Strain Modulation of Electronic Properties in Monolayer SnP2S6 and GeP2S6

1. Introduction

Two-dimensional (2D) materials, such as graphene [1,2] have attracted immense interest because of the exotic physical properties and potential application in nanoelectronic and optoelectronic devices [3]. However, graphene is a semimetal with zero band gap [4], and the absence of bandgap will limit its application in nanoscale optoelectronic and next-generation ultra-high-speed electronic devices [5]. Hence, searching for two-dimensional (2D) materials with suitable bandgap is significant for device applications. The transition metal dichalcogenides (TMDs) [6], hexagonal boron nitride (b-BN) [7], germanene (2D germanium) [8], metal halogenides [9,10] and so on, have received a lot of attention in the fields of materials science, microelectronics, physics, etc. Among these promising candidates, 2D nanoporous metal chalcogen phosphates MP₂S₆ (M = metal, X = S, Se) also gained considerable attention because of their moderate bandgap [11]. Moreover, the metal chalcogen phosphates MP₂X₆ have rich properties, such as topological magnetism [12], ferroelectric ordering [13], photocatalytic properties [14], H2 storage and Li intercalation for batteries [15], etc. For example, SnP₂S₆ is a promising 2D photocatalyst for water splitting as well as a good candidate for thin film electronics and photoelectronics [16]. The novel physical properties of 2D nanoporous metal chalcogen phosphates material have the potential to expand the range of applications in nanoelectronics. [17]

The development of two-dimensional (2D) materials has gained significant attention due to their distinctive properties, such as high surface-to-volume ratio and tunable electronic properties. Strain is a promising avenue for tuning the electric properties of 2D materials [18,19]. Theoretical studies have shown that transition metal dichalcogenides (TMDs) are quite sensitive to tensile strain [20], and strain engineering can shift the conduction band minima (CBM) and valence band maxima (VBM) [20,21,22,23]. For instance, it has been reported that the bandgap of MoS₂ can be narrowed under tensile strain in monolayer system [24,25,26]. Moreover, the direct-to-indirect bandgap transition can occur in monolayer MoS₂ as the tensile strain increases [27]. The strain-induced band-gap transition in 2D materials has significant implications for the development of next-generation nanoelectronic and optoelectronic devices [28,29,30]. The metal chalcogen phosphates MP₂X₆ with intrinsic nanoporous structure is expected to be able to effectively tune the electronic properties under strain [31].

In this study, the electronic properties of monolayer metal chalcogen phosphates SnP₂S₆ and GeP₂S₆ are explored through first-principles calculations. Monolayer SnP₂S₆ is found be indirect band-gap type semiconductors with gaps of 1.35eV in equilibrium. While monolayer GeP₂S₆ is a direct band-gap type semiconductor with a gap of 1.06 eV. The electronic properties of monolayer semiconductors can be effectively engineered by strain with direct-to-indirect or indirect-to-direct band-gap transition. For example, monolayer SnP₂S₆ undergoes an indirect-to-direct band-gap transition at 4.0% of biaxial compressive (BC) strains. While monolayer GeP₂S₆ exhibits a direct-to-indirect transition at 2.0% biaxial tensile (BT) strain. These results provide valuable insights into the strain engineering in tunning the electronic structures of the monolayer systems.

2. Calculation method

Density functional theory (DFT) [32] calculation was performed to investigate the electronic properties of monolayer metal chalcogen phosphates of SnP₂S₆ and GeP₂S₆ using the Vienna ab-initio simulation package (VASP) [33]. The projector-augmented wave method was adopted with a cutoff energy of 450 eV [33]. The Perdew-Burke-Ernzerhof (PBE) [34] exchange-correlation functional within the generalized gradient approximation (GGA) was utilized. To minimize interactions between vertically periodic layers, a vacuum layer of 25 Å was set in the z direction for the monolayer structures. A 15×15×1 Monkhorst-Pack k-grid mesh was employed for Brillouin zone sampling. Atomic positions were fully optimized until all the Hellmann-Feynman forces on all atoms were less than 0.01 eV/Å.

3. Result and discussion

SnP₂S₆ and GeP₂S₆ are members of the family of novel 2D metal thiophosphates. These monolayers are characterized by space group P312 and contain one metal cation (Sn or Ge) and one anionic [P₂S₆]^4- unit as illustrated in Figure 1(a) and (b) [31]. The metal cation is coordinated with six S atoms to form a hexahedron, while each P atom is coordinated with three S atoms in a tetrahedral arrangement as depicted in Figure 1(b). The optimized lattice parameters are 6.13 and 5.99 Å for monolayer SnP₂S₆ and GeP₂S₆, respectively, which is consistent with the previous result [35].

The biaxial strain is applied to explore the strain effect on the electronic properties of monolayer SnP₂S₆ and GeP₂S₆. The biaxial strain is defined as

$$\begin{array}{c}\delta =\frac{\Delta a}{a_0} \end{array}$$

(1)

where a₀ represents the optimized lattice constant when the structure is unstrained and Δa represents the change of the lattice constant after applying a certain strain in the xy plane. Electronic property calculations are presented within a range of δ=−6% to δ=+6%. The negative value of δ denotes compressive strain whereas the positive sign refers to tensile strain.

The electronic band structures of monolayer SnP₂S₆ and GeP₂S₆ structures under biaxial strain are investigated. Our calculations reveal that the total energy of the system exhibits a weak dependence on the applied biaxial strain as depicted in Figure 2. The total energy of the relaxed monolayer structures SnP₂S₆ and GeP₂S₆ is found to be -42.6808 eV and-42.4794806 eV, respectively. The maximum change of total energy is only around 0.5eV and 0.6eV within the considered strain range. Even though the total energy change may be minimal as the strain is applied, it can still have a substantial impact on the material properties.

The electronic band structure of the unstrained SnP₂S₆ is presented in Figure 3(a), where the VBM and CBM are located at the K and Γ points, respectively, with an indirect band gap of 1.346 eV. The contribution of different orbitals to the VBM and CBM are investigated by calculating the orbitals resolved density of states. S-p orbitals contribute mostly to the VBM, while Sn-s orbitals have the highest contribution to the CBM, along with a minor contribution from S-p orbitals, as illustrated in Figure 3(a). We investigate the impact of applying homogeneous biaxial strain on the electronic structure of SnP₂S₆. At 4.0% BC strain, the CBM shifts from the Γ point to the K point, while the VBM remains at the K point, leading to an indirect-to-direct band-gap transition as shown in Figure 3(b).

Similarly, we investigated the electronic structure of the unstrained GeP₂S₆ and strained system as illustrated in Figure 3(c) and 3(d). Notably, one can notice that both the VBM and CBM are located at the K points for unstrained GeP₂S₆ monolayer, indicating a direct bandgap semiconductor. As depicted in Figure 3(c), the majority of the orbital contribution to the VBM sources from S-p orbitals, whereas Ge-s orbital dominates the CBM along with a minor contribution from S-p orbitals. Under a 2.0% biaxial tension (BT) strain, we observed a shift of the CBM from the K point to the Γ point, while the VBM remains at the K point. Hence a direct-to-indirect band-gap transition emerges under 2.0% biaxial tension (BT) strain.

To gain further insights into the orbital contributions to the band structure, we evaluate the projected band structure without strain. It is clear that the conduction band edge of system SnP₂S₆ is primarily contributed by Sn-s orbitals, with additional small contributions from S-p_z orbitals and a small contribution from S-p_x/p_y orbitals, while the valence band edge is mainly contributed by S-p_x orbital with a small contribution from S-p_y orbital in Figure 4(a-d). Similarly, the conduction band edge of the GeP₂S₆ monolayer is mainly contributed by the Ge-s orbital, while the valence band edge is mainly contributed by the S-p_x orbital with a small contribution from S-p_z orbitals as depicted in Figure 5(a-d).

According to Figure 3(a-d), the transition from indirect to direct bandgap for monolayer SnP₂S₆ and the transition from direct to indirect bandgap for monolayer GeP₂S₆ is primarily caused by the shift of the conduction band minimum. To further investigate this phenomenon, we plotted the variation of the energy of the conduction band edge state at the Γ point (CB-Γ) and at the K point (CB-K) as a function of strain as depicted in Figure 6(a)and(b). One can find that both systems exhibit an approximately linear decrease between the energy and strain for both Γ and K points, decreasing with increasing tensile strain and increasing with increasing compressive strain. The high-symmetry point Γ exhibits a higher rate under strain as compared to the K point, indicating the band edge near Γ point is more sensitive to strain. Hence the relative position of the energy bands at Γ and K points reverses under certain strain. In the case of system SnP₂S₆, when the applied strain is less than -4%, E_CB-Γ is smaller than E_CB-K with located at K. when the applied strain exceeds -4% E_CB-Γ is larger than E_CB-K with the CBM is located at the Γ point. In contrast, when the strain is less than 1%, E_CB-Γ is larger than E_CB-K for monolayer GeP₂S₆ with the CBM located at the K point. When the strain exceeds 2%, E_CB-Γ becomes smaller than E_CB-K, and the CBM shifts to the Γ point.

We also studied the variation in the band gap along the different symmetry directions K-K and K-Γ with the strain. The band gaps of SnP₂S₆ along the symmetric directions K-K and K-Γ direction are very close when the strain is less than -4%, and the difference between the two distinct band gaps along K-K and K-Γ becomes larger when the strain is greater than -4% as illustrated in Figure 7(a). The bandgap changes slightly with compressive strain and significantly with tensile strain. Differently, the difference of bandgap is relatively larger between K-K and K-Γ for monolayer GeP₂S₆ under compressive strain as compared with that of monolayer SnP₂S₆. The bandgap changes significantly with both compressive strain and tensile strain as shown in Figure 7(b). These findings provide valuable insights into the design and optimization of 2D materials for electronic and optoelectronic applications.

4. Conclusion

In summary, we have conducted a comprehensive investigation on the electrical properties of monolayer SnP₂S₆ and GeP₂S₆ under biaxial strain. The results demonstrate that the monolayer SnP₂S₆ with an indirect bandgap of 1.346 eV exhibit an indirect-to-direct band-gap transition under 4.0% uniform biaxial compressive (BC) strain. Additionally, we report a direct-to-indirect band-gap transition in the monolayer semiconductor GeP₂S₆ under a uniform BT strain of 2.0%. The transition occurs because the high-symmetry point Γ is more sensitive to strain than K. Our findings suggest that biaxial strain can effectively tune the electrical properties of monolayer systems which is a promising approach for designing high-performance ultra-fast nanoelectronic and optoelectronic devices based on these materials.