Vertically stacked GaN/WX₂ (X = S, Se, Te) heterostructures for photocatalysts and photoelectronic devices

Abstract

Tremendous attention has been paid to vertically stacked heterostructures owing to their tunable electronic structures and outstanding optical properties. In this work, we explore the structural, electronic and optical properties of vertically stacked GaN/WX₂ (X = S, Se, Te) heterostructures using density functional theory. We find that these stacking heterostructures are all semiconductors with direct band gaps of 1.473 eV (GaN/WTe₂), 2.102 eV (GaN/WSe₂) and 1.993 eV (GaN/WS₂). Interestingly, the GaN/WS₂ heterostructure exhibits a type-II band alignment, while the other two stackings of GaN/WSe₂ and GaN/WTe₂ heterostructures have type-I band alignment. The optical absorption of GaN/WX₂ heterostructures is very efficient in the visible light spectrum. Our results suggest that GaN/WX₂ heterostructures are promising candidates for photocatalytic water splitting and photoelectronic devices in visible light.

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Introduction

Van der Waals (vdW) heterostructures (HS) are used to design unusual electronic devices because of their peculiar physical properties and immense performances.¹ Additionally, vertically stacked heterostructures have innovative applications in electronic devices, such as ultrathin photodetectors,² solar cells,³ memory devices,⁴ flexible sensors and transistors^5,6 etc. Specifically, two-dimensional (2D) vdW heterostructures with type-II band alignments have promising potential in photovoltaics devices and photocatalysts^7–11 due to their fascinating electronic and optical properties. In type-II heterostructures, the photogenerated holes and electrons become spatially located in different layers. As a result, the recombination of carriers can be effectively prevented and the light energy utilization is significantly enhanced.¹² Moreover, 2D WX₂ (X = S, Se, Te) is a typical layered transition metal dichalcogenide family, which has a direct band gap from 1.0 eV to 2.4 eV.^13–22 Among the transition metal dichalcogenides (TMD) materials, monolayer WS₂, WSe₂, and 1H WTe₂ are typically semiconductors with direct band gaps of 2.38 eV,^18,19 2.11 eV,^20,21 1.46 eV.²²

Motivated by 2D graphene-like planar honeycomb structures, 2D group III–V compound semiconductors with planar hexagonal structures have been predicted to be stable.^23–26 In particular, the monolayer hexagonal structure of gallium nitride (GaN) has recently received growing attractions, which has been directly experimentally synthesized via graphene encapsulation.²⁵ Onen et al. reported that the indirect band gap of 2D GaN is 3.42 eV with HSE06 calculation,²⁶ but the indirect bandgap hindered the practical applications in optoelectronics. In addition, heterostructures based on 2D GaN, such as GaN/blueP, GaN/MoS₂, GaN/MoSe₂, GaN/WS₂, MoSe₂/blueP, GaN/ZnO and GaN/BP heterostructures, are able to be formed to type-II band structures, which show good electronic and optical behaviors in photocatalyst and optoelectronic applications.^27–32

It is also worth to note that 2D WX₂, together with 2D GaN, can form vdW heterostructures for their similar structures and same lattice constants. Generally, the superior structures and excellent properties of GaN/WX₂ (X = S, Se, Te) heterostructures are significantly valuable to explore, which could potentially provide a platform for applications in photocatalyst and optoelectronic devices.

Computational methods

Ab initio calculations were performed within the framework of density functional theory (DFT),^33,34 as implemented in the Vienna Ab Initio Simulations Package (VASP).³⁵ Electronic exchange and correlation effects were described with the Perdew–Burke–Ernzerhof (PBE)³⁶ functional of generalized gradient approximation (GGA)³⁷ and HSE06 hybrid function.³⁸ Electron–ion interaction were treated with the projector augmented wave (PAW) method,^39,40 with an energy cutoff of 550 eV. And Brillouin zone sampling of K-mesh was set to 9 × 9 × 1 for relaxation. Subsequently, K-mesh points for density of states (DOS) and energy band structures were set to 13 × 13 × 1 and the energy criteria were set as 10⁻⁵ eV until the residual force was smaller than 10⁻³ eV Å⁻¹. Especially, the vacuum layer thickness was set more than 25 Å to avoid spurious interactions in the neighboring images. As the long-range vdW interaction is important to hold the 2D heterostructure together, the vdW-D3 approach⁴¹ was used to describe long-range electron correlation effects.

The optical properties of 2D GaN/WX₂ heterostructures are described by the complex dielectric function ε(ω) = ε₁(ω) + iε₂(ω), where ε₁(ω) and ε₂(ω) are real and imaginary parts, respectively. At the same time, the imaginary part is calculated by summing up all possible transitions from the occupied to unoccupied states, which is closely related to the band structure in the absorption behaviors.⁴² The imaginary part is given by:

where e, m and ω are the charge, mass of free electrons, and the frequency of incident photons, respectively. Meanwhile, M, i, j and f_i are the dipole momentum, indices of initial and final states, and the Fermi–Dirac distribution function for ith state with wave vector k, respectively. The real part ε₁(ω) is obtained from the imaginary ε₂(ω) by Kramers–Kronig relation:^43,44where P is the principal value. Absorption coefficient is then obtained as:^43,44

Results and discussion

Stability and structures

Stacking patterns can modulate the electronic properties of the vdW heterostructures. Therefore, four typical stacking configurations (AA, AB, AC, AD) have been constructed. In the AA stacking, the Ga atom sits on the top of S/Se/Te atom, while the N atom is on top of W atom. In the AB stacking, the Ga atom is placed on the top of W atom, while the N atom is on the center of the hexagonal site. In the AC stacking, the N atom sits on the top of W atom, while the Ga atom is located on the center of the hexagonal site. In the AD stacking, the Ga atom sits on the top of W atom, while the N atom is on top of S/Se/Te atom. These relaxed structures are shown in Fig. 1. For GaN/WS₂ heterostructure, the interface binding energies of AA, AB, AC and AD stacking patterns are −27.72 meV Å⁻², −27.01 meV Å⁻², −26.69 meV Å⁻², and −22.58 meV Å⁻² respectively. In consistence with other reports,^27,28 after relaxation, AA stacking of GaN/WX₂ heterostructures are the most stable due to the lowest interface binding energies. AA stacking patterns are only taken into consideration in the next calculation. The equilibrium lattice constants a(b), bond lengths, bond angles of GaN monolayer, WX₂ monolayer and AA stacking GaN/WX₂ heterostructures, calculated with GGA–PBE, are listed in Table 1. From Table 1, the calculated lattice constants, bond lengths/angles accord well with previous reports.^{13,14,16,23,24,26,28} And the relaxed crystal structures of the GaN, WS₂, WSe₂, and WTe₂ monolayers and GaN/WX₂ bilayers are hexagonal. It is clear that the hexagonal unit parameters of GaN/WS₂, GaN/WSe₂, GaN/WTe₂ heterostructures are 3.194 Å, 3.285 Å, 3.388 Å, respectively, which agree well with previous results.^28,29 The lattice mismatches are expressed as Where a and c are lattice constants of GaN/WX₂ heterostructure and individual WX₂ layer or GaN layer. The lattice mismatches of GaN/WS₂, GaN/WSe₂, GaN/WTe₂ heterostructures are 1.7%, 3.0% and 3.4%, meaning that the differences are negligible.

Fig. 1 Relaxed structures of four typical stacking patterns of GaN/WX₂ (X = S, Se, Te) heterostructures. Cyan, yellow, dark blue, and brown spheres indicate W, X, N and Ga atoms, respectively.

Table 1 Lattice parameters a(b), bond lengths l_X–W(l_Ga–N), bond angles Θ_XWX, interface equilibrium distances d_eq and the interface binding energies ΔE were calculated using PBE in comparison to previous theoretical and experimental values

Name		a (b)/Å	lX–W/Å	lGa–N/Å	ΘXWX/°	deq/Å	ΔE/meV·Å^−2
a Ref. ^26.b Ref. 23.c Ref. 25.d Ref. 16.e Ref. 14.f Ref. 28.g Ref. 13.h Ref. 29.
GaN	Theo.	3.21^a, 3.25^b		1.85^a	—	—	—
	Cal.	3.248	—	1.858	—	—	—
	Expt.	3.20^c			—	—	—
WS2	Theo.	3.18^d, 3.14^f	2.42^d		81.01^d	—	—
	Cal.	3.185	2.411	—	81.023	—	—
	Expt.	3.155^e				—	—
WSe2	Theo.	3.32^d, 3.31^g	2.55^d		82.43^d	—	—
	Cal.	3.295	2.517	—	82.749	—	—
	Expt.	3.286^e			—	—	—
WTe2	Theo.	3.51^g			—	—	—
	Cal.	3.502	2.736	—	83.334	—	—
GaN/WS2	Theo.	3.200^f	2.433^f	1.852^h	—	3.479^f	−33.36^f, −19.61^h
	Cal.	3.194	2.431	1.845	81.144	3.081	−27.72
GaN/WSe2	Theo.	3.29^h	—	—	—	—	−21.87^h
	Cal.	3.285	2.543	1.897	82.417	3.139	−28.05
GaN/WTe2	Cal.	3.388	2.810	1.906	83.799	3.236	−37.63

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To describe the vdW interactions, the interface binding energies (ΔE) of GaN/WX₂ heterostructures are calculated as:

ΔE = (E_HS − E_GaN − E_WX2)/S₀ (4)

where ΔE refers to the interface binding energies at the interface of GaN/WX₂ heterostructures, and E_HS, E_GaN, E_WX2, S₀ represent the total energies of heterostructures, GaN monolayer, WX₂ monolayer, the interface areas of the heterostructures, respectively. The interface areas of the heterostructures are calculated by multiplying a and b vectors in hexagonal unit cells. Then, the interface binding energies of GaN/WX₂ heterostructures are listed in Table 1, consistent with other theoretical reports.^28,29 As is shown in Fig. 2, the optimal distances between N atom in the GaN layer and X atom in the WX₂ layer are 3.081 Å, 3.139 Å, 3.236 Å, respectively, indicating that no bonds between Ga and X atoms are formed and all these heterostructures are formed by the same magnitude order of van der Waals (vdW) forces as others, such as GaN–blueP,²⁷ GaN/WS₂,²⁸ GaN/BP³⁰ and typical vdW graphite.⁴⁵

Fig. 2 Plot of interface binding energies as function of interlayer distances for GaN/WS₂, GaN/WSe₂, and GaN/WTe₂ heterostructures. 5th order polynomial has been employed for fitting. In order to clarify the equilibrium distances between the GaN layer and WX₂ layer, the values of interface binding energies of both the GaN/WSe₂ and GaN/WTe₂ heterostructures are shifted downwards by 1.80 eV, 5.40 eV, respectively.

Obviously, the interface binding energies of GaN/WS₂, GaN/WSe₂ and GaN/WTe₂ heterostructures are −27.72, −28.05, and −37.63 meV Å⁻², demonstrating that the interactions between two layers belong to physically vdW forces. All the interface binding energies are negative, suggesting that the GaN/WX₂ heterostructures have favorable energies during the formation.

Electronic properties

In the following section, projection-resolved band structures of GaN/WX₂ heterostructures are depicted in Fig. 3. All the GaN/WX₂ heterostructures are direct band gap semiconductors. Both the valence band maximum (VBM) and the conduction band minimum (CBM) of the GaN/WX₂ (X = S, Se, Te) heterostructures locate at the K point of Brillouin zone (BZ). The band gaps of GaN/WS₂, GaN/WSe₂, GaN/WTe₂ heterostructures are 1.993 eV, 2.102 eV, 1.473 eV, smaller than both individual GaN (3.241 eV) layer and individual WS₂ (2.357 eV), WSe₂ (2.119 eV), WTe₂ (1.594 eV) layer according to HSE06 calculations, which agrees well with the theoretical values of GaN (3.23 eV),²³ WTe₂ (1.49 eV)²² and experimental values of WS₂ (2.38 eV),⁵ WSe₂ (2.11 eV).⁸ Specially, GaN/WS₂ heterostructure has a type II band alignment, which is beneficial to the separation of the photogenerated holes and electrons in different layers, the prevention of the recombination of carriers, and the enhancement of the light energy utilization. It is also found that the GaN/WSe₂ and GaN/WTe₂ heterostructures have type-I band alignment semiconductors for both the VBM and CBM of GaN/WSe₂ and GaN/WTe₂ heterostructures come from the W-dz² orbitals of the WSe₂ and WTe₂ layer, which can be used in light emitting diodes (LED),⁴⁶ indicating that the interlayer interactions between the GaN layer and the WX₂ (X = Se, Te) layer reduce the band gap values. Therefore, the band gaps of the GaN/WX₂ heterostructures could be significantly changed by vertically stacked heterostructures, which could provide a good opportunity to work on band engineering and electronic device designs. It is interesting that the band gap of GaN/WS₂ heterostructure is larger than the minimum required energy of the photocatalytic reaction (1.23 eV), which is potential for a photocatalyst in water splitting.

Fig. 3 Projection-resolved band structures of (a) GaN/WS₂, (b) GaN/WSe₂, and (c) GaN/WTe₂ heterostructures. Blue and red lines indicate contributions from GaN and WX₂ layer, respectively.

As reflected in the projection-resolved band structures, the band gap of WX₂ monolayer is decreased by the downshift of CBM as well as the upshift of VBM at K point. The contribution of VBM of GaN/WS₂ heterostructure is GaN layer and that of CBM is WS₂ layer. In Fig. 4(a), the blue and red lines present the DOS of GaN and WS₂ layer in GaN/WS₂ heterostructure. Both the contributions of VBM and CBM of GaN/WSe₂ and GaN/WTe₂ heterostructures are derived from WSe₂ and WTe₂ layer, as shown in Fig. 4(b and c). Obviously, for GaN/WS₂ heterostructure, the VBM and CBM are respectively confined in GaN and WS₂ layer, which also demonstrates that GaN/WS₂ heterostructure has a type-II band alignment.

Fig. 4 Projected density of states (PDOS) of (a) GaN/WS₂, (b) GaN/WSe₂, and (c) GaN/WTe₂ heterostructures. Fermi level is set to zero as indicated by the black dashed line.

Photocatalyst and optoelectronic performances

The absorption coefficients of GaN/WX₂ heterostructures are calculated, as illustrated in Fig. 5(a). It is clear that the first peaks in absorption spectrum of GaN/WS₂, GaN/WSe₂, GaN/WTe₂ heterostructures locate at 3.03, 2.69, 2.25 eV, which are mainly contributed by WX₂ layers. The absorption spectrum of GaN/WX₂ heterostructures covers the whole incident solar spectrum,⁴⁷ which makes well suitable applications for optoelectronic devices in visible light.

Fig. 5 (a) Absorption spectrum of GaN/WS₂, GaN/WSe₂, and GaN/WTe₂ heterostructures. Incident AM 1.5 G solar flux⁴⁸ is plotted in orange solid line. (b) Schematic plot of the migration of photogenerated electrons and holes at the GaN/WS₂ interface. (c) Band-edge alignments of GaN/WX₂ heterostructures.

A schematic plot of migrating carriers to depict the dynamic processes of photogenerated carriers at the GaN/WS₂ interface is shown in Fig. 5(b). In the GaN/WS₂ heterostructure, the photogenerated electrons start to transfer from the GaN layer the WS₂ layer in the conduction band, which is motivated by the conduction band offset (CBO) (0.71 eV). Meanwhile, the photogenerated holes in the valence band move from the WS₂ layer to the GaN layer, which are driven by a large valence band offset (VBO) (1.60 eV). Hence, the GaN/WS₂ heterostructure, owing a type-II band alignment, could be utilized as a photocatalyst. As for the GaN/WSe₂ and GaN/WTe₂ heterostructures, one can see that all the photogenerated carriers of the GaN layer are likely to move to the WSe₂ (WTe₂) layer. The VBO and CBO between GaN and WSe₂ (WTe₂) layers are 1.98 eV (2.97 eV) and 0.86 eV (1.72 eV), respectively. As a result, the photogenerated carriers can be located in the WSe₂ (WTe₂) layers to build light-emitting diodes (LEDs).⁴⁶ The band edge positions of GaN/WS₂, GaN/WSe₂, GaN/WTe₂ heterostructures are illustrated in Fig. 5(c). The CBMs of GaN/WS₂, GaN/WSe₂, GaN/WTe₂ heterostructures are −4.09, −3.99, −4.26 eV, respectively, whereas the VBMs of GaN/WS₂, GaN/WSe₂, GaN/WTe₂ heterostructures are −6.08, −6.09, −5.73 eV, respectively. Those are within the oxidation potential (E_O2/H2O, −5.67 eV) of water and the reduction potential (E_H⁺/H2, −4.44 eV). Especially, the redox reaction in the GaN/WS₂ heterostructure occurs in different layers: water oxidation occurs in the GaN layer, meanwhile water reduction takes place in the WS₂ layer.

It is well known that the lifetime of photogenerated carriers is significantly influenced by the build-in electric field. Hence, build-in electric field induced by ground state charge transfer were investigated. Based on Bader charge analysis,⁴⁸ the charge transfer from the GaN layer to the WS₂ layer is 0.029e, leading to an electric field pointing to GaN from WS₂. This electric field will promote the migration of electrons from the GaN layer to WS₂ layer and holes from the WS₂ layer to GaN layer. The build-in electric field E = P/ε₀ε_rS₀d_eq of 3.69 × 10⁹ V m⁻¹ is acquired in the junction region of GaN/WS₂ heterostructure. Where P = Δq·d_eq = 0.089e·Å is the size of dipole moment, ε₀ = 8.850 × 10⁻¹² F m⁻¹ refers to the permittivity of free space, ε_r = 1 represents the relative dielectric constant, S₀ = 8.835 × 10⁻²⁰ m² is the interfaces area of the WS₂/GaN heterostructure, d_eq = 3.081 × 10⁻¹⁰ m denotes the interlayer equivalent distance.

Conclusions

In summary, the electronic and optical properties of GaN/WX₂ heterostructures have been performed within density functional theory. It is found that all the hexagonal GaN/WX₂ heterostructures are stable semiconductors with direct band gaps. Interestingly, among them, the GaN/WS₂ heterostructure has a type-II band alignment, which is beneficial in photocatalysts for water splitting. However, both the GaN/WSe₂ and GaN/WTe₂ heterostructures exhibit type-I band alignment, which can be utilized in LED. In the GaN/WS₂ heterostructure, the charge transport from the GaN layer to the WS₂ layer is 0.029e, based on Bader charge analysis, forming a build-in electric field favorable for charge separation. The build-in electric field E = P/ε₀ε_rS₀d_eq of 3.69 × 10⁹ V m⁻¹ is acquired in the junction region of GaN/WS₂ heterostructure. The absorption behaviors of GaN/WX₂ heterostructures are also performed, and results show that GaN/WX₂ heterostructures are very efficient at absorbing the visible light to expand the application to photocatalyst and photoelectronic devices.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work is supported by the Natural Science Foundation of China with grants no. 1186040026, Incubation Project for High-Level Scientific Research Achievements of Hubei Minzu University with grants no. 4205009 and the Educational Commission of Hubei Province of China with grant no. T201914.

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