The First-Principles Study of External Strain Tuning the Electronic and Optical Properties of the 2D MoTe2/PtS2 van der Waals Heterostructure

Two-dimensional van der Waals (vdW) heterostructures reveal novel properties due to their unique interface, which have attracted extensive focus. In this work, the first-principles methods are explored to investigate the electronic and the optical abilities of the heterostructure constructed by monolayered MoTe₂ and PtS₂. Then, the external biaxial strain is employed on the MoTe₂/PtS₂ heterostructure, which can persist in the intrinsic type-II band structure and decrease the bandgap. In particular, the MoTe₂/PtS₂ vdW heterostructure exhibits a suitable band edge energy for the redox reaction for water splitting at pH 0, while it is also desirable for that at pH 7 under decent compressive stress. More importantly, the MoTe₂/PtS₂ vdW heterostructure shows a classy solar-to-hydrogen efficiency, and the light absorption properties can further be enhanced by the strain. Our results showed an effective theoretical strategy to tune the electronic and optical performances of the 2D heterostructure, which can be used in energy conversion such as the automotive battery system.

Introduction

Graphene shows unique electronic and thermal performances after being prepared as a two-dimensional (2D) material (Geim and Novoselov, 2007), which has also attracted other layered materials (Cui et al., 2021a; Cui et al., 2021b; Ren et al., 2022a; Wang et al., 2022a). However, its zero bandgap restricts the applications as electronic switch and other devices. Therefore, 2D semiconducting materials include transition metal dichalcogenides (TMDs) (Shen et al., 2022), phosphorene, and MXenes. MoS₂ possesses excellent electronic and photoelectric properties similar to or even more advantageous than graphene in some aspects (Butler et al., 2013; Zhang et al., 2018). After the successful synthesis of graphene and MoS₂, more and more 2D materials have been found and synthesized. Its direct bandgap is about ∼1.8 eV (Wickramaratne et al., 2014), which can be widely used in transistors, optoelectronics, and photocatalysts (Radisavljevic et al., 2011; Qiu et al., 2013; Ma et al., 2020). Black phosphorene has intrinsic direct bandgap and high carrier mobility (Li et al., 2014). Due to the anisotropic structure, black phosphorene shows remarkable anisotropic electronic, mechanical, and thermal properties. All these excellent properties endow its application in high-performance photovoltaic (Liu et al., 2017), spin-filter devices (You et al., 2016), thermal rectifiers (Ren et al., 2020a), field-effect transistors (Hong et al., 2014), etc.

To expand the family of 2D materials, tremendous investigations have been conducted to predict the structure and properties of these layered materials (Sun et al., 2020; Sun and Schwingenschlögl, 2020; Sun et al., 2021; Sun and Schwingenschlögl, 2021). In addition, the formation of the van der Waals (vdW) heterostructure by different 2D materials is also a popular strategy to extend the applications of the 2D materials (Wang et al., 2022b). The vdW interactions in the heterostructure result in novel interfacial performances, which can improve the electronic (Ren et al., 2021a), optical (Ren et al., 2019a), and catalytic (Wang et al., 2018a; Wang et al., 2020a; Wang et al., 2020b) characteristics. Furthermore, such excellent properties of the heterostructure can even be tuned by the electric field (Sun et al., 2017a), strain (Ren et al., 2019b; Wang et al., 2020c; Wang et al., 2020d), stacking (Ren et al., 2022b), doping (Ren et al., 2022c),and defect (Sun et al., 2017b). When applied, the external strain is an effective tactic; for example, the band structure of the MXene/blue phosphorene vdW heterostructure can result in the transformation from type-I to type-II by the strain (Guo et al., 2017). The external strain also possesses a significant influence on the layer distance, which further decides the interfacial performances (Guo et al., 2020). Under the strain, the evolution of Schottky barriers of the GaN/graphene heterostructure can be converted from the n-Schottky to Ohmic type (Deng and Wang, 2019). Recently, the TMD materials of MoTe₂ and PtS₂ monolayers have been prepared experimentally (Qu et al., 2017; Zhao et al., 2019). The MoTe₂ and PtS₂ monolayers present the novel electronic (Qu et al., 2017; Sajjad et al., 2018) and thermoelectric (Shi et al., 2017) properties, which have been widely studied. The 2D MoTe₂ can be obtained from mechanically exfoliated bulk crystals (Chang et al., 2016), which have potential usages in electronics, such as inverters and amplifiers, and in logic and digital circuits. Moreover, the electronic property of MoTe₂ is sensitive to atomic doping (Kanoun, 2018), suggesting tunable electronic and optical performances. The PtS₂ monolayer also presents tunable properties by the strain (Liu et al., 2018) and electric field (Nguyen et al., 2019). In addition, the PtS₂ monolayer is reported to be formed as a vdW heterostructure such as PtS₂/arsenene (Ren et al., 2020b), PtS₂/InSe (Nguyen et al., 2019), and HfS₂/PtS₂ (Colibaba et al., 2019). Furthermore, the MoTe₂ and PtS₂ monolayers share a honeycomb hexagonal structure with a small lattice mismatch, explaining the advantage to be formed as a heterostructure. Therefore, the MoTe₂ and PtS₂ monolayers have been decided to be used for constructing the heterostructure in this work. The first-principles calculations are developed to investigate the band structure of the MoTe₂/PtS₂ (MP) heterostructure. Importantly, the tunable electronic, charge density, potential, light absorption ability, and the solar-to-hydrogen efficiency (STH) by the external biaxial strain are addressed.

Computational Methods

In this investigation, the Vienna ab initio simulation software package (VASP) was used to find the first-principles simulations by the density functional theory (DFT) (Kresse and Furthmüller, 1996a; Kresse and Furthmüller, 1996b). In the generalized gradient approximation (GGA), the projector augmented wave (PAW) potentials were used with the Perdew–Burke–Ernzerhof (PBE) functional to describe the core electrons and the exchange–correlation functional (Perdew et al., 1996; Kresse and Joubert, 1999). The cut-off energy was used by 550 eV, and the Monkhorst–Pack k-point was 15 × 15 × 1 in the calculations. Furthermore, the Heyd–Scuseria–Ernzerhof hybrid method was adopted to calculate the electronic and optical properties (Heyd et al., 2005). The weak dispersion forces were described by the DFT-D3 method proposed by Grimme et al. (2010). Due to the ignorable effect of the spin–orbit coupling (SOC) on the electronic properties of the studied system, shown in Supplementary Figure S1, the SOC is not employed in the calculations. The vacuum thickness was set as 25 Å to prohibit the interaction adjacent layers. Besides, the convergence criterion of the force in the simulations was 0.01 eV Å⁻¹, while the energy was controlled in 0.01 meV.

Results and Discussion

The lattice parameters of the MoTe₂ and PtS₂ monolayers are optimized as 3.564 and 3.529 Å, respectively, showing a low lattice mismatch of about 0.1%, which are suitable to be constructed as a heterostructure. Supplementary Figure S2 shows the band structures of the pristine MoTe₂ and PtS₂ monolayers calculated using the HSE06 functional with the indirect and direct bandgaps of 1.22 and 2.60 eV, respectively, demonstrating an agreement with the previous reports (Shao et al., 2022). Then, the MP heterostructure is constructed by considering six different highly symmetrical structures, as shown in Supplementary Figure S3. By calculating the binding energy, the most stable stacking configuration is decided, as shown in Figure 1A, that the Mo atoms are located on top of the upper S atoms, while the Te atoms are set on top of the lower S atoms. The MoTe₂/PtS₂ heterostructure is built by vdW forces because of the weak binding energy of about −28.10 meV Å⁻² (Ren et al., 2022b), which is lower than that in graphites (about −18 meV Å⁻²) (Chen et al., 2013). The projected band structure of the MP vdW heterostructure is obtained in Figure 1B, suggesting an indirect bandgap of about 1.26 eV. The CBM and the VBM of the MP vdW heterostructure result from the PtS₂ and MoTe₂ monolayers, respectively, showing a type-II band alignment, which can separate the photogenerated electrons and holes using as a photocatalyst for water splitting (Ren et al., 2021b). In detail, when the MP vdW heterostructure obtains the energy from the light, the photogenerated electrons will move to the conduction band of the MoTe₂ and PtS₂ monolayers, as shown in Figure 1C, resulting in photogenerated holes staying at the valence band. Then, the conduction band offset (CBO) can promote the photogenerated electrons from MoTe₂ to PtS₂ at the conduction band, while the photogenerated holes will be transferred from PtS₂ to MoTe₂ at the valence band. Thus, the photogenerated charges in the MP vdW heterostructure are prevented from recombination.

FIGURE 1

FIGURE 1. (A) Geometric and (B) band structure of the MP heterostructure with the lowest binding energy. (C) Photogenerated charge migration path in the MP vdW heterostructure. The yellow, gray, orange, and blue spheres represent the Te, Mo, S, and Pt atoms, respectively. The Fermi level is decided as 0 shown by the gray dashed line.

Next, the external biaxial strain is applied in the MP vdW heterostructure to explore its effect on the electronic structure. In Figure 2, the projected band structure of the MP vdW heterostructure under the external biaxial strain from –4 to 2% is obtained, where negative and positive values represent pressure and tension, respectively. One can see that the type-II band structure is retained in the MP vdW heterostructure with that strain, which still can separate the photogenerated electrons and holes, while the bandgap decreased from 1.454 to 1.150 eV by the external biaxial strain from –4 to 2%, as shown in Figure 3A. In addition, the binding energy (E_b) is also investigated, which is decided by

$E_{\mathrm{b}}=E_{\mathrm{H}}-E_{\mathrm{M}}-E_{\mathrm{P}},(1)$

where E_H, E_M, and E_P represent the total energy of the MP vdW heterostructure, pristine MoTe₂, and PtS₂, respectively. The calculated binding energy change of the MP vdW heterostructure applied by different external biaxial strains is demonstrated by Figure 3B, which shows the stability of the MP vdW heterostructure, and the lowest binding energy of the MP vdW heterostructure is the unstressed state.

FIGURE 2

FIGURE 2. Band structures of the MP vdW heterostructure under the external strains of (A) –4%, (B) –3%, (C) –2%, (D) –1%, (E) 1%, and (F) 2%.

FIGURE 3

FIGURE 3. (A) Band alignment of the MP vdW heterostructure by the external strain comparing the energy potential of the redox reaction at pH values 0 and 7. (B) Binding energy and the bandgap difference of the MP vdW heterostructure tuned by the external strain.

The band edge positions of the MP vdW heterostructure under different strains are also calculated by the HSE06 functional, demonstrated in Figure 3B. The potential energy values of the oxidation and reduction reactions for water splitting are –5.67 eV and –4.44 eV, respectively, at pH 0. The energy of the redox potential can be decided by the pH level with: E = −4.44 eV + pH × 0.059 eV for the reduction reaction, while the potential of the oxidation is obtained by E = −5.67 eV + pH × 0.059 eV. Thus, the calculated potentials of the oxidation and reduction reactions at pH 0 are −5.26 eV and −4.03 eV, respectively, at pH 7. As a decent photocatalyst, the band edge positions of the CBM (or VBM) of the heterostructure should be higher (or lower) than the potential of the reduction (or oxidation) for water splitting (Ren et al., 2021c). In Figure 3B, one can see that the MP vdW heterostructure possesses suitable band edge positions to promote the redox reaction at pH 7 for water splitting by the external biaxial strains of –3% and –2%, while the MP vdW heterostructure can be used as a promising photocatalyst for water splitting at pH 0 without the external strain.

The charge density difference (Δρ) of the MP vdW heterostructure tuned by the strain is also investigated, which is calculated as follows:

$\mathrm{\Delta }\rho =\rho \mathrm{H}-\rho \mathrm{M}-\rho \mathrm{P,}(2)$

where ρ_H, ρ_M, and ρ_P are used as the charge densities of the MP vdW heterostructure, pristine MoTe₂, and PtS₂, respectively. Under these strains, the PtS₂ layer still gains the electrons from the MoTe₂ layer, and the charge density difference between the interface of the MP vdW heterostructure under –4%, –2%, and 2% is demonstrated in Figures 4A–C, respectively. In addition, the quantitative analysis of the charge transfer in the MP vdW heterostructure is explored by the Bader charge method (Sanville et al., 2007). The calculated charge transfers between the interface of the MP vdW heterostructure under –4%, –2%, and 2% are 0.0463 |e|, 0.0475 |e|, and 0.052 |e|, respectively.

FIGURE 4

FIGURE 4. Isosurface of the charge density difference of the MP vdW heterostructure under the strains of (A) –4%, (B) –2%, and (C) 2%; red and green marks demonstrate the losing and gaining of electrons, respectively. The isosurface parameter is 0.001 |e|.

The charge density difference between the interface of the MoTe₂ and PtS₂ monolayers can induce a potential drop. The potential energy of the MoTe₂ and PtS₂ in the heterostructure by the different strains is investigated in Figure 5, showing that the strain can increase the potential energy of the MoTe₂ and PtS₂ from pressure to tension. The potential drop across the interface of the MP vdW heterostructure is obtained as 4.962, 4.720, 4.672, and 4.500 eV by the external biaxial strains of –4%, –2%, –0%, and 2%, respectively, which demonstrates the decreased charge density difference. It is worth emphasizing that such a potential drop in the MP vdW heterostructure can also provide a critical boost for the separation of the photogenerated electrons and holes.

FIGURE 5

FIGURE 5. Potential drop of the MP vdW heterostructure across the interface by different external strains.

We also studied the light absorption coefficient (α) of the MP vdW heterostructure by external strain using the HSE06 method, which is calculated as follows:

$\alpha \left(\omega \right)=\frac{\sqrt{2}\omega }{c}{\left\{{\left[{\epsilon }_1^2\left(\omega \right)+{\epsilon }_2^2\left(\omega \right)\right]}^{1/2}-{\epsilon }_1\left(\omega \right)\right\}}^{1/2},(3)$

where ω is the angular frequency, and c is the speed of light. The real and imaginary parts are represented by ε₁(ω) and ε₂(ω), respectively. Moreover, ε₁(ω) and ε₂(ω) can be obtained as follows:

${\epsilon }_2\left(q\to O_{\widehat{u}},\hslash \omega \right)=\frac{2e^2\pi }{\mathrm{\Omega }{\epsilon }_0}{{\displaystyle \sum _{k,v,c}\left|\langle {\mathrm{\Psi }}_k^c\right|\widehat{u}\cdot r\left|{\mathrm{\Psi }}_k^v\rangle \right|}}^2\times \delta \left(E_k^c-E_k^v-E\right),(4)$

$\epsilon \left(\omega \right)={\epsilon }_1\left(\omega \right)+i{\epsilon }_2\left(\omega \right),(5)$

where ${\Psi }_k$, $E_k$, and $\widehat{u}$ are the wave function, energy, and unit vector of the electric field of the incident light, respectively. The superscripts (v and c) in ${\Psi }_k$ and $E_k$ are labeled as the conduction bands and valence bands, respectively. The calculated light absorption performance of the strained MP vdW heterostructure is explained by Figure 6 marked by a visible spectrum (Wang et al., 2018b). Evidently, applying the external compressive stress can improve the light absorption capacity at the absorption wavelength ranging from 480 to 550 nm. In detail, the light absorption peaks of the MP vdW heterostructure are obtained as 3.79 × 10⁵ cm⁻¹, 3.13 × 10⁵ cm⁻¹, and 2.60 × 10⁵ cm⁻¹ locating the wavelength at 509 nm, 519, and 527 nm, respectively, by the strains of –0.04, –0.02, and 0, while the light absorption performance of the MP vdW heterostructure can be enhanced by tensile stress when the absorption wavelength exceeds 550 nm. Furthermore, these obtained absorption performances are also higher than those of other 2D heterostructures, such as CdO/HfS₂ (3.51 × 10⁵ cm⁻¹) (Zhang et al., 2022), arsenene/PtSe₂ (2.23 × 10⁵ cm⁻¹) (Zheng et al., 2021), and MoSSe/GaN (2.74 × 10⁵ cm⁻¹) (Ren et al., 2020c).

FIGURE 6

FIGURE 6. Calculated optical absorption of the MP vdW heterostructure under the external strain.

Furthermore, the solar-to-hydrogen efficiency of the MP vdW heterostructure is calculated by η_STH = η_abs × η_cu (Fu et al., 2018), where η_abs is the efficiency of light absorption, and η_cu demonstrates carrier utilization. As for the light absorption, it can be decided by

${\eta }_{\mathrm{a}\mathrm{b}\mathrm{s}}=\frac{{\displaystyle {\int }_{E_g}^{\infty }P\left(\hslash \omega \right)\mathrm{d}\left(\hslash \omega \right)}}{{\displaystyle {\int }_0^{\infty }P\left(\hslash \omega \right)\mathrm{d}\left(\hslash \omega \right)}},(6)$

where E_g means the bandgap of the studied material. $\hslash \omega$ is used to explain the photon energy, while the AM1.5G solar energy flux is P(hω). The carrier utilization is obtained by

${\eta }_{\mathrm{cu}}=\frac{\mathrm{\Delta }G{\displaystyle {\int }_E^{\infty }\frac{P\left(\hslash \omega \right)}{\hslash \omega }}\mathrm{d}\left(\hslash \omega \right)}{{\displaystyle {\int }_{E_g}^{\infty }P\left(\hslash \omega \right)\mathrm{d}\left(\hslash \omega \right)}}.(7)$

To describe the potential difference in water splitting, ΔG is used by 1.23 eV here. Importantly, the photon energy of E is calculated by

$E=\{\begin{array}{r}\hfill E_g,\left(\chi \left({\mathrm{H}}_2\right)\ge 0.2,\chi \left({\mathrm{O}}_2\right)\ge 0.6\right),\\ \hfill E_g+0.2-\chi \left({\mathrm{H}}_2\right),\left(\chi \left({\mathrm{H}}_2\right)<0.2,\chi \left({\mathrm{O}}_2\right)\ge 0.6\right),\\ \hfill E_g+0.6-\chi \left({\mathrm{O}}_2\right),\left(\chi \left({\mathrm{H}}_2\right)\ge 0.2,\chi \left({\mathrm{O}}_2\right)<0.6\right),\\ \hfill E_g+0.8-\chi \left({\mathrm{H}}_2\right)-\chi \left({\mathrm{O}}_2\right),\left(\chi \left({\mathrm{H}}_2\right)<0.2,\chi \left({\mathrm{O}}_2\right)<0.6\right).\end{array}(8)$

The overpotential for the reduction and oxidation reactions for water splitting is explained by χ(H₂) and χ(O₂), respectively. In addition, previous experimental investigations provide the necessary overpotentials for the reduction and oxidation reactions as 0.2 and 0.6 eV (Fu et al., 2018), respectively. The efficiencies of light absorption of the MP vdW heterostructure under the strains of –0.03, –0.02, and 0 are calculated by 89.44, 89.80, and 93.26%, respectively. Furthermore, the carrier utilization of the MP vdW heterostructure is 33.66, 33.53, and 32.28%, respectively, by the strains of –0.03, –0.02, and 0. Thus, the solar-to-hydrogen efficiencies are obtained as 30.10, 30.11, and 30.10%, respectively, at pH values 7, 7, and 0, as shown in Table. 1, which is higher than other 2D heterostructures such as CdO/arsenene (about 11.67%) (Ren et al., 2021b) and GaS/arsenene (about 25.46%) (Li et al., 2021).

TABLE 1

TABLE 1. Energy conversion efficiency of light absorption, carrier utilization, and the solar-to-hydrogen efficiency of the MP vdW heterostructure under the external strain.

Conclusion

In this work, the first-principles method is employed to investigate the electronic and optical performances of the MP vdW heterostructure. The external strain is also applied on the MP vdW heterostructure, and the results show that the MP vdW heterostructure maintains the type-II band alignment and decreased bandgap. In addition, the external compressive stress can tune the MP vdW heterostructure as a potential for water splitting at pH 7 because of the decent band edge positions. The strain also has a significant influence on the interfacial properties of the MP vdW heterostructure. Furthermore, the MP vdW heterostructure possesses excellent light absorption capacity and light conversion efficiency, which can also be enhanced by the strain. The results show that the MP vdW heterostructure possesses potential energy conversion used in the automotive battery system.

Data Availability Statement

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

Author Contributions

All the authors listed have made a substantial, direct, and intellectual contribution to the work and approved it for publication.

Conflict of Interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher’s Note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors, and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Acknowledgments

The author LZ thanks the Zhejiang Provincial Natural Science Foundation of China (Grant No. LZY21E060002).

Supplementary Material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fchem.2022.934048/full#supplementary-material

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