Enhancing the electronic and optical properties of the metal/semiconductor NbS2/BSe nanoheterostructure towards advanced electronics

Metal–semiconductor (M–S) contacts play a vital role in advanced applications, serving as crucial components in ultracompact devices and exerting a significant impact on overall device performance. Here, in this work, we design a M–S nanoheterostructure between a metallic NbS2 monolayer and a semiconducting BSe monolayer using first-principles prediction. The stability of such an M–S nanoheterostructure is verified and its electronic and optical properties are also considered. Our results indicate that the NbS2/BSe nanoheterostructure is structurally, mechanically and thermally stable. The formation of the NbS2/BSe heterostructure leads to the generation of a Schottky contact with the Schottky barrier ranging from 0.36 to 0.51 eV, depending on the stacking configurations. In addition, the optical absorption coefficient of the NbS2/BSe heterostructure can reach up to 5 × 105 cm−1 at a photon energy of about 5 eV, which is still greater than that in the constituent NbS2 and BSe monolayers. This finding suggests that the formation of the M–S NbS2/BSe heterostructure gives rise to an enhancement in the optical absorption of both NbS2 and BSe monolayers. Notably, the tunneling probability and the contact tunneling-specific resistivity at the interface of the NbS2/BSe heterostructure are low, indicating its applicability in emerging nanoelectronic devices, such as Schottky diodes and field-effect transistors. Our findings offer valuable insights for the practical utilization of electronic devices based on the NbS2/BSe heterostructure.


Introduction
Two-dimensional (2D) materials, including graphene, 1 phosphorene 2 and transition metal dichalcogenides, 3 have received much attention from the research community owing to their exceptional properties and diverse potential applications.As the rst successfully fabricated 2D material, graphene emerges as a promising candidate in various next-generation applications, including electronic, 4 optoelectronic 5 and spintronic 6 applications.However, the absence of a desirable band gap in graphene is crucial, especially in the design of high-frequency applications, where it plays a signicant role.Hence, many different strategies, such as doping, 7 functionalization 8 and strain 9 have been proposed to open an intrinsic band gap in graphene.It's worth noting that these strategies may potentially result in a reduction in the carrier mobility of graphene. 10Therefore, seeking 2D materials with an appropriated band gap for highspeed applications remains a challenging endeavor.
Recently, the construction of a van der Waals (vdW) heterostructure by stacking two or more 2D materials has emerged as a common strategy to improve the properties and extend the application possibilities of 2D materials. 11,12VdW heterostructures can be synthesized in experiments by the chemical vapor deposition (CVD) method, 13,14 one-step growth 15 or twostep growth. 16Additionally, these heterostructures also can be predicted through rst-principles calculations. 17,188][29] The 2D vdW heterostructures can be categorized into metal/semiconductor (M-S) and semiconductor/semiconductor heterostructures (S-S), which depend on the characteristics of 2D materials.It's worth noting that the M-S heterostructure is one of the most crucial components in electronic devices.Hence, the characteristics of the M-S heterostructure signicantly impact the performance of electronic devices.Therefore, there is growing attention on the search for M-S heterostructures towards next-generation electronic devices aiming for high performance.
Recently, many different M-S heterostructures have been proposed and investigated, involving the combination of both traditional 3D metals or novel 2D metals with 2D semiconductors, such as 3D and 2D metals/MSi 2 N 4 (M = Mo, W) 30 and 3D metals/MoS 2 . 31Notably, the traditional 3D metals/ semiconductor oen exhibit unmodulated Schottky barriers, leading to high contact resistance and lower carrier mobility, thus diminishing device performance.3][34][35][36] Hence, there is a growing focus on the discovery of novel 2D metals and semiconductors, which can be combined to form an M-S contact with enhanced performance.
8][39][40] 2D metallic NbS 2 was synthesized in recent experiments by different methods, such as chemical vapor deposition 41,42 and mechanical/chemical exfoliation. 43The electronic and optical properties of the NbS 2 monolayer have also been investigated through rst-principles calculations 44 along with its tunable properties via doping 45 and intercalations. 46All these ndings suggest that a metallic NbS 2 monolayer can be considered as a promising material for future applications, including gas sensors 47,48 and energy storage. 49Furthermore, a promising BSe semiconducting monolayer has been predicted to be mechanically and thermally stable at room temperature. 50It is evident that the BSe monolayer exhibits a semiconducting feature with an indirect band gap.Additionally, the BSe monolayer is considered as a promising semiconductor for forming contacts with various other 2D materials such as graphene, 51 phosphorene, 52 MoS 2 (ref.17) and so forth. 53,54However, to date, a combination between a BSe semiconductor and other 2D metals has not yet been extensively predicted and investigated.Therefore, in this work, we perform rst-principles calculations to design a M-S heterostructure by combining 2D metal NbS 2 and a BSe semiconductor.Our ndings offer valuable insights for the practical utilization of electronic devices based on the NbS 2 /BSe heterostructure.

Computational model and methods
In this work, we performed rst-principles calculations based on the density functional theory (DFT).We use the Quantum Espresso simulation package 55 in the framework of the generalized gradient approximation (GGA). 56In addition, we employed the Perdew-Burke-Ernzerhof (PBE) functional 57 to calculate the exchange and correlation energy with the projected augmented wave (PAW) pseudopotential. 58The vdW interactions that may exist in layered nanostructures can be described by using the Grimme correction DFT-D3 method. 59he Heyd-Scuseria-Ernzerhof (HSE) functional 60 is also used to achieve more accurate band gaps of 2D semiconductors.A cutoff energy of 510 eV and a (9 × 9 × 1) k-point mesh are used in all our calculations.A vacuum thickness of 30 Å is included to prevent unnecessary interactions caused by the periodic boundary conditions.Dipole correction is also applied in all calculations.

Results and discussion
We rst examine the atomic and electronic structures of NbS 2 and BSe monolayers, as illustrated in Fig. 1.Both the NbS 2 and BSe monolayers show hexagonal atomic crystals.In the NbS 2 monolayer, one Nb atom is sandwiched between two S atoms on both sides, whereas in the BSe monolayer, each B atom is bonded with one Se atom on one side.The calculated lattice parameters of the NbS 2 and BSe monolayers are 3.31 and 3.23 Å, respectively.These results are in good agreement with previous reports. 50,61The NbS 2 monolayer is characterized by its metallic properties, featuring a band that crosses the Fermi level.In contrast, the BSe monolayer exhibits a semiconducting behavior with an indirect band gap of 2.62/3.46eV, obtained by using the PBE/HSE functional.These values are in good agreement with previous measurements. 50The valence band maximum (VBM) and conduction band minimum (CBM) of the BSe monolayer are located at the G point and G-M path, respectively.Interestingly, we nd that both the PBE and HSE functionals predict the similar behavior of NbS 2 and BSe monolayers.The main difference between PBE and HSE methods is in a shi of the VBM of the BSe monolayer.The VBM of the BSe monolayer in the PBE functional is positioned closer to the Fermi level than that in the HSE functional.
We now combine the NbS 2 and BSe monolayers to generate the metal/semiconductor NbS 2 /BSe heterostructure by stacking NbS 2 on top of the BSe monolayer.The possible stacking congurations of the NbS 2 /BSe heterostructure are depicted in Fig. 2. Due to a small difference in the lattice parameters between NbS 2 and BSe monolayers, the NbS 2 /BSe heterostructure has a small lattice mismatch of only 1.2% for all stacking congurations.Aer the geometric optimization process, the interlayer spacing d between NbS 2 and BSe layers in

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Paper their heterostructure can be obtained, as listed in Table 1.It is evident that the interlayer spacing in the AC1 stacking conguration is d = 2.95 Å, which is the shortest among the eight stacking congurations.In addition, it should be noted that the interlayer spacing d in all stacking congurations is larger than the sum of covalent radii between S (0.99 Å) and Se (1.14 Å) atoms, conrming that there is no covalent bond between the two constituent NbS 2 and BSe layers.Furthermore, to examine the interfacial stability of the NbS 2 /BSe heterostructure for all stacks, we calculate the binding energy as follows: Here, E NbS 2 /BSe , E NbS 2 and E BSe are the total energies of the NbS 2 / BSe heterostructure, and isolated NbS 2 and BSe monolayers, respectively.S = 10.69Å 2 is the surface area of the heterostructure.The calculated E b for all stacks of the NbS 2 /BSe heterostructure is listed in Table 1.The binding energy of the NbS 2 / BSe heterostructure is approximately averaged at about −20 meV Å −2 .The negative binding energy suggests that the NbS 2 / BSe heterostructure is stable.Interestingly, this binding energy is comparable to that in graphite 62 and other typical 2D van der Waals (vdW) heterostructures. 63,64This nding indicates that the NbS 2 /BSe heterostructure can be synthesized in future experiments by different strategies, including mechanical exfoliation 12 and CVD. 65For instance, using the CVD method, Fu et al. 37 successfully synthesized a metal/semiconductor NbS 2 / MoS 2 heterostructure with high quality and a clean interface.Among these stacks, the AC2 stack has the lowest binding energy of −23.89 meV Å −2 .The shortest interlayer spacing and the lowest binding energy in the AC1 stacking conguration of the NbS 2 /BSe heterostructure indicate that the AC1 stack is the most energetically feasible stacking conguration.Furthermore, to check the mechanical stability of the NbS 2 / BSe heterostructure, we consider its independent elastic constants (C ij ).The C ij of the perfect NbS 2 and BSe monolayers are also calculated for comparison, as illustrated in Fig. 3 We nd that the Young's modulus of the NbS 2 /BSe heterostructure is calculated to be 289.74N m −1 , which is greater than that of the NbS 2 (109.95N m −1 ) and BSe (178.90N m −1 ) monolayers.The phonon dispersion curves of the NbS 2 /BSe heterostructure are depicted in Fig. 3(c).We observe that there are no imaginary frequencies in the phonon spectrum of the NbS 2 /BSe heterostructure, indicating that such a heterostructure is dynamically stable.All these ndings indicate that the NbS 2 / BSe heterostructure can be considered as a promising candidate for the design of electronic devices.
The projected band structures of the NbS 2 /BSe heterostructure for all stacks are depicted in Fig. 4, in which red and blue bubbles show the contributions of the NbS 2 and BSe layers, respectively.It is obvious that the band structures of the NbS 2 / BSe heterostructure appear to be a combination of the band structures of the constituent monolayers.The reason for such a combination is weak interactions between the NbS 2 and BSe layers.These weak interactions play a pivotal role in stabilizing the heterostructure, making it readily obtainable in experiments.Furthermore, the combination between the metallic NbS 2 monolayer and semiconducting BSe monolayer might give rise to the formation of either a Schottky or ohmic contact, depending on the position of the band edges of the BSe semiconductor in relation to the Fermi level of the metallic NbS 2 layer.As depicted in Fig. 4, the Fermi level of the metallic NbS 2 monolayer lies between the band edges of the semiconductor BSe monolayer.This arrangement leads to the formation of a Schottky contact.In a Schottky contact, Schottky barriers exist, and these barriers can be determined as follows: and Here, E CBM and E VBM are the band edge energies of the CBM and VBM of the BSe semiconductor, respectively.E F is the Fermi level of the heterostructure.The obtained Schottky barriers F n and F p of the heterostructure are listed in Table 1 and Fig.

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Fermi level than that calculated by using the PBE functional.Interestingly, it's worth noting that both the PBE and HSE functional predictions indicate a p-type Schottky contact with the same Schottky barrier F p .This suggests that the PBE functional can be effectively used in the subsequent calculations without compromising the accuracy of the results.Furthermore, in order to verify the thermal stability of the NbS 2 /BSe heterostructure, we perform ab initio molecular dynamics (AIMD) simulation.The AIMD simulation of the NbS 2 /BSe heterostructure is displayed in Fig. 6(b).It is evident that the uctuation in the total energy of the NbS 2 /BSe heterostructure as a function of time steps is small.In addition, the atomic structure of the NbS 2 /BSe heterostructure aer heating for 5 ps is preserved without any distortion.All these ndings conrm that the NbS 2 /BSe heterostructure is thermally stable.The stability indicates that the NbS 2 /BSe heterostructure could be synthesized and used in recent nanoelectronic and optoelectronic devices, such as Schottky diodes, eld-effect transistors and photodetectors.Furthermore, the charge transfers between the NbS 2 and BSe layers in their heterostructure are also explored by calculating the charge density difference (CDD) as follows: Here, the charge densities of the NbS 2 /BSe heterostructure and isolated NbS 2 and BSe monolayers are denoted as r NbS 2 /BSe , r NbS 2 and r BSe , respectively.The CDD of the NbS 2 /BSe heterostructure is depicted in Fig. 6(c).One can nd that the charges are accumulated mainly around the NbS 2 layer and depleted mainly around the BSe layer.This nding implies that the electrons are transferred from the NbS 2 to the BSe layer in their corresponding NbS 2 /BSe heterostructure.Based on Bader charge analysis, there is a small amount of charge transfer of only 0.02 electrons that ow from the NbS 2 to the BSe layer.The electrostatic potential of the NbS 2 /BSe heterostructure is depicted in Fig. 6(d).One can observe that the NbS 2 layer has a deeper potential that the BSe layer in their heterostructure.The charge transfer between metallic NbS 2 and BSe layers at the interface of the NbS 2 /BSe heterostructure gives rise to the formation of an interfacial dipole, which can be obtained using DV = W NbS 2 − W NbS 2 /BSe , where the work functions of the metallic NbS 2 layer and the NbS 2 /BSe heterostructure are denoted as the W NbS 2 and W NbS 2 /BSe , respectively.The interfacial dipole at the interface of the NbS 2 /BSe heterostructure is obtained to be 0.02 eV.The formation of the interfacial dipole at the interface can change the Schottky barriers.However, our results show that both the amount of charge transfer and interface dipole are small; hence, the change in the Schottky barriers at the interface of the NbS 2 /BSe heterostructure can be considered negligible.Furthermore, both the charge transfer and interfacial dipole in the NbS 2 /BSe heterostructure may give rise to the formation of a built-in electric eld at the interface.The built-in electric eld can be calculated as follows: 67 Nanoscale Advances where P stands for the interface dipole.3, S and d are the dielectric constant, surface area and interlayer distance of the NbS 2 /BSe heterostructure, respectively.We can observe that the built-in electric eld is directly proportional to the interface dipole.As we have discussed above, the amount of charge transfer and interface dipole of the NbS 2 /BSe heterostructure are small; hence, the built-in electric eld across the interface of the heterostructure is also small and can be considered negligible.Furthermore, in order to evaluate the efficiency of electron injection through the contact of the NbS 2 /MoSSe heterostructure, we add the calculations on the tunneling probability ðTÞ and the tunneling-specic resistivity (r t ) as follows: and Here, ħ is the reduced Planck's constant.e and m e are the electron magnitude and mass of a free electron, respectively.h TB and w TB are the tunneling barrier height and width, respectively, which can be obtained directly from the electrostatic potential of the NbS 2 /BSe heterostructure.The calculated h TB and w TB of the NbS 2 /BSe heterostructure for the most energetically favorable stacking conguration are 3.68 eV and 1.35 Å, respectively.Hence, the tunneling probability and contact tunneling-specic resistivity at the interface of the NbS 2 /BSe heterostructure are about 7% and 2.09 × 10 −10 U cm 2 , respectively.We also observe that the value of the tunneling-specic resistivity at the interface of the NbS 2 /MoSSe heterostructure exhibits a magnitude similar to that in other metal/ semiconductor contacts, such as Bi/MoS 2 , 68 semimetals/ TMDs, 69 metal/MSi 2 N 4 (M = Mo, W) 29 and 2D (3D) metals/ GeSe. 70This nding also suggests that the NbS 2 /BSe heterostructure could serve as an efficient contact for electronic devices.Furthermore, we calculate the optical absorption of the NbS 2 /BSe heterostructure as well as that of the constituent NbS 2 and BSe monolayers for comparison.The optical absorption can be obtained as follows: Here, the real and imaginary parts of dielectric functions are denoted ass 3 1 and 3 2 , respectively.The optical absorption of the NbS 2 /BSe heterostructure and the constituent NbS 2 and BSe monolayers are depicted in Fig. 7.We can nd that the optical absorption coefficient of the NbS 2 /BSe heterostructure can reach up to 5 × 10 5 cm −1 at a photon energy of about 5 eV, which is still greater than that in the constituent NbS 2 and BSe monolayers.Hence, the formation of the M-S NbS 2 /BSe heterostructure gives rise to an enhancement in the optical absorption of both NbS 2 and BSe monolayers.The enhancement in the optical absorption of the M-S NbS 2 /BSe heterostructure indicates that it can be considered as a promising candidate for the design of optoelectronic devices.

Conclusions
In summary, we have designed a metal/semiconductor heterostructure between two different materials 2D NbS 2 metal and 2D BSe semiconductor using rst-principles prediction.The combination between NbS 2 and BSe monolayers gives rise to the formation of a metal/semiconductor NbS 2 /BSe heterostructure with different stacking congurations.All these stacking congurations of the NbS 2 /BSe heterostructure are considered to be structurally, mechanically and thermally stable, suggesting their potential as components in electronic devices.The formation of the NbS 2 /BSe heterostructure leads to the generation of a Schottky contact with the Schottky barrier ranging from 0.36 to 0.51 eV, depending on the stacking congurations.
In addition, the optical absorption coefficient of the NbS 2 /BSe heterostructure can reach up to 5 × 10 5 cm −1 at a photon energy of about 5 eV, which is still greater than that in the constituent NbS 2 and BSe monolayers.This nding suggests that the formation of the M-S NbS 2 /BSe heterostructure gives rise to an enhancement in the optical absorption of both NbS 2 and BSe monolayers.Notably, the tunneling probability and the contact tunneling-specic resistivity at the interface of the NbS 2 /BSe heterostructure are low, indicating its applicability in emerging nanoelectronic and optoelectronic devices, such as Schottky diodes, eld-effect transistors and photodetectors.Our ndings offer valuable insights for the practical utilization of electronic and optoelectronic devices based on the NbS 2 /BSe heterostructure.

Fig. 1 (
Fig. 1 (From left to right) Atomic structure, PBE and HSE band structures of (a) NbS 2 and (b) BSe monolayers.Orange and purple balls represent the S and Nb atoms, respectively.Dark green and green balls stand for the Se and B atoms, respectively.
. The calculated elastic constants C 11 , C 12 and C 66 of monolayers NbS 2 and BSe are 183.31,28.40, 77.45 and 120.10, 34.91 and 42.59 N m −1 , respectively.According to the Born-Huang stability criteria, 66 i.e.C 11 > C 12 , C 66 > 0 and C 11 2 -C 12 2 > 0, both the NbS 2 and BSe monolayers are mechanically stable.Interestingly, the formation of the NbS 2 /BSe heterostructure leads to an increase in the elastic constants C ij , as shown in Fig. 3(a).The calculated C 11 , C 12 and C 66 of the NbS 2 /BSe heterostructure are about 300, 65 and 130 N m −1 , respectively.These values of the elastic constants are still larger than those of the NbS 2 and BSe monolayers.In addition, the elastic constants of the NbS 2 /BSe heterostructure meet the Born-Huang stability criteria.This nding suggests that the NbS 2 /BSe heterostructure exhibits outstanding mechanical stability.Furthermore, the angledependent Young's modulus of NbS 2 and BSe monolayers and their combined NbS 2 /BSe heterostructure for the most energetically favorable stacking conguration are depicted in Fig. 3(b).
5. It is evident that the Schottky barrier F p of the heterostructure is always narrower than the Schottky barrier F n , indicating that the NbS 2 /BSe heterostructure tends to exhibit p-type ShC.The ptype Schottky barrier in the NbS 2 /BSe heterostructure ranges from 0.34 to 0.51 eV.The AC4 stacking pattern exhibits the narrowest Schottky barrier F p of 0.34 eV, while the AA2 and AC3 stacking patterns exhibit the highest Schottky barrier F p of 0.51 eV.As previously discussed, the AC1 stacking pattern of the NbS 2 /BSe heterostructure is the most favorable among the stacking congurations.Hence, we will focus on this stacking conguration in our subsequent calculations.The projected band structures of the NbS 2 /BSe heterostructure for the most energetically favorable stacking patterns using PBE and HSE methods are illustrated in Fig.6(a).The calculated Schottky barriers F n and F p of the NbS 2 /BSe heterostructure are 1.97/2.88and 0.42/0.43eV, obtained using the PBE/HSE functional.It is clear that both the PBE and HSE functionals predict the similar behavior of the NbS 2 /BSe heterostructure.The CBM calculated using the HSE functional of the NbS 2 /BSe heterostructure is positioned further away from the

Fig. 3
Fig. 3 (a) Calculated independent elastic constants (C ij ) of the NbS 2 /BSe heterostructure for different stacking configurations and (b) angledependent Young's modulus and (c) phonon dispersion curves of the NbS 2 /BSe heterostructure for the most energetically favorable stacking configuration.

Fig. 5
Fig. 5 The Schottky barriers of the NbS 2 /BSe heterostructure for different stacking patterns.

Fig. 6
Fig. 6 (a) Projected band structures, (b) AIMD simulation, (c) charge density difference and (d) electrostatic potential of the AC1 stacking pattern of the NbS 2 /BSe heterostructure.Red and blue lines represent the contribution of metallic NbS 2 and semiconducting BSe monolayers, respectively.The inset of (c) shows the atomic structure of the heterostructure before and after heating for 5 ps.Yellow and cyan regions in (c) indicate the charge accumulation and depletion, respectively.

Fig. 7
Fig. 7 Calculated optical absorption as a function of the photon energy of the NbS 2 /BSe heterostructure and the constituent BSe and NbS 2 monolayers.