Potential Visible-Light Driven PtO₂/GaN vdW Hetero-Bilayer Photocatalysts for Water Splitting Using First-Principles

Novel two-dimensional (2D) PtO2/GaN van der Waals (vdW) hetero-bilayers (HBL) are studied here for photocatalytic water splitting (PWS) application under first-principles density functional theory (DFT). We proposed six HBLs due to the atomic orientational variations and two of them are found dynamically stable confirmed by phonon dispersion curves. The two stable HBLs, HBL1, and HBL6 also show negative binding energy depicted by the interlayer distance-dependent binding energy curves. Among them, HBL1 has the lowest binding energy, suggesting the exothermic practicability of the material. Electronically both materials show a visible ranged indirect bandgap of ~2.65 (2.69) eV for HBL 1 (HBL6), lowered by ~2 times compared to their intrinsic constituents (2D PtO2, 2D GaN). The bandgaps also have type-II band orientation, which is highly required for efficient spatial carrier separation in photocatalytic water splitting (PWS) applications. The optical properties of the HBLs were also calculated, and it’s found that the HBLs have $\sim 2\times 10 ^{5}{\mathrm {cm}}^{-1} $ of perovskite material-like absorption coefficient in the visible spectrum, a key requirement for efficient photocatalysis. Reflectivity is as low as ~7% in the visible spectrum, suggesting the low-loss nature of the materials. Photocatalytic band-edges with type-II band alignments show sufficient kinetic overpotential for hydrogen evolution reaction (HER) and oxygen evolution reaction (OER) in both HBLs, suggesting effective water-splitting capacity. Moreover, we have explored the biaxial strain-induced tunability of the electronic bandgap, absorption coefficients, and photocatalytic band edges. They all found responsive due to homogeneous biaxial strain and show bandgap-lowering, absorption coefficient visible shifting, and band-edges tuning from compressive to tensile strains in the −6 % to +6% range. These studies suggest that the novel PtO2/GaN vdW layered material can be a probable efficient material for visible-light-driven photocatalytic water-splitting technology.


I. INTRODUCTION
The incremental energy consumption is made globally, causing a detrimental environmental effect as the energy sources The associate editor coordinating the review of this manuscript and approving it for publication was Guijun Li . are mainly from fossil fuels [1]. This leads to CO 2 emission worldwide to the extent that was never before, resulting in serious global warming [2], [3]. An energy alternative, potentially high-efficient, renewable, and facilitated by low-or zero CO 2 -emission is highly demanding to reduce this negative effect. This leads to an eloquently simple concept of hydrogen (H 2 ) fuel production from water using a semiconductor-based splitting mechanism [4], [5]. The core attractiveness of the concept is that harnessing the two-dimensional (2D) semiconductor and layered materials-based photocatalysts, the water can be split into oxygen (O 2 ) and H 2 with zero CO 2 -emission while the traditional biomass-gasification process of H 2 fuel production comes up with CO 2 byproduct [6]. However, finding an efficient photocatalyst is on the search, and many scientists are exploring newer and newer possibilities. In this regard, the key challenge is to seek a material having all the attributes for photocatalytic water splitting (PWS). The attributes are the following: the material must possess (i) suitable bandgap (∼1.23 eV) and band-edges so that the kinetic overpotential become sufficient for hydrolysis, (ii) spatial carrier separation capability and high-surface to volume ratio so that photocatalytic sites can be increased, and (iii) highoptical absorption in the visible or near ultra-violet (NUV) spectrum so that the peak solar irradiations can be utilized. To acquire these features, nanostructured 2D materials are the best candidates as they have suitable band-gap, highsurface to volume ratio, superior carrier mobility, and considerable absorption co-efficient [5], [7]- [9]. The prominent proof regarding it is the first nanostructured (nanoparticle) photocatalysts, TiO 2 outperforms in water splitting with better hydrogen yield than its bulk structure [7], [10]. From these evidences, many 2D materials are coming into the light for PWS application. Among them, a nonmetallic graphenelike C 3 N 4 shows ∼3.2 µmol/h/g of H 2 production at ∼ λ > 420 nm visible lights with ∼10 m 2 /g surface area and ∼2.7 eV near-ultraviolet (NUV) bandgap [9], [11]. It shows almost by ∼35 (∼106 µmol/h/g) times more yields when Pt co-catalysts are added. Bandgap engineered graphene outperforms in this respect almost by ∼100 (∼1050 µmol/h/g) times more yields than the previous one [5]. Besides, 2D transition metal dichalcogenides (TMDs) show a tangible change (∼26000, ∼62000, and ∼2580 µmol/h/g of yields for MoS 2 , MoSe 2 , and WS 2 , correspondingly) in H 2 yields using their self-polarizing properties [5], [12], [13]. However, the spatial carrier separation, another key requirement for PWS cannot be acquired by only 2D materials. Here, comes another alluring concept, vdW stacked layered materials, as with the properties like 2D materials, they also have bandgap tunability due to stacking patterns, spatial carrier separation capability, and superior optical absorption [14], [15]. With the advent of nanotechnology, emergent materials, precisely, graphene, 2D oxides, 2D transition metals dichalcogenides (TMDs), and 2D group III-V are experimentally realized and unleashed the astonishingly unique properties of the materials [12], [16], [17]. As such material is 2D PtO 2 , having superior thermo-mechanical stability with ∼175.78 N/m of mechanical stiffness, two valley bandgap of ∼1.67 eV (PBE), ∼3.15 eV (HSE06), and ∼3.59 eV (GW), superior optical absorption and carrier mobility, is numerously used as substrate material for many-layered materials, hetero-bilayers for photovoltaics and PWS applications [18]. For example, ZnO/PtO 2 vdW hetero-bilayer (HBL), with direct type-II 0.47 eV of bandgap, can be used in photodetector application [19], PtO 2 /MoS 2 vdW HBL with indirect bandgap shows photocatalysis property [20], experimentally synthesized Ni(OH) 2 /PtO 2 nanostructured array show enhanced hydrogen evolution reaction (HER) [21], and PtO 2 based nanoparticle show improved HER [22]. Besides, the PtO 2 based 2D and vdW structures show altering bandgap, enhanced HER, and improved optical absorption. Another promising 2D material, 2D planar GaN with a large ultraviolet (UV) ranged bandgap ∼4.42 eV (GW), and ∼4.18 eV-5.2 eV (experimental) bandgap, high thermal and chemical stability, mechanically robustness (∼108.37 mechanical stiffness and 0.410 Poisson's ratio), self-polarizing capability, and ultra-high carrier mobility makes it available in wide ranges of application namely, photovoltaics, coating material, UV-detector, and dielectric material for nano-transistors [23]- [26]. It is also experimentally realized [24], [27]. Moreover, the vdW concept of 2D GaN is widely used as direct-Z scheme type-II bandgap photocatalysts for water splitting [15], [28]- [30]. Some of the shreds of evidence are compiled in TABLE 1. Among them, 2D GaN stacked with TMDs, and transition metal oxides (TMO) outperforms due to their visible driven PWS capability with cross-plane spatial carrier separation (SCS). Besides, MoS 2 /GaN, phosphorene/GaN, GeC/GaN, BAs/GaN, and BP/GaN are all show tunable electronic, optical properties VOLUME 9, 2021 with tunable PWS band edges due to stacking variations and external perturbation (biaxial strain, and cross-plane electric field) [29], [31]- [33].
However, to our best knowledge, the vdW PtO 2 /GaN hetero-bilayer is not studied yet for the PWS application, though 2D PtO 2 and 2D GaN possess astounding intrinsic and tunable optoelectronic properties. Therefore, in this study, we have introduced the novel vdW PtO 2 /GaN hetero-bilayer with all of its stacking variants and explore the PWS attributes of the materials. Also, to unlock tunability in electronic, optical, and photocatalytic properties, biaxial strain is introduced. These studies suggest that the novel vdW PtO 2 /GaN heterobilayer, with visible ranged bandgap, high-optical absorption, and tunable photocatalytic properties can be a promising material for advanced PWS technology.

II. COMPUTATIONAL METHODOLOGY
For the density functional theory (DFT) calculations, CAmbridge Serial Total Energy Package (CASTEP), an academic opensource version, is used which utilizes a planewave basis set [37]. Electron-ion interactions are described by the norm-conserving pseudopotential (NCP). To predict electronic properties, we initially implemented Perdew-Burke-Erzernhof (PBE) functional with generalized gradient approximation (GGA) exchange-correlation [38]. Conventionally, GGA-PBE exchange-correlation functional predict bandgap underestimated from experimental bandgap of a semiconductor. Heyd-Scusena-Ernzerhof's (HSE 06) nonlocal hybrid functional was introduced to minimize the bandgap problem [39]. Besides, customized meta-GGA (MGGA) functional with 2D PRHG and regularized PBE is utilized to further reduce the deviation between theoretical and experimental bandgap [40]. We have also evaluated the predicted bandgap value with experimental and quasi-particle (QP) bandgap values. The vdW interaction, significant in the stacked HBLs, is defined by semi-empirical Grimme dispersion corrected density functional theory (DFT-D3) [41]. To model the vdW stacked HBLs, a 2 × 2 supercell of 2D PtO 2 and 2D GaN are chosen and oriented in six different ways. For each 2D layer, a 30 Å vacuum slab model is used.
For structural relaxation Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm is used with energy cut-off 800 eV. The energy, stress, force, and displacement tolerance cutoff are 1 × 10 −5 eV/atom, 0.05 GPa, 0.03 eV/Å, and 0.001 Å, correspondingly. The K-points sampling for reciprocal space are 9 × 9 × 1, 15 × 15 × 1, and 30 × 30 × 1 for electronic band structure, projected density of states (PDOS), and optical properties calculations, respectively. For predicting the exothermic feasibility of the stacking, the binding energy is introduced equated by the following equation, where, E heterobilayer is the dispersion corrected total energy of the hetero-bilayer system, and i E i (layer i ) is the sum of the energies of i numbers of 2D layers for stacking the hetero-bilayer. Likewise, the formula used for charge density difference calculation is the following, here, ρ hetrobilayer is the vdW HBL's charge density and i ρ i (layer) is the accumulated charge density of the 2D layer used for vdW stacking. Besides, to predict the dynamical stability of the HBLs, density functional perturbation theory (DFPT) initiated phonon dispersion curves are introduced.
For strain-dependent tunability of the properties, the following equation is applied, where, a s and a u denotes strained and unstrained lattice constants, correspondingly. The e with +ve (−ve) sign signifies the tensile (compressive) strains. For calculating density functional theory (DFT) based dielectric function, ε (ω) = ε 1 (ω) + iε 2 (ω), the complex dielectric constant is evaluated first. Interestingly, a singularity between inter-band transition energies and complex dielectric function is found evaluated by [42], [43], where, e = electronic charge,û = vector defining the polarization of incident filed, = polarization density, r = spatial position, ψ c k and ψ v k = the conduction band (CB) and valence band (VB) wave-function at k respectively. E c k = the conduction band energy, E v k = valance band energy, and E = Fermi energy.
To reveal the exothermic feasibility of the HBLs, the interlayer spacing dependent binding energy is calculated by the following equation, where, E PtO2/GaN HBL = dispersion corrected total energy of the HBL, E GaN = the energy of 2D GaN and E PtO2 = the total energy of 2D PtO 2 . The binding energy curves are shown in Fig.2 (i). The binding energies, respective interlayer distances, optimized lattice constants, and buckling heights, bond lengths are enlisted in   Fig. 3 (a)-(h), (i)   MGGA band structures of the HBLs are also depicted in Fig. 3 (e)-(h). As depicted, the bandgap values are highly receptive in the value due to stacking. The HBL 1 and HBL 6 both have indirect bandgap with almost ∼2 times lowering of the bandgap values from their constituents, facilitating for the PWS application.
To evaluate the photocatalytic water splitting activity of the VdW HBL, the relative band edges are to be calculated.  Fig 3 (j) demonstrates the VBE and CBE for the 2D GaN, 2D PtO 2 , HBL 1, and HBL 6. The relative band-edge positions suggest that VBE is contributed by 2D GaN, and CBE contributed by 2D PtO 2 , outlining the type-II band edge (staggering). At, pH level zero, the standard potential with respect to vacuum for (2H + /H 2 ) reduction and (H 2 O/O 2 ) oxidation potentials are at −4.46 eV, and −5.67 eV energy levels, respectively. In comparison with these reference values, both HBL 1 and HBL 6 have adequate kinetic overpotential for initiating the reduction and oxidation (redox) reactions, facilitating the hydrolysis potentiality. Moreover, the valance band offset (VBO) (conduction band offset (CBO)) is ∼2.25 eV (1.69 eV), high enough to separate the carrier spatially. This high-VBO and CBO thus facilitates the potentiality of the photocatalysis of the water.
For the deep insights, we have evaluated the atomic orbital projected density of states (PDOS) (as shown in Fig. 4 (a), and (b)) so that the band-edge contributing atoms and their orbitals can be revealed. In both HBLs, the CBE is mainly subsidized by the d-orbital of Pt atom of the 2D PtO 2 layer, and the VBE is dominantly donated by p-orbital of N atom of the 2D GaN layer, marking the type-II (staggering) band positions. This finding is also theoretically in line with the relative band-edge calculation mentioned in the previous paragraph. To gain the insights of charge transfer and contributing layers, the charge density difference is shown using, ρ = ρ HBLs − ρ 2D PtO2 − P 2D GaN , where, ρ HBLs is the charge density of HBL, ρ 2D PtO2 is the charge density of 2D PtO 2 and P 2D GaN is the charge density of the 2D GaN. The yellow (green) region refers to the charge depletion (accumulation). In both HBL (Fig 5. (a), (b)), N (O) predominantly depletes (accumulates) the charges. This nature signifies the charge transfer direction from N atoms of 2D GaN to O atoms of 2D PtO 2 . The transfer is also confirmed by the comparative electro-negativities of the atom. As, the O atoms (∼3.44) have higher electro-negativity than N atoms (∼3.04), resulting in the charge transfer from N to O direction.
To find out the effective carrier separation capability, the spatial effective average potential along the cross-plane direction is calculated from the Poison equation. It turns out that 2D PtO 2 has a higher potential than 2D GaN which is reliable with the charge transmission as well. A significant amount of effective potential difference ∼3.25 V is found. A strong electrostatic electric field arises due to the highpotential difference which results in spatially discretizing the charge carriers, operating as anti-recombinant, highly suggestive for photocatalysis applications. To proceed further, we have calculated the electron and hole effective masses of the HBLs and comprising 2D layer from dispersion band theory as summarized in TABLE 3. The values reveal that the electron and hole effective masses are highly responsive to the stacking orientation of the HBLs. However, the HBLs show a low value of effective masses compared with their constituents, suggesting high-carrier mobility in the HBLs. Moreover, effective carrier separation is also suggestive due to the low recombination time as mobility is higher, also confirming the potential of spatial carrier separation and facilitating the PWS.

C. ELECTRONIC PROPERTIES OF HBLS: BIAXIAL STRAIN CONTRIBUTION
Biaxial strain, an intrinsic feature of vdW stacked HBL, arisen from the lattice mismatch is used here to alter the electronic properties. The biaxial strain tuned band structures for HBL l and HBL 6 are shown in Fig. 6 (a), (b). Unstrained HBL 1 shows an indirect bandgap ∼2.65 eV at K (VBM) to M * (CBM). With increasing the compressive strains, the bands at the K point become lower and at the gamma (G) point pushed up, resulting in the bandgap increment from ∼2.65 eV to 2.82 eV at 4% compressive strain. Simultaneously, the conduction band minima (CBM) are shifted toward the G point and pushed down due to the application of compressive strains. This trends also lower the bandgap value at 6% compressive strain and the bandgap becomes ∼2.71 while at 4% compressive strain it is ∼2.82 eV. Tensile strains, on the other hand, push up the band near the K point in the VBM and shift the band in the CBM from M * to M, resulting in the bandgap lowering with the increase of tensile strains. As a whole, both compressive and tensile strains seem to lower the bandgap value. In HBL 6, a similar fashion is observed with compressive and tensile strains. However, the highest bandgap is attained ∼2.87 eV at 4% compressive strain.
To evaluate the band edge tunability due to the biaxial strain, we have calculated the CBE and VBE upon applying biaxial strains as depicted in Fig 7 (a), (b). It is found that  the HBL 1 has sufficient photocatalytic overpotential (PO) up until 4% tensile strain. It has sufficient PO from 6% compressive to 4% tensile strains. The highest PO is attained at 4% compressive strain, and the overpotential for hydrogen evolution reaction (HER) is ∼0.13 eV, and that for oxygen evolution reaction (OER) is ∼1.47 eV. Conversely, the HBL6 has sufficient PO in all the biaxial strains either compressive or tensile in the 6% compressive to 6 % tensile strains range. Again, the highest PO is achieved at 4% compressive strain and the potential for HER (OER) is ∼0.15 eV (1.50 eV). Interestingly, 4% compressive strain the PO, facilitating the visible-light-driven PWS.

D. OPTICAL PROPERTIES AND ITS TUNABILITY UPON BIAXIAL STRAINS
Exploring optical properties and tunability of it is significant to evaluate the key performance of photocatalysts. To do so, we have calculated the core optical properties namely, real and imaginary part of the dielectric function, absorption coefficients, and reflectivity using density functional theory (DFT). The complex and imaginary part of the dielectric functions is calculated for 0 eV to 15 eV of photon energy range as demonstrated in Fig. 8 (a), (b). Amazingly, no negative portion is found within the energy range in the real part of the dielectric function, revealing the semiconducting nature of the HBLs in the energy range. This property signifies the high refraction of light through the HBLs, suggesting higher photocurrent in the HBLs. The imaginary part of the dielectric function shows the nature of the peak in the HBLs. The first peaks are also depicted in the imaginary part of the dielectric function is shown in Fig. 8 (b). The first peaks are at ∼1.8 eV, and ∼2.01 eV for HBL 1, and HBL 6, respectively, denoting the exciton energy of the materials. Both the parts of the dielectric function follow the trend of the dielectric function of 2D PtO 2 in a red-shifted manner, suggesting a strong influence on the HBL's optical property of the substrate material. Static dielectric constant, signifying electric field supporting capability, is also calculated for the HBLs and the constituent 2D layer and the HBLs show higher value compared with the constituents. The values are as following: In HBL 1 ∼2.74, in HBL 6 ∼2.5, in 2D PtO 2 ∼1.8, and in 2D GaN ∼1.45. Clearly, a ∼1.89 times increment of the static dielectric function value upon stacking of the layer, which indicates a significant amount of photo-induced charge supporting capability.
The optical absorption coefficient is also calculated with respect to photon wavelength which signifies the photon conversion efficacy. In our proposed HBLs, ∼10 6 cm −1 of absorption coefficient, 10 times greater than the perovskite materials, is attained at the ultra-violet (UV) photon wavelength, suggesting the material's high-absorption capability of photons [48], [49]. The absorption peaks again follow the trends of 2D PtO 2 in a red-shifted way. The gray lines in the Fig. 8(c), (d) represents solar flux (spectral irradiance), adopted in the curves for pointing out the spectrum range utilizes the most of the solar flux. It turns out that visible VOLUME 9, 2021 and near infrared (NIR) hold most of the solar irradiances. The absorption coefficients and reflectivity values calculated in our work, hence compared and commented with the flux value so that the optical performance improvements of the material can be revealed.
Surprisingly, though both comprising 2D layers have zero absorption coefficient in the visible spectrum, the HBLs have ∼2 × 10 5 cm −1 (at 380 nm) of absorption coefficient, highly recommended for PWS application. To proceed further, the reflectivity of the HBLs is calculated and the highest reflectivity is ∼7% (at 407 nm) in the visible spectrum, significantly low, suggesting the low-loss nature of the materials. These high-absorption and low-reflectivity in the visible spectrum for the HBLs suggest the visible-light-driven PWS capability of the material, as well.
To find the further visible shifting of the absorption coefficients, we have calculated the biaxial strain-dependent absorption coefficients with respect to photon wavelength. The biaxial strain tuned absorption coefficients are shown in Fig 9 (a), (b). In HBL 1, the unstrained absorption peak ∼9×10 5 cm −1 is at 210 nm in the UV range and in the visible range it is 2 × 10 5 cm −1 . Upon applying compressive strains from −2% to −6%, the absorption coefficients are shifted towards the UV spectrum. Interestingly, due to the tensile strains ranges from 2% to +6%, the absorption coefficient is increased by almost ∼2 times in the visible spectrum (from 290 nm to 400 nm), significant for the PWS application. The highest absorption peak achieved in the visible spectrum for HBL 1 is ∼4.1 × 10 5 cm −1 , comparable to perovskite materials. In the HBL 6, the same phenomenon is observed for the absorption co-efficient, precisely, at 6% of tensile strain, the absorption peaks in the visible region appear almost ∼2.1 times more compared with the unstrained condition, emulating high-photocatalytic carrier generations. In the visible spectrum for HBL 6, the tensile strain tuned absorption becomes as high as ∼4.2 × 10 5 cm −1 , predicting enhanced carrier generation probability of HBL 6 compared with HBL 1. Interestingly, in both HBLs, for 6% tensile strain, another absorption peak is arisen at ∼300 nm. This peak is due to the extra inter-band transition states originated by the proximal transition of CBM from M * to M and the bandgap lowering. These values also suggest that within the permissible bandgap and PO range, tensile strains in the HBL6 are more advantageous than in the HBL 1.
Concisely, the key performance factors of a photocatalysts are namely, the highest obtained bandgap, E g , the highest optical absorption attained in the visible spectrum at a specific wavelength, α s , reflectivity, r, photocatalytic overpotential (PO), conduction band offset (CBO), and valance band offset (VBO) are summarized in the TABLE 4 for benchmarking of this PtO 2 /GaN with other 2D GaN (2D PtO 2 ) based vdW HBLs. These values also suggest that the PtO 2 /GaN vdW HBLs can be more potential compared with their constituent layer based vdW HBLs.

IV. CONCLUSION
Harnessing first-principles density functional theory (DFT), we have explored the novel GaN/PtO 2 vdW HBL and its electronic, optical, and photocatalytic water splitting (PWS) capability. Two HBLs, HBL 1, and HBL 6 are found dynamically stable confirmed by phonon dispersion curves. Among them, the HBL 1 shows the lowest binding energy (∼820 meV), suggesting the chemical formation feasibility of the vdW stacking. Both HBLs show visible ranged type-II bandgap. The bandgap becomes biaxial strains responsive in a manner that for both compressive and tensile strain, it tends to lower. However, some anomaly is found at 4% compressive strains due to the CBM-VBM shifting, forming the highest bandgap at this strain (∼2.82 eV for HBL 1, and ∼2.87 eV for HBL 6). The low-effective masses and interlayer effective potential show the spatial carrier separation probability of the HBL. Both the HBLs have sufficient photocatalytic overpotential (PO) for the HER and OER. The overpotentials are also responsive to the biaxial strains and HBL 1 has the permissible strain range is −6 % to +4 % while for HBL 6 it is −6% to + 6%. The optical absorption coefficient in the visible spectrum is ∼2 × 10 5 cm −1 (at ∼380 nm) and the value can be further improved by ∼2 (at ∼383 nm) times upon applying 6% tensile strain, suggesting visible-lightdriven PWS capability. Concisely, the visible ranged type-II bandgap, spatial carrier separation capability, improved visible ranged absorption coefficient and tunability of the properties suggest that the novel GaN/PtO 2 VdW HBL can be a potential visible-light-driven photocatalysts candidate, fulfilling almost all the PWS attributes.