α-tellurene van der Waals heterostructure via biaxial strain and external electric field

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S0169-4332(19)33641-4 https://doi.org/10.1016/j.apsusc.2019.144824 APSUSC 144824

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Please cite this article as: M.M. Obeid, Tuning the Electronic and Optical Properties of Type-I PbI2/α-Tellurene Van der Waals Heterostructure via Biaxial Strain and External Electric Field, Applied Surface Science (2019), doi: https://doi.org/10.1016/j.apsusc.2019.144824

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Tuning the Electronic and Optical Properties of Type-I PbI2/αTellurene Van der Waals Heterostructure via Biaxial Strain and External Electric Field Mohammed M. Obeid Department of Ceramics, College of Materials Engineering, University of Babylon, 51002, Hilla, Iraq

Abstract Using density functional theory (DFT), we systematically studied the impact of biaxial strain and an external electric field on the electronic and optical properties of two-dimensional PbI2/α-Te van der Waals (vdW) heterostructures. The stability of the constructed PbI2/α-Te heterostructures has been predicted based on the binding energy, phonon spectrum, and molecular dynamics simulation. Our results have revealed that the most stable PbI2/α-Te vdW heterostructure has a distinct type-I band alignment with an indirect bandgap of 0.64 eV. The intrinsic type-I band alignment can be transformed to either type-II or type-III by applying a strong external electric field, which holds great potential for designing multifunctional devices. Furthermore, the compressive and tensile strains can be varied to effectively tune the bandgap value between 0.55 eV and 0.85 eV. Additionally, the constructed PbI2/α-Te vdW heterostructure exhibits excellent optical absorption properties in the UV-Vis regions under biaxial strain and external electric field. Overall, the constructed PbI2/α-Te heterostructure is expected to find potential applications in nanoelectronic devices. Corresponding author. Tel: +9647812307281 E-mail address: [email protected] (Mohammed M. Obeid, volunteer researcher)

Keywords: Type-I band alignment; Van der Waals heterostructures; DFT; Optical properties; Nanomaterials; Strain engineering.

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1. Introduction The successful isolation of graphene has attracted research interest in discovering various types of ultrathin two-dimensional (2D) nanomaterials [1]. Such interest is attributed to graphene's excellent chemical and physical properties [2, 3]. However, the gapless characteristic of graphene has limited its functional applications. Therefore, new 2D materials, such as transition metal dichalcogenides (TMDCs), transition metal carbides (TMCs), transition metal oxides (TMOs), hexagonal boron nitride (h-BN), phosphorene, and arsenene, have been investigated [4-13]. Among them, the most investigated are TMDCs, which exhibit intriguing electronic, optical, mechanical, and thermal properties [4, 5, 14]. But, the relatively low carrier mobility of the TMDCs limits their practical applications [15]. Several studies have revealed that van der Waals (vdW) heterostructures with two or more 2D materials would be likely to overcome the limitation of the monolayer materials [16-18]. Moreover, there are already many theoretical and experimental attempts to study 2D vdW heterostructures, such as graphene/phosphorene [19], MoS2/PbI2 [20-22], α-tellurene/MoS2 [23], MoS2/h-BN [24], MoSe2/phosphorene [25], graphene/GeC [26], GaN/TDMs [27], TDMs/Mg(OH)2 vdW heterostructures [28] and so on. These studies have suggested that vdW heterostructure is an effective alternative for tuning the fundamental properties of 2D materials because the resulting electronic, optical, and magnetic properties of these heterostructures surpass those of the individual monolayers. The most important characteristic of such heterostructures is the bandgap alignment, which can be assorted into three different types, i.e., straddling type-I, staggered type-II, and broken-gap type-III [29]. And each type of band alignment suits specific device applications. Type-I band alignment is valuable for spatially confining electrons and holes so that efficient recombination can be feasible, and hence type-I 2

band alignment is favorable for practical applications in light-emitting diodes and semiconductor lasers [30, 31]. Unlike the type-I band alignment, the large band offset in type-II band alignment offers significant carrier separation, which is beneficial for photovoltaic and photocatalytic devices [32, 33]. Band offset in type-III band alignment can facilitate the engineering of the conduction-to-valence band transition energy. As a result, this type may be useful in designing novel tunnel field-effect transistors and wavelength photodetectors [34]. Most recently, lead iodide (PbI2) and α-tellurene (Te) were successfully fabricated and added to the library of 2D monolayer materials [15, 35]. PbI2 is a typical layered semiconductor material with important applications as a nuclear radiation detector, photodetector, and a lead‐halide perovskite solar cell [36-39]. Moreover, PbI2 is a very soft and flexible material, which can be used in flexible optoelectronics [40, 41].

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α-tellurene monolayer has been theoretically predicted and experimentally synthesized on highly oriented pyrolytic graphite (HOPG) substrates [35]. This material has also been studied for both its unique properties and a wide range of potential applications [23]. Specifically, α-Te monolayer possesses higher electron and hole mobility than MoS2 and demonstrates outstanding optical absorption performance [35]. Both PbI2 and α-Te monolayers have a stable 1T-MoS2-like structure, where the intermediate Pb (Te) atoms act as a metal-like and the two outer I (Te) atoms as more semiconductor-like. Based on these excellent characteristics of 2D PbI2 and α-Te monolayers, we have created new PbI2/α-Te vdW heterostructures to investigate their relevant strengths in electronic and optoelectronic devices. In this paper, the structural, electronic, and optical properties of a newly designed vdW heterostructure, composed of single layers of PbI2 and α-Te, were studied using the first-principles calculations. The results showed that this heterostructure has a 3

distinct type-I band alignment. Then, we tuned the electronic and optical properties of the constructed heterostructure by varying the interlayer distance, biaxial strain, and an external electric field. The results have shown that the intrinsic type-I band alignment can be altered to either type-II or type-III by applying a strong external electric field. Moreover, the bandgap value can be tuned by applying vertical and biaxial strains. 2. Computational methodology All the density functional theory (DFT) calculations have been performed using the Cambridge Serial Total Energy Package (CASTEP) code [42, 43]. Ultrasoft pseudopotentials were used for geometry optimizations [44, 45]. All electrons contributing to exchange-correlation energy were treated via the generalized gradient approximation within the scheme of Perdew–Burke–Ernzerhof (GGA-PBE) [46, 47]. The vdW density functional correction procedure proposed by Tkatchenko and Scheffler (TS-vdW) [48] was adopted in our calculations to describe the long-range vdW interactions. The cutoff energy for the plane-waves was chosen to be 500 eV. A sufficiently large vacuum space (20 Å) was applied to avoid any interactions between neighboring layers along the z-axis. For geometry optimizations, the Brillouin zone was sampled by 5×5×2 mesh points in k-space based on the Monkhorst-Pack scheme [49, 50]. For optical properties and the density of states (DOS) calculations, a sufficiently dense k-points mesh of 7×7×2 was used. In the geometry relaxation process, the convergence criteria for the total energy and residual forces were set to 10 −6 eV/atom and 0.03 eV/Å, respectively. The valence states for Pb, I, and Te atoms were selected to be 5d106s26p2, 5s25p5 and 5s25p4, respectively. Furthermore, the hybrid Heyd– Scuseria–Ernzerhof (HSE06) [51, 52] method was used to ascertain the validity of the results achieved by the PBE scheme.

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. The optical absorption curves of PbI2/α-Te vdW heterostructure were predicted using the formula below [53, 54]: 12

  ( )  2 ( )   22 ( )   n ( )   1  1 2  2 

(1)

where ε1 and ε2 are the real and imaginary parts of the dielectric function, respectively, and ω is the photon frequency. 3. Results and discussion 3.1. Geometric structures and the stability of heterostructures PbI2/α-Te vdW the structural parameters of PbI2 and α-Te monolayers were optimized. It was found that the single-layer PbI2 sheet has a hexagonal structure with optimized lattice constants a = b = 4.558 Å, and the Pb─I bond length is 3.249 Å. These calculated values are consistent with the previous experimental and theoretical reports [55-60]. On the other hand, the optimized lattice constants and the Te─Te bond length of α-tellurene are estimated to be 4.15 Å and 3.009 Å, respectively. Our findings are in uniform agreement with the recent experimental and theoretical results [23, 35]. A good lattice match between two or more 2D materials is essential for the construction of ideal vdW heterostructures. However, it should be noted that there is a large lattice mismatch (~10%) between PbI2 and α-Te monolayers, see Fig. 1(a). Since the electronic properties of PbI2 are sensitive to strain [61], the lattice constants of PbI2 were kept fixed and the lattice constants of α-Te for constructing the M-type PbI2/α-Te vdW heterostructure were varied [62], see Fig. 1(b). Consequently, the lattice mismatch of the M-type heterostructure is about 2.5 %, and the lattice parameters of the primitive 5

cell are a = b = 4.39 Å after the relaxation. The corresponding structural parameters, binding energies, and bandgap values are given in Table S1. To quantitatively assess the relative stability of PbI2/α-Te vdW heterostructures, the binding energies (Eb) are calculated as, E b  E PbI 2 / Te  E PbI 2  E  Te

(2)

where E PbI 2 / Te , E PbI 2 , and E  Te are the total energies of the heterostructures and freestanding PbI2 and α-Te monolayers, respectively. A negative value of the binding energy proves the stability of the heterostructure. As depicted in Fig. 1(a) and (b), both S-type and M-type heterostructures have negative binding energies at their optimum interlayer distances. However, the binding energies of the M-type PbI2/α-Te vdW heterostructure are all negative under different interlayer distances. This observation confirms the higher stability of M-type over S-type. The obtained values are consistent with other similar vdW heterostructures [58, 61, 63]. For M-type heterostructure, the optimized vertical interlayer distance between the PbI2 and α-Te layers is 3.561 Å, while it is 3.982 Å for the S-type. These distances are larger than the sum of the covalent radii of I and Te atoms [64], indicating that the two building blocks are beyond the bonding range. Generally, the electronic properties of a heterostructure can be modulated by the interaction between the stacked monolayers. Hence, the variation of bandgap (Eg) as a function of different interlayer distances (d) has been studied. With vertical compressive strains, the bandgap increased progressively as the interlayer distance decreases, see Fig. 1(a) and (b). On the other hand, the vertical tensile strains have a minor effect on the variation of the bandgap values. The results may indicate that the bandgap of PbI2/α-Te vdW heterostructure is more sensitive to compressive strain than 6

tensile one. The obtained results showed that the bandgap type and bandgap alignment character are retained under the effect of vertical strains. To further validate the stability of the M-type vdW heterostructure, phonon calculations and ab initio molecular dynamics (AIMD) simulations were performed, see Fig. 2. The phonon dispersion curve along the full Brillouin zone (Γ-M-K- Γ) shows that the M-type heterostructure exhibits no imaginary frequency mode, indicating the dynamic stability of the constructed heterostructure, see Fig. 2(a). The AIMD calculations were achieved under the canonical NVT ensemble at 300 K for 6 ps, as illustrated in Fig. 2(b). The thermal stability was confirmed by the time-dependent calculation of temperature. It can be deduced from the snapshots of the structure (before and after heat treatment) that the atoms are displaced around their equilibrium positions throughout the simulations. Moreover, neither broken bond nor structural reconstruction takes place at 300 K, indicating the thermal stability of the constructed heterostructure at room temperature. Thus, in the next subsections, we choose to discuss the electronic and optical properties of M-type vdW heterostructure. 3.2. Electronic band structure To analyze the electronic band structure of the PbI2/α-Te vdW heterostructure, firstly, the corresponding results of the individual monolayers of lead iodide and αtellurene are studied. As presented in Fig. 3 (a) and (b), monolayers PbI2 and α-Te are indirect band semiconductors with the bandgap values of 2.57 eV and 0.78 eV, respectively. For both monolayers, the valence band maximum (VBM) is positioned between K and Γ points, whereas the conduction band minimum (CBM) is located at Γ' point. The obtained results are in close agreement with the recent experimental and theoretical reports [15, 35, 65, 66]. The partial density of states (PDOS) of both PbI2

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and α-Te monolayers revealed that the conduction and valence bands are dominated by p-orbitals. Next, the electronic band structure of the PbI2/α-Te vdW heterostructure was calculated. This heterostructure is a semiconductor material with an indirect bandgap of 0.64 eV, see Fig. 3(c). The PDOS showed that the VBM and CBM are dominated by Te-p orbitals. It can be argued that the intrinsic electronic properties are preserved when α-Te monolayer transforms into type-I PbI2/α-Te vdW heterostructure. Also, it should be noted that the bandgap value of this type of heterostructure is lower than that of the individual monolayers, indicating the weak charge transfer between PbI2 and αTe layers. The influence of SOC interaction on the electronic band structure of the individual monolayers and heterostructure has also been investigated using the PBE-SOC scheme. reduction in the bandgap of PbI2 (1.77eV) with SOC has been observed, see Fig. 3. On the other hand, the bandgap of α-Te with SOC is about 0.62 eV, which is less than that without SOC. The calculated values are in line with other published data [15, 35, 59]. For PbI2/α-Te vdW heterostructure, the calculated bandgap value has been reduced down to 0.28 eV, which confirms the effect of SOC interaction in heavy elements. The hybrid HSE06 method with 25% Hartree–Fock exchange energy has been employed to predict the electronic band structure of the individual monolayers and that of the heterostructure, see Fig. S1, Supporting Information. It is found that the bandgap values of PbI2 and α-Te monolayers are 3.59 eV and 1.1 eV, respectively, which are overestimated the experimental bandgap values. Moreover, the bandgap value of PbI2/α-Te vdW heterostructure is 1.00 eV. Interestingly, one can observe that the obtained bandgap values from the PBE method are in good agreement with the experimental results [15, 35]. Therefore, PBE is sufficient to estimate the correct trend in bandgap variation and well validates the physical mechanisms. 8

The band alignments of the PbI2/α-Te vdW heterostructure are determined using the vacuum level as an energy reference. As shown in Fig. 3(d), the calculated band alignment revealed the formation of type-I heterojunction, which is favorable to attain the practical applications in the light-emitting diodes (LEDs). A similar trend has been found in the experimental results of MoS2/PbI2 [20, 21] and theoretical report of αTe/MoS2 vdW heterostructures [23]. The work function of a crystalline solid is an important parameter and is widely used as an intrinsic reference to predict the type of bandgap alignment [67]. The calculated work functions of PbI2 and α-Te monolayers are 6.28 eV and 5.20 eV, which are consistent with the previous reports [23, 60]. Additionally, the calculated work function of the PbI2/α-Te vdW heterostructure is 5.18 eV. It can be seen that the work function of the constructed heterostructure is lower than that of both individual monolayers, which indicates the strong interaction at the interface. A large potential difference (ΔV = 10.9 eV) between PbI2 and α-Te indicates a strong built-in electric field at the interface (see Fig. S2, Supporting Information). This behavior leads to extensive modifications of the electronic band structure near the Fermi level [68]. As shown in Fig. 3(d), the Fermi level (EF) of PbI2 is positioned near the valence band because it is a p-type semiconductor, whereas the EF of α-Te approaches the conduction band since it is an n-type semiconductor. Thus, PbI2 loses electrons, whereas α-Te gains electrons after the contact. A charge density difference was used to study the interfacial charge transfer of the PbI2/α-Te vdW heterostructure, see Fig. S2(d). The latter shows clear charges accumulation at the PbI2/α-Te vdW heterostructure interface, while they are depleted in individual monolayers. The conduction band offset (CBO), and valence band offset (VBO) between the PbI2 and α-Te layers are 0.755 eV and 0.75 eV, respectively. With these band offsets, both electrons and holes excited in the PbI2 layer transfer to the α-Te layer, whereas the 9

carriers excited in the α-Te layer are prevented from interlayer transfer because of their lower energies, see Fig. 3(d). Hence, the quantum confinement of electrons and holes is likely to recombine again, which is valuable in LED applications [62]. The results showed that the predicted band edge positions are in line with the recent reports of similar vdW heterostructures [20, 21]. 3.3. Band structure of strained heterostructure The electronic properties of vdW heterostructures can be modulated under the effect of tensile or compressive strains, which have been widely used in 2D systems [69-71]. These strains can be applied to such heterojunctions by mechanical loading or lattice mismatch on a substrate [69, 72]. Accordingly, it is necessary to study the effect of strain on the electronic band structure of PbI2/α-Te vdW heterostructure. The biaxial strain can be defined as ε = a-a0/a0 [73], where a0 and a are the lattice constants of the unstrained and strained heterostructure, respectively. The positive and negative signs correspond to tensile and compressive strains, respectively. Starting with the optimized PbI2/α-Te vdW heterostructure, we select strain within the range of ± 8% to investigate its influence on the bandgap variation. Fig. 4(a) displays the variation of the bandgap and strain energy of PbI2/α-Te vdW heterostructure with biaxial strains, Es = (Estrained − Eunstrained)/n, with n being the number of atoms in the unit cell. The results revealed that the biaxial strain is in perfect quadratic function with the energy per atom, indicating that the system is flexible and all the strains considered are within the elastic limit and, hence, are completely reversible [74]. Therefore, the bandgap value of the PbI2/α-Te vdW heterostructure can be effectively tuned by applying moderate biaxial strains. The same trends can be found in PbI2 and α-Te monolayers [59, 75]. The calculations showed that the locations of

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CBM and VBM are not changed under the effect of tensile and compressive stresses. Thus, the unstrained heterostructure preserved its indirect bandgap character under the influence of strains, see Fig. 4(b) and (c). Under increasing compressive strain, the VBM is always located between the K and Γ points. On the other hand, the energy of the conduction band minimum at Γ'-point is shifted to higher energy levels compared to the original CBM. Similarly, the VBM is positioned between K and Γ points with the increasing of applied tensile strain, but the CBM at Γ'-point tends to shift to lower energy levels. It can be concluded that the applied strains cannot induce indirect-direct bandgap transition, semiconductor-metal transition, and band alignments transition. However, suitable bandgap values in the range of 0.55 eV to 0.85 eV can be achieved by applying tensile and compressive strains. As a result, the stained PbI2/α-Te vdW heterostructure is anticipated to find its potential applications in optoelectronic devices. 3.4. Electric field effects on the band structure of the PbI2/α-Te heterojunction It is well known that the electronic band structure of heterojunctions can be effectively modulated by applying an external electric field (Eext.) [2]. Therefore, the impact of Eext. on the electronic properties of the PbI2/α-Te vdW heterostructure has been evaluated. Two opposite electric fields (positive and negative) were studied in the direction normal to the stacking (along the z-axis). The positive electric field is taken as pointing from the bottom of the PbI2 layer to the top of the α-Te layer, while that of the negative electric field represents the opposite direction, see Fig. 5. One may note that positive Eext. values have a significant effect on the variation of the electronic properties. When the negative electric field is applied, the bandgap is enlarged linearly and reaches its maximum value of ~0.65 eV at -0.15 V/Å. This is caused by the slight

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shifting of CBM towards higher energy levels, as plotted in Fig. 5(b). Beyond -0.15 V/Å, a bandgap reduction is observed and reaches a minimum value of approximately 0.57 eV at -0.9 V/Å. This is caused by the slight shifting of CBM towards lower energy levels. On the other hand, when a positive electric field is applied, the bandgap decreased linearly at Eext.  +0.2 V/Å. This is caused by the slight shifting of CBM towards lower energy levels, see Fig. 5(c). At +0.3 V/Å, the bandgap increased slightly. This increase may be ascribed to the counterbalance of external electric field up to some extent with the internal electric field. The results show that PbI2/α-Te vdW heterostructure preserved the type-I band alignment under the effect of Eext. from -0.9 to +0.5 V/Å. Interestingly, type-I to type-II indirect bandgap alignment transition is observed at +0.5 V/Å  Eext. < +0.68 V/Å, see Fig. S3(a). The CBM is dominated by the PbI2 s-orbitals, while the VBM predominated by the p-orbitals of Te monolayer, resulting in the formation of type-II alignment, see the inset of Fig. 5(a). It is worth noting that the application of a stronger external electric field (Eext.  +0.68 V/Å) can induce a typical broken-gap type-III band alignment in the constructed heterostructure, see the inset of Fig. 5(a) and Fig. 5(c). Under the effect of such an external electric field, the CBM of PbI2 moves down to the VBM of the α-Te (Fig. S3(b)). Overall, the three types of bandgap alignments can be achieved in the PbI2/α-Te vdW heterostructure under diverse external electric fields, indicating multi-band alignment modulations in a single heterostructure. It can be concluded that the variation of the external electric field is an effective technique for designing high-performance optoelectronic devices.

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3.5. Optical properties The analysis of optical absorption responses can be used to evaluate the performance of a material in optoelectronic devices [10, 76]. In this work, the effect of biaxial strain and external electric field on the absorption response of the PbI2/α-Te vdW heterostructure has been studied, see Fig. 6. The results showed that the strainfree heterostructure has an intense absorption peak in the UV region. As shown in Fig. 6(a), the absorption edges have been shifted towards higher wavelengths under the effect of tensile strains, causing a reduction in the bandgap values (redshift). This observation is in excellent agreement with previous theoretical and experimental results [56, 77]. The results also revealed that the optical absorption intensity of the strained heterostructure is lower than that of the strain-free PbI2/α-Te vdW heterostructure. On the other hand, the absorption edges are found to be significantly blue-shifted under the effect of compressive strains. This observation is consistent with the bandgap variations. Moreover, the compressive strain can be varied to enhance the optical absorption response of the strain-free heterostructure. As shown in Fig. 6(a), the range of light absorption by each strained heterostructure overlaps the wavelength range of the incident AM 1.5 G solar flux. Interestingly, the positive and negative external electric fields give rise to redshift, especially at ±0.68 V/Å, with an obvious enhancement of the absorption capability, see Fig. 6(b). In conclusion, the biaxial strain and external electric field can be varied to effectively improve the visible light response of the PbI2/α-Te vdW heterostructure, indicating potential applications of such heterostructures in low-dimensional optoelectronics devices.

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4. Conclusions In this work, we examined the electronic and optical characteristics of PbI2/α-Te vdW heterostructure under the effects of biaxial strain and an external electric field. The results indicated that such heterostructure belongs to type-I band alignment, and hence, the quantum confinement of electrons and holes is likely to recombine again, which is useful in light-emitting applications. The use of SOC calculations has revealed that the bandgap value of PbI2/α-Te vdW heterostructure is reduced to 0.28 eV. Furthermore, the bandgap structure can be tuned by applying strains and external electric fields. The application of the external electric field was found to be more effective in the bandgap modulation of the constructed heterostructure, where type-II and type-III characteristics could be achieved. Furthermore, the biaxial strain and an external electric field can be varied to enhance the visible light response of the PbI2/αTe vdW heterostructure, indicating potential applications of such heterostructures in the novel 2D optoelectronics devices. References [1] H. Chen, J. Zhao, J. Huang, Y. Liang, Computational understanding of the structural and electronic properties of the GeS–graphene contact, Physical Chemistry Chemical Physics, 21 (2019) 7447-7453. [2] W. Xiong, C. Xia, J. Du, T. Wang, Y. Peng, Z. Wei, J. Li, Band engineering of the MoS2/stanene heterostructure: strain and electrostatic gating, Nanotechnology, 28 (2017) 195702. [3] H.T. Nguyen, T.V. Vu, N.T. Binh, D. Hoat, N.V. Hieu, N.T. Anh, C.V. Nguyen, H.V. Phuc, H.R. Jappor, M.M. Obeid, Strain-tunable electronic and optical properties of monolayer GeSe: Promising for photocatalytic water splitting applications, Chemical Physics, 529 (2019) 110543. [4] O. Lopez-Sanchez, D. Lembke, M. Kayci, A. Radenovic, A. Kis, Ultrasensitive photodetectors based on monolayer MoS 2, Nature nanotechnology, 8 (2013) 497. [5] N. Huo, J. Kang, Z. Wei, S.S. Li, J. Li, S.H. Wei, Novel and enhanced optoelectronic performances of multilayer MoS2–WS2 heterostructure transistors, Advanced Functional Materials, 24 (2014) 7025-7031. [6] J. Tao, T. Luttrell, M. Batzill, A two-dimensional phase of TiO 2 with a reduced bandgap, Nature chemistry, 3 (2011) 296. [7] C. Xu, L. Wang, Z. Liu, L. Chen, J. Guo, N. Kang, X.-L. Ma, H.-M. Cheng, W. Ren, Large-area high-quality 2D ultrathin Mo 2 C superconducting crystals, Nature materials, 14 (2015) 1135.

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Figures caption Fig. 1. (a) Top and (b) side views of the atomic structure of the S-type and M-type PbI2/α-Te vdW heterostructures with the variation of bandgap values and binding energies as a function of interlayer distance. Fig. 2. (a) The phonon spectrum of the M-type heterostructure and (b) the fluctuation of temperature as a function of molecular dynamics simulation steps at 300 K. Fig. 3. (a)–(c) The projected band structures and PDOS of single-layers of PbI2, α-Te, and PbI2/α-Te heterostructure using PBE functional with and without SOC effect. The Fermi level (EF) is set as zero. (d) The band alignment of singlelayers of PbI2, α-Te, and PbI2/α-Te heterostructure. The vacuum level is used as a reference. Fig. 4. (a) In-plane biaxial strain effects on the bandgap and strain energy of the PbI2/αTe heterostructure. (b) and (c) the projected band structures of the PbI2/α-Te heterostructure as a function of compressive and tensile strain, respectively. The Fermi level (EF) is set to zero. Fig. 5. (a) The bandgap values of the PbI2/α-Te heterostructure variation with the external electric field. (b) and (c) the evolution of the electronic band structure as a function of negative and positive Eext., respectively. The insets represent the positive direction of Eext. and the types of the bandgap alignments. The EF is set to zero. Fig. 6. The absorption spectra of PbI2/α-Te heterostructure as a function of (a) biaxial strain ε and (b) external electric field Eext.; the range of light absorption by each heterostructure overlaps the wavelength range of the incident AM 1.5 G solar flux.

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Highlights 

The most stable structures of the vertical heterostructures of PbI2/α-Te were obtained..

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Van der Waals interaction was predicted in this heterostructure.

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Type-I band alignment was observed in the studied vdW heterostructure.

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The effect of biaxial strain and external electric field has been investigated..

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Band gap alignment transition has been observed under the effect of external electric field.

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The heterostructure shows high optical absorption in the visible region under the effect of biaxial strain.

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Graphical Abstract

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Declaration of interest

There is no conflict of interests to be declared.

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Authorship contribution section Mohammed M. Obeid: Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Software, Supervision, Validation, Visualization, Writing-original draft, Writing- review editing.

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