First-principles investigations of the controllable electronic properties and contact types of type II MoTe2/MoS2 van der Waals heterostructures

Two-dimensional (2D) van der Waals (vdW) heterostructures are considered as promising candidates for realizing multifunctional applications, including photodetectors, field effect transistors and solar cells. In this work, we performed first-principles calculations to design a 2D vdW MoTe2/MoS2 heterostructure and investigate its electronic properties, contact types and the impact of an electric field and in-plane biaxial strain. We find that the MoTe2/MoS2 heterostructure is predicted to be structurally, thermally and mechanically stable. It is obvious that the weak vdW interactions are mainly dominated at the interface of the MoTe2/MoS2 heterostructure and thus it can be synthesized in recent experiments by the transfer method or chemical vapor deposition. The construction of the vdW MoTe2/MoS2 heterostructure forms a staggered type II band alignment, effectively separating the electrons and holes at the interface and thereby extending the carrier lifetime. Interestingly, the electronic properties and contact types of the type II vdW MoTe2/MoS2 heterostructure can be tailored under the application of external conditions, including an electric field and in-plane biaxial strain. The semiconductor–semimetal–metal transition and type II–type I conversion can be achieved in the vdW MoTe2/MoS2 heterostructure. Our findings underscore the potential of the vdW MoTe2/MoS2 heterostructure for the design and fabrication of multifunctional applications, including electronics and optoelectronics.


Introduction
The advent of two-dimensional (2D) materials, characterized by their atomic structures and unique properties, has ushered in a new era of exploration and innovation in condensed matter physics and materials science.This burgeoning class of materials, with graphene 1 as a pioneering example, has captivated both fundamental and industrial researchers.Following the success of graphene, a plethora of 2D materials have been exfoliated and investigated, both in terms of fundamental understanding and practical applications.9][30] Among them, the exploration of vdW heterostructures between different 2D TMD materials has received much more consideration and interest.Many 2D TMDbased vdW heterostructures have been successfully fabricated and explored, such as MoS 2 /WSe 2 , 31,32 HfS 2 /MoS 2 , 33 MoS 2 /WS 2 , 34 MoTe 2 /ReS 2 (ref.35) and black phosphorus/MoS 2 . 36One can nd that the 2D vdW TMD heterostructures can be synthesized in experiments by various strategies, including top-down 37 and bottom-up 38,39

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PAPER experiments by various methods, such as one-step CVD, 40 mechanical exfoliation 41,42 and direct imprinting. 43Using the one-step CVD technique, Ding et al. 40 fabricated a MoTe 2 /MoS 2 heterostructure and demonstrated that the photodetector based on such a heterostructure exhibits outstanding photoresponsivity and external quantum efficiency.Lately, Ji et al., 41 utilizing mechanical exfoliation, fabricated a 2D vdW MoTe 2 / MoS 2 heterostructure.These ndings proved that such a heterostructure can be considered as a promising candidate for optoelectronic devices and integrated photonics.In addition, the MoTe 2 /MoS 2 heterostructure can also be fabricated by combining the mechanical exfoliation and transfer methods 42 or direct imprinting. 43All these experimental ndings highlighted the potential applications of MoTe 2 /MoS 2 heterostructures for multifunctional devices, including electronics and optoelectronics.Despite experimental successes in the fabrication of MoTe 2 /MoS 2 heterostructures, a comprehensive computational investigation into the depth of their atomic structure, electronic properties and the formation of contact types is notably lacking.Therefore, in this work, we perform rst-principles calculations to design a MoTe 2 /MoS 2 heterostructure and investigate its structures and electronic properties and the formation of type II band alignment.The impact of external conditions is also explored to examine the potential applications of the MoTe 2 /MoS 2 heterostructure for multifunctional devices.Our ndings underscore the potential of the vdW MoTe 2 /MoS 2 heterostructure for the design and fabrication of multifunctional applications, including electronics and optoelectronics.

Computational methods
In this work, the rst-principles calculations are performed using the Quantum Espresso simulation package. 44,45The geometric optimization process and electronic property calculations are performed in the framework of the Perdew-Burke-Ernzerhof (PBE) functional 46 within the projector augmentedwave (PAW) pseudopotential. 47A cut-off energy of 510 eV and a Monkhorst-Pack (9 × 9 × 1) K-point mesh are employed for all the processes and calculations.The hybrid Heyd-Scuseria-Ernzerhof (HSE) functional 48 is also employed to get a more accurate band gap value of materials.The weak vdW interactions that may occur in layered materials can be described by adding the long-range dispersion correction of the Grimme DFT-D3 method. 49The convergence threshold for the force and energy in all the calculations is set at 0.01 eV Å −1 and 10 −6 eV, respectively.A vacuum thickness of 27 Å is applied along the z direction of materials to avoid any unnecessary interlayer interactions.A dipole correction is also employed for all the calculation processes.

Results and discussion
We rst investigate the atomic structure and electronic properties of MoX 2 (X = Te, S) monolayers.The atomic structures of MoX 2 are depicted in Fig. 1.The MoX 2 monolayer consists of an X-Mo-X layer, where a Mo atom is sandwiched between two X atoms on different sides.Similar to graphene, the MoX 2 monolayer shows a hexagonal atomic structure.The lattice parameters of MoTe 2 and MoS 2 monolayers are calculated to be 3.50 and 3.16 Å, respectively.These values are consistent with the experimental measurement. 50The electronic band structures of MoS 2 and MoTe 2 monolayers are depicted in Fig. 1

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Nanoscale Advances the PBE and HSE06 functionals yield consistent behavior for the MoS 2 and MoTe 2 monolayers.Hence, we employed the PBE functional for the subsequent calculations due to its low computational resource.The phononic spectrum of MoS 2 and MoTe 2 monolayers is illustrated in Fig. 1(e) and (f).One can observe that there are no negative frequencies in the phonon spectrum of both the MoS 2 and MoTe 2 monolayers, predicting that these monolayers are dynamically stable.
The atomic structures of the MoTe 2 /MoS 2 heterostructure are illustrated in Fig. 2. The MoTe 2 /MoS 2 heterostructure is designed by using (2 × 2) unit cells of a MoS 2 monolayer and Þ unit cells of a MoTe 2 monolayer.The lattice mismatch is calculated to be 2.1%, which is small and can be considered negligible.Aer geometric optimization, the interlayer spacing d between the two constituent MoTe 2 and MoS 2 monolayers is obtained to be 3.33 Å.This interlayer spacing is consistent with that in other typical vdW heterostructures [51][52][53] and the experimental value. 42This indicates that the MoTe 2 / MoS 2 heterostructure is characterized by weak vdW interactions.Furthermore, to examine the stability of the MoTe 2 /MoS 2 heterostructure, we calculate the binding energy as follows: Here, E H and E M are the total energies of the MoTe 2 /MoS 2 heterostructure and isolated MoX 2 (X = S, Te) monolayers, respectively.A stands for the surface area of the heterostructure.
The E b of the MoTe 2 /MoS 2 heterostructure is obtained to be −32.23 meV Å −2 .The negative value of the binding energy indicates that the MoTe 2 /MoS 2 heterostructure is structurally stable.In addition, we nd that the value of the binding energy is consistent with that in graphite 54 and other vdW-based systems. 55,56All these ndings conrm that the weak vdW interactions are mainly dominated at the interface of the MoTe 2 /MoS 2 heterostructure.It is noteworthy that the weak vdW interactions keep the MoTe 2 /MoS 2 heterostructure stable and can be synthesized in recent experiments by the transfer method 42 or chemical vapor deposition (CVD) method. 40urthermore, to check the thermal and mechanical stability of the MoTe 2 /MoS 2 heterostructure, we perform Ab initio molecular dynamics (AIMD) simulation and elastic constant calculation.The uctuation in the total energy as a function of time steps of the MoTe 2 /MoS 2 heterostructure is depicted in Fig. 3(a).It is evident that the change in the total energy of the MoTe 2 /MoS 2 heterostructure before and aer heating for 6 ps is small.Additionally, there is no distortion in the atomic structure of the MoTe 2 /MoS 2 heterostructure aer heating for 6 ps.All these ndings conrm that the MoTe 2 /MoS 2 heterostructure is thermally stable at room temperature of 300 K.The elastic constants C ij of the MoTe 2 /MoS 2 heterostructure are also calculated to evaluate its mechanical stability.The elastic constants of the MoTe 2 /MoS 2 heterostructure are depicted in Fig. 3

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Paper monolayers, exhibiting that the construction of the MoTe 2 / MoS 2 heterostructure leads to an enhancement in the in-plane stiffness, as depicted in Fig. 3(c).
The projected band structure of the MoTe 2 /MoS 2 heterostructure is depicted in Fig. 4(a).The MoTe 2 /MoS 2 heterostructure possesses a semiconducting behavior with an indirect band gap.The VBM is located at the G point, whereas the CBM is at the K point.The band gap of the MoTe 2 /MoS 2 heterostructure is 0.97 eV.Such a band gap is still smaller than that of both the constituent MoTe 2 and MoS 2 monolayers.This implies that the formation of the MoTe 2 /MoS 2 heterostructure gives rise to a reduction in the band gap.A narrower band gap corresponds to stronger optical absorption.Therefore, the construction of the MoTe 2 /MoS 2 heterostructure could lead to an enhancement in the optical properties.More interestingly, the band edges of the MoTe 2 /MoS 2 heterostructure are contributed by distinct layers.The VBM is mainly contributed by the MoTe 2 layer, while the CBM comes from the MoS 2 layer.This nding suggests that the MoTe 2 /MoS 2 heterostructure forms a type II band alignment.The formation of a type II band alignment was also observed in previous experiments. 41,42herefore, the type II MoTe 2 /MoS 2 heterostructure can be considered as a promising candidate for the design of optoelectronic and electronic devices, such as photodetectors and transistors.
We further consider the charge redistribution at the interface of the MoTe 2 /MoS 2 heterostructure by analyzing the charge density difference (CDD) as follows: The electrostatic potential of the MoTe 2 /MoS 2 heterostructure is displayed in Fig. 4(c).One can nd that the difference in the potential of the MoS 2 and MoTe 2 layers is small, verifying a small amount of charge transfer between the two layers.In addition, the potential of the MoS 2 layer is deeper than that of the MoTe 2 layer, conrming that the electrons move from the MoS 2 to the MoTe 2 layer.Such charge transfer leads to the formation of a built-in electric eld, pointing from the MoS 2 to the MoTe 2 layer in their combined heterostructure.Furthermore, we examine how the external conditions impact the electronic properties and contact types of the MoTe 2 / MoS 2 heterostructure.Therefore, external electric elds and biaxial strains are applied to the heterostructure.The electric elds are applied along the z direction of the heterostructure, as depicted in the inset of Fig. 5(a).The positive direction of the electric elds is dened as from the MoTe 2 to the MoS 2 layer in their combined heterostructure.It is evident that an electric eld can be used to modify the band gaps and change the contact types in the MoTe 2 /MoS 2 heterostructure, as shown in Fig. 5(a).The band gap of the MoTe 2 /MoS 2 heterostructure increases with applying a negative electric eld and decreases with applying a positive electric eld.The physical mechanism of such change can be described as follows: the direction of the built-in electric eld is opposite to that of the negative electric Furthermore, it should be mentioned that a high strength electric eld can be generated from the tabletop terahertz source within an electrolyte top gate. 58Additionally, a high strength electric eld always requires high-k and a back (top)gated device architecture. 59All these ndings prove that the electric eld can be considered as an effective tool to manipulate the electronic properties and contact type of the MoTe 2 / MoS 2 heterostructure, thereby expanding its potential applications in electronics and optoelectronics. 60he biaxial in-plane strain is derived from 3 b = (a − a 0 )/a 0 × 100%, where a and a 0 are the lattice parameters of the MoTe 2 / MoS 2 heterostructure with and without the application of the biaxial strain, respectively.The negative and positive values refer to the compressive and tensile strains, respectively.The schematic model of the in-plane biaxial strain is depicted in the inset of Fig. 6.It is obvious that the strain causes a change in both the band gap values and contact types of the MoTe 2 /MoS 2 heterostructure.The biaxial strain gives rise to a reduction in the band gap of the MoTe 2 /MoS 2 heterostructure, as depicted in Fig. 6(a).The band gap of the MoTe 2 /MoS 2 heterostructure can be reduced down to zero under the application of either a compressive strain of −12% or a tensile strain of +16%.This observation indicates that the transition from semiconductor to metal can be achieved in the MoTe 2 /MoS 2 heterostructure under the application of biaxial strain.Additionally, the tensile strain can also lead to the transformation between type II and type I band alignment in the MoTe 2 /MoS 2 heterostructure.

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To have a better understanding of the impact of the strain, we further analyze the projected band structures of the MoTe 2 / MoS 2 heterostructure under different strain ratios, as illustrated in Fig. 6(b).When the compressive strain is applied, both the VBM and CBM of the MoTe 2 /MoS 2 heterostructure shi towards the Fermi level, giving rise to a reduction in the band gap values.Similarly, the band edges of both the MoTe 2 and MoS 2 layers in the MoTe 2 /MoS 2 heterostructure move closer to the Fermi level under the tensile strain.Under a tensile strain of 3 b = +3%, the CBM of the MoTe 2 /MoS 2 heterostructure shis from the K to the G point.Thus, the indirect-to-direct transition is achieved in the MoTe 2 /MoS 2 heterostructure.In addition, both the VBM and CBM of the MoTe 2 /MoS 2 heterostructure now come from the MoTe 2 layer, indicating that there occurs a transition from type II to type I band alignment.The type I band alignment is maintained in the MoTe 2 /MoS 2 heterostructure under tensile strains ranging from +3% to +6%.When the tensile strain is larger than +6%, the CBM of the MoTe 2 /MoS 2 heterostructure is recovered from the G to the K point, while the VBM is preserved at the G point.This recovery indicates that there is a transition from direct to indirect semiconductor and a conversion from type I to type II band alignment because the band edges of the MoTe 2 /MoS 2 heterostructure are contributed by the MoTe 2 layer.When the tensile strain is larger than 16%, the band edges of the MoTe 2 /MoS 2 heterostructure cross the Fermi level, leading to a transition from semiconductor to metal.Our ndings prove that the in-plane biaxial strain can effectively be used to tailor the electronic properties and contact types in the MoTe 2 /MoS 2 heterostructure, thereby expanding its potential applications in multifunctional devices.

Conclusions
In conclusion, we have performed rst-principles calculations to design a 2D vdW MoTe 2 /MoS 2 heterostructure with the formation of a type II band alignment.Our results indicate that the MoTe 2 / MoS 2 heterostructure is structurally, thermally and mechanically stable.The weak vdW interactions are found to be dominated at the interface of the MoTe 2 /MoS 2 heterostructure and thus it can be synthesized in recent experiments by the transfer method or chemical vapor deposition.The vdW MoTe 2 /MoS 2 heterostructure exhibits a staggered type II band alignment, effectively separating the electrons and holes at the interface and thereby extending the carrier lifetime.Furthermore, our ndings reveal that the electronic properties and contact types of type II vdW MoTe 2 /MoS 2 heterostructures can be tailored under the application of external conditions, including an electric eld and in-plane biaxial strain.The semiconductor-semimetal-metal transition and type II-type I conversion can be achieved in the vdW MoTe 2 /MoS 2 heterostructure.Our ndings underscore the potential of the vdW MoTe 2 / MoS 2 heterostructure for the design and fabrication of multifunctional applications, including electronics and optoelectronics.

Conflicts of interest
There are no conicts to declare.The inset shows the schematic model of the applied in-plane biaxial strain to the heterostructure.

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Nanoscale Advances Fig. 1 (a) Top view and (b) side view of the atomic structures of a MoX 2 (X = S, Te) monolayer.Calculated electronic band structures of (c) MoS 2 and (d) MoTe 2 monolayers from PBE and HSE functionals.Phonon spectrum of (e) MoS 2 and (f) MoTe 2 monolayers.

Fig. 2
Fig. 2 (a) Top view and (b) side view of the atomic structure of the MoTe 2 /MoS 2 heterostructure.

Fig. 3
Fig. 3 (a) The fluctuation in the total energy as a function of time steps of the MoTe 2 /MoS 2 heterostructure.The insets show the atomic structures of the MoTe 2 /MoS 2 heterostructure before and after heating for 6 ps.(b) Elastic constants and (c) angle-dependent Young's modulus of the MoTe 2 /MoS 2 heterostructure and the isolated MoTe 2 and MoS 2 constituent monolayers.
) Here, r H and r M are the charge densities of the MoTe 2 /MoS 2 heterostructure and isolated MoX 2 (X = S, Se) monolayers, respectively.The planar-averaged CDD of the MoTe 2 /MoS 2 heterostructure is depicted in Fig. 4(b).The dark blue and dark orange regions represent charge accumulation and depletion, respectively.It is evident that the charges are mainly accumulated in the MoTe 2 layer and depleted in the MoS 2 layer.It indicates that the MoTe 2 gains electrons, while the MoS 2 layer loses electrons.The electrons ow from the MoS 2 to the MoTe 2 layer, whereas the holes are transferred in the opposite direction, i.e. from the MoTe 2 to the MoS 2 layer.Bader charge analysis indicates that there is a small amount of charge transfer of about 10 −3 electrons between the two constituent layers.Furthermore, to conrm the charge transfers in the MoTe 2 /MoS 2 heterostructure, we also calculate the work functions of the MoTe 2 /MoS 2 heterostructure and the constituent MoX 2 monolayers.The work function of a material can be calculated as: F = E vac − E F , where E vac and E F represent the vacuum energy and Fermi energy, respectively.The work functions of the MoTe 2 and MoS 2 monolayers are calculated to be 4.76 eV and 4.08 eV, respectively.The lower work function of the MoS 2 monolayer compared to that of the MoTe 2 monolayer conrms that the electrons move from the MoS 2 to the MoTe 2 layer upon the formation of the heterostructure.The work function of the MoTe 2 /MoS 2 heterostructure is calculated to be 4.98 eV, which is larger than that of the MoS 2 and MoTe 2 layers.

Fig. 4
Fig. 4 (a) Projected band structure, (b) planar-averaged charge density difference and (c) electrostatic potential of the MoTe 2 /MoS 2 heterostructure.Red and blue balls stand for the contributions of the MoS 2 and MoTe 2 layers, respectively.The dark blue and dark orange represent the charge accumulation and depletion, respectively.

Fig. 5
Fig. 5 (a) The variation of the band gaps and (b) the projected band structures of the MoTe 2 /MoS 2 heterostructure under electric fields of different strengths.The inset shows the schematic model of applied electric fields along the z direction of the heterostructure.

Fig. 6
Fig. 6 (a) The variation of the band gaps and (b) the projected band structures of the MoTe 2 /MoS 2 heterostructure under different ratios of strain.The inset shows the schematic model of the applied in-plane biaxial strain to the heterostructure.