Strain-Induced Tunable Band Offsets in Blue Phosphorus and WSe 2 van der Waals Heterostructure

: The electronic structure and band offsets of blue phosphorus/WSe 2 van der Waals (vdW) heterostructure are investigated via performing ﬁrst-principles calculations. Blue phosphorus/WSe 2 vdW heterostructure exhibits modulation of bandgaps by the applied vertical compressive strain, and a large compressive strain of more than 23% leads to a semiconductor-to-metal transition. Blue phosphorus/WSe 2 vdW heterostructure is demonstrated to have a type-II band alignment, which pro-motes the spontaneous spatial separation of photo-excited electrons and holes. Furthermore, electrons concentrating in BlueP and holes in WSe 2 can be enhanced by applied compressive strain, resulting in an increase of carrier concentration. Therefore, these properties make blue phosphorus/WSe 2 vdW heterostructure a good candidate for future applications in photodetection.

Therefore, in this work, a BlueP/WSe 2 vdW heterostructure is constructed. The electronic structure and band offsets are investigated via utilizing first-principles calculations. Therefore, in this work, a BlueP/WSe2 vdW heterostructure is constructed. The electronic structure and band offsets are investigated via utilizing first-principles calculations. It is illustrated that BlueP/WSe2 vdW heterostructure exhibits modulation of bandgaps by applying vertical compressive strain, which is accompanied by a semiconductor-to-metal transition under a large compressive strain more than 23%. A type-II band alignment of BlueP/WSe2 vdW heterostructure is demonstrated, since the band positions of BlueP and WSe2 straddle each other. In other words, the CBM and the VBM are contributed by BlueP and WSe2, respectively. Compared with other types of band alignments, the type-II band alignment is beneficial to the spatial separation of excited electrons and holes. Furthermore, the compressive strain can facilitate electrons in BlueP and holes in WSe2, resulting in an increase of carrier concentration.

Computational Model and Methods
The first-principles calculations are performed by using the projector-augmented plane-wave (PAW) method with the framework of density functional theory (DFT) in the VASP code. The GGA of PBE is adopted to describe the electron exchange and correlation. The pairwise force field in DFT-D2 method is used to describe the vdW interlayer interactions. The vacuum layer, the cutoff energy, the force tolerance, and the first Brillouin zone are 12 Å , 500 eV, 0.01 eV/Å and (9 × 9 × 1) Monkhorst-Pack grid. Figure 1a,b shows the top and side views of the 4 × 4 supercell structure of BlueP/WSe2 vdW heterostructure. The optimized lattice constants of BlueP and WSe2 are 3.28 and 3.29 Å [33,36], respectively, which indicates a very good lattice matching in this system. The effect of applied vertical strain on the electronic and optical properties of BlueP/WSe2 vdW heterostructure is study. The strain is calculated as ε = (d − d0)/d0, where d and d0 are the instantaneous and equilibrium distances between the bottom phosphorus atom layer and the tungsten atom layer, as shown in Figure 1b. So, a negative ε represents compressive strain and a positive one represents tensile strain. Figure 1c exhibits the Brillouin zone of hexagonal cell with high-symmetry points (M, K, and Γ) labeled, and the point between M and Γ is defined as Λ.

Results and Discussion
To determine the stable structure of BlueP/WSe 2 vdW heterostructure, a variation of the total energy with the applied vertical strains is calculated in Figure 1d. The curve indicates the minimum under zero strain, and the equilibrium distance is d 0 = 4.79 Å. Figure 1d also illustrates that the total energy of BlueP/WSe 2 vdW heterostructure is sensitively tuned by compressive strain rather than tensile strain.
Band structures of monolayer BlueP, monolayer WSe 2 , and BlueP/WSe 2 vdW heterostructure are exhibited in Figure 2. To explore the optoelectronic properties of BlueP/WSe 2 vdW heterostructure, its band alignment is also calculated in Figure 2b. In the projected band structure in Figure 2a, lines in blue and red dots are the electronic bands dominated by BlueP and WSe 2 , respectively. Our results show that monolayer BlueP has an indirect bandgap of 1.94 eV, and monolayer WSe 2 shows a direct bandgap of 1.55 eV. After combination, the indirect band gap of BlueP/WSe 2 vdW heterostructure is reduced to 1.11 eV, with the conduction band minimum (CBM) and the valence band maximum (VBM) localizing at the Λ and K points, respectively. More importantly, the CBM and the VBM are mainly contributed by BlueP and WSe 2 , respectively, which indicates that BlueP/WSe 2 vdW heterostructure is type-II heterostructure. As a result, spontaneous spatial separation of the lowest energy electron-hole pairs will occur in the vdW heterostructure with electrons and holes concentrating in BlueP and WSe 2 , respectively, as shown in Figure 2b. Further insight can be obtained from the band decomposed charge density of CBM and VBM of the BlueP/WSe 2 vdW heterostructure in Figure 2c. It can be seen that the wavefunctions of the CBM and the VBM are localized on BlueP and WSe 2 , respectively. These results are also supported by the projected density of states (DOS) of BlueP/WSe 2 vdW heterostructure, as displayed in Figure 2d. According to our results, the spatially separated photoexcited electrons and holes can effectively improve the carrier concentrations and photocurrent in the vdW heterostructure and further improve the optoelectronic property of BlueP/WSe 2 vdW heterostructure.

Results and Discussion
To determine the stable structure of BlueP/WSe2 vdW heterostructure, a variation of the total energy with the applied vertical strains is calculated in Figure 1d. The curve indicates the minimum under zero strain, and the equilibrium distance is d0 = 4.79 Å . Figure  1d also illustrates that the total energy of BlueP/WSe2 vdW heterostructure is sensitively tuned by compressive strain rather than tensile strain.
Band structures of monolayer BlueP, monolayer WSe2, and BlueP/WSe2 vdW heterostructure are exhibited in Figure 2. To explore the optoelectronic properties of BlueP/WSe2 vdW heterostructure, its band alignment is also calculated in Figure 2b. In the projected band structure in Figure 2a, lines in blue and red dots are the electronic bands dominated by BlueP and WSe2, respectively. Our results show that monolayer BlueP has an indirect bandgap of 1.94 eV, and monolayer WSe2 shows a direct bandgap of 1.55 eV. After combination, the indirect band gap of BlueP/WSe2 vdW heterostructure is reduced to 1.11 eV, with the conduction band minimum (CBM) and the valence band maximum (VBM) localizing at the Λ and K points, respectively. More importantly, the CBM and the VBM are mainly contributed by BlueP and WSe2, respectively, which indicates that BlueP/WSe2 vdW heterostructure is type-II heterostructure. As a result, spontaneous spatial separation of the lowest energy electron-hole pairs will occur in the vdW heterostructure with electrons and holes concentrating in BlueP and WSe2, respectively, as shown in Figure 2b. Further insight can be obtained from the band decomposed charge density of CBM and VBM of the BlueP/WSe2 vdW heterostructure in Figure 2c. It can be seen that the wavefunctions of the CBM and the VBM are localized on BlueP and WSe2, respectively. These results are also supported by the projected density of states (DOS) of BlueP/WSe2 vdW heterostructure, as displayed in Figure 2d. According to our results, the spatially separated photoexcited electrons and holes can effectively improve the carrier concentrations and photocurrent in the vdW heterostructure and further improve the optoelectronic property of BlueP/WSe2 vdW heterostructure.  Projected band structures of BlueP/WSe 2 vdW heterostructure under different vertical strains are illustrated in Figure 3. The bands contributed by BlueP and WSe 2 are plotted by blue and red balls, respectively. The CBM is found to localize on the Λ and the VBM is found to localize on the K when BlueP/WSe 2 vdW heterostructure is under a tensile strain of 0.08, as shown in Figure 3a. However, the VBM is changed from K to Γ when the strain is changed to a compressive strain of 0.08, but the CBM remains on Λ, as shown in Figure 3c. Interestingly, Figure 3d displays that the CBM is localized on both Λ and K, when continue increasing the compressive strain to 0.12. And after that, the CBM is changed to K, while the VBM remains on Γ, as displayed in Figure 3e. It is also proved that both the CBM and VBM move towards the Fermi level under applying vertical compressive strain, leading to a decreasing bandgap.
found to localize on the K when BlueP/WSe2 vdW heterostructure is under a tensile strain of 0.08, as shown in Figure 3a. However, the VBM is changed from K to Γ when the strain is changed to a compressive strain of 0.08, but the CBM remains on Λ, as shown in Figure  3c. Interestingly, Figure 3d displays that the CBM is localized on both Λ and K, when continue increasing the compressive strain to 0.12. And after that, the CBM is changed to K, while the VBM remains on Γ, as displayed in Figure 3e. It is also proved that both the CBM and VBM move towards the Fermi level under applying vertical compressive strain, leading to a decreasing bandgap.
The corresponding evolution of the bandgap of BlueP/WSe2 vdW heterostructure with the applied vertical strain is exhibited in Figure 4a. The bandgap reaches its maximum at the equilibrium state, and it decreases under tensile or compressive strain. Interestingly, compared with the tensile strain, the compressive strain shows much more remarkable tunability on the bandgap of BlueP/WSe2 heterostructure. Results in Figure 3 show that both the CBM and VBM move towards the Fermi level under applying vertical compressive strain, leading to a decreasing bandgap. When the compressive strain increases to more than 0.23, BlueP/WSe2 vdW heterostructure experiences a transition from semiconductor to metal, which can result in improved conductivity and enhanced transport properties.  The corresponding evolution of the bandgap of BlueP/WSe 2 vdW heterostructure with the applied vertical strain is exhibited in Figure 4a. The bandgap reaches its maximum at the equilibrium state, and it decreases under tensile or compressive strain. Interestingly, compared with the tensile strain, the compressive strain shows much more remarkable tunability on the bandgap of BlueP/WSe 2 heterostructure. Results in Figure 3 show that both the CBM and VBM move towards the Fermi level under applying vertical compressive strain, leading to a decreasing bandgap. When the compressive strain increases to more than 0.23, BlueP/WSe 2 vdW heterostructure experiences a transition from semiconductor to metal, which can result in improved conductivity and enhanced transport properties.  The integrated charge density difference of BlueP/WSe2 vdW heterostructure under compressive strains is calculated in Figure 4b. The integrated charge density difference is calculated as: ,, x y z  are the charge density at the point of (x, y, z) in BlueP/WSe2, BlueP, and WSe2, respectively. It can be seen that the charge exchange at the interface of BlueP/WSe2 vdW heterostructure is weak at the equilibrium state. Then, more charge exchange appears with the increase of compressive strain. To quantify interlayer charge transfer in the vdW heterostructure, Bader charge analysis is employed to determine the resulted charge density of BlueP/WSe2 vdW heterostructure. The results indicated that the number of electrons transferred from WSe2 to BlueP is 0.0068, 0.008, and 0.0091 under the compressive strain of 0, 0.08, and 0.18, respectively. Therefore, it suggests that the compressive strain can facilitate electrons in BlueP and holes in WSe2, resulting in an increase of carrier concentration, as shown in Figure 4c.
Calculated optical properties of absorption coefficient and reflectivity of BlueP/WSe2 vdW heterostructure under different compressive strain are exhibited in Figure 5. The same optical properties are observed in x and y directions, due to the isotropy of the hexagonal lattice, as shown in Figure 5a,b. From the absorption spectrum, it can be found that BlueP/WSe2 vdW heterostructure would have excellent application in ultraviolet light (above 5 eV) detecting. Furthermore, Figure 5c indicates that the applied vertical compressive strain shows obvious influence on the optical properties in the z direction, while The integrated charge density difference of BlueP/WSe 2 vdW heterostructure under compressive strains is calculated in Figure 4b. The integrated charge density difference is calculated as: ∆ρ(z) = ρ BlueP/WSe 2 (x, y, z)dxdy − ρ BlueP (x, y, z)dxdy − ρ WSe 2 (x, y, z)dxdy (1) where ρ BlueP/WSe 2 (x, y, z), ρ BlueP (x, y, z), and ρ WSe 2 (x, y, z) are the charge density at the point of (x, y, z) in BlueP/WSe 2 , BlueP, and WSe 2 , respectively. It can be seen that the charge exchange at the interface of BlueP/WSe 2 vdW heterostructure is weak at the equilibrium state. Then, more charge exchange appears with the increase of compressive strain. To quantify interlayer charge transfer in the vdW heterostructure, Bader charge analysis is employed to determine the resulted charge density of BlueP/WSe 2 vdW heterostructure. The results indicated that the number of electrons transferred from WSe 2 to BlueP is 0.0068, 0.008, and 0.0091 under the compressive strain of 0, 0.08, and 0.18, respectively. Therefore, it suggests that the compressive strain can facilitate electrons in BlueP and holes in WSe 2 , resulting in an increase of carrier concentration, as shown in Figure 4c.
Calculated optical properties of absorption coefficient and reflectivity of BlueP/WSe 2 vdW heterostructure under different compressive strain are exhibited in Figure 5. The same optical properties are observed in x and y directions, due to the isotropy of the hexagonal lattice, as shown in Figure 5a,b. From the absorption spectrum, it can be found that BlueP/WSe 2 vdW heterostructure would have excellent application in ultraviolet light (above 5 eV) detecting. Furthermore, Figure 5c indicates that the applied vertical compressive strain shows obvious influence on the optical properties in the z direction, while exerts little influence in x and y directions. The reason is that the applied vertical compressive strain only enhances the interlayer interaction while having a negligible effect on the in-plane interaction.
Crystals 2021, 11, x FOR PEER REVIEW 6 of 8 exerts little influence in x and y directions. The reason is that the applied vertical compressive strain only enhances the interlayer interaction while having a negligible effect on the in-plane interaction.

Conclusions
In summary, we have constructed a BlueP/WSe2 vdw heterostructure and investigated its electronic structure and band offsets via first-principles calculations. BlueP/WSe2 vdW heterostructure exhibits tunable bandgap by applied vertical compressive strain and even a semiconductor-to-metal transition is observed, which suggests a great application potential in future nano-electronics. Moreover, the type-II band alignment of BlueP/WSe2 vdW heterostructure facilitates the spatial separation of the photo-excited electron-hole pairs. The compressive strain facilitates electrons in BlueP and holes in WSe2, which results in an increase of carrier concentration. According to these results, BlueP/WSe2 vdW heterostructure presents a variety of opportunities for applications in future nano-and optoelectronic devices such as photodetectors and solar cells.

Data Availability Statement:
The data presented in this study are available within the article.

Conflicts of Interest:
The authors declare no conflicts of interest.

Conclusions
In summary, we have constructed a BlueP/WSe 2 vdw heterostructure and investigated its electronic structure and band offsets via first-principles calculations. BlueP/WSe 2 vdW heterostructure exhibits tunable bandgap by applied vertical compressive strain and even a semiconductor-to-metal transition is observed, which suggests a great application potential in future nano-electronics. Moreover, the type-II band alignment of BlueP/WSe 2 vdW heterostructure facilitates the spatial separation of the photo-excited electron-hole pairs. The compressive strain facilitates electrons in BlueP and holes in WSe 2 , which results in an increase of carrier concentration. According to these results, BlueP/WSe 2 vdW heterostructure presents a variety of opportunities for applications in future nano-and optoelectronic devices such as photodetectors and solar cells.

Data Availability Statement:
The data presented in this study are available within the article.

Conflicts of Interest:
The authors declare no conflict of interest.