Strain engineering the electronic and photocatalytic properties of WS₂/blue phosphene van der Waals heterostructures

Abstract

The effects of −8–8% in-plane uniaxial and biaxial strains on the electronic and photocatalytic activity of tungsten disulfide/blue phosphene (WS₂/BlueP) are investigated within the framework of first-principles calculations. The most energetically stable configuration of WS₂/BlueP exhibits type I band alignment with a direct band gap of 1.779 eV. Compared with WS₂ and BlueP, WS₂/BlueP has the strongest absorption in the entire visible light region with a red-shifted absorption edge. The in-plane −8–8% uniaxial and biaxial strains cause elastic deformation of the heterostructures. The strains can affect the band gap, band edge arrangement, band type (type-I, type-II, Z-scheme) and electron transition type (direct, indirect) of WS₂/BlueP. The −2% uniaxial (or biaxial) strain can engineer the band gap to reach the maximum and achieve full water decomposition. At pH = 0, only the −2% and −4% uniaxial and −2% biaxial strained WS₂/BlueP (Z-scheme) heterostructures are thermodynamically feasible, while at pH = 7, all the strained heterostructures are viable for photocatalytic water decomposition. The −2% uniaxial and biaxial strained WS₂/BlueP heterostructures at pH = 0 and pH = 7 are proved to be potential candidates for achieving full water decomposition. The lower potential determining step, higher electro-chemical driving forces and lower effective mass of carriers can promote the transition performance and improve the photocatalytic efficiency. Therefore, the in-plane uniaxial and biaxial strains can effectively adjust the electronic and photocatalytic performances of the heterostructures.

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1. Introduction

Since the successful mechanical exfoliation from graphite in 2004,¹ two-dimensional (2D) graphene has attracted worldwide attention due to its fascinating physical properties, such as unique hexagonal symmetry structure,² extremely high carrier mobility³ and anomalous quantum Hall effect.⁴ Unfortunately, the zero band gap has greatly limited the practical application of graphene. Meanwhile, other 2D materials varying from insulators to semiconductors and semimetals have been explored, such as bismuth oxyhalides (BiOBr),⁵ transition metal dichalcogenides (TMDs)⁶ and phosphenes,^7–9 which possess large specific surface area, high surface activity and excellent photocatalytic properties.¹⁰ S. V. Prabhakar Vattikuti et al. found that the hexagonal WS₂ nanosheet has good photocatalytic activity for degrading rhodamine B under visible light irradiation. WS₂ has a suitable band gap of 1.91 eV and can be mechanically peeled easily due to its weak van der Waals (vdW) interactions in the layered S–W–S sandwich structure.¹¹ However, the large effective mass and low carrier mobility have hindered its real application in the photocatalytic field. Moreover, it can only achieve the oxygen evolution reaction (OER) since the reduction and oxidation potentials are 0.08 eV and 1.99 eV, respectively. Strain is one of the effective ways to adjust the electronic and optical properties of WS₂ to meet the photocatalytic requirements. For instance, as the tensile strain on 1T-WS₂ reaches 2.7%, the electron state density near the Fermi level increases significantly, and the free energy of adsorbed atomic hydrogen is close to thermoneutral (ΔG_H ≈ 0), which is the benchmark of a good catalyst. In contrast, even when the strain on 2H–WS₂ increases to 4%, the free energy remains at about 2 eV, presenting great thermodynamic resistance to hydrogen production.

Recently, large-scale blue phosphorus (BlueP) monolayers on Au (111) and GaN (001) substrates^12,13 were fully synthesized via molecular beam epitaxy. BlueP exhibits extremely high carrier mobility and can achieve water decomposition as an ideal photocatalyst with a reduction and oxidation center of −0.47 eV and 2.27 eV, respectively.¹⁴ However, the photocatalytic efficiency is greatly limited by an inherent band gap of 2.74 eV, resulting in ultraviolet absorption. Moreover, the poor stability limits its application in an open-air environment.^15,16

For the sake of better performance, researchers have thought of stacking two-dimensional materials together to form a heterostructure, which not only has the properties of each constituent monolayer, but also exhibits significant electronic and optical properties missing in isolated monolayers.¹⁷ The “face-to-face” stacked heterostructure has a larger interface area and stronger electronic couplings between the layers, which can improve the electronic properties¹⁸ and eliminate the surface pollution.¹⁹ Supposing WS₂ (strong absorption, weak redox ability) and BlueP (weak absorption, strong redox ability) are constructed to form a heterostructure, they can complement each other, achieve strong absorption and exhibit redox capabilities. Moreover, BlueP and WS₂ have a small interface mismatch due to the same hexagonal structures with similar lattice constants, which can effectively reduce the dangling bonds and interface states. Qiong Peng et al. found that the WS₂/BlueP heterostructure exhibits abnormally strong absorption rate and energy conversion efficiency in the visible light range.²⁰

Previous experimental and theoretical studies have shown that in-plane uniaxial and biaxial strains can further effectively adjust the band gap, absorption, charge transfer and redox capabilities of nanosheets or heterostructures, such as Ga₂SSe,²¹ SnSe₂,²² MoSe₂/PtS₂ (ref. 23) and PtS₂/MoS₂.²⁴ Long Lin et al. found that the biaxial strain on the group VA/VA 2D vdW heterostructures can convert the indirect band gap into a direct one, and finally cause the heterostructure to become metal with excellent electrical conductivity.²⁵ Jiaxin Ye et al. found that the in-plane biaxial tensile strain on g-C₃N₄/WSe₂ can reduce the band gap and promote the red-shift of the absorption peak.²⁶ Xiaolong Wang et al. found that strain can adjust the energy band arrangement of C₂N/MTe (M = Ga, In) heterostructures and improve the redox potential.²⁷ Afterwards, Wenxue Zhang et al. found that the plane biaxial strain not only maintains the high carrier mobility of BlueP/WS₂, but also changes the band structure from type-II to type-I as a potential photocatalytic switch.²⁸ So far, the Heyd–Scuseria–Ernzerhof 2006 (HSE06) hybrid functional has not been used to discuss the electronic and photocatalytic properties of WS₂/BlueP heterostructures, nor have there been any studies to adjust the photocatalytic activity of WS₂/BlueP heterostructures by in-plane uniaxial and biaxial strains.

Therefore, in-plane uniaxial and biaxial strains within the range of −8–8% are applied to investigate the influences of strain on the WS₂/BlueP heterostructure. The electronic and optical properties including the band structure, density of states, light absorption, charge density difference, band arrangement, the carrier mobility are systematically analyzed. Furthermore, the photocatalytic properties is investigated and in particular the Gibbs free energy (ΔG) during the OER process is calculated to explore the thermodynamic feasibility of photocatalytic water splitting. The conclusions might help people to find and design photocatalysts with excellent performance for photocatalytic water splitting.

2. Computational methods

The electronic, optical and photocatalytic properties of WS₂, BlueP nanosheets and WS₂/BlueP heterostructures are explored based on the density functional theory, which is performed using the Vienna ab initio simulation package (VASP)^29,30 with the projector augmented wave (PAW). The generalized gradient approximation (GGA) of the Perdew–Burke–Ernzerhof (PBE) functional is used to deal with the exchange–correlation interactions between the electrons.³¹ The optB88-vdW functional is adopted to evaluate the vdW interaction, where the exchange functionals were optimised for the correlation part.^32,33 The cut-off energy of the plane-wave basis is set to be 400 eV. The WS₂/BlueP heterostructures are fully relaxed until the force and the total energy decrease to −0.02 eV Å⁻¹ and 1 × 10⁻⁴ eV, respectively. A vacuum spacing of 25 Å is added to avoid the interlayer interactions caused by the periodicity along the direction perpendicular to the 2D nanosheets.

While calculating the electronic properties, the Heyd–Scuseria–Ernzerhof (HSE06) hybrid functional is adopted to avoid the underestimation of the band gap by the PBE functional. The exchange–correlation energy E^HSE_XC in the HSE06 function is given by^34–36E^HSE_XC = αE^SR_X(μ) + (1 − α)E^PBE,SR_X(μ) + E^PBE,LR_X(μ) + E^PBE_C, where α is taken as the default value of 0.25, the SR and LR stand for short-ranged and long-ranged parts of the electron–electron interactions, and the screening parameter μ is the ratio of SR and LR, which is set as 0.20 Å⁻¹.

3. Results and discussion

3.1 Geometric configurations and interface formation energy

Fig. 1a and b show the fully relaxed structure of WS₂ and BlueP nanosheets, with lattice constants of 3.185 Å and 3.278 Å, respectively, which are consistent with the previous results.^20,37 For the construction of ideal heterostructures, the lattice constants of constituent materials should match as well as possible, however, a mismatch is inevitable, which will induce large dangling bonds, interfacial states and stress.^38,39 The heterostructure is constructed with 3 × 3 supercells of WS₂ and BlueP nanosheets. Fig. 1c–f show four optimized stacking patterns of WS₂/BlueP: (I) S atoms are on top of the hollow sites of BlueP, (II) P–P bonds and W–S bonds cross each other from the top view, (III) P atoms are exactly on top of W and S sites, (IV) W atoms are on top of the hollow sites of BlueP.

Fig. 1 The relaxed geometrical configurations of WS₂ (a), BlueP nanosheets (b) and WS₂/BlueP heterostructures of model I (c), II (d), III (e) and IV (f).

The interface formation energy is utilized to evaluate the stability of the heterostructure, which is defined as:⁴⁰

E_f = E_WS2/BlueP − E_WS2 − E_BlueP (1)

where E_WS2/BlueP, E_WS2 and E_BlueP are the total energy of the WS₂/BlueP heterostructures, WS₂ and BlueP nanosheets, respectively.

The interface binding energies of four configurations of WS₂/BlueP are calculated by the absolute value of E_f per unit interface area.

According to eqn (1), the formation and binding energies of four configurations of WS₂/BlueP are obtained and shown in Table 1. It can be found that the formation energies are all less than 0, indicating that the formation processes are exothermic and they are stable. Among them, the configuration of model III has the smallest formation energy, proving that this heterostructure is the most stable one. The binding energies are all in the range of the typical vdW binding energy (13–21 meV Å⁻²), indicating that WS₂/BlueP has a typical vdW heterostructure. Hence, WS₂/BlueP of model III is chosen for further investigation in the following context. The corresponding lattice mismatch is calculated by η = 2(a₁ − a₂)/(a₁ + a₂), where α₁ and α₂ are the lattice parameters of WS₂ and BlueP nanosheets, respectively. The lattice mismatch is estimated to be 2.88%, which is acceptable (<5%) to create vdW heterostructures. The minimum distance (d) between the interfacial layers of WS₂/BlueP is 3.22 Å, which is in the range of the vdW interaction distance (3–5 Å), indicating that WS₂/BlueP belongs to typical vdW heterostructure.

Table 1 The formation and binding energies of WS₂/BlueP heterostructures

	Model I	Model II	Model III	Model IV
E f (eV)	−1.507	−1.317	−1.663	−1.171
E b (meV Å^−2)	18.176	15.886	20.058	14.121

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3.2 Optoelectronic properties

The band gaps of WS₂ and BlueP nanosheets are 2.037 eV and 2.910 eV, respectively. The projected density of state (PDOS) shows that the orbitals near the Fermi level are mainly occupied by W-5d of WS₂ (Fig. 2a) and P-3p of the BlueP nanosheet (Fig. 2b). The valence band maximum (VBM) and the conduction band minimum (CBM) of the WS₂/BlueP heterostructure are both located at high symmetry k-point Γ, showing a direct band gap of 1.779 eV, which is smaller than the band gaps of WS₂ and BlueP. The direct transition without the phonon's participation makes WS₂/BlueP respond to visible light. Moreover, the band gap is greater than the minimum energy (1.23 eV) required by thermodynamics, making it an ideal candidate in photocatalysis (Fig. 2c). The band decomposed charge density (Fig. 2d) shows that the CBM and VBM are mainly contributed by W atoms in the WS₂ layer, besides, the VBM is also contributed by a small amount of S atoms in WS₂ and P atoms in BlueP. Meanwhile, the S atoms on each side of the isolated WS₂ have similar electronic states due to the symmetric configuration. However, it is completely different in the heterostructure, the corresponding energy band is not a simple superposition of the isolated WS₂ and BlueP, which is mainly affected by the interfacial interactions and charge transfer resulting in the shift of the electronic states. The PDOS of WS₂/BlueP (Fig. 2e) further points out that the VBM is mainly occupied by W-5d with a small degree of hybridization of S-3p and P-3p, however, the CBM is totally occupied by the W-5d orbital, demonstrating that the WS₂/BlueP heterostructure has a type-I band arrangement.

Fig. 2 The projected density of states of WS₂ (a) and BlueP (b). The band structures (c), the decomposed charge densities of the VBM and CBM (d) and the projected density of states (e) of WS₂/BlueP. The absorption spectra of WS₂, BlueP and WS₂/BlueP (f). The Fermi level is set to be zero.

In order to decompose water efficiently by photocatalysts, it is expected that light absorption covers a significant portion of the visible spectrum (380–780 nm). The light response range of WS₂/BlueP is expanded as shown in the absorption spectra (Fig. 2f), and the absorption intensity in the entire visible light region is greater than that of WS₂ and BlueP. The enhanced light absorption may be caused by the overlap of the electronic states in the VB of the heterostructure due to the charge redistribution and interface coupling. Moreover, the absorption edge is red-shifted. The excellent optical performance will improve the photoelectric conversion efficiency and the photocatalytic activity of WS₂/BlueP.

The electrons participate in the redox reaction via transition from the Fermi level (inside) to the vacuum level (surface), and the required minimum energy is the work function, which is defined as:

ϕ = E_vac − E_F (2)

where E_vac and E_F are the electrostatic potential of the vacuum level and Fermi level, respectively. The work functions of WS₂, BlueP and WS₂/BlueP are 6.196 eV, 5.933 eV and 5.536 eV, respectively. Since BlueP has a smaller work function than WS₂, the electrons at the interface of WS₂/BlueP will flow from BlueP to WS₂ until they have the same work function or Fermi level, establishing a dynamic equilibrium. The directional movement of electrons generates a potential difference and forms a built-in electric field from BlueP to WS₂, which is conducive to the separation of photogenerated carriers.

3.3 Interfacial electronic and photocatalytic properties

There is no doubt that WS₂/BlueP has different interfacial electronic properties with respect to the surfaces of the isolated nanosheets, which may be caused by the atomic electronegativity and charge redistribution. Since the S atom has a greater electronegativity (6.22 eV) than the P atom (5.62 eV),⁴¹ the lone pair of electrons on the lower surface of BlueP is pulled closer to the upper surface of WS₂, which makes the electrons (holes) accumulate on the upper (lower) surface of WS₂ (BlueP), and thereby forms a built-in electric field. The charge redistribution is reflected by the three-dimensional charge density difference (Δρ) and the planar-averaged charge density difference along the Z direction (Δρ_avg(z)), which is defined as

Δρ = ρ_WS2/BlueP − ρ_WS2 − ρ_BlueP (3)

where ρ_WS2/BlueP, ρ_WS2 and ρ_BlueP are the charge densities of WS₂/BlueP, WS₂ and BlueP, respectively. Fig. 3 shows the diagrams of Δρ and Δρ_avg(z), where yellow (positive value) and cyan (negative value) represent electron accumulation and depletion, respectively. The amount of charge transfer across the interfaces is further quantitatively evaluated by the Bader charge analysis, which demonstrates that the electrons with 0.135 |e| transfer across the interface from BlueP to WS₂, leaving the same amount of holes in BlueP. This directional movement forms a built-in electric field pointing from BlueP to WS₂, which has also been analyzed using the work function and the atomic electronegativity. Moreover, with respect to BlueP, the gain and loss of electrons between W and S atoms of WS₂ are greater, resulting in larger peaks and valleys (Fig. 3b).

Fig. 3 The side view of the three-dimensional charge density difference (a) and the planar-average charge density difference perpendicular to the Z direction of WS₂/BlueP (b).

The photocatalytic activity of the material is estimated by the energy band arrangement, which is related to the position of the CBM (E_CB) and VBM (E_VB) versus the vacuum level, expressed as follows:

E_CB = −χ + 0.5E_g (5)

E_VB = −χ − 0.5E_g (6)

where χ is the absolute electronegativity and E_g is the band gap of the semiconductor. The values of χ are calculated to be 5.62 eV and 5.54 eV for BlueP and WS₂, respectively. According to eqn (5) and (6), the band edges of (E_CB, E_VB) are evaluated to be (−4.52 eV, −6.56 eV) and (−4.16 eV, −7.08 eV) for WS₂ and BlueP, respectively. Thus, the absolute values of the conduction band offset (|E_CBO|) and the valence band offset (|E_VBO|) are obtained as 0.36 eV and 0.52 eV, respectively. On the absolute vacuum scale, the energy band arrangements of WS₂, BlueP and WS₂/BlueP are schematically shown in Fig. 4, where the CBO and VBO are the simplified labels of |E_CBO| and |E_VBO|. The CBM (VBM) of BlueP is higher (lower) than the CBM (VBM) of WS₂, indicating that WS₂/BlueP is a type-I heterostructure. Moreover, since WS₂ and BlueP have different dielectric constants, the built-in electric field at the interface is discontinuous, which causes different electric potentials and the energy band bending near the interface. Different band gaps and absolute electronegativity make the amount of bending different, resulting in “spikes” and “notches”, with the heights equal to the E_|CBO| and E_|VBO|, which correspond to the potential barriers of electrons and holes, respectively. Under the sunlight, the electrons of WS₂ and BlueP will be excited from the VBM to CBM as they absorb the energy greater than the band gaps, thus leaving an equal amount of holes in the VBM, and generating photogenerated carriers. For the type-I heterostructure, the band alignment promotes the photogenerated electrons (holes) to flow from the CBM (VBM) of BlueP into the CBM (VBM) of WS₂, respectively. Thus the electrons and holes are all accumulated in the WS₂ layer. However, the built-in electric field pointing from BlueP to WS₂ will hinder (enhance) the movement of electrons (holes). Moreover, the E_|CBO| of WS₂/BlueP is only 0.36 eV, which cannot hold the electrons in WS₂ tightly, and the built-in electric field leads the electrons to flow from the CBM of WS₂ to BlueP, therefore, there is a small degree of separation of the photogenerated carriers, which is still unfavourable for photocatalytic activity.

Fig. 4 The equilibrium energy band arrangement of WS₂ and BlueP nanosheets before and after contact.

3.4 Strain effects on the electronic properties of WS₂/BlueP

The in-plane uniaxial and biaxial strains can effectively adjust the electronic properties of 2D heterostructures, which can be achieved by adjusting the lattice parameters of the heterostructures. The strain is evaluated by:

ε = (a − a₀)/a₀ × 100% = Δa/a₀ × 100% (7)

where a₀ and a represent the lattice constants of the ideal and the strained heterostructures, respectively. The positive and negative values of ε correspond to the tensile and compressive strain, respectively.

The strain energy is defined as:

E_s = E_strain − E_ideal (8)

where E_strain and E_ideal are the total energy of the strained and ideal WS₂/BlueP, respectively.

The in-plane uniaxial and biaxial strains in the range of −8% to 8% are chosen to study their effects on the band gaps of WS₂/BlueP. The variations of strain energies and band gaps with different tensile and compressive strains are shown in Fig. 5. The relationship of strain energy and strain can be approximately stated with a quadratic function, demonstrating that the system has undergone elastic deformation, and the applied strains are within the elastic limit (Fig. 5a and b). That is to say, the heterostructure can be stretched and compressed in a reversible way and it will be restored to the original state as the strain is reduced to zero. Fig. 5c and d show that, both the −2% and −4% uniaxial and biaxial strains can enlarge the band gaps, while the other strains diminish them compared with WS₂/BlueP free of strain. Notably, the band gap reaches the maximum as the heterostructure is under the −2% uniaxial (or biaxial) strain.

Fig. 5 The strain energy and the band gap as a function of the uniaxial strain (a and c) and biaxial strain (b and d).

The applied external strain is also one of the effective ways to adjust the band edge arrangement. Under the uniaxial and biaxial strains, the CBM and VBM of BlueP and WS₂ in WS₂/BlueP, as shown in Fig. 6, are compared with each other and the band edge arrangement can be summarized into four categories: (I) CBM_BlueP < CBM_WS2, VBM_BlueP > VBM_WS2, (II) CBM_BlueP > CBM_WS2, VBM_BlueP > VBM_WS2, (III) CBM_BlueP > CBM_WS2, VBM_BlueP < VBM_WS2, (IV) CBM_BlueP < CBM_WS2, VBM_BlueP < VBM_WS2. The specific comparisons between the CBM and VBM of BlueP and WS₂ under each strain are marked with mathematical symbols “<” and “>” as shown in Table 2. According to the band arrangement, the electron transition type and the band type are obtained and listed in Table 2. The −4%, −6%, −8% and 8% uniaxial strains alter the direct bandgaps of WS₂/BlueP to indirect ones, while the other strains maintain the same direct bandgaps as the ideal WS₂/BlueP. The indirect transition needs the assistance of phonons to excite the electrons from the VBM to CBM, which is unfavourable for the generation of carriers. Remarkably, even the same transition type of the electron does not necessarily correspond to the same band type. The band types of the ideal and strained WS₂/BlueP can be categorized as type-I, type-II and Z-scheme, which may be caused by the strains with different magnitudes and loading modes. It is worth noting that there are two cases of type I band arrangement: (I) CBM_BlueP < CBM_WS2, VBM_BlueP > VBM_WS2 due to the −8%, −6% uniaxial and −4% biaxial strains and (II) CBM_BlueP > CBM_WS2, VBM_BlueP < VBM_WS2 due to the 2%, 6% and 8% uniaxial and biaxial strains. The type-II heterostructures correspond to the band arrangement of CBM_BlueP < CBM_WS2, VBM_BlueP < VBM_WS2 resulting from the −8% and −6% biaxial strains, while the Z-scheme heterostructures correspond to the case of CBM_BlueP > CBM_WS2, VBM_BlueP > VBM_WS2 resulting from the −2% and −4% uniaxial strains and −2% biaxial strain.

Fig. 6 The band edges (CBM and VBM) of each constituent in WS₂/BlueP under the uniaxial strain (a) and biaxial strain (b).

Table 2 The band edges, transition type and band type of WS₂/BlueP under strains

Strain (%)		BlueP versus WS2		Transition type	Band type
		CBM	VBM
Uniaxial strain	−8, −6	<	>	Indirect	Type-I
	−4	>	>	Indirect	Z-Scheme
	−2	>	>	Direct	Z-Scheme
	2, 6	>	<	Direct	Type-I
	8	>	<	Indirect	Type-I
Biaxial strain	−8, −6	<	<	Direct	Type-II
	−4	<	>	Direct	Type-I
	−2	>	>	Direct	Z-Scheme
	2, 6, 8	>	<	Direct	Type-I

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The type-I heterostructure is disadvantageous to the separation of photogenerated carriers because the reduction (Re) and oxidation (Ox) centers are located in the same layer. In contrast, the Re and Ox centers of the type-II and Z-scheme heterostructures are located in different layers, which can effectively separate the photogenerated carriers in space and greatly improve the photocatalytic activity of the heterostructures. Therefore, in the subsequent context, we only focus on the type II and Z-scheme heterostructures involving the −2% and −4% uniaxial strains and −2%, −6%, and −8% biaxial strains.

The band edges and carrier transfer pathways of the −2% and −4% uniaxial and −2% biaxial strained WS₂/BlueP (Fig. 7a) show that as WS₂ and BlueP absorb the solar energies greater than their band gaps, the electrons will transition from the VB to the corresponding CB, leaving an equal number of holes in the VB. The energy band offset promotes the electrons to transfer from the CB of BlueP to WS₂ and the holes from the VB of WS₂ to BlueP. However, the built-in electric field impedes this kind of movement, and promotes the electrons from the CB of WS₂ to recombine with the holes from the VB of BlueP. Therefore, a large number of electrons and holes are separated and accumulated in the CB of BlueP and VB of WS₂, which become the Re and Ox centers, respectively. The above analyzed mechanism indicates the −2% and −4% uniaxial and −2% biaxial strained WS₂/BlueP belong to the typical direct Z-scheme photocatalysts.

Fig. 7 Schematic diagrams of the band edges and carrier transfer pathways of the Z-scheme (a) and type-II (b) heterostructures.

The band edges and carrier transfer pathways of the −6% and −8% biaxial strained WS₂/BlueP (Fig. 7b) show that both the band offset and the built-in electric field promote the electrons to transfer from the CB of WS₂ to BlueP and the holes from the VB of BlueP to WS₂, thus a large number of electrons and holes are accumulated in the CB of BlueP and VB of WS₂, which become the Re and Ox centers, respectively. Therefore, the −6% and −8% biaxial strained WS₂/BlueP heterostructures are type-II photocatalysts. It is worth noting that the Re and Ox centers of the Z-scheme WS₂/BlueP are relatively higher than those of type-II heterostructures due to the applied strains, demonstrating that the direct Z-scheme photocatalysts have higher oxidation and reduction capabilities, which will be better candidates for optoelectronic devices.

The planar-average charge density difference along the Z direction of uniaxial (−2% and −4%) and biaxial (−2%, −6%, and −8%) strained WS₂/BlueP shows that, near the interface, BlueP loses and WS₂ gains electrons, which is similar to the case of the ideal heterostructure. The directional movement of the electrons forms the space charge region together with a built-in electric field pointing from BlueP to WS₂. This indicates that the strains do not reverse the built-in electric field. Bader charge analysis further provides the amount of charge transfer across the interface (Table 2), which demonstrates that the −2% and −4% uniaxial and −2% biaxial strained WS₂/BlueP heterostructures have more charge transfer than the ideal one, indicating that the strain induced built-in electric field is stronger and the corresponding heterostructures can separate the photogenerated carriers more efficiently. This is mainly caused by the stronger interfacial interactions due to the smaller interlayer distances as shown in Table 2, thus the electrons pass through the interface easily. In contrast, with respect to ideal WS₂/BlueP, the −6% and −8% biaxial strains have less charge transfer due to the larger interlayer distances, which reduces the interfacial interactions and is not conducive to the charge movement (Fig. 8).

Fig. 8 The planar-average charge density difference along the Z-direction of ideal, uniaxial and biaxial strained WS₂/BlueP heterostructures.

3.5 Strain effects on the photocatalytic properties

As is well known the Re center of a catalyst should be greater than H⁺/H₂ (−4.5 eV), and the Ox center should be less than O₂/H₂O (−5.73 eV) referring to full water decomposition. Analyzing the Re and Ox centers of strained WS₂/BlueP in Table 3, it can be seen that both the −2% uniaxial and biaxial strains lead to strong reduction capacities (Re > −4.5 eV) of the heterostructures, which can easily undergo the hydrogen evolution reaction (HER), while the −4% uniaxial and −6% and −8% biaxial strained heterostructures cannot undergo such reactions spontaneously. To adjust the Re centers of the heterostructures, in general, the cocatalyst is added during the reaction process in the experiment. The Ox centers of strained WS₂/BlueP are all less than −5.73 eV, which is beneficial to the OER and the degradation of organic pollutants. Therefore, −2% uniaxial and biaxial strains can achieve full water decomposition.

Table 3 The Bader charge, interlayer distance, Re and Ox center, and PDS and EDF of the OER at pH = 0 and pH = 7, the effective mass of electrons and holes for ideal and strained WS₂/BlueP

Physical quantity		Uniaxial strain		Biaxial strain
		−2%	−4%	−2%	−6%	−8%
Bader (e)		−0.140	−0.140	−0.136	−0.124	−0.121
d (Å)		3.206	3.192	3.191	3.248	3.225
Re center (eV)		−4.298	−4.574	−3.615	−4.899	−5.216
Ox center (eV)		−7.283	−7.144	−7.288	−5.816	−5.923
pH = 0	PDS (eV)	0.585	0.639	0.610	0.527	0.607
	EDF (eV)	1.553	1.414	1.558	0.086	0.193
pH = 7	PDS (eV)	0.172	0.226	0.197	0.114	0.194
	EDF (eV)	1.966	1.827	1.971	0.499	0.606
m e/m0		0.132	0.183	0.354	0.162	0.150
m h/m0		0.590	0.770	0.314	0.970	0.177

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The thermodynamic feasibility is crucial to photocatalytic water splitting, and the HER is relatively easy under the influence of potential, therefore, the feasibility of the OER in thermodynamics is only considered. As U = 0 V, 1.23 V (minimum potential difference required for water decomposition) and pH = 0, the variation of Gibbs free energy ΔG with reaction steps of *H₂O, *OH, *O, *OOH and O₂ release are shown in Fig. 9a–e, where ‘*’ stands for the substrate (WS₂/BlueP). As U = 0 V and pH = 0, ΔG goes up with each step of the reaction, and eventually reaches 4.920 eV for all the strained heterostructures. For each strained WS₂/BlueP, the curve of U = 1.23 V and pH = 0 is obtained by ΔG_U=1.23 = ΔG_U=0 −1.23. The potential determining step (PDS) is adopted to evaluate the feasibility of the OER, which refers to the largest energy difference of every two adjacent steps at U = 1.23 V. The values of the PDS for −2% and −4% uniaxial and −2%, −6%, and −8% biaxial strained WS₂/BlueP are obtained and listed in Table 3. This shows that the −6% biaxial strained WS₂/BlueP heterostructure has the smallest PDS, indicating that it is the best choice for achieving the OER. Notably, in the case of pH = 7, the correction term ΔG_pH = −K_bT ln 10 × pH = −0.059 pH should be considered during the calculation of the ΔG and PDS. As shown in Table 3, the ΔG_U=1.23 declines in the first and second reactions while increases in the third and fourth reactions except −6% biaxial strained WS₂/BlueP, where ΔG_U=1.23 only decreases in the second reaction. The actual electrochemical driving forces (EDFs) of the OER are calculated as (E^NHE_VBM − 1.23) and (E^NHE_VBM − 1.23 + 0.059 × pH) for pH = 0 and pH = 7, respectively, where the NHE refers to the normal hydrogen electrode. The calculated values of the EDF are listed in Table 3. Our analytic conclusion suggests that when the EDF is equal or greater than the PDS, the ΔG of each reaction step is equal or less than zero, thus the OER can be conducted spontaneously. As shown in Fig. 9f, the values of the EDF at pH = 0 are greater than the PDS for −2% and −4% uniaxial and −2% biaxial strained WS₂/BlueP, which indicates that the Z-scheme heterostructure is feasible in thermodynamics for photocatalytic water decomposition. In contrast, the EDF of −6%, −8% biaxial strained WS₂/BlueP (type II) is less than the PDS, indicating that the external energy is needed to achieve water decomposition. The above conclusion further demonstrates that the Z-scheme heterostructure is a better choice for photocatalytic water splitting due to its stronger oxidation and reduction potential. When pH = 7, the values of the EDF are greater than the PDS for all the strained heterostructures, which proved to be thermodynamically feasible during photocatalytic water decomposition. Therefore, it is an effective way to improve the photocatalytic activity of the strained heterostructure by adjusting the pH value.

Fig. 9 The Gibbs free energy of each reaction step at U = 0, U = 1.23 and pH = 0 for WS₂/BlueP under the uniaxial strain of −2% (a) and −4% (b) and biaxial strain of −2% (c), −6% (d), and −8% (e). The EDF and PDS of uniaxial and biaxial strained WS₂/BlueP during the OER at pH = 0 and pH = 7 (f).

The applied strains can also adjust the transfer rate of the photogenerated carriers, reflected by the carrier mobility (μ) under an electric field, which is defined as:

where e, τ and m* are the electronic charge, scattering time and effective mass of carriers, respectively. Since μ is inversely proportional to m*, we can use m* to qualitatively analyze the variation tendency of μ. The effective mass of electrons (m_e/m₀) and holes (m_h/m₀) in Table 3 show that the −2% uniaxial strained WS₂/BlueP heterostructure has the smallest m_e/m₀, while the −8% biaxial strained WS₂/BlueP heterostructure has the smallest m_h/m₀, corresponding to the largest μ_e and μ_h, respectively, which can reduce the recombination rate of photogenerated carriers and improve the efficiency of catalytic reaction. Except for the −2% biaxial strained WS₂/BlueP, the m_e/m₀ of the other strained heterostructures are greater than m_h/m₀, demonstrating that electrons more easily migrate than holes. It should be noted that although the −6% and −8% biaxial strained WS₂/BlueP (type II) heterostructures have smaller m_e/m₀ and m_h/m₀, unfortunately they cannot achieve water decomposition through the previous analysis. Therefore, we only focus on −2% and −4% uniaxial and −2% biaxial strained heterostructures, among them, the −2% uniaxial strained WS₂/BlueP heterostructure has the smallest m_e/m₀, while the −2% biaxial strained heterostructure has the smallest m_h/m₀, moreover, their PDS values are relatively smaller and EDF values are greater, hence they could be potential candidates for electron-driven HER and hole-driven OER.

4. Conclusions

In summary, the effects of in-plane uniaxial and biaxial strains on the electronic and photocatalytic activity of WS₂/BlueP are systematically studied through first-principles calculations. The most energetically stable configuration of WS₂/BlueP is “P atoms exactly on top of W and S sites” (model III), which exhibits a direct band gap of 1.779 eV, and both the VBM and CBM are occupied by W-5d, with the characteristic of type I heterostructure. Moreover, WS₂/BlueP not only expands the light response to the entire visible light region, but also enhances the absorption intensity and red-shifts the absorption edge. The charge density difference, work function and Bader analysis can prove the built-in electric field pointing from BlueP to WS₂. The WS₂/BlueP is further confirmed as a type-I heterostructure by the band arrangement, and its redox centers are located in the WS₂ layer, which is not conducive to the separation of carriers.

The in-plane −8–8% uniaxial and biaxial strains make the heterostructure undergo elastic deformation. The strains can affect the band gap, band edge arrangement, band type (type-I, type-II, Z-scheme) and electron transition type (direct, indirect) of WS₂/BlueP, even though the same electron transition type does not correspond to the same band type. The −2% uniaxial (or biaxial) strain can engineer the band gap to reach the maximum and achieve full water decomposition. At pH = 0, only the −2% and −4% uniaxial and −2% biaxial strained WS₂/BlueP (Z-scheme) heterostructures are thermodynamically feasible for photocatalytic water splitting, while at pH = 7, all the strained heterostructures are feasible. Hence, it is an effective way to improve the photocatalytic activity by adjusting the pH value of the strained heterostructures. The −2% uniaxial and biaxial strained WS₂/BlueP are potential candidates for electron-driven HER and hole-driven OER, respectively. Moreover, the lower PDS, EDF and m* values can promote the transition performance and improve the photocatalytic reaction efficiency. In conclusion, the electronic and photocatalytic properties of WS₂/BlueP can be engineered by in-plane uniaxial and biaxial strains.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 51771144), the Natural Science Foundation of Shaanxi Province in China (No. 2017JZ015), the Fundamental Research Funds for the Central Universities (No. GK GK202003017, 2019CSLY004) and the Comprehensive Teaching Reform Research Project of Shaanxi Normal University (No. 19JG27).

References

1. X. Gao, Y. Shen, Y. Ma, S. Wu and Z. Zhou, First-principles insights into efficient band gap engineering of the blue phosphorus/g-C₃N bilayer heterostructure via an external vertical strain, Appl. Surf. Sci., 2019, 479, 1098–1104.
2. X. Wang, X. Yang, B. Wang, G. Wang and J. Wan, Significant band gap induced by uniaxial strain in graphene/blue phosphorene bilayer, Carbon, 2018, 130, 120–126.
3. A. K. Geim and K. S. Novoselov, The rise of graphene, Nanosci. Technol., 2009, 11–19.
4. Y. Zhang, Y. W. Tan, H. L. Stormer and P. Kim, Experimental observation of the quantum Hall effect and Berry's phase in graphene, Nature, 2005, 438, 201–204.
5. M. M. Obeid, C. Stampfl, A. Bafekry, Z. Guan, Z. H. R. Jappor, C. V. Nguyen, M. Naseri, D. M. Hoat, N. N. Hieu, A. E. Krauklis, T. V. Vu and D. Gogova, First-principles investigation of nonmetal doped single-layer BiOBr as a potential photocatalyst with a low recombination rate, Phys. Chem. Chem. Phys., 2020, 22(27), 15354–15364.
6. Y. Cai, G. Zhang and Y. W. Zhang, Electronic properties of phosphorene/graphene and phosphorene/hexagonal boron nitride heterostructures, J. Phys. Chem. C, 2015, 119, 13929–13936.
7. L. Li, Y. Yu, G. J. Ye, Q. Ge, X. Ou, H. Wu, D. Feng, X. H. Chen and Y. Zhang, Black phosphorus field-effect transistors, Nat. Nanotechnol., 2014, 9, 372–377.
8. H. O. Churchill and P. Jarillo-Herrero, Two-dimensional crystals: phosphorus joins the family, Nat. Nanotechnol., 2014, 9, 330–331.
9. A. Goswami and M. B. Gawande, Phosphorene: current status, challenges and opportunities, Front. Chem. Sci. Eng., 2019, 13(2), 296–309.
10. S. L. Li, K. Tsukagoshi, E. Orgiu and P. Samorì, Charge transport and mobility engineering in two-dimensional transition metal chalcogenide semiconductors, Chem. Soc. Rev., 2016, 45, 118–151.
11. Q. H. Wang, K. Kalantar-Zadeh, A. Kis, J. N. Coleman and M. S. Strano, Electronics and optoelectronics of two-dimensional transition metal dichalcogenides, Nat. Nanotechnol., 2012, 7, 699–712.
12. J. L. Zhang, S. Zhao, C. Han, Z. Wang, S. Zhong, S. Sun, R. Guo, X. Zhou, C. D. Gu, K. D. Yuan, Z. Li and W. Chen, Epitaxial growth of single layer blue phosphorus: a new phase of two-dimensional phosphorus, Nano Lett., 2016, 16, 4903–4908.
13. J. Zeng, P. Cui and Z. Zhang, Half layer by half layer growth of a blue phosphorene monolayer on a GaN(001) substrate, Phys. Rev. Lett., 2017, 118, 046101.
14. B. J. Wang, X. H. Li, R. Q. Zhao, X. L. Cai, W. Y. Yu, W. B. Li, Z. S. Liu, L. W. Zhang and S. H. Ke, Electronic structures and enhanced photocatalytic properties of blue phosphorene/BSe van der Waals heterostructures, J. Mater. Chem. A, 2018, 6(19), 8923–8929.
15. G. Wang, W. J. Slough, R. Pandey and S. P. Karna, Degradation of phosphorene in air: understanding at atomic level, 2D Mater., 2016, 3, 025011.
16. W. Zhang and L. Zhang, Electric field tunable band-gap crossover in black(blue) phosphorus/g-ZnO van der Waals heterostructures, RSC Adv., 2017, 7, 34584–34590.
17. C. Li, J. Gao, Y. Zi, F. Wang, C. Niu, J. H. Cho and Y. Jia, Asymmetric quantum confinement-induced energetically and spatially splitting Dirac rings in graphene/phosphorene/graphene heterostructure, Carbon, 2018, 140, 164–170.
18. Y. Zheng, Y. Jiao, Y. Zhu, L. H. Li, Y. Han, Y. Chen, A. Du, M. Jaroniec and S. Z. Qiao, Hydrogen evolution by a metal-free electrocatalyst, Nat. Commun., 2014, 5, 3783.
19. A. K. Geim and I. V. Grigorieva, Van der Waals heterostructures, Nature, 2013, 499, 419–425.
20. Q. Peng, Z. Wang, B. Sa, B. Wu and Z. Sun, Electronic structures and enhanced optical properties of blue phosphorene/transition metal dichalcogenides van der Waals heterostructures, Sci. Rep., 2016, 6, 31994.
21. H. R. Jappor, M. M. Obeid, T. V. Vu, D. M. Hoat, H. D. Bui, N. N. Hieu, S. J. Edrees, Y. Mogulkoc and R. Khenata, Engineering the optical and electronic properties of Janus monolayer Ga₂SSe by biaxial strain, Superlattices Microstruct., 2019, 130, 545–553.
22. N. D. Hien, N. Q. Cuong, L. M. Bui, P. C. Dinh, C. V. Nguyen, H. V. Phuc, N. V. Hieu, H. R. Jappor, L. T. T. Phuong, B. D. Hoi, L. C. Nhan and N. N. Hieu, First principles study of single-layer SnSe₂ under biaxial strain and electric field: Modulation of electronic properties, Phys. E, 2019, 111, 201–205.
23. A. O. M. Almayyali, B. B. Kadhim and H. R. Jappor, Stacking impact on the optical and electronic properties of two-dimensional MoSe₂/PtS₂ heterostructures formed by PtS₂ and MoSe₂ monolayers, Chem. Phys., 2020, 532, 110679.
24. A. O. M. Almayyali, B. B. Kadhim and H. R. Jappor, Tunable electronic and optical properties of 2D PtS₂/MoS₂ van der Waals heterostructure, Phys. E, 2020, 118, 113866.
25. L. Lin, S. F. Li, W. Y. Yu, L. H. Zhu, J. T. Huang, Z. Y. Zhang, H. L. Tao and W. B. Zhang, Electronic structures and strain responses of group VA/VA two-dimensional van der waals heterostructures, Vacuum, 2020, 176, 109296.
26. J. X. Ye, J. W. Liu and Y. K. An, Electric field and strain effects on the electronic and optical properties of g-C₃N₄/WSe₂ van der Waals heterostructure, Appl. Surf. Sci., 2020, 501, 144262.
27. X. L. Wang, Y. Y. Wang, R. G. Quhe, Y. N. Tang, X. Q. Dai and W. H. Tang, Designing strained C₂N/GaTe(InTe) heterostructures for photovoltaic and photocatalytic application, J. Alloys Compd., 2020, 816, 152559.
28. W. X. Zhang, W. H. He, J. W. Zhao and C. He, Electronic properties of blue phosphorene/transition metal dichalcogenides van der Waals heterostructures under in-plane biaxial strains, J. Solid State Chem., 2018, 265, 257–265.
29. G. Kresse and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B: Condens. Matter Mater. Phys., 1996, 54, 11169–11186.
30. G. Kresse and J. Furthmüller, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mater. Sci., 1996, 6, 15–50.
31. J. P. Perdew, K. Burke and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett., 1996, 77, 3865.
32. J. Klimes, D. R. Bowler and A. Michaelides, Chemical accuracy for the van der Waals density functional, J. Phys.: Condens. Matter, 2010, 22, 022201.
33. T. Thonhauser, V. R. Cooper, L. Shen, A. Puzder, P. Hyldgaard and D. C. Langreth, Van der Waals density functional: self-consistent potential and the nature of the van der Waals bond, Phys. Rev. B: Condens. Matter Mater. Phys., 2007, 76, 125112.
34. J. Heyd, G. E. Scuseria and M. Ernzerhof, Hybrid functionals based on a screened Coulomb potential, J. Chem. Phys., 2003, 118, 8207–8215.
35. J. Liu, Origin of high photocatalytic efficiency in monolayer g-C₃N₄/CdS heterostructure: a hybrid DFT study, J. Phys. Chem. C, 2015, 119, 28417–28423.
36. J. N. Wang, Y. H. Huang, F. Ma, J. M. Zhang, X. M. Wei and G. Q. Zhu, Electronic states and photocatalytic performances of SnS₂-based binary and ternary vdW heterostructures, J. Alloys Compd., 2020, 849, 156627.
37. B. J. Wang, X. H. Li, X. L. Cai, W. Y. Yu, L. W. Zhang, R. Q. Zhao and S. H. Ke, Blue phosphorus/Mg(OH)₂ van der Waals heterostructures as promising visible-light photocatalysts for water splitting, J. Phys. Chem. C, 2018, 122, 7075–7080.
38. W. Oldham and A. Milnes, Interface states in abrupt semiconductor heterojunctions, Solid-State Electron., 1964, 7, 153–165.
39. W. W. Dai and Z. Y. Zhao, Understanding the interfacial properties of graphene-based materials/BiOI heterostructures by DFT calculations, Appl. Surf. Sci., 2017, 406, 8–20.
40. B. Ghosh, S. Nahas, S. Bhowmick and A. Agarwal, Electric field induced gap modification in ultrathin blue phosphorus, Phys. Rev. B: Condens. Matter Mater. Phys., 2015, 91, 115433.
41. G. Ralph, Pearson, Absolute Electronegativity and Hardness: Application to Inorganic Chemistry, Inorg. Chem., 1988, 27, 734–740.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/d0cy01656j

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