Stacked van der Waals (vdW) heterostructures (HSs) often lead to new physics and to promising opportunities for the design of unusual electronic devices.^[1] Therefore, two-dimensional (2D) vertically stacked vdW HSs have drawn the attention of many researchers because of their tunable band gaps and thicknesses of several atomic layers.^[2] For example, MoS₂–ZnO,^[3] MoS₂–WSe₂,^[4] BP–BN,^[5] MoSe₂–graphene,^[6] and AlGaN–GaN^[7] have provided novel material platforms to explore a range of innovative applications, including ultrathin photodetectors,^[8] solar cells,^[9] and tunneling transistor-based memory devices.^[10] However, the application of these 2D materials is enabled by their outstanding physical properties. In addition, the electronic structures of these materials are highly sensitive to both thickness and external strain.^[11–15] Miwa et al. demonstrated that MoS₂–graphene HSs could be grown epitaxially on a semiconducting silicon carbide substrate under ultrahigh vacuum conditions.^[16] In a recent work by He et al., the band gap of the MoSe₂–WSe₂ HS was reduced to 1.48 eV, which was lower than the band gaps of the individual WSe₂ (1.60 eV) and MoSe₂ (1.50 eV) layers, and the direct or indirect band gaps of HSs have shown redshifts under tensile strains.^[17] Overall, strain can be feasibly used to tune the band gaps of these 2D materials.

GaN has recently drawn considerable interest and 2D GaN has been used in optoelectronic applications. Unlike other 2D materials, wurtzite structured bulk GaN is unsuitable for 2D structure formation through exfoliation.^[18] Fortunately, 2D GaN has been experimentally synthesized directly via a graphene encapsulation process.^[19] Sun et al. systematically investigated the electronic properties of a graphene-g-GaN HS based on first-principles calculations and discovered that an increase in the interlayer distance from 2.5 Å to 4.5 Å led to a transition from a p-type to an n-type Schottky contact.^[20] Subsequently, the stability properties of 2D GaN have also been confirmed theoretically.^[21–23] Sanders et al. investigated the electronic and optical properties of both monolayer and bilayer 2D GaN.^[24] Accurate band gaps, excitonic properties, and the luminescence energies of 2D GaN under various strains were studied via first-principles calculations based on density functional theory (DFT) and many-body perturbation theory, and it was revealed that the quantum confined Stark effect was amplified by the strong polarization field of the material. With its excellent properties, 2D GaN could be applied in fields including energy-efficient display applications, nonlinear optics, and water purification.^[24] In addition, 2D GaN and transition metal dichalcogenides can be combined to provide superior physical properties.

2D MoS₂, a typical direct band gap (1.8 eV) semiconductor, has also received significant attention.^[25,26] Monolayer MoS₂ can absorb light in the 510 nm–780 nm range with absorbance of 5%–10%.^[26] Therefore, the exploration of the novel structures and excellent properties of GaN–MoS₂ HSs is of great importance. To the best of our knowledge, the electronic and optical properties of GaN–MoS₂ HS have not been investigated previously. The study of the structural, electronic, and optical properties of GaN–MoS₂ HSs is very valuable because of the potential applications of these structures in the fields of photovoltaic cells and photocatalysis.

All the properties of GaN–MoS₂ HSs were studied using first-principles calculations based on DFT. The generalized gradient approximation of the Perdew–Burke–Ernzerhof functional^[27] was adopted and implemented in Vienna ab initio simulation package software.^[28–31] The projector augmented wave method was used to solve the Kohn–Sham equations.^[32] An energy cutoff of 600 eV and Brillouin zone sampling of a K-mesh of 11 ×11×1 were set. Additionally, a K-mesh of 15×15×1 was used for the energy band structure calculations. In the relaxation process, the energy criterion was set at 10⁻⁵ eV and the residual force was less than 10⁻³ eV/Å. The vacuum layer thickness was more than 20 Å to prevent spurious interactions with the neighboring image structures. The long-range vdW interactions were important in holding the 2D HS together.^[33] The vdW-DF2 functional was selected here to describe the long-range electron correlation effects.^[34]

In the optical properties calculations, the Fourier transform of the dielectric function was given as^[35]

The wurtzite GaN structure is cleaved along [0001] to form a planar structure, which was previously predicted to be stable.^[19] After optimization, the lattice constants of monolayer GaN and MoS₂ were determined to be 3.18 Å and 3.20 Å, respectively; these values are consistent with previously reported results.^[12,24] The structure of the GaN–MoS₂ HS is depicted in Fig. 1. The GaN–MoS₂ HS can be formed with only a small lattice mismatch (0.3%). The lattice parameter of the GaN–MoS₂ HS is 3.19 Å, as calculated using DFT. A supercell (4 × 4) is then adopted to calculate the properties of the HS.

Fig. 1.

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	Fig. 1. Structure (4 × 4 supercells) of GaN–MoS2 HS from (a) the top view and (b) the side view, where the purple, gray, blue, and brown balls represent the Mo, S, N, and Ga atoms, respectively.

To assess the vdW interactions between the GaN and MoS₂ layers, the distance D between the Ga and S atoms and the binding energy Δ E are calculated for the GaN–MoS₂ HS as follows:

Next, the band structure of the GaN–MoS₂ HS is derived, as shown in Fig. 2. Both the valence band maximum (VBM) and the conduction band minimum (CBM) of the GaN–MoS₂ HS remain at the K point, as shown in Fig. 2(b). The band gap of the GaN–MoS₂ HS is 1.95 eV, while that of monolayer GaN is 3.48 eV and that of monolayer MoS₂ is 2.03 eV, based on HSE06 hybrid functional calculations. It is thus demonstrated that the GaN–MoS₂ HS is a typical type-II band semiconductor, as illustrated in Fig. 2(a). In the type-II band alignment, the positions of the valence and conduction bands of the GaN semiconductor are higher than the corresponding bands of the MoS₂ semiconductor. In addition, the steps in the conduction and valence bands are oriented in the same direction. Importantly, the difference in the chemical potential between semiconductor GaN and MoS₂ causes band bending at the junction interface. This band bending induces a built-in field that drives the photogenerated electrons and holes to move in opposite directions, which leads to spatial separation of the electrons and holes on the different sides of the heterojunction.^[37] Type-II HSs are of particular interest because of this spatial separation of the electrons and holes following photoexcitation, which is a highly desirable property for photovoltaic applications.^[38] Therefore, the type-II band behavior of the GaN–MoS₂ HS could be applicable in the photovoltaic and photocatalytic fields.

Fig. 2.

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	Fig. 2. (a) Schematic diagram of a typical type-II band and (b) band structure of the GaN–MoS2 HS, where the purple and red balls represent the MoS2 and GaN contributions, respectively.

To gain an insight into the electronic properties of the GaN–MoS₂ HS, the total density of states and the projected density of states are presented in Fig. 3. The red and blue lines represent the DOSs of GaN and MoS₂ in the GaN–MoS₂ HS, respectively. The figure clearly shows that the VBM and the CBM are confined within the GaN and MoS₂ layers, respectively.

Fig. 3.

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	Fig. 3. Total density of states of GaN, MoS2, and the GaN–MoS2 HS.

For further clarification of the interactions, the electronic band structure of the GaN–MoS₂ HS is calculated under various biaxial strains. Strain is known to be one of most effective means to tailor the properties of 2D materials.^[11–13,17] Yu et al. calculated the electronic properties of RbGeI₃ under strains ranging from −6% to 6% and found that the band gap of the material decreased monotonically.^[11] In Fig. 4, the lattice parameters with strains of −5.0% to +5.0% have been added to the structure of the GaN–MoS₂ HS and the band gap properties of the GaN–MoS₂ HS as it varies from compressed to stretched have been investigated. First, the strain may not be transferred entirely from the GaN layer to the MoS₂ layer. Second, to avoid the symmetry of the HS being destroyed, the use of biaxial strain of less than 5% is considered. Both stretching and compression can lead to a reduction of the band gap of the GaN–MoS₂ HS. The calculated band gap shifts with respect to the strain and the band gap are significantly reduced under application of biaxial tensile or compressive strain at 2.0%. The rate of reduction of the direct band gap of the GaN–MoS₂ HS under tensile strain is found to be much higher than that under compressive strain. This is the reason why the VBM at the K point is predominantly contributed by the N p_z and Ga p_z, d_z2, and d_yz orbitals, while the CBM at the K point contains a proportion of the metal S p_x and Mo d_z2 and d_yz orbitals. Obviously, the tensile strain results in in-plane expansion of the lattice because of the reduction in the overlap of the metal Ga d orbitals and Mo d orbitals. As a result, the rate of change in the direct band gap of the GaN–MoS₂ HS induced by strain at the K point is relatively slow. As indicated by the calculated band structures, the direct band gap is reduced by strain because of the contributions from the upshifted CBM at the K point and the downshifted VBM at the K point. In particular, the direct band gap peak intensity decreases monotonically under the application of strain, and the +5.0% and −5.0% strains ensure that the stretched and compressed GaN–MoS₂ HSs remain semiconductors. These results agree well with those reported for the WSe₂/MoSe₂ HS.^[17]

Fig. 4.

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	Fig. 4. Band gap of the GaN–MoS2 HS under various biaxial strains.

The imaginary part of the dielectric constant ε₂ for the GaN–MoS₂ HS from −5% to 5% strain is then calculated, as shown in Fig. 5. The imaginary part of the dielectric constant can represent the absorption coefficient and the first absorption peak is located at 3.30 eV, which is in the ultraviolet light range. The optical band gap is 1.89 eV, which agrees well with the calculated electronic band gap. It is clearly shown that the optical band gap of the GaN–MoS₂ HS suffers from redshifts under tensile and compressive strain. When the tensile and compressive strain is increased, the absorption intensity is also enhanced. This means that GaN–MoS₂ HS will be suitable for application to photovoltaic cells and photodetectors in the future.

Fig. 5.

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	Fig. 5. Imaginary dielectric function of the GaN–MoS2 HS with strains ranging from −5% to 5%.

In summary, the electronic and optical properties of the GaN–MoS₂ HS have been determined from first-principles calculations. The lattice parameter of the GaN–MoS₂ HS is 3.19 Å and the structure of this HS is stable. The GaN–MoS₂ HS is found to be a typical type-II band structure semiconductor. The application of tensile or compressive strain leads to a reduction of the direct band gap of the GaN–MoS₂ HS. These results can offer insights into the interactions between the stacked GaN and MoS₂ monolayers in the GaN–MoS₂ HS and will help to guide the design of future applications of these HSs in solar cells and photocatalysts.