Effect of external electric field on the electronic structure of MoSe₂/Arsenene heterojunction

1. Introduction

Graphene has received a lot of attention since it was first prepared in 2004 by Geim and Novoselov et al.¹ using a mechanical exfoliation method. Its unique two-dimensional structure and physical properties make it an important application in energy conversion, hydrogen storage, and sensors.^2,3 However, the zero bandgap of graphene limits its application in solar cells, photocatalysis and integrated circuits. New two-dimensional materials have been therefore developed, which possess a wide bandgap and a graphene-like structure. Transition metal disulfides (TMDs) are considered to meet these requirements and have thus become an attractive research hotspot.^4,5,6,7,8 TMDs have the ability to achieve direct-indirect bandgap conversion by controlling the number of layers. As a type of TMDs, MoSe₂ has the advantages of high electron mobility, catalytic efficiency, and mechanical properties, showing wide application prospects in many fields.^9,10,11,12

In 2013, the concept of heterojunctions was first proposed by Geim and Grigorieva.¹³ The heterojunctions are formed through stacking one monolayer structure on top of another monolayer or multilayer crystal by van der Waals force instead of chemical bonding. In addition to maintaining their excellent individual physical properties, the formation of a heterojunction between two materials often results in the acquisition of even more enhanced physical properties. This synergistic effect contributes to the overall improved performance of the materials. Once the concept of heterojunction was introduced, novel heterojunctions composed of two materials emerged, causing a surge of exploration in the field.^14,15 Researchers have found that heterojunctions exhibit superior electrical and optical properties, of which the electronic structure and optical properties can be effectively tuned by strain and external electric fields.^{16,17,18,19,20}

Recently, TMDs (e.g. MoS₂ and WS₂) have been favored in the study of heterojunctions due to their excellent physical properties. Compared to MoS₂ and WS₂, MoSe₂ has been less comprehensively studied due to its later emergence, especially in the study of heterojunctions, of which application has rarely been reported.

Two-dimensional material phosphorene exhibits excellent physical properties, inspired by which arsenene as a member of the same main-group has also received extensive attention. arsenene has a similar folded structure as phosphorene and the corresponding high carrier mobility. arsenene-based field-effect transistor shows a higher $L_{\text{on}}$/$L_{\text{off}}$ ratio and better stability than phosphorene-based field-effect transistors.²¹ Therefore, the studies on arsenene-based heterojunctions have been a hot research topic.^22,23

Herein, a novel type-II heterojunction MoSe₂/Arsenene heterojunction is synthesized by stacking a arsenene single layer on top of MoSe₂ single layer. The stability and band structure of the heterojunction are calculated based on the first-principles. When MoSe₂ and arsenene form heterojunctions, band bending occurs, leading to the formation of an internal electric field, which drives photogenerated electrons and holes to move in opposite directions, effectively separating them on different sides of the heterojunction, leading to the extended carrier lifetime. Therefore, this phenomenon in MoSe₂/Arsenene heterojunctions enables efficient electron transfer and enhances photocatalytic activity. Furthermore, MoSe₂/Arsenene heterojunctions, being type-II, exhibit strong confinement of carrier transport, which is suitable for the fabrication of transistors with high electron mobility. Overall, MoSe₂/Arsenene heterojunctions hold great potential for applications in the field of electronic devices. It is well known that when a heterojunction is applied to an electronic device, it will inevitably be affected by an external electric field. Therefore, the band structure and differential charge density of the heterojunction under an external electric field are also calculated. The results show that the external electric field can effectively modulate the electronic structure between the layers of the heterojunction. MoSe₂/Arsenene heterojunctions hold great potential for the application in electronic devices.

2. Calculation Methods

All calculations were performed by the CASTEP module in Materials Studio software, using the GGA-PBE functional for structural optimization.²⁴ However, as the generalized gradient approximation (GGA) may underestimate the bandgap, the Heyd-Scuseria-Ernzerhof (HSE06) hybrid functional was used to calculate the band structure.²⁵ The cut-off energy was set as 450eV, and the energy convergence criterion was $1.0\times 10^{-6}$eV/atom. The Monkhorst–Pack mesh grid was set as $7\times 7\times 1$. The structure was optimized with atomic forces converge of 0.01eV/Å. To avoid the molecular interactions between layers, the vacuum layer between the molecular layers was set as 20Å. The spin–orbit coupling (SOC) effect was taken into account in the calculations. The band structure was calculated comparatively with and without SOC effect: the bandgap errors of monolayer MoSe₂, monolayer arsenene, and MoSe₂/Arsenene heterojunction were 0.0072eV, 0.0037eV, and 0.0057eV, respectively. The difference under the two conditions was negligible, but the computational speed was significantly decreased when the SOC effect was taken into account. To ensure speed and accuracy, the SOC effect was not considered in the subsequent calculations.

3. Results and Discussion

3.1. Geometry and stability

Before constructing the MoSe₂/Arsenene heterojunction, the monolayer MoSe₂ and arsenene structure were optimized with a lattice constant of 3.22Å and 3.64Å, respectively, which is mostly consistent with the previous literatures.^26,27 To minimize the lattice mismatch, $2\times 2\times 1$ for MoSe₂ and $\sqrt{3}\times \sqrt{3}\times 1$ for arsenene supercells were used to construct a heterojunction, where the lattice mismatch was 2.15%, satisfying the calculation requirements. The MoSe₂/Arsenene heterojunction was constructed by stacking arsenene on top of MoSe₂. Three different stacks of arsenene were obtained by translating it in the x and y directions (Fig. 1), where the purple atoms and red atoms are the top and bottom As atoms of arsenene, respectively. The three stacking configurations are: (1) A: the top As atom is located on top of the Mo and Se atoms (Figs. 1(a) and 1(b)); (2) B: the bottom As atom is located on top of the Mo and Se atoms (Figs. 1(c) and 1(d)); and (3) C: the As–As bond is located on top of the MoSe₂ six-ring (Figs. 1(e) and 1(f)).

To investigate the stability of MoSe₂/Arsenene heterojunction, the binding energy of different stacking configurations was calculated by the following equation²⁸ :

where $E_b$ represents the binding energy of the system, $E_{M∕A}$, $E_M$, and $E_A$ represent the total energies of the MoSe₂/Arsenene heterojunction, MoSe₂, and arsenene, respectively. A negative value of the binding energy indicates a stable structure, and the smaller one indicates better stability.

The binding energy and interlayer distance for the different stacking configurations after structural optimization are presented in Table 1. All three stacking configurations exhibit interlayer distances larger than 3Å, which surpasses the bonding range of As and Se atoms. Thus, MoSe₂ and arsenene are bound together by van der Waals force, forming van der Waals heterojunction. Furthermore, the binding energy is negative for all three stacking configurations, of which the C-configuration with an interlayer distance of 3.21Å shows the lowest binding energy, indicating it is the most stable at this point. Therefore, the calculations below were carried out all in the C-configuration.

In order to comprehensively verify the kinetic and thermal stability of MoSe₂/Arsenene heterojunction at room temperature, the phonon dispersion curve was calculated and molecular dynamics simulations of the heterojunction were carried out. Figure 2(a) shows the phonon dispersion curve of the heterojunction, with no imaginary frequency observed, which proves that the heterojunction has good kinetic stability. The above molecular dynamics simulations of 10ps at 300K were carried out using the NVT system. As shown in Fig. 2(b), the total energy of the system fluctuates slightly during the first 2ps and oscillates after 2ps above and below −4267.00eV. During the whole simulations, no structural deformation is observed in the heterostructure, indicating that the MoSe₂/Arsenene heterojunction is thermally stable at room temperature.

3.2. Band structure

To investigate the band structure of MoSe₂/Arsenene heterojunction, the band structures of monolayer MoSe₂, monolayer arsenene, and MoSe₂/Arsenene heterojunction were calculated and are shown in Fig. 3. The bandgaps of monolayer MoSe₂ and arsenene are 1.59eV and 1.61eV, respectively, in agreement with the literatures.^29,30 When the monolayer MoSe₂ and arsenene form a heterojunction, the band structure (Fig. 3(c)) keeps both that of monolayer MoSe₂ and arsenene well.

Heterojunctions can be classified into three types³¹: type-I, type-II, and type-III, according to the band arrangement of two different materials forming a heterojunction. Figure 4 shows the three types of band arrangement. For type-I heterojunction, the conduction band bottom of A lies above B and the valence band top lies below B; for type-II heterojunction, the band arrangement of A and B is staggered; for type-III heterojunction, the valence band top of A lies above the conduction band bottom of B. It can be seen from the band structure of MoSe₂/Arsenene heterojunction (Fig. 3) that the MoSe₂/Arsenene heterojunction presents a conduction band bottom contributed by arsenene and a valence band top contributed by MoSe₂, consistent with the band arrangement of a type-II heterojunction. Therefore, the MoSe₂/Arsenene exhibits a type-II heterojunction.

The electronic orbital diagram of the heterojunction is shown in Fig. 5, in which the isosurface value is 0.04e/Å.³ It can be seen that the top of valence band and the bottom of conduction band are contributed by MoSe₂ and arsenene, respectively, consistent with the results in Fig. 3. The two combine to form a type-II heterojunction. Due to interlayer coupling, the bandgap reduces to 0.89eV.

To investigate the electron transfer between monolayer MoSe₂ and arsenene more deeply, the average potential of the MoSe₂/Arsenene heterojunction along the z-direction and differential charge density were calculated. As shown in Fig. 6(a), the MoSe₂ monolayer in the heterojunction has a deeper potential, Fig. 6(b) shows the differential charge density of the heterojunction, with the blue and the yellow part representing electron accumulation and dissipation, respectively, at an electron isosurface value of 0.002e/Å.³ The isosurface for electron accumulation (in blue) is closer to the arsenene, so that electrons are transferred from the MoSe₂ layer to the arsenene layer, while holes are transferred in the opposite direction. Due to the diffusion of electrons and holes, an internal electric field is formed between the two monolayers, promoting the drift movement of electrons and holes in the opposite direction. Finally, the electron and hole diffusion achieve equilibrium with the same drift rates, and the Fermi levels of MoSe₂ and arsenene monolayers stabilize at the same height.

Furthermore, the work functions were also calculated for monolayer MoSe₂ and arsenene, both at 4.62eV and 5.09eV, respectively, in agreement with previous reports.^32,33 The work function of MoSe₂/Arsenene heterojunction was calculated as 4.94eV, in-between the former two. When a heterojunction is formed, the arsenene monolayer generally has a higher work function compared to the MoSe₂ monolayer. This leads to the diffusion of electrons from the MoSe₂ monolayer to the arsenene monolayer and the diffusion of holes from the arsenene monolayer to the MoSe₂ monolayer. Therefore, the Fermi level of MoSe₂ decreases while the Fermi level of arsenene increases until reaching an equality, consistent with the previous results. The electron transfer during the heterojunction formation is shown in Fig. 7, which explains the results of the top of valence band and the bottom of conduction band are contributed by arsenene and MoSe₂, respectively, and the two combine to form a type-II heterojunction.

3.3. Effect of external electric fields on the electronic structure

When heterojunctions are applied in electronic devices, they will inevitably be affected by an external electric field ($E_{\text{ext}}$), thus the effect of the external electric field on the electronic structure for MoSe₂/Arsenene heterojunction is discussed in this section. The vertical direction from the MoSe₂ monolayer to the arsenene monolayer is taken as the positive direction. Figure 8(a) shows the bandgaps of the heterojunction with the different external electric field, in which the bandgap decreases to zero when the value of the external electric field is sufficiently large. Due to the presence of the internal electric field in the heterojunction, the positive and negative electric fields play distinct roles on the band structure.

The band structures at $E_{\text{ext}}=-0.4$V/Å, $E_{\text{ext}}=0$, $E_{\text{ext}}=0.4$V/Å, and $E_{\text{ext}}=0.8$V/Å are presented in Fig. 8(b) and the band structures under other conditions are presented in Fig. S1. The electronic orbital diagrams of the MoSe₂/Arsenene heterojunction under different electric fields are shown in Figs. 8(c) and 8(d), in which the isosurface value is 0.04e/Å.³ It can be seen that the conduction band bottom of the heterojunctions at $E_{\text{ext}}=-$0.4V/Å, $E_{\text{ext}}=0$, and $E_{\text{ext}}=0.4$V/Å are contributed by arsenene and the valence band tops are contributed by MoSe₂; the conduction band bottoms of the heterojunctions at $E_{\text{ext}}=0.8$V/Å are contributed by MoSe₂ and the valence band tops are contributed by arsenene. Figure 8(e) presents the band arrangement under different electronic fields. When the electric field is negative, electrons are transferred from the MoSe₂ monolayer to the arsenene monolayer and holes from the arsenene monolayer to the MoSe₂ monolayer. The Fermi level of arsenene moves downwards and that of MoSe₂ moves upwards. The relative movement of the Fermi level leads to a narrowed bandgap of the MoSe₂/Arsenene heterojunction (Fig. 8(e)). As shown in Fig. S1(a), the bandgap decreases to 0 when $E_{\text{ext}}<-0.8$V/Å. This is because that the too-large reverse electric field renders an enhanced carrier drift in the barrier region, leading to a large kinetic energy. During the drifting, the carriers collide out electrons from other valence bonds, leading to the generation of new carriers and the eventual dielectric breakdown of the heterojunction. The heterojunction then transforms into type-III.

When the electric field is positive, electrons are transferred from arsenene monolayer to the MoSe₂ monolayer and holes from the MoSe₂ monolayer to the arsenene monolayer. The Fermi level of MoSe₂ moves downwards and that of arsenene moves upwards. The relative movement of the Fermi level leads to a widened and then narrowed bandgap of the MoSe₂/Arsenene heterojunction. As shown in Fig. 8(e), the bandgap of the heterojunction increases when 0 < $E_{\text{ext}}<0.6$V/Å. At this point, the top of the valence band is contributed by MoSe₂ and the bottom of the conduction band is contributed by arsenene. As shown in Fig. S1(f), the bandgap of the heterojunction reaches a maximum value of 1.08eV when $E_{\text{ext}}=0.6$V/Å. The bandgap of the heterojunction begins to decrease when $E_{\text{ext}}>0.6$V/Å, with a transition of the valence band top and conduction band bottom, namely, the top of the valence band is contributed by arsenene and the bottom of the conduction band by MoSe₂. As $E_{\text{ext}}$ continues to increase, the valence band top of arsenene and the conduction band bottom of MoSe₂ gradually move closer to the middle. As shown in Fig. S1(g), the bandgap decreases to zero when $E_{\text{ex}}=1.0$V/Å, and the MoSe₂/Arsenene heterojunction completes the semiconductor-metal transition into type-III.

The partial density of states under $E_{\text{ext}}=-0.4$V/Å, $E_{\text{ext}}=0$, $E_{\text{ext}}=0.4$V/Å, and $E_{\text{ext}}=0.8$V/Å are presented in Fig. 9, while the other conditions are listed in Fig. S1. The density of states near the Fermi level of the heterojunction is mainly contributed by Mo-4d, Se-4p, and As-4p orbitals. When the electric field $E_{\text{ext}}=-0.4$V/Å, $E_{\text{ext}}=0$ and $E_{\text{ext}}=0.4$V/Å, the valence band top of the heterojunction is mainly contributed by Mo-4d and Se-4p orbitals and the conduction band bottom is mainly contributed by As-4p orbitals. It can be observed in Fig. S2, as the electric field enhances, the density of states in the As-4p orbitals gradually moves towards the higher energy region. When $E_{\text{ext}}=0.8$V/Å, the valence band top of the heterojunction is mainly contributed by As-4p orbitals and the conduction band bottom is mainly contributed by Mo-4d and Se-4p orbitals. The remaining partial density of states has been listed in Fig. S2.

To further investigate the effect of the external electric field on the electronic structure of the MoSe₂/Arsenene heterojunction, the average differential charge density in the z-direction was calculated as follows³⁴ :

where ${\rho }_H$, ${\rho }_M$, and ${\rho }_A$ denote the charge density of the MoSe₂/Arsenene heterojunction, MoSe₂, and arsenene, respectively; the positive and negative values of $\mathrm{\Delta }\rho (z)$ represent the accumulation and dissipation of charge, respectively. The 3D planar average differential charge density under different electronic fields is provided in Fig. S3. Figure 10 shows the average differential charge density along the z-direction of the MoSe₂/Arsenene heterojunction. It can be obtained in Figs. S3 and 10 that, when the electric field is positive, electrons are transferred from arsenene monolayer to the MoSe₂ monolayer and holes from the MoSe₂ monolayer to the arsenene monolayer. When the electric field is negative, electrons and holes are transferred along the opposite directions. Moreover, the larger the electric field, the greater the number of electrons transferred and the more pronounced the interlayer interactions. Electron transfer in heterojunctions under different electric fields is shown in Table 2. The electron transfer from the MoSe₂ layer to the arsenene layer represents positive, and that from the arsenene layer to the MoSe₂ layer represents negative.

4. Conclusions

The binding energy of MoSe₂/Arsenene heterojunction with different stacking configurations was calculated. The thermostability, band structure, and the effect of the external electric field on the band structure and electron transfer were calculated using the most stable configuration. The calculation results show that, when MoSe₂ combines with arsenene, electrons are transferred from MoSe₂ to arsenene, forming a heterojunction by van der Waals force. The type-II MoSe₂/Arsenene heterojunction shows a bandgap of 0.89eV and an excellent thermostability at room temperature. External electric fields can effectively modulate the electron transfer and band structure of heterojunction. When the external electric field is negative, electrons are transferred from the MoSe₂ to arsenene, and the bandgap of the heterojunction decreases as the electric field increases. The Fermi level of arsenene moves downwards and that of MoSe₂ moves upwards. When the electric field is positive, the direction of electrons transfer is opposite to that when the electric field is negative, with a first increased and then decreased bandgap of MoSe₂/Arsenene heterojunction. The Fermi level of MoSe₂ moves downwards and that of arsenene moves upwards. The greater external electric field can lead to a larger number of electrons transferred, and as the external electric field increases, the heterojunction can achieve a semiconductor-metal transition.

Supplemental Materials

The Supplemental Materials are available at: https://www.worldscientific.com/doi/suppl/10.1142/S0217984923502627