed by the Mo-4d orbitals in the BP-SMoSe vdW heterostructure. For BP-SeMoS vdW heterostructure, Fig. 3(c) shows that the VBM is dominated by MoSSe layer, while the CBM is mainly contributed by BP layer. Fig. 3(d) further indicates that the VBM and CBM of BP-SeMoS vdW heterostructure are from Mo-4d and P-3p orbitals, respectively. To further clearly see the electronic properties of BP-SMoSe and BPSeMoS vdW heterostructures, the weighted band structures were examined using PBE-vdW level, respectively, as shown in Fig. 4(a) and

(d). The size of green and blue lines illustrates the projected weight of electrons in MoSSe and BP layer, respectively. For BP-SMoSe vdW heterostructure, Fig. 4(a) shows an indirect bandgap of 0.95 eV with the VBM at the Γ-point and the CBM at the K-point. The bandgap is significantly smaller than that of isolated BP and MoSSe monolayer, indicating that the electronic properties of BP-SMoSe vdW heterostructure are different from those of their components. To further gain insights, the band decomposed charge density of the VBM and CBM in BP-SMoSe vdW heterostructure have been calculated in Fig. 4(b). It is obvious that both the photogenerated electrons of CBM and the photogenerated holes of VBM are localized on MoSSe layer, indicating that BP-SMoSe vdW heterostructure forms a type-I band alignment. In Fig. 4(c), we present the band alignment of BP-SMoSe vdW heterostructure to deeply understand its carrier separation. It can be seen that the CBM of MoSSe is lower than that of BP, while the VBM of MoSSe is higher than that of BP, which confirms that BP-SMoSe vdW Fig. 4. Weighted band structures of BP-SMoSe vdW heterostructure (a) and BP-SeMoS vdW heterostructure (d) calculated using PBE-vdW. The Fermi energy is set to 0 eV. The size of green and blue lines illustrates the projected weight of MoSSe and BP electrons, respectively. The band decomposed charge density of VBM and CBM in BP-SMoSe vdW heterostructure (b) and BPSeMoS vdW heterostructure (e). The isovalue is 0.013 eÅ−3. Type-I band alignment of BP-SMoSe vdW heterostructure (c) and Type-II band alignment of BP-SeMoS vdW heterostructure (f). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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heterostructure features a typical type-I band alignment. The conduction-band offset (CBO) and valence-band offset (VBO) are approximately 0.13 and 0.98 eV respectively. Therefore, both photogenerated electrons and holes tend to migrate from BP to MoSSe driven by the band offsets, leading to photogenerated electrons and holes tend to recombine. This band characteristic enables the BP-SMoSe vdW heterostructure can be applied for electric device such as light-emitting diodes and LEDs [19,20,89]. For BP-SeMoS vdW heterostructure, Fig. 4(d) demonstrates an indirect bandgap of 0.93 eV with the VBM at the Γ point and the CBM at the Γ-M path. This is also supported by the band decomposed charge densities in Fig. 4(e), it is clear that the CBM and VBM are localized on BP layer and MoSSe layer, respectively, indicating a typical type-II band alignment. As shown in Fig. 4(f), the CBO and VBO are about 0.41 and 0.60 eV respectively. The photogenerated electrons in MoSSe layer are tend to move to the conduction band of BP layer with the CBO, while the photogenerated holes in BP layer are readily migrated to the valence band of MoSSe layer with the VBO. Thus the energy band alignment of BP-SeMoS vdW heterostructure just like BP/g-ZnO, BP/g-GaN, and BP/BlackP heterostructures, can efficiently separate electrons and holes in BP-SeMoS vdW heterostructure, making them apply in the field of optoelectronics devices, solar energy conversion and so on [23,24]. Furthermore, to check the effects of lattice mismatch on the electronic properties of heterostructures consisting of BP and MoSSe monolayer, we also calculated the band structures of BP-SMoSe and BPSeMoS vdW heterostructures with the lattice constant of 3.26 Å (the lattice constant of MoSSe) and 3.28 Å (the lattice constant of BP), respectively, and compared them with the present results calculated at the lattice constant of 3.27 Å. As shown in Fig. S6, for BP-SMoSe and BP-SeMoS vdW heterostructures, although the values of bandgap are slightly different (the error ranges: 1.1%–4.3%), the band structures are almost the same under different lattice constants, thus the effects of the lattice mismatches on the band structures can be neglected. This means an acceptable lattice mismatch between MoSSe and BP layers. From the above analysis, it can be concluded that the BP-SMoSe vdW heterostructure features type-I band alignment, while the BPSeMoS vdW heterostructure displays type-II band alignment. In order to further understand this, we plotted in-plane average electrostatic potential of BP-SMoSe and BP-SeMoS vdW heterostructures, respectively,

as shown in Fig. 5(a)–(b). The inset panel represents schematic illustration of built-in electric field. As we know that Janus MoSSe monolayer has an intrinsic dipole moment of 0.18 Debye pointing from Se layer to S layer. At the same time, there exists a weak dipole moment at the interface region pointing to S/Se layer from BP layer due to the disparity in the electronegativities of S/Se and P atoms. Therefore, the BP-SMoSe vdW heterostructure has a small dipole moment of 0.11 Debye pointing to BP layer due to the opposite dipole moments of MoSSe and BP layer, while the BP-SeMoS vdW heterostructure has a large dipole moment of −0.24 Debye pointing to MoSSe layer due to the same direction of dipole moments of MoSSe and BP layer. Therefore, BP-SMoSe vdW heterostructure forms a weak in-plane averaged electrostatic potential at the interface region, which results in the small built-in electric field from MoSSe layer to BP layer. This intrinsic builtin electric field slightly increases the interlayer coupling and promotes the electron transition from BP to MoSSe layer, and thus the electrostatic potential of MoSSe layer decreases by about 0.53 eV due to acceptance of electrons (see Fig. 5(a)). Contrary to BP-SMoSe vdW heterostructure, a strong electrostatic potential is formed at the interface of BP-SeMoS vdW heterostructure. As a result, a large built-in electrical field pointing to MoSSe layer from BP layer has been built in BP-SeMoS vdW heterostructure interface, leading to the significant charge transfer from MoSSe to BP. Therefore, the electrostatic potential of BP layer is 0.73 eV lower than that of MoSSe layer due to obtaining electrons (see Fig. 5(b)).Another evidence of charge transfer is the integrated charge density differences between heterostructure and its component monolayers. Therefore, we calculated the integrated charge density differences of BP-SMoSe and BP-SeMoS vdW heterostructures using ∆ρ(z) = ∫ ρhetero(x, y, z)dxdy − ∫ ρMoSSe(x, y, z)dxdy − ∫ ρBP(x, y, z)dxdy, where ρhetero(x, y, z), ρMoSSe(x, y, z), and ρBP(x, y, z) are charge densities in heterostructure, MoSSe monolayer, and BP monolayer at the (x, y, z) point, respectively, and the results are plotted in Fig. 5(c)–(d). The inset shows the corresponding isosurfaces of charge density difference, yellow and blue areas denote the electron accumulation and depletion, respectively. For BP-SMoSe heterostructure, as seen in Fig. 5(c), evidently, the charges transfer from BP layer to MoSSe layer, and thus the holes accumulate at BP region. On the contrary, distinct charge transfer from MoSSe layer to BP layer is observed in BP-SeMoS vdW heterostructure, as seen in Fig. 5(d), and thus more charges are accumulated Fig. 5. In-plane average electrostatic potential of BP-SMoSe vdW heterostructure (a) and BPSeMoS vdW heterostructure (b). The inset represents the schematic illustration of built-in electric field. Integrated charge density difference along the direction perpendicular to the interface of BP-SMoSe (c) and BP-SeMoS vdW heterostructures (d). The inset shows the corresponding isosurfaces of charge density difference. The isovalue is 1.25 × 10−4 eÅ−3. Yellow and blue areas denote electron accumulation and depletion, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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Fig. 6. The evolution of bandgap (a) and band edges (b) for BP-SMoSe vdW heterostructure, and of bandgap (c) and band edges (d) for BPSeMoS vdW heterostructure under external electric field. EC-BP, EC-SMoSe and EC-SeMoS are the CBMs of BP and MoSSe in BP-SMoSe and BPSeMoS heterostructures, respectively, and EV-BP, EV-SMoSe and EV-SeMoS are the VBMs of BP and MoSSe in BP-SMoSe and BP-SeMoS heterostructures, respectively. The Fermi level is set as zero.

−0.6–+0.8 V/Å, and reaches the maximum at E⊥=−0.6 V/Å. When the positive and negative E⊥ increase to +1.0 and −0.8 eV, respectively, dielectric breakdown as well as charge tunneling will occur. As a result, the bandgap decreases sharply and very quickly turns BP-SeMoS heterostructure into a metal. To get further insights, changes of the band edge position as a function of external E⊥ are shown in Fig. 6(d). As seen from Fig. 6(d), the EC-BP decreases and the EV-SeMoS increases with the change of E⊥ from −0.6 V/Å to +0.8 V/Å, and thus the CBM and VBM of BP-SeMoS vdW heterostructure are getting closer to each other, resulting in a gradual decline in the bandgap. Interestingly, BPSeMoS vdW heterostructures can keep its type-II band alignment under external E⊥ in the wide range of −0.6–+0.8 V/Å. Based on above analysis, we believe that the modulations of electronic structures of BP-SMoSe and BP-SeMoS vdW heterostructures can be realized by applying an external E⊥. Especially for BP-SMoSe vdW heterostructure, the type-I band alignment can be transformed to typeII under a moderate positive E⊥ (e.g., +0.2 V/Å). Further observation of the evolution of bandgap under external E⊥, we found that the modulations of electronic band structure in BPSMoSe and BP-SeMoS vdW heterostructures are the synergistic effects of intrinsic built-in electric field and external perpendicular electric field. As shown in Fig. 7(a), after applying a positive E⊥ on BP-SMoSe vdW heterostructure, the direction is the same as that of built-in electric field, strengthening the total electric field, thus the bandgap increases until positive E⊥ reaches +0.2 V/Å. Then the bandgap decreases due to the exchange of EC-SMoSe and EC-BP at E⊥=0.2 V/Å. However, the direction of negative E⊥ is opposite to that of built-in electric field, weakening the total electric field, therefore the bandgap decreases with the increase of negative E⊥. Contrary to BP-SMoSe vdW heterostructure, for BP-SeMoS vdW heterostructure, as shown in Fig. 7(b), the direction of positive E⊥ is opposite to that of built-in electric field, which decreases the total electric field, and thus the bandgap decreases with the increase of positive E⊥. However, after applying a negative E⊥, the direction is the same as that of built-in electric field, which increases the total electric field, therefore the bandgap increases with increasing of negative E⊥.

in BP layer, and depleted in Se atom layer of MoSSe monolayer. Bader charge analysis indicates that the charges of only 0.021 |e| are transferred from BP to MoSSe layer for BP-SMoSe vdW heterostructure, while there are 0.033 |e| transferred from MoSSe to BP layer for BPSeMoS vdW heterostructure. Such small amount of charge transfer again demonstrates the weak vdW interactions in BP-SMoSe and BPSeMoS vdW heterostructures. 3.3. Effects of electric field on BP-SMoSe and BP-SeMoS vdW heterostructures Applying an external electric field is an effective way to tune the electronic structure and enhance the performance of materials. Thus we investigate the effects of an external perpendicular electric field (E⊥) applied on BP-SMoSe and BP-SeMoS vdW heterostructures, respectively. The direction of E⊥ from MoSSe layer to BP layer has been taken as the positive direction (z direction), and vice versa. For BP-SMoSe vdW heterostructure, evolution of the bandgap as a function of applied external E⊥ is shown in Fig. 6(a). It is found that the bandgap increases monotonously at first in the E⊥ ranging from −0.8 to +0.2 V/Å, reaches the maximum at E⊥=+0.2 V/Å, then the bandgap decreases gradually with the increase of external E⊥, and rapidly drops to 0.18 eV at E⊥=+0.8 V/Å. To clearly understand the physics mechanism for the modulations of bandgap, changes of the band edge position under external E⊥ are shown in Fig. 6(b). Clearly, the EV-SMoSe and EV-BP decrease monotonously in the electric field range of −0.8–+0.6 V/Å, then increase in the E⊥ ranging from +0.6 to +0.8 V/Å. On the other hand, the EC-SMoSe increases monotonously in the electric field range of −0.8–+0.8 V/Å, while the EC-BP decreases monotonously in the same electric field range, and the EC-SMoSe and EC-BP cross at E⊥=+0.2 V/Å. As a result, the bandgap increases with the increase of E⊥, and reaches its maximum at +0.2 V/Å, then the bandgap decreases as the E⊥ increases. When under a strong electric field of 0.8 V/Å, the EV-SMoSe and EC-BP shift rapidly towards Fermi level, which significantly reduces the bandgap and BP-SMoSe heterostructure has a tendency to transition to a metal. In addition, the band alignment can be switched to typical type-II from its primary type-I when the E⊥ is larger than +0.2 V/Å. For BP-SeMoS vdW heterostructure, as shown in Fig. 6(c), we can see that the bandgap decreases linearly in the electric field range of 6

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Fig. 7. Schematic illustration of synergistic effects of the intrinsic built-in electric field and the external perpendicular electric field for BP-SMoSe and BP-SeMoS heterostructures, respectively.

3.4. Strain effects on BP-SMoSe and BP-SeMoS vdW heterostructures

energy is decreased. In the meantime, the VBM of MoSSe layer at Γ point continues to decrease, whereas the VBM of BP layer at Γ point increases and is higher than that of MoSSe layer at ε = −6%. This leads to a slightly enlarged bandgap of 1.41 eV at ε = −4% and a significantly decreased bandgap of 0.88 eV at ε = −6%, and a transformation of band alignment from type-II to type-I at ε = −6%. For the tensile strain in the range of +2%−+6%, the CBM of MoSSe layer at K point decreases, while the VBM of MoSSe layer at Γ point increases, resulting in a transformation of BP-SMoSe vdW heterostructure from a semiconductor to zero bandgap at ε = +4% and to a metal at ε = +6%. For strained BP-SeMoS vdW heterostructure, as shown in Fig. 8(b), after application of −2% compress strain, the CBM of BP transforms to K point and increases slightly, at the same time, the VBM of MoSSe at Γ point decreases, resulting in the larger indirect bandgap of 1.13 eV. It is noted that the valence band of MoSSe at K point also increases at ε = −2%, causing to the direct bandgap of 1.14 eV. With the increase of compressive strain, the CBM of BP layer at K point decreases, while the VBM of MoSSe layer at K point increases. Therefore, the bandgap of BP-SeMoS vdW heterostructure decreases, and converts the bandgap from indirect bandgap to direct bandgap at ε = −4% and ε = −6%. Interestingly, the indirect bandgap is the same as the direct bandgap at ε = −6% due to the increase of the VBM of BP at Γ point. In the case of tensile strain, the tensile strain of +2% decreases the CBM of BP layer

Strain is a facile and powerful tool to modulate the electronic properties of materials. To further explore the possibilities of tuning electronic structure under biaxial strain, we examined the electronic structures of BP-SMoSe and BP-SeMoS vdW heterostructures with a series of biaxial strains (ε) from −6% to +6% with a step of 2%. The biaxial strains is defined as (a-a0)/a0, where a and a0 are the lattice constants of the strained and pristine structures, respectively. In previous studies [90], both methods of the PBE and HSE06 calculated the same gap variation trends and near-gap states in phosphorene with strain, including the direct-indirect bandgap transition. Therefore, we believe that the PBE can correctly predict the general trends of strain effect on the band structures and band edges in BP-SMoSe and BPSeMoS vdW heterostructures. Fig. 8 shows the weighted band structures of strained BP-SMoSe and BP-SeMoS vdW heterostructures, respectively. For strained BP-SMoSe vdW heterostructure, as shown in Fig. 8(a), the −2% compressive strain decreases the CBM of BP layer at the Γ-M path, and thus changes the CBM of BP-SMoSe heterostructure from MoSSe layer to BP layer. At the same time, the VBM of MoSSe layer at Γ point greatly decreases. As a result, the bandgap enlarges to 1.33 eV and the band alignment transforms to type-II from its original type-I. With the increase of compressive strain, the CBM of BP layer transfers to K point and the

Fig. 8. Weighted band structures of BP-SMoSe and BP-SeMoS vdW heterostructures under −6%–+6% compressive strain and tensile strain, respectively. (a) BP-SMoSe vdW heterostructures, and (b) BP-SeMoS vdW heterostructures. The Fermi energy is set to 0 eV. The size of green and blue lines illustrates the projected weight of MoSSe and BP electrons, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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Fig. 9. The evolution of bandgap (a) and band edges (b) for BP-SMoSe vdW heterostructure, and bandgap (c) and band edges (d) for BP-SeMoS vdW heterostructure under strain. EC-BP, EC-SMoSe and EC-SeMoS are the CBM of BP and MoSSe in BP-SMoSe and BP-SeMoS vdW heterostructures, respectively, and EV-BP, EV-SMoSe and EV-SeMoS are the VBM of BP and MoSSe in BP-SMoSe and BP-SeMoS vdW heterostructures, respectively. The Fermi level is set as zero.

at Γ-M path and increases the VBM of MoSSe layer at Γ point, which leads to a reduced bandgap of 0.76 eV. With the increase of tensile strain, the CBM of MoSSe layer at K point moves downwards and the VBM of MoSSe layer at Γ point moves upwards, leading to the reduced bandgap of 0.57 and 0.26 eV at +4% and +6% tensile strain, respectively. Furthermore, when the tensile strain exceeds +4%, the transformation of band alignment from pristine type-II to type-I is observed. To unravel the transition mechanism of band alignment, the evolution of bandgap and band edge position of BP and MoSSe with biaxial strain were further studied, the results are shown in Fig. 9. For BPSMoSe vdW heterostructure, Fig. 9(a) indicates that the bandgap decreases with the increase of tensile strain, and when the tensile strain reaches +4%, the BP-SMoSe vdW heterostructure is transformed to a metal. On the contrary, the bandgap increases at first and then decreases with the increase of compressive strain, and reaches the maximum at ε = −4%. To further elaborate the tuning mechanism, the changes of band edge as a function of strain are shown in Fig. 9(b). Clearly, the EC-SMoSe decreases while the EV-SMoSe increases with the increase of tensile strain, causing the bandgap to narrow gradually and reaches zero when the tensile strain reaches +4%. Therefore the tensile strain can tune the electronic structure and convert the BP-SMoSe vdW heterostructure from a semiconductor to a metal when the tensile strain is larger than +4%. On the other hand, the EC-SMoSe increases with the increase of compressive strain and is higher than the EC-BP at about ε = −1%, whereas the EV-SMoSe decreases with the increase of compressive strain and is lower than the EV-BP at about ε = −4%. As a result, the bandgap increases at first with the increase of compressive strain, and then decreases when the compressive strain exceeds −4%. Moreover, the band alignment is transformed to type-II when ε = −2%, and to a new type-I when ε = −6%. As for BP-SeMoS vdW heterostructure, Fig. 9(c) shows that the bandgap increases with varying of the strain from −6% to −2%, and decreases linearly as the strain varies from −2% to +6%. In Fig. 9(d), it clearly indicates that the EV-SeMoS decreases and the EC-BP increases as the strain varies from −6% to −2%, resulting in the increase of bandgap in the same strain range. On the contrary, the EV-SeMoS increases and the EC-BP decreases as the strain varies from −2% to 4%, resulting in the decrease of bandgap in this strain range. Furthermore, the decrease of the EC-SeMoS and the increase of the EV-SeMoS cause to narrow the bandgap at ε = +6%. As a result, the BP-SeMoS vdW heterostructure keeps its primary type-II band alignment under biaxial

strain in the wide range of −6% < ε < +4%, and transforms to typeI heterostructure when ε > +4% because that the EC-SeMoS is lower than the EC-BP. 4. Conclusions In summary, we have systematically investigated the structural and electronic properties of BP-SMoSe and BP-SeMoS vdW heterostructures and their modulations under external electric field and strain based on the first principles calculations. The negative formation energies and FPMD results indicate that the thermodynamic and dynamic stabilities of BP-SMoSe and BP-SeMoS vdW heterostructures. For pristine BPSMoSe vdW heterostructure, the VBM and CBM are contributed by MoSSe layer, resulting in typical type-I heterostructure and implying the recombination of photogenerated electrons and holes. Whereas for pristine BP-SeMoS vdW heterostructure, the VBM and CBM are from MoSSe and BP layer, respectively, which leads to typical type-II heterostructure and indicates the spatial separation of photogenerated electron-hole pairs. Moreover, as characterized by the band structures, bandgap and band edges position, for BP-SMoSe vdW heterostructure, we predicted that type-I heterostructure can be converted to type-II heterostructure under moderate external electric field (e.g. +0.2 V/Å), and a semiconductor to a metal can be achieved by applying moderate tensile strain (e.g. +4%). For BP-SeMoS vdW heterostructure, an indirect to direct bandgap transition can be achieved under moderate compress strain (e.g. -4%), and type-II heterostructure can be transformed to type-I heterostructure under moderate tensile strain (e.g. +4%). The present study for the modulation of electronic structures of BP-SMoSe and BP-SeMoS vdW heterostructures will benefit the further development of vdW heterostructures for multi-functional device applications. Acknowledgements The authors thank the National Science Foundation of China (Grant No. 11764019, 11664013, 11664012, 11564016) for major financial support of the current work. The partial computations were performed on TianHe-1 (A) at the National Supercomputer Center in Tianjin.

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Appendix A. Supplementary data [26]

Supplementary data to this article can be found online at https:// doi.org/10.1016/j.apsusc.2019.143809.

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