Investigating the Impact of Stress on the Optical Properties of GaN-MX₂ (M=Mo, W; X=S, Se) Heterojunctions Using the First Principles

Abstract

This study used the first-principles-based CASTEP software to calculate the structural, electronic, and optical properties of heterojunctions based on single-layer GaN. GaN-MX₂ exhibited minimal lattice mismatches, typically less than 3.5%, thereby ensuring lattice coherence. Notably, GaN-MoSe₂ had the lowest binding energy, signifying its superior stability among the variants. When compared to single-layer GaN, which has an indirect band gap, all four heterojunctions displayed a smaller direct band gap. These heterojunctions were classified as type II. GaN-MoS₂ and GaN-MoSe₂ possessed relatively larger interface potential differences, hinting at stronger built-in electric fields. This resulted in an enhanced electron–hole separation ability. GaN-MoSe₂ exhibited the highest value for the real part of the dielectric function. This suggests a superior electronic polarization capability under an electric field, leading to high electron mobility. GaN-MoSe₂ possessed the strongest optical absorption capacity. Consequently, GaN-MoSe₂ was inferred to possess the strongest photocatalytic capability. The band structure and optical properties of GaN-MoSe₂ under applied pressure were further calculated. The findings revealed that stress significantly influenced the band gap width and light absorption capacity of GaN-MoSe₂. Specifically, under a pressure of 5 GPa, GaN-MoSe₂ demonstrated a significantly narrower band gap and enhanced absorption capacity compared to its intrinsic state. These results imply that the application of stress could potentially boost its photocatalytic performance, making it a promising candidate for various applications.

1. Introduction

In contemporary society, while individuals embrace the convenience bestowed by advanced technology, they are simultaneously confronted with grave environmental pollution issues [1,2,3,4]. Photocatalytic technology enables the conversion of solar energy into chemical energy and possesses the capability to degrade environmental pollutants. Therefore, extensive research has been conducted on various photocatalyst materials, including TiO₂ [5], g-C₃N₄ [6], CdS [7], and GaN [8]. Among these, GaN has garnered significant attention from researchers due to its cost-effectiveness, facile preparation process, and exceptional catalytic activity [9]. However, the wide bandgap (approximately 3.4 eV [10]) of this material restricts its absorption range for solar radiation and poses a challenge to its practical implementation in everyday applications. Consequently, multiple enhancement techniques such as doping, defect engineering, and heterojunction formation have emerged successively [11]. By employing these technologies, the bandgap width of the system can be effectively reduced, thereby broadening the absorption spectrum range of solar radiation for the material and further augmenting its photocatalytic activity. Among these, the construction of heterojunctions facilitates catalysts to exhibit enhanced carrier mobility, thereby endowing them with remarkable visible light absorption capability and facilitating efficient electron–hole pair separation. Zhang et al. [12] theoretically investigated the electronic structure of GaN/AlN. The determined band gap width of the material was 2.44 eV, exhibiting a lower value compared to that of monolayer AlN (2.79 eV). This indicates that constructing heterojunctions can effectively reduce the band gap width of the system, increasing the probability of electron transitions. Fu et al. [13] conducted computational studies on the electronic structure and optical properties of monolayer g-C₃N₄ and the GaN/g-C₃N₄ heterojunction. They found that the band gap value of GaN/g-C₃N₄ (1.658 eV) was less than that of monolayer g-C₃N₄. Han et al. [14] devised a synthesis pathway to fabricate GaN/ZnO solid solution nanocrystals through nitridation of a uniform Ga-Zn-O nanoprecursor, leading to the achievement of a reduced band gap (2.21 eV) in comparison to individual counterparts (GaN and ZnO) possessing approximate band gaps around 3.3 eV. Butté et al. [15] reported on the synthesization of an AlInN/GaN heterostructure via chemical deposition, demonstrating a remarkably low lattice mismatch of 0.18%. This heterostructure also exhibited an intrinsic electric field strength of 3.64 mV/cm and achieved high two-dimensional electron mobility of approximately 1170 cm²/V·s at room temperature. The enhancement of photocatalytic activity relies on optimizing a relatively narrow band gap and fast electron mobility. Therefore, the utilization of GaN-based heterojunctions as photocatalysts exhibits exceptional performance, exemplified by their remarkable achievements in GaN-AlN [16], GaN/g-C₃N₄ [17], GaN/ZnO [18], and GaN/AlInN [19]. The objective of the first part of this study was to computationally simulate the construction of GaN and chalcogenide heterojunctions, denoted as GaN-MX₂, where M signifies a transition metal and X represents a chalcogen element. Subsequently, an assessment of their respective physical properties was conducted.

Furthermore, the photocatalytic efficiency of heterojunctions can be further enhanced by applying stress. The application of pressure on heterojunctions has been demonstrated to effectively modulate the bandgap width in previous research. Wang et al. [20] conducted theoretical calculations and observed that the application of 30 GPa of pressure on Cu-N co-doped TiO₂/MoS₂ led to a reduction in the bandgap width by 0.35 eV, from 1.38 eV (without pressure) to 1.03 eV (under pressure). Moreover, the absorption band edge was redshifted, thereby expanding the optical response range. Guo et al. [21] experimentally investigated the photocatalytic performance of the BiVO₄/Bi_0.6Y_0.4VO₄ system under applied pressure. They found that applying pressure induced a structural transition of the solid solution from the tetragonal to the monoclinic phase. BiVO₄/Bi_0.6Y_0.4VO₄ under pressure exhibited a maximum hydrogen evolution rate of 45.5 μmol/h and an oxygen evolution rate of 22.8 μmol/h, the values of which are three times higher than those of BiVO₄/Bi_0.6Y_0.4VO₄ without applied pressure (hydrogen ≈ 15.1 μmol/h, oxygen ≈ 7.5 μmol/h). This indicates that the application of pressure enhances the carrier migration rate of the system, thereby improving the photocatalytic activity of the heterojunction system [22]. The subsequent investigation in this study aimed to explore the impact of applied pressure on the photocatalytic performance of GaN-MX₂.

We employed the CASTEP [23] package (version 2017), which is based on density functional theory, to conduct this study. Since its publication in the 1990s, this method has garnered recognition for its user-friendly interface compared to other software, as well as its precise calculation results that closely align with experimental values. Consequently, it has been extensively utilized in designing and predicting periodic materials. This comprehensive software suite alone can fulfill the research objectives outlined in this paper, specifically encompassing heterojunction construction and stress implementation.

While previous studies focused solely on investigating the modulation effect of constructing heterojunctions on the optical properties of GaN, this study explored the impact of superimposing two methods of constructing heterojunctions and applying stress on GaN to elucidate alterations in its optical properties. The results can provide theoretical guidance for future experimental research.

2. Results

2.1. Geometric Parameters and System Stability

Geometric Parameters and Stability

The lattice parameters of GaN-MX₂ are shown in

Table 1. Lattice constants of GaN-MX₂ after optimization.

Model	GaN-MoS2	GaN-MoSe2	GaN-WS2	GaN-WSe2
σ /%	0.5	3.3	0.1	3.2
Eb/eV	−0.1385	−0.1512	−0.1347	−0.1498
Cell volume/Å3	786.404	826.206	825.014	846.888
Length (Å)	2.9505	2.5270	2.4218	2.4838

. The lattice mismatch rate (σ) of the four heterostructures was calculated in this study to investigate their lattice matching, following Formula (1) [24].

$$\sigma ={\displaystyle \frac{({\mathrm{a}}_1-{\mathrm{a}}_2)}{{\mathrm{a}}_1}}\times 100\%$$

(1)

where a₁ and a₂ are the lattice constants of single-layer GaN and MX₂ supercells, respectively. The calculated σ values for the four different heterojunctions are presented in Table 1, all of which remained below 3.5%, satisfying the conditions of complete coherence (|σ| < 5%).

Meanwhile, to investigate the stability of heterojunctions, we performed calculations on the binding energies (E_b) of GaN-MX₂, where a more negative value indicates a higher degree of system stability. The mathematical expression for the E_b of heterojunctions can be formulated as follows [25]:

$$E_b=E\left[{\mathrm{GaN}\text{-}\mathrm{MX}}_2\left(M=Mo,W;X=S,Se\right)\right]-E(\mathrm{GaN})-E\left[{\mathrm{MX}}_2\left(M=Mo,W;X=S,Se\right)\right]$$

(2)

where E(GaN-MX₂) denotes the energy of GaN-MX₂, while E(GaN) and E(MX₂) represent the energies of GaN and MX₂, respectively. The calculated values of E_b are presented in Table 1. It is evident that all heterojunctions exhibited negative E_b values, indicating their inherent structural stability. Among the four systems, GaN-MoSe₂ demonstrated the lowest binding energy, implying its superior structural stability.

2.2. Electronic Structure Analysis

In order to facilitate the investigation of the electronic structure of GaN-MX₂, we defined the Fermi level at 0 eV, as depicted in Figure 1. Figure 1a illustrates the band diagram of a monolayer GaN. The figure demonstrates that the conduction band minimum (CBM) of single-layer GaN is situated at the high symmetry point G, while the valence band maximum (VBM) is located at the high symmetry point K. This observation indicates an indirect band gap with a width of 2.133 eV for the system.

The energy band diagram of GaN-MoS₂ is depicted in the left image of Figure 1b. It was observed that both the CBM and VBM were situated at the high symmetry point Q, indicating a direct band gap with a forbidden bandwidth of 0.856 eV for GaN-MoS₂. Moreover, this material exhibited a downward shift toward lower energy levels, thereby reducing the energy required for electron transitions from the valence band to the conduction band. This is consistent with the results calculated by Tian et al. [26], which proves that the parameter selection in this study is reasonable. In conjunction with the density of states (DOS) plot presented in the left picture of Figure 1b, it was observed that GaN predominantly contributed to VBM, while MoS₂ primarily contributed to CBM in GaN-MoS₂, indicating distinct system-specific contributions to VBM and CBM. Consequently, GaN-MoS₂ exhibiting this band characteristic was classified as a type II heterojunction.

The left panel in Figure 1c illustrates the band structure of GaN-MoSe₂. Compared to single-layer GaN, the conduction band exhibited a downward shift in energy and a reduction in the band gap by 1.426 eV. The DOS plot for GaN-MoSe₂ is depicted in the image on the right-hand side (Figure 1c). The analysis revealed that the VBM was primarily determined by contributions from GaN, while the CBM was predominantly influenced by MoSe₂. Their combined effect led to a reduced bandwidth. This system exhibited a similar electric structure to GaN-MoS₂ and was also classified as a type II heterojunction.

The band diagram of GaN-WS₂ (left image) in Figure 1d exhibited a downward shift in energy, revealing a narrower bandgap, measured at 1.161 eV, compared to that of single-layer GaN. Additionally, it was observed that GaN-WS₂ exhibited a distinct characteristic of having a direct bandgap. The DOS plot in Figure 1d (right image) reveals that the VBM was mainly contributed by GaN, while the CBM was primarily influenced by WS₂. Therefore, this system can be classified as a type II heterojunction material.

The energy bands of GaN-WSe₂ in Figure 1e (left image) transitioned from an indirect to a direct bandgap, resulting in a reduced width of 1.622 eV compared to single-layer GaN. This reduction effectively lowered the energy required for electron transition [27]. Furthermore, based on the DOS plot in Figure 1e (right image), it is evident that WSe₂ significantly contributed to the CBM, while GaN dominated the VBM, confirming this system as a type II heterojunction material.

2.3. Work Function

The work function (Φ), as defined by Equation (5), quantifies the energy required to overcome the surface potential barrier, enabling electrons to escape from a solid surface (Fermi level, E_F) and reach the vacuum energy level (E_vac) [28]. This formula is as follows:

$$\Phi =E_{\mathrm{vac}}-E_{\mathrm{F}}$$

(3)

Therefore, we calculated the work functions for four GaN-MX₂ systems and compared the results of this study with both the calculated and experimental values of other studies, as shown in

Table 2. Summary of the work functions of GaN-MoS₂, GaN-MoSe₂, GaN-WS₂, and GaN-WSe₂.

	GaN-MoS2	GaN-MoSe2	GaN-WS2	GaN-WSe2
Φ (this work)	5.042 eV	5.077 eV	4.699 eV	4.735 eV
Φ (calculated values)	5.17 eV [26]	5.091 eV [29]	4.57 eV [30]	4.92 eV [31]
Φ (experimental values)	5.26 eV [26]	-	-	-

. It was found that the calculated values in this study are very close to those obtained by others, indicating that the calculated results presented in this paper are reliable, as illustrated in Figure 2. In GaN-MoS₂, the minimum work function of MoS₂ exhibited an 11.06 eV reduction compared to that of GaN. Electrons were required to undergo transfer from MoS₂, characterized by a lower potential, to GaN, characterized by a higher potential, until the same E_F was reached. MoS₂ accumulated positive charges on its surface, while GaN accumulated negative charges on its surface during the process. Consequently, a built-in electric field was present at the interface, oriented from GaN toward MoS₂. This built-in field facilitated the efficient separation of electron–hole pairs, thereby significantly enhancing the photocatalytic activity of the system.

Through extrapolation, the other three heterojunctions exhibited varying potential differences at the interface, indicating the generation of distinct built-in electric fields. Notably, the interface potential differences of GaN-MoS₂ and GaN-MoSe₂ were significantly larger than those of the other two heterojunctions. Although GaN-MoSe₂ demonstrated a slightly smaller potential difference compared to GaN-MoS₂, this disparity was not statistically significant. Consequently, it can be inferred that among these four heterojunctions, GaN-MoS₂ exhibited superior electron–hole separation ability, followed by GaN-MoSe₂. Based on this observation, it can be speculated that both GaN-MoS₂ and GaN-MoSe₂ possess commendable photocatalytic capabilities.

2.4. Optical Properties

2.4.1. Alignment with Band Structure Edges

Typically, photocatalysts are evaluated based on the relative positions of their semiconductor conduction band max (CBM) and valence band min (VBM) values with respect to the standard hydrogen electrode (NHE). Determining the band-edge potential on the NHE scale commonly relies on Equations (4) and (5) [32]. In the two equations, X represents the absolute electronegativity of the material. The energy level of free electrons on the NHE scale, which is approximately 4.5 eV, is denoted as E_elce. On the contrary, E_g refers to the band gap of a semiconductor.

$$E_{\mathrm{CBM}}=X-E_{\mathrm{elec}}-0.5E_g$$

(4)

$$E_{\mathrm{VBM}}=\mathrm{VBM}+E_g$$

(5)

The band-edge potential on the NHE scale of the four heterojunctions is depicted in Figure 3, revealing that the CBMs of GaN-MoS₂ and GaN-WS₂ lie above the H⁺/H₂ potential, indicating their capability to evolve hydrogen. However, the VBMs of both systems did not fall below the O₂/H₂O potential, suggesting their inability to evolve oxygen. Conversely, GaN-WSe₂ solely possessed the ability to evolve oxygen, while only GaN-MoSe₂ exhibited simultaneous hydrogen and oxygen evolution capabilities. Consequently, it can be inferred that, among these four heterojunctions, GaN-MoSe₂ has superior photocatalytic activity for water splitting.

2.4.2. Dielectric Function

The variation in the real and imaginary parts of the dielectric function for GaN-MX₂ with incident photon energy is depicted in Figure 4. In Figure 4a, the real part of the dielectric function for GaN-MX₂ is presented. The stronger the static dielectric constant, the greater the binding ability and polarization capability toward charges in the system. This figure reveals that the static dielectric constants for monolayer GaN and GaN-MX₂ systems were 1.938, 6.195, 6.663, 5.574, and 6.153, respectively, satisfying the equation $\epsilon (0)\approx 1+{({\displaystyle \frac{\hslash \omega }{Eg}})}^2$ [14]. The GaN-MX₂ system exhibited a higher static dielectric constant compared to that of single-layer GaN, suggesting enhanced charge confinement and polarization capabilities in the GaN-MX₂ heterojunctions. Among these systems, GaN-MoSe₂ demonstrated the highest static dielectric constant, indicating faster migration of photogenerated carriers within the crystal, thus enhancing its photocatalytic activity. The imaginary part of the dielectric function for GaN-MX₂ is depicted in Figure 4b. As the value increased, the likelihood of electron absorption of photons in the system also increased, resulting in a higher population of electrons in an excited state. From the graph, it is evident that single-layer GaN, GaN-WS₂, GaN-WSe₂, GaN-MoS₂, and GaN-MoSe₂ manifested their first noticeable peak within the visible light range at energy levels of 3.146, 2.827, 2.798, 3.137, and 2.991 eV, respectively. This observation highlights a redshift phenomenon in the GaN-MX₂ systems, which may have significant implications for future research in this field. Among them, GaN-MoSe₂ presented the highest imaginary part of the dielectric function value, indicating a greater propensity for electron absorption of photons and consequently possessing a higher population of excited electrons. Therefore, it can be inferred that this system has superior photocatalytic performance.

In summary, compared to monolayer GaN, GaN-MX₂ exhibited an increased static dielectric constant and a redshift phenomenon, indicating an enhanced polarization ability and binding energy. Consequently, there is a higher likelihood of electron absorption of photons and an increase in excited state electrons. Therefore, the probability of electron transition is also amplified. Thus, constructing heterojunctions serves as a means to enhance the photocatalytic performance of the system.

2.4.3. Absorption Spectra

The absorption spectra of GaN-MX₂ as a function of incident wavelength are depicted in Figure 5. It can be observed from the graph that within the visible light range, all four systems of GaN-MX₂ exhibited significantly higher absorption intensity compared to monolayer GaN. The constructed GaN-MX₂ heterojunctions exhibited superior photocatalytic activity compared to monolayer GaN. Among these systems, it is noteworthy that GaN-MoSe₂ demonstrated the highest absorption intensity due to enhanced interaction between the 4d state of Mo and the 4p state of Se, as well as between the 4p state of Ga and the 2p state of N in this particular heterojunction. Consequently, there was an increased number of electron transitions, which beneficially impacted the photocatalytic efficiency of GaN-MoSe₂. Importantly, this result aligns with analysis based on dielectric functions [5].

2.5. Applying Pressure

Based on the aforementioned analysis, it is evident that GaN-MoSe₂ exhibited a commendable photocatalytic performance. In general, applying stress engineering to a photocatalyst can further enhance its photocatalytic capability. Consequently, GaN-MoSe_2, with superior photocatalytic performance, was chosen for subsequent implementation of stress engineering regulations. As illustrated in Figure 6, variations in Eg of GaN-MoSe₂ were observed under stress levels ranging from 3 to 6 GPa. The effect of stress on the electronic structure of GaN-MoSe₂ was highly significant, as evidenced by the observed increase in Eg followed by a gradual decrease with increasing pressure. The aforementioned observation suggests that stress exerts a robust influence on the catalytic activity of GaN-MoSe₂, as convincingly demonstrated by the light absorption spectra (Figure 7) obtained under various stress conditions. The results depicted in Figure 7 indicate that the light absorption capacity of GaN-MoSe₂ was enhanced under pressures of 3 and 6 GPa, compared to GaN-MoSe₂ without pressure. Therefore, the implementation of stress engineering can further enhance the photocatalytic activity of GaN-MoSe₂, which exhibited superior photocatalytic performance compared to the other three heterojunctions.

3. Computational Methods and Theoretical Model

The selected GaN structure in this study was wurtzite, belonging to the P63mc (No. 186) space group, with lattice constants of a = b = 0.318 nm and c = 0.517 nm and angles of α = β = 90° and γ = 120° [33]. The transition metal chalcogenide MX₂ exhibited the 2H phase [34]. First, geometric optimization of both GaN and MX₂ unit cells was performed individually. Subsequently, they were cleaved along the (001) direction to fabricate heterostructures. Additionally, a vacuum layer with a thickness of 18 Å was incorporated along the c-axis to mitigate interlayer coupling effects. Based on the convergence test diagram (Figure 8), the supercell size of GaN-MX₂ was set to 2 × 2 × 1, ensuring calculation accuracy while conserving computing resources. Therefore, we constructed GaN-MX₂ models using a 2 × 2 × 1 supercell while ensuring computational accuracy, as illustrated in Figure 9. The valence electron configurations for the six atoms involved in this study were as follows: Ga (4s²4p¹), N (2s²2p³), Mo (4d⁵5s¹), W (5d⁴6s²), S (3s²3p⁴), and Se (4s²4p⁴).

The calculation in this article was based on density functional theory (DFT), utilizing the CASTEP module within the Materials Studio software package (version 2017). The plane wave super soft pseudo potential was employed to describe the interaction between valence electrons and ions, while the generalized gradient approximation GGA-PBE was utilized for exchange–correlation energy during geometry optimization [35]. Considering the limitations of DFT in accurately describing van der Waals (vdW) interactions, the incorporation of Tkatchenko–Scheffler (TS) dispersion correction is essential during the calculation process [31]. The plane wave cutoff energy was set to 550 eV. The K-point grid was set as 5 × 5 × 1 under the Monkhorst–Pack scheme [36]. The BFGS algorithm was employed, incorporating a self-consistent field (SCF) convergence criterion of 2.0 × 10⁻⁶ eV/atom and a maximum interatomic stress limit of 0.1 GPa. All calculations were conducted within the reciprocal lattice space [37].

4. Conclusions

The structural stability, electronic structure, and optical properties of GaN-MX₂ (M=Mo, W; X=S, Se) heterojunctions were investigated in this study using the CASTEP module. Through first principle calculations, it was shown that GaN-MX₂ exhibited low lattice mismatches (<3.5%), thereby ensuring lattice coherence. Notably, GaN-MoSe₂ demonstrated the lowest binding energy, indicating its high stability. The four heterojunctions exhibited a smaller direct band gap compared to single-layer GaN, which had an indirect band gap. All heterojunctions were of type II. Calculation of the work functions revealed that GaN-MoS₂ and GaN-MoSe₂ have relatively larger interface potential differences, indicating stronger built-in electric fields and, thus, the strongest electron–hole separation ability. Among the four heterojunctions, GaN-MoSe₂ exhibited the highest real part value of the dielectric function, indicating its superior electronic polarization ability under an electric field and, consequently, the highest electron mobility, as well as the most pronounced optical absorption capacity. Therefore, it can be inferred that GaN-MoSe₂ possesses the strongest photocatalytic capability. The primary distinction between this investigation and prior ones lies in the computation of the band structure and optical properties of GaN-MoSe₂ under applied pressure. The findings demonstrate that the application of stress significantly impacted the band gap width and light absorption capacity of GaN-MoSe₂. Specifically, when subjected to a pressure of 5 GPa, it demonstrated a significantly narrower band gap and heightened absorption capacity in comparison to its intrinsic state. These results suggest that the application of stress has the potential to further enhance its photocatalytic performance. Future studies could explore the application of biaxial strain on GaN-MoSe₂ to observe changes in its electronic structure and optical properties so as to speculate on the modulation effect of its photocatalytic capacity.