Tunable type-I band alignment and electronic structure of GaSe/MoSi₂N₄ van der Waals heterostructure

INTRODUCTION

Van der Waals heterostructures^[1-4] (vdWHs) are stacked structures made of atomically two-dimensional (2D) layered materials. Such structures are of intense interest to the scientific community because these structures may integrate 2D materials^[5,6] with varied properties at the atomic scale, thereby offering a standard platform for applications in electronics and optoelectronics. Using van der Waals forces, it is possible to construct structures with specific functions by stacking various 2D monolayers of materials. Researchers are able to govern the interface and electronic characteristics of materials by modifying the stacking order of different materials thanks to the adaptability of this structure, which enables various applications^[7-9]. The band alignment (When the band alignment appears below, it is denoted by the abbreviation b-a) of heterostructures is a crucial characteristic that can be categorized into three distinct types: straddling type-I, staggered type-II, and broken-gap type-III. Each specific b-a is associated with certain applications for electronic devices. Type-I b-a is advantageous for spatially restricting electrons and holes, which allows for more effective recombination to be achieved; optical device applications benefit from type-I b-a^[10,11]. In contrast to type-I b-a, type-III b-a engineering facilitates the transition of energy between the conduction band and the valence band. Consequently, type-III b-a holds a unique potential for use in photodetectors and tunnel field effect transistors^[12,13]. However, for type-II b-a, it is evident that the shifting of bands facilitates the separation of carriers, which is ideal for attaining efficient electron-hole separation and thus proves advantageous for applications involving electronic devices and photocatalysis^[14,15]. Much research has been done on 2D layered materials and vdWHs because of these worthwhile applications.

Gallium selenide (GaSe) is a widely studied layered structure that has garnered significant interest in the fields of optoelectronics, terahertz radiation detection, and nonlinear optics^[16]. The crystal structure of GaSe is hexagonal with the space group P-3m1. In recent times, there have been successful endeavors to extract high-quality single and few-layer GaSe nanosheets using different methods, including chemical and mechanical exfoliation, as well as vapor phase deposition or epitaxy growth^[17,18]. The 2D GaSe nanosheets exhibit a remarkable on-off current ratio of approximately 10⁵, together with a significantly high photoresponsivity of up to 2.8 A W^-1. This photoresponsivity surpasses that of MoS₂ and graphene^[17,19]. Recent theoretical and experimental investigations have demonstrated that the monolayer form of GaSe exhibits promising characteristics as a potential photocatalyst^[20,21]. Nevertheless, the significant experimental bandgap range of 3-3.5 eV could potentially impede the practical implementation of this material as a promising photocatalyst, primarily due to its limited ability to effectively utilize visible light^[22,23]. Moreover, it has been experimentally verified that the bulk carrier mobility of GaSe is 215 cm² V^-1 s ^-1, and there is potential for a substantial increase in mobility when GaSe is reduced to a few layers^[24]. The acquisition of single-layer GaSe represents a significant advancement in the realm of 2D materials, thereby broadening the scope of this material family. This development also paves the way for novel opportunities in the field of optoelectronic device applications^[25-30].

Recently, the successful fabrication of a MoSi₂N₄ monolayer has been achieved by the process of chemical vapor deposition^[31]. Using first-principles calculations, Hong et al.^[31] were able to make a prediction regarding the electronic properties of the MoSi₂N₄ monolayer. Specifically, they determined that this monolayer possesses the characteristics of a direct bandgap semiconductor. The calculated bandgap value, acquired using the Perdew, Burke, and Ernzerhof (PBE)/Heyd-Scuseria-Ernzerhof (HSE06) method, was found to be 1.744/2.297 eV. Theoretical investigations have been conducted to examine the electrical and optical characteristics of the MoSi₂N₄ monolayer^[32-34]. The investigation of contact heterostructures using MoSi₂N₄ and various 2D and 3D materials has been conducted. Examples of such heterostructures include MoSi₂N₄/graphene^[35,36], MoSi₂N₄/MoS(Se)₂^[37,38], and MoSi₂N₄/metals^[39]. The electrical and optical properties of the MoSi₂N₄ monolayer are significantly influenced when it comes into contact with other 2D materials. Cai et al.^[38] conducted a study on the construction of the MoSi₂N₄/MoSe₂ vdWH. Their findings indicate that the MoSi₂N₄/MoSe₂ vdWHs exhibit a type-I b-a, resulting in improved optical absorption and carrier mobility when compared to the individual monolayers.

Tunable b-a and electronic properties of GaSe/MoSi₂N₄ vdWHs have not been studied to date. The objective of this investigation is to perform first-principles research on the electronic structure of GaSe/MoSi₂N₄ vdWHs. In addition, we explored the potential to adjust its b-a through the application of interlayer distance, biaxial strain, and applied electric fields. The results show that the GaSe/MoSi₂N₄ vdWHs exhibit stability under ambient conditions and possess characteristics of an indirect bandgap semiconductor. Furthermore, it was observed that the band edges of the heterostructure, which consists of a monolayer of GaSe and MoSi₂N₄, exhibit type-I b-a. Through the control of biaxial strain and the action of applied electric field, the direction type of the band can be effectively adjusted from type-I to type-II. This adjustment facilitates the efficient separation of electrons and holes that are created. Our results show that the GaSe/MoSi₂N₄ vdWH has good properties as a multifunctional material and has great potential in the field of optoelectronics.

COMPUTATIONAL METHODS

This study presents the outcomes of our investigation into the geometric optimization, electrical structures, and b-a of the GaSe/MoSi₂N₄ vdWHs, employing first-principles calculations. The density functional theory framework^[40] is utilized for structure optimization and property computations. These calculations are performed using the standard version of Vienna ab initio simulation package (VASP.5.4.4)^[41], which employs the projector-augmented plane wave (PAW) approach^[42] to account for the ion-electron interaction. The software program known as Visualisation for Electronic Structural Analysis (VESTA)^[43] is widely employed for the manipulation and analysis of various forms of data pertaining to structural models, volumetric data encompassing electron and nuclear densities, and crystal morphologies. The electronic exchange-correlation functional is addressed in this study by employing the generalized gradient approximation (GGA)^[44] as determined by PBE^[45]. The energy cutoff of the plane waves is established at 550 eV with an energy accuracy of 10^-6 eV, and the k-point mesh of the Brillouin zone is set to be 8 × 8 × 1. The atomic locations undergo complete relaxation until the magnitude of the force acting on each atom is below 10^-3 eV/Å. The supercell technique is commonly employed for simulating monolayers, wherein a vacuum separation of around ~40 Å is employed to mitigate the interaction between neighboring layers. Given that the GGA tends to underestimate bandgaps, we employ the HSE06 hybrid functional^[46] for the computation of band structures. The computation of dynamic stabilities and phonon dispersion curves is carried out using the supercell technique, which is implemented in the Phonopy code^[47]. The inclusion of the dipole correction was also accounted for in the calculations.

RESULTS AND DISCUSSION

Figure 1 shows the atomic structure, phonon spectrum, projected band structure and state density of semiconductor GaSe and MoSi₂N₄ monolayers. After geometric optimization, both GaSe (γ’ phase, in these papers as 1T phase)^[48] and MoSi₂N₄ (1T, 2H) showed layered atomic structures with lattice constants of 3.64 Å, 2.90 Å and 2.89 Å. As illustrated in Figure 1A-C, for the optimized GaSe geometry, it is observed that the Ga atom is connected to two Se atoms, while in the MoSi₂N₄ geometry, the Mo-N₂ layer is situated in between the Si-N double layer. By calculating the band structure of the GaSe monolayer through HSE06 and PBE, it can be found in Figure 1G and J that GaSe has semiconductor characteristics and is an indirect bandgap semiconductor. The locations of the conduction band minimum (CBM) and valence band maximum (VBM) are identified to be at the M and Γ points. The PBE and HSE06 approaches both anticipate the identical features of the GaSe monolayer, with a bandgap value of 2.32 eV for each calculation method. The contribution of the atoms in the GaSe monolayer is shown in Figure 1J. The red and green lines correspond to the respective contributions made by gallium and selenium atoms. It is shown that both VBM and CBM of GaSe monolayers are predominantly contributed by the p-orbital of Se atoms. Figure 1D illustrates the phonon spectrum of the monolayer GaSe. The figure illustrates that the frequency of the 2D GaSe monolayer is positive and there is an absence of virtual frequency, so indicating the dynamic stability of the material.

Figure 1. (A-C) Shows the optimized atomic structure, phonon dispersion curve (D-F); (G-I) HSE06 projected band structure and state density are 1T-GaSe, 1T-MoSi₂N₄, 2H-MoSi₂N₄; (J-L) are the PBE projected band structure and state density of 1T-GaSe, 1T-MoSi₂N₄, 2H-MoSi₂N₄. The green, orange, red, blue, and silver spheres represent selenium, gallium, molybdenum, silicon, and nitrogen atoms. HES06: Heyd-scuseria-ernzerhof; GaSe: Gallium selenid; PBE: Perdew, burke, and ernzerhof.

Additionally, the MoSi₂N₄ monolayer is also an indirect bandgap semiconductor, and the CBM and VBM of 1T- MoSi₂N₄ and 2H- MoSi₂N₄ are located at the K and Γ points. In the ground state, the band structures of 1T-MoSi₂N₄ and 2H-MoSi₂N₄ monolayers were calculated by HSE06 and PBE [Figure 1H, I, K and L]. The bandgap values obtained by HSE06 methods are 2.38 eV and 2.61eV, and those obtained by PBE methods are 1.81 eV and 2.02 eV. It is imperative to acknowledge that conventional PBE techniques frequently underestimate the bandgap of 2D semiconductors. To address this limitation, the HSE06 approach can be employed to acquire a more precise and reliable bandgap. However, the bandgap measurement of the MoSi₂N₄ monolayer in the experiment yielded a value of 1.94 eV^[31], which is in greater agreement with our PBE calculation. Therefore, we used the PBE method for subsequent related calculations. Furthermore, we found that the bandgap of 1T-MoSi₂N₄ is closer to the experimental value compared to that of 2H-MoSi₂N₄. Meanwhile, the total energy of 1T-MoSi₂N₄ is lower than that of 2H-MoSi₂N₄. Hence, we will further investigate the correlated electronic properties of the vdWH formed by monolayers of 1T-MoSi₂N₄ and 1T-GaSe in the following sections. The contribution of atoms in the monolayer of MoSi₂N₄ is shown in Figure 1K and L. The red and blue lines represent the contributions of molybdenum and nitrogen atoms. This suggests that the p-orbital of the N atom contributes most to the VBM of the MoSi₂N₄ monolayer, while the d-orbital of the Mo atom contributes most to the CBM. The phonon spectrum of the MoSi₂N₄ monolayer is shown in Figure 1E and F, illustrating that the frequency of the 2D MoSi₂N₄ monolayer is positive, indicating its dynamic stability. Additionally, there is no presence of virtual frequency, further supporting its stability.

GaSe/MoSi₂N₄ vdWHs can be obtained by stacking the GaSe monolayer in the z direction on top of the MoSi₂N₄ monolayer. The initial equilibrium layer spacing D is set to 3.39 Å, which is larger than the sum of covalent radii between Se and N atoms, thus providing evidence that there is no formation of a covalent bond between the two constituent monolayers. Due to the difference in lattice parameters between GaSe and MoSi₂N₄ monolayers, we use a supercell composed of (√3 × √3) GaSe and (2 × 2) MoSi₂N₄. Additionally, we consider three potential stack configurations, AA-stacking, AB-stacking and AC-stacking modes, which correspond to Figure 2A-C. As illustrated in Figure 2, in the AA-stacking configuration, Se atoms correspond to Mo atoms; in the AB-stacking configuration, Se atoms are in the center of Mo and Si atoms, and in the AC-stacking configuration, Si atoms correspond to Se atoms at the center point. The calculation results show that the energy in Figure 2C is relatively low (E_b about -7.26972 eV). Because the lattice parameters of GaSe and MoSi₂N₄ monolayers are different, we use a supercell composed of (√3 × √3) GaSe and (2 × 2) MoSi₂N₄. Based on m-n/m+n < 5% (m, n is the lattice constant of monolayer GaSe and MoSi₂N₄), the lattice parameter of the combination of GaSe/MoSi₂N₄ is 6.30 Å, resulting in a lattice mismatch rate of 4.1% < 5%, which proves the rationality of the heterostructure. Furthermore, to assess the stability of the structure, we determined the binding energy using E_b = E_vdWHs - E_GaSe - $$ E_{M_{0} S i_{2} N_{4}} $$, where E_vdWHs, E_GaSe and $$ E_{M_{0} S i_{2} N_{4}} $$ are the total energy of the corresponding vdWHs and GaSe and MoSi₂N₄ monolayer. The binding energy of GaSe/MoSi₂N₄ is -2.19 eV. The binding energy of vdWHs is negative, indicating that their energy is stable. In order to assess the mechanical stability of GaSe/MoSi₂N₄ vdWHs, we additionally computed the elastic constants. The elastic constants C₁₁, C₁₂ and C₆₆ = (C₁₁ - C₁₂)/2 of GaSe/MoSi₂N₄ vdWHs are calculated as 387 N/m, 90 N/m and 148 N/m. The Born-Huang criterion^[49,50] suggests that the elastic constants C₁₁ > C₁₂ and C₆₆ > 0 of vdWHs demonstrate stability. We also calculate Young’s modulus and Poisson’s ratio of Y = (C₁₁² - C₁₂²)/C₁₁, V = C₁₂/C₁₁ and other systems. The Supplementary Figure 1 describes the orientation-dependent Young’s modulus and Poisson’s ratio of vdWHs, showing that the Young’s modulus and Poisson’s ratio of GaSe/MoSi₂N₄ is isotropic. The average Young’s modulus of GaSe/MoSi₂N₄ vdWHs is 366 N/m and Poisson’s ratio is 0.23. The results show that the vdWHs have high in-plane stiffness. Additionally, another key factor is the stability at high temperatures. Ab initio molecular dynamics (AIMD) simulations were performed to investigate the thermal stability of the heterostructure. The results of the energy fluctuations over 20 ps, along with the final snapshot, are presented in Supplementary Figure 2. The GaSe/MoSi₂N₄ heterostructure maintained structural integrity and stable energy at temperatures up to 1000 K. The well-preserved geometric structure suggests that the GaSe/MoSi₂N₄ heterostructure may have practical applications even under high-temperature conditions.

Figure 2. (A-C) Three different stacking forms of GaSe/MoSi₂N₄ vdWHs. The green, orange, red, blue, and silver spheres represent selenium, gallium, molybdenum, silicon, and nitrogen atoms. vdWHs: van der Waals heterostructures; GaSe: Gallium selenid; PBE: Perdew, burke, and ernzerhof; HES06: Heyd-scuseria-ernzerhof; CBM: Conduction band minimum; VBM: Valence band maximum.

Figure 3A and B Depicts the band structure of GaSe/MoSi₂N₄ vdWHs. The band structure calculated by PBE and HSE06 methods shows that GaSe/MoSi₂N₄ vdWHs demonstrate characteristics of a semiconductor, with the CBM situated at the K point and the VBM situated at the Γ point. This suggests that GaSe/MoSi₂N₄ vdWHs are an indirect bandgap semiconductor. The band shape and b-a type of GaSe/MoSi₂N₄ vdWHs remain unchanged when utilizing the HSE calculation approach in contrast to the PBE method. Therefore, the PBE method can accurately predict the electronic structure of GaSe/MoSi₂N₄ vdWHs. Due to computational cost savings, we decided to use the PBE method for all subsequent calculations. In addition, according to the band structure diagram shown in Figure 3, we find that both VBM and CBM are contributed by the MoSi₂N₄ layer. Thus, GaSe/MoSi₂N₄ vdWHs form a type-I b-a.

In order to gain a deeper comprehension of the charge distribution within GaSe/MoSi₂N₄ vdWHs, the electron density difference is computed using^[51,52]: Δρ = ρ_vdWHs - ρ_GaSe - ρ_MoSi2N4, where ρ_vdWHs, ρ_GaSe and ρ_MoSi2N4 represent the charge density of GaSe/MoSi₂N₄ vdWHs, a single GaSe monolayer, and MoSi₂N₄ monolayer, respectively. Charge depletion is represented by the cyan zone and charge accumulation is represented by the yellow region. The electron redistribution that takes place at the contact surface is clearly depicted in Figure 4A. More specifically, the predominant concentration of charge distribution occurs at the interface between the GaSe monolayer and MoSi₂N₄, where electrons are consumed in the Ga-Se layer and accumulate in the Si-N layer. Thus, The charge transfer occurs from the GaSe layer to the MoSi₂N₄ layer. The electrostatic potential of GaSe/MoSi₂N₄ vdWHs is shown in Figure 4B and C. The MoSi₂N₄ layer exhibits a greater potential depth compared to the GaSe layer, leading to the establishment of a built-in electric field at the interface. To have a better understanding of the interface’s charge redistribution, we further calculate the GaSe/MoSi₂N₄ vdWHs and the work function of the composition of the monolayer using:

Figure 3. (A and B) Weighted projected band structures of GaSe/MoSi₂N₄ vdWHs calculated by PBE and HES06. vdWHs: van der Waals heterostructures; PBE: Perdew, burke, and ernzerhof; HES06: Heyd-scuseria-ernzerhof.

Figure 4. (A) In-plane average charge density difference of GaSe/MoSi₂N₄ vdWHs; (B and C) in-plane average electrostatic potential of GaSe/MoSi₂N₄ vdWHs. Inset represents the 3D charge density difference in the heterostructure. The yellow and cyan regions represent charge accumulation and depletion, respectively. vdWHs: van der Waals heterostructures; GaSe: Gallium selenide.

Here, E_VAC and E_F stand for vacuum energy and Fermi energy, respectively. The calculated work functions of isolated GaSe and MoSi₂N₄ layers are 5.28 eV and 6.86 eV, while the work functions of GaSe/MoSi₂N₄ vdWHs are 6.41 eV. The work function of GaSe/MoSi₂N₄ vdWHs is shown in Figure 5. It is observed that the work function of single-layer MoSi₂N₄ is higher than that of GaSe/MoSi₂N₄ vdWHs, indicating that electrons accumulate on the MoSi₂N₄ side and are consumed on the GaSe side, both of which are transferred from GaSe to MoSi₂N₄. The observed direction of charge transfer aligns with the findings shown in Figure 4. The presence of the built-in electric field is attributed to the phenomenon of interfacial charge transfer. Hence, the mobility of carriers and the injection of charges may be influenced. Besides, to establish carrier migration, we calculate the effective mass in such vdWHs. Using VBM and CBM fitting for band edge dispersion, we calculate the effective mass of the electron (m_e*) and hole (m_h*) using

Figure 5. The work functions of GaSe, MoSi₂N₄ monolayer and their vdWHs. vdWHs: van der Waals heterostructures; GaSe: Gallium selenide.

In this context, E(k) represents the energy dispersion, $$ \hbar $$denotes Planck’s constant, and k represents the wave vector. The calculated electrons and holes of GaSe/MoSi₂N₄ vdWHs and the effective masses of the monolayer are listed in Table 1. It can be found that the calculated electron effective mass of GaSe/MoSi₂N₄ vdWHs is 0.38 m₀, which is still smaller than the value of GaSe and MoSi₂N₄ monolayer, thus indicating that GaSe/MoSi₂N₄ vdWHs has a higher carrier migration mobility. Furthermore, the carrier mobility of the GaSe/MoSi₂N₄ heterostructure calculated in this study (489 cm² V^-1 s^-1) is slightly higher than that of MoS₂ (410 cm² V^-1 s^-1), yet it is lower than that of silicon (1,400 cm² V^-1 s^-1). These findings suggest that our work holds significant potential for applications in the field of optoelectronics.

It is commonly recognized that controlling mechanical strain can effectively control the physical characteristics of 2D materials. In this study, we investigate the impact of strain engineering on GaSe/MoSi₂N₄ vdWHs by adjusting the interlayer distance, as shown in Figure 6A. Notably, interlayer distance in 2D-based vdWHs can be controlled using scanning tunneling microscopy^[53] or vacuum thermal annealing^[54]. We also calculated three stacking modes of GaSe/MoSi₂N₄ vdWHs at different interlayer distances in Supplementary Table 1. The results show that AC-stacking in GaSe/MoSi₂N₄ vdWHs has the lowest binding energy. Here, the strain is applied by adjusting the interlayer distance, defined as ΔD = D - D₀, where the value of the original D is 3.4 Å and D₀ is the interlayer distance after the strain. By increasing the interlayer distance D, the tensile strain is specified, and by reducing D, the compressive strain is defined. ΔD < 0 indicates compressive strain, while ΔD > 0 indicates tensile strain. As illustrated in Figure 6A, the bandgap of GaSe/MoSi₂N₄ vdWHs gradually increases as the interlayer distance gradually rises from 2.8 Å to 4.0 Å. By studying the band structure in Figure 6B, the underlying mechanism of GaSe/MoSi₂N₄ vdWHs bandgap variation under strain engineering can be described. By applying tensile strain (i.e., as D increases), the CBM and VBM of GaSe/MoSi₂N₄ vdWHs barely change, indicating that the bandgap remains unchanged, and the type-I band structure is also retained in GaSe/MoSi₂N₄ vdWHs. Under compressive strain, as D (3.4 Å) decreases to 2.8 Å, VBM and CBM in the red GaSe layer shift slightly upward, while VBM and CBM in the green MoSi₂N₄ layer hardly change and still maintain the band structure of type-I. These results show that there is no change in b-a from type-I to type-II by changing the interlayer distance.

Figure 6. (A) GaSe/MoSi₂N₄ vdWH bandgap variation with interlayer distance. The illustration is a schematic model of applying strain in the z-direction; (B) GaSe/MoSi₂N₄ vdWH band structure at different interlayer distances. vdWHs: van der Waals heterostructures; GaSe: Gallium selenide.

Furthermore, the effect of in-plane strain on the electronic structure of GaSe/MoSi₂N₄ vdWHs is considered. The in-plane strain is defined as:

Here, a and a_S denote the lattice parameters of GaSe/MoSi₂N₄ vdWHs without and in-plane strain, respectively. The bandgap change of GaSe/MoSi₂N₄ vdWHs is shown in Figure 7A. We found that the bandgap of GaSe/MoSi₂N₄ vdWHs decreased due to the in-plane strain. The bandgap of GaSe/MoSi₂N₄ vdWHs is reduced to 0.24 eV when ε = +6% tensile strain is applied. By applying in-plane compression strain, the bandgap of GaSe/MoSi₂N₄ vdWHs increases gradually and reaches a maximum value of 0.88 eV at -6% in-plane compression strain. Even more intriguingly, we found that the in-plane strain includes not only a change in the GaSe/MoSi₂N₄ vdWHs bandgap, but also a shift between type-I and type-II b-a. To better understand the underlying mechanism of the above behavior, we further mapped the projected band structure of GaSe/MoSi₂N₄ vdWHs under different tensile and compressive strains, as shown in Figure 7B. With the compression strain ε = -2% to -6% in the applied plane, the CBM of the MoSi₂N₄ layer shifts upward, causing it to move away from the Fermi level (E_F), and the VBM position hardly changes, while the VBM and CBM of GaSe layers are close to the E_F. In this instance, GaSe/MoSi₂N₄ vdWHs exhibit a type-I b-a; both VBM and CBM are contributed by the MoSi₂N₄ layer and have an indirect bandgap semiconductor at the Γ, K point. Besides, the CBM of the MoSi₂N₄ layer moves downward towards the E_F, VBM moves downward away from the E_F, and both VBM and CBM of the GaSe layer move closer to the E_F with the in-plane tensile strain ε = +2% to +4%. In this case, GaSe/MoSi₂N₄ vdWHs exhibit a type-I b-a; both VBM and CBM are contributed by the MoSi₂N₄ layer and have an indirect bandgap semiconductor at the K, Γ point. More interestingly, when ε = +4%, we find that GaSe layer CBM changes from the original M point to Γ point, and VBM changes from the original Γ point to between M and Γ point. Noteworthy is the fact that the positions of CBM and VBM in the MoSi₂N₄ layer almost do not change with the in-plane tensile strain ε reaching +6%, while the VBM in the GaSe layer moves upward to the E_F and the VBM in the GaSe layer is higher than that in MoSi₂N₄ layer. The results show that there is a shift from type-I to type-II b-a in GaSe/MoSi₂N₄ vdWHs. According to the above results, in-plane strain can effectively regulate the b-a and electronic structure of GaSe/MoSi₂N₄ vdWHs, which will be conducive to the design of high-efficiency nanoscale devices.

Figure 7. (A) Variation of GaSe/MoSi₂N₄ vdWH bandgap with in-plane strain. The illustration is a schematic model of the applied in-plane strain; (B) Projected band structure of GaSe/MoSi₂N₄ vdWHs under in-plane strain of ε = -6%, -4%, -2%, +2%, +4%, +6%. vdWHs: van der Waals heterostructures; GaSe: Gallium selenide.

The use of external vertical electric fields presents an additional efficacious approach for controlling the electronic structure of 2D materials and vdWHs. We explore the effects of an electric field applied perpendicular to the GaSe/MoSi₂N₄ vdWHs, as shown in Figure 8A. The direction of the electric field from MoSi₂N₄ towards the GaSe layer is defined as the positive direction (from bottom to top in the illustration). In Figure 8A, we find that the application of a negative electric field hardly causes a large change in the bandgap of GaSe/MoSi₂N₄ vdWHs. However, when a positive electric field is applied, we can observe that a decrease in the bandgap is observed as the field is intensified. When a positive electric field greater than +0.2 V/Å is applied, the bandgap of GaSe/MoSi₂N₄ vdWHs decreases to zero, resulting in a transition from semiconductor to metal (Supplementary Figure 3 describes the projected band structure of GaSe/MoSi₂N₄ vdWHs at an electric field of +0.3 V/Å). Interestingly, we found that applying an external electric field included not only a change in the GaSe/MoSi₂N₄ vdWHs bandgap, but also a shift between type-I and type-II b-a. In order to better understand the underlying mechanism of the above behavior, the projected band structure of GaSe/MoSi₂N₄ vdWHs was also plotted to describe the bandgap trend, as shown in Figure 8B. With the application of a negative electric field of - 0.1 to - 0.2 V/Å, the position of CBM and VBM in the MoSi₂N₄ layer hardly changes, while the GaSe layer CBM moves downward towards the E_F and VBM moves downward away from the E_F. In this case, the CBM of the GaSe layer in vdWHs is above the CBM of MoSi₂N₄, and the VBM of the GaSe layer is below the VBM of MoSi₂N₄, so there is a type-I b-a (where both VBM and CBM are contributed by the MoSi₂N₄ layer). On the other hand, with the application of a positive electric field of +0.1 to +0.2 V/Å, the CBM and VBM of the MoSi₂N₄ layer move downward to the lower energy level, and the VBM and CBM of the GaSe layer move upward to the higher energy level. In this case, both CBM and VBM of the GaSe layer in vdWHs are above MoSi₂N₄, so it appears as a type-II b-a (where CBM is contributed by MoSi₂N₄ layer and VBM is contributed by GaSe layer). These discoveries imply that the electric field is an effective regulating knob for the type of b-a between type-I and type-II.

Figure 8. (A) Variation of bandgap of GaSe/MoSi₂N₄ vdWHs with electric field. The illustration is a diagram of applying an electric field along the vdWHs z-direction; (B) Projected band structure of GaSe/MoSi₂N₄ vdWHs under different electric field intensities. vdWHs: van der Waals heterostructures; GaSe: Gallium selenide.

CONCLUSIONS

In a word, we investigate the structural characteristics and electronic properties of GaSe/MoSi₂N₄ vdWHs by first-principles calculations and explore the interlayer distance, in-plane strain, adjustable electronic structure and band alignment under external electric fields. The results show that the heterostructure exhibits stability at standard room temperature and possesses characteristics of an indirect bandgap semiconductor. Notably, we observed that both CBM and VBM of GaSe/MoSi₂N₄ vdWHs are derived from monolayer MoSi₂N₄, thus forming a type-I b-a. Furthermore, by applying in-plane strain, the external vertical electric field can separate the band edges of GaSe/MoSi₂N₄ vdWHs from the GaSe and MoSi₂N₄ layers, leading to a shift from type-I to type-II b-a types. Our results reveal the great potential of GaSe/MoSi₂N₄ vdWHs as a tunable material in optoelectronic applications.