
==== Front
Sci Rep
Sci Rep
Scientific Reports
2045-2322
Nature Publishing Group UK London

72757
10.1038/s41598-024-72757-6
Article
Photocatalytic water splitting and charge carrier dynamics of Janus PtSSe/ζ-phosphorene heterostructure
Chauhan Poonam
Kumar Ashok ashokphy@cup.edu.in

https://ror.org/02kknsa06 grid.428366.d 0000 0004 1773 9952 Department of Physics, Central University of Punjab, VPO Ghudda, Bathinda, 151401 India
16 9 2024
16 9 2024
2024
14 2161826 6 2024
10 9 2024
© The Author(s) 2024
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
On the basis of first-principles calculations and non-adiabatic molecular dynamics (NAMD) simulations, we explore the photocatalytic water splitting properties of PtSSe/ζ-Phosphorene heterostructure. This heterostructure possess semiconducting nature with high carrier mobility (≈ 103 cm2V− 1s− 1). The calculated high value of electron-hole recombination rate as compared to electron transfer rate and hole transfer rate, establish the Type-II mechanism more favorable for PtSSe/ζ-Phosphorene heterostructure. Further, the calculated value of solar-to-hydrogen (STH) conversion efficiency of PtSSe/ζ-Phosphorene exceeds to 10%, which makes it the potential candidate for commercial production of hydrogen for industrial use. STH conversion efficiency is further tunable on rotating one monolayer over other with specific angles in the heterostructure. Our study demonstrates PtSSe/ζ-Phosphorene heterostructure to be efficient Type II-scheme photocatalyst for water splitting.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-024-72757-6.

Subject terms

Materials science
Physics
http://dx.doi.org/10.13039/501100001843 Science and Engineering Research Board EEQ/2022/000047-C issue-copyright-statement© Springer Nature Limited 2024
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pmcIntroduction

The photocatalysts materials gathered researcher’s attention due to their stupendous ability to breakdown water by utilizing solar energy and produce hydrogen with pollution-free zero by-products1. Due to superior physical and chemical properties of two-dimensional (2D) monolayer materials, they act as potential candidates for photocatalytic water splitting2–4. The high carrier’s recombination rate and narrow optical absorption, limits the use of 2D materials as photocatalyst for water splitting5, however, the 2D van der Waals heterostructures (vdWHs) can overcome the limitation of 2D monolayers for water splitting6–8.

To evaluate the staggered arrangement of valance band maximum (VBM) and conduction band minimum (CBM) of each monolayers in conjunction with the built-in electric field (EF) in vdWHs, the two photocatalytic mechanisms namely Type-II9 and Z-scheme10 are implemented in the heterostructures. The accumulation of electrons and holes on different monolayer surface of heterostructures results in reduction and oxidation reaction of water splitting for both Type-II and Z-scheme, however, the charge transfer pathways remains different for these mechanisms9. Both the mechanisms possess excellent carrier utilization capability; however, Type-II is limited by low redox ability. Thus Z-scheme is preferred over Type-II for the high redox ability and high solar-to-hydrogen (STH) conversion efficiency11.

The presence of EF in the heterostructure and non-adiabatic coupling (NAC) of photogenerated charge carriers are the key parameters that influence the STH conversion efficiency of heterostructure photocatalysts12. The presence of EF in the heterostructure provide additional degree of freedom to tailor the photocatalytic properties of photocatalyst materials13,14. Stronger the NAC between the interface photogenerated charge carriers, more rapidly the charge carriers combine that results into a decrease in the STH conversion efficiency. The NAC effect in vdWHs is demonstrated in previous studies15–19. Also, the different stacking patterns significantly affects the NAC between the charge carriers20,21.

The experimental synthesis 2D Janus PtSSe monolayer22 and tendency of occurring phosphorene in a variety of allotropic forms23–25 motivated to investigate the Janus PtSSe/ζ-Phosphorene heterostructure. Due to difference in the electronegativity of surface atoms in Janus PtSSe, an intrinsic electric field get induced which is beneficial to improve photocatalytic water splitting properties26. Besides Janus PtSSe monolayer, the α- and β-phosphorene synthesized experimentally23,24 and the various stable allotropes such as γ, δ, ζ, red, hexa and ψ-phosphorene are predicted using density functional theory25.

However, the phosphorene is thermodynamically less stable as comparison to its oxide (P2O5) or phosphates. The stability of these compounds can be attributed to the strong P = O bonds in P2O5 and the robust P-O bonds in phosphates27. Also, the weak van der Waals forces between phosphorene layers make it prone to structural instability28. The phosphorene stability is also affected by environmental conditions such as moisture and oxygen that accelerates its degradation28. Despite of that the stability of phosphorene is enhanced by various methods such as chemical functionalization, doping with metals, and creating 2D heterostructures29. These modifications can enhance both the stability and catalytic activity of phosphorene for water splitting29. Under different ambient condition, various oxide configuration of phosphorene are stable27. Also, the van der Waals substrate and vertical electric field significantly enhance the stability of phosphorene by suppressing oxidation30.

Despite of that, the ζ- phase of phosphorene which is dynamically and thermally stable31, has not been much explored. Herein, various stacking patterns of the heterostructure of Janus PtSSe with ζ-phosphorene are considered, out of which energetically most stable configuration of heterostructure is adopted for further study. The thermal stability of the heterostructure is confirmed using ab initio molecular dynamics (AIMD) simulations. Non-adiabatic molecular dynamics (NAMD) simulations32, are adopted to estimate the electron transfer, hole transfer and recombination rate of photogenerated charge carriers. Gibbs free energy profiles are obtained to evaluate hydrogen evolution reaction (HER) and oxygen evolution reaction (OER) on the surface of vdWHs. Also, the experimental and theoretical feasibility of rotation of one monolayer over other monolayer at large angles33–35, we inspect the effect of specific rotation on the electronic properties and STH conversion efficiency of PtSSe/ ζ-phosphorene heterostructures is also demonstrated.

Computational details

All the simulations of PtSSe/ζ-Phosphorene heterostructure are performed using Vienna ab initio simulation package (VASP)36,37. To include electrons and ions interactions, we used projected augmented-wave (PAW) potentials, while generalized gradient approximation (GGA) parameterized by Perdew-Burke-Ernzerhof (PBE) has been implemented to calculate exchange-correlation functionals38. The electronic band structure and bands alignments are also obtained using HSE06 hybrid functional. The structures were relaxed until the Hellmann-Feynman forces decrease below 0.01 eV/Å. The energy convergence criteria between sequential steps for structural relaxation was fixed at 10− 5 eV. For the sampling of the Brillouin zone, the Γ-centred k-mesh of 12 × 12 × 1 has been implemented39. A vacuum of ~ 25 Å is used to exterminate the interactions between neighbouring images along perpendicular direction. To model the vdW interactions between the monolayers in heterostructures, DFT-D3 method40 was implemented in the calculations. AIMD simulations controlled by Nose-Hoover thermostat41,42 under NVT ensemble were performed using 3 × 3 × 1 supercell up to 5 ps with time step of 3 fs. For the optical absorption spectra, 32 × 32 × 1 k-point grid was used in the calculations. NAMD simulations were performed within decoherence-induced surface hopping (DISH) method as implemented in Hefei-NAMD package43. We sampled 4000 trajectories for the simulation in DISH method. We also included the solvent effect in Gibbs free energy calculations. The rotation of one layer over other in heterostructure is demonstrated using the method proposed by Lazic et al.44. The number of atoms in the calculations corresponding to 40, 80 and 120 rotation are 220, 170 and 186, respectively. The information about the calculations of excitonic binding energy, Gibbs free energy and STH conversion efficiency is provided in ESI.

Results and discussion

The Janus PtSSe monolayer possess trigonal structure with hexagonal unit cell, while ζ-phosphorene possess the rectangular unit cell. Their lattice parameters (a = b = 3.66 Å for PtSSe; and a = 6.40 Å and b = 5.25 Å for ζ-Phosphorene) are consistent with the literature45–47. The AIMD simulations confirm their thermodynamic stability as depicted in Fig. S1. Both PtSSe and ζ-Phosphorene monolayers are indirect bandgap semiconductor having bandgap value of 1.52 eV and 1.20 eV, respectively (Fig. S2), which are also consistent with literature47,48. Furthermore, the average electrostatic potential curves of these monolayers are depicted in Fig. S3.

Next, a Janus PtSSe/ζ-Phosphorene heterostructure is generated in rectangular unit cell (Fig. 1 (a) and Fig. S4 (a)) having 34 atoms with minimal lattice mismatch (along a = 1.84% and along b = 4.23%). The lattice parameter of heterostructure unit cell is: a = 6.59 Å and b = 11.41 Å. Seven different types of stacking patterns of PtSSe/ζ-Phosphorene heterostructure are considered, out of which AA stacking is more stable as depicted in Fig. S5. Therefore, AA-stacked heterostructure is considered for further study. The interlayer distance of most stable stacked heterostructure is calculated to be 2.96 Å and 3.25 Å corresponding to S-side and Se-side of PtSSe contacting ζ-Phosphorene. To determine the energetically stability of PtSSe/ζ-Phosphorene heterostructure, the binding energy is calculated as: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{E}}_{\text{b}}={\text{E}}_{\text{P}\text{t}\text{S}\text{S}\text{e}/{\upzeta}-\text{P}\text{h}\text{o}\text{s}\text{p}\text{h}\text{o}\text{r}\text{e}\text{n}\text{e}}-({\text{E}}_{\text{P}\text{t}\text{S}\text{S}\text{e}}+{\text{E}}_{{\upzeta}-\text{P}\text{h}\text{o}\text{s}\text{p}\text{h}\text{o}\text{r}\text{e}\text{n}\text{e}})$$\end{document}; where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{E}}_{\text{P}\text{t}\text{S}\text{S}\text{e}/{\upzeta}-\text{P}\text{h}\text{o}\text{s}\text{p}\text{h}\text{o}\text{r}\text{e}\text{n}\text{e}}$$\end{document}, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{E}}_{\text{P}\text{t}\text{S}\text{S}\text{e}}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{E}}_{{\upzeta}-\text{P}\text{h}\text{o}\text{s}\text{p}\text{h}\text{o}\text{r}\text{e}\text{n}\text{e}}$$\end{document} are the total energy of PtSSe/ζ-Phosphorene heterostructure, PtSSe monolayer and ζ-Phosphorene monolayer, respectively. The binding energy of PtSSe/ζ-Phosphorene heterostructure is calculated to be -23.82 meV/Å2 and − 22.66 meV/ Å2 corresponding to S-side and Se-side contacting ζ-Phosphorene, which is comparable with most common vdW crystals graphite (-12 meV/Å2)49 and MoS2 (-26 meV/Å2)50, which indicates that PtSSe/ζ-Phosphorene heterostructure is dominated by the vdW interactions. The electrostatic potential difference between two surfaces of PtSSe/ζ-Phosphorene heterostructures is obtained to be 0.5 eV and a charge of 0.028 electron/atom is accumulated around the Se atom of PtSSe (Fig. S6).

Fig. 1 (a) Structure (top view and side view) and (b)AIMD simulation curves representing the fluctuation of energy with time step along with initial and final structure corresponding to Se-side contacting ζ-Phosphorene of PtSSe/ζ-Phosphorene heterostructure.

Furthermore, the mechanical stability of vdWH is quantified by computing Young’s modulus (Y2D), Poisson ratio (ν), and elastic constants (Cij). PtSSe/ζ-Phosphorene heterostructure satisfies the Born and Huang requirements (C11 (= 94.71 N/m) > |C12| (= 25.03 N/m) and C66 = (C11 − C12 ) /2 > 0)51, confirming its mechanical stability. The calculated value of Youngs modulus of PtSSe/ζ-Phosphorene heterostructure is 88.07 N/m. The Poisson ratio (ν = 0.25) indicates PtSSe/ζ-Phosphorene heterostructure to be brittle in nature according to Frantsevich rule (ν < 1 /3)52. Next, the thermal stability of vdWH is determined by AIMD simulations as depicted in Fig. 1 (b) and Fig. S4 (b). The fluctuation of temperature and energy is around a constant value of temperature and energy w.r.t. the time steps. The initial and final structure of heterostructure is maintained without any distortion along with nearly the same interlayer distance of vdWH.

Next, the electronic structure is obtained at HSE06 level of theory and the calculated value of bandgap is 0.67 eV and 0.80 eV corresponding to S-side and Se-side contacting ζ-Phosphorene as shown in Fig. S7. Now, we implement Z-scheme and Type-II mechanism53 to investigate the band alignment of PtSSe/ζ-Phosphorene heterostructure for photocatalytic water splitting. In Z-scheme mechanism, the recombination of photogenerated charge carriers takes place at upper VBM and lower CBM in vdWH as depicted in Fig. 2 and Fig. S8 corresponding to Se-side and S-side, respectively. The VBM of ζ-Phosphorene and CBM of PtSSe properly engulf the redox potential of water and recombination of charge carriers takes place in between the VBM of PtSSe and CBM of ζ-Phosphorene. While in Type-II mechanism, the electron transfer takes place in between higher CBM to lower CBM and transfer of holes takes place in between lower VBM to higher VBM (Fig. 2 and Fig. S8).

Fig. 2 Band alignments of PtSSe/ζ-Phosphorene heterostructure within (a) Z-scheme and (b) traditional Type-II mechanism at HSE06 level of theory corresponding to Se-side of PtSSe contacting ζ-Phosphorene. The VBM and CBM of PtSSe and ζ-Phosphorene monolayers are shifted by vacuum potential. The orange dashed lines correspond to water redox potential and E is built-in electric field in heterostructure.

In order to evaluate the different charge transfer pathways, interlayer transfer of electrons and holes are investigated by utilizing NAMD simulations and evaluating the time-dependent Kohn-Sham (TDKS) equation at different time T corresponding to Kohn-Sham (KS) orbitals, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\uppsi}}_{\text{E}}(\text{r},\text{T})$$\end{document}, as43:1 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\uppsi}}_{\text{E}}\left(\text{r},\text{T}\right)=\sum\limits_{\text{k}}{\text{C}}_{\text{k}}\left(\text{T}\right){{\upphi}}_{\text{k}}\left(\text{r},\text{R}\left(\text{T}\right)\right)$$\end{document}

The electron transfer, hole transfer and electron-hole recombination at VBM, CBM and VBM-CBM interface is represented by 1, 2 and 3 in KS orbital plot (Fig. 3). The photogenerated charge carriers recombination rate depends upon decoherence time (DT) and NAC43. The calculated value of decoherence time is 19.67 fs. Lesser the decoherence time, higher is the carrier’s recombination rate. Further, the NAC of charge carriers is evaluated as:2 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{d}}_{\text{x}\text{y}}=\left\langle{{\uppsi}}_{\text{x}} \left|\frac{\partial}{\partial\text{t}} \right|{{\uppsi}}_{\text{y}}\right\rangle=\frac{\left\langle{{\uppsi}}_{\text{x}}|{\nabla}_{\text{r}}\text{H}|{{\uppsi}}_{\text{y}}\right\rangle}{{{\upvarepsilon}}_{\text{y}}-{{\upvarepsilon}}_{\text{x}}}\dot{\text{r}}$$\end{document}

where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\dot{\text{r}}$$\end{document} is the velocity of the nuclei. NACs is calculated by electron-phonon coupling elements (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle {{\uppsi}}_{\text{x}}|{\nabla}_{\text{r}}\text{H}|{{\uppsi}}_{\text{y}}\rangle$$\end{document}), the energy gap (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\upvarepsilon}}_{\text{y}}-{{\upvarepsilon}}_{\text{x}}$$\end{document}) and velocity (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\dot{\text{r}}$$\end{document}). The calculated value of NAC for electron-hole recombination (7.38 meV) is higher than the electron transfer (5.35 meV) and hole transfer (2.02 meV), that may lead to the high electron-hole recombination rate. The similar trend of NAC is also appeared in CrS3/GeSe15 and Sc2Cl2/Hf2CO210 heterostructures.

Fig. 3 (a) Kohn-sham energy orbitals, (b) average energy, (c) dephasing time and (d) non-adiabatic coupling (NAC) corresponding to Se-side contacting ζ-Phosphorene of PtSSe/ζ-Phosphorene heterostructure. In KS-Orbital energy plots, the blue and red energy levels correspond to the PtSSe and ζ-Phosphorene, respectively. 1, 2 and 3 in Kohn-Sham energy levels represent the electron transfer, hole transfer and electron-hole recombination.

Next, we calculate the electron transfer rate, hole transfer rate and electron-hole recombination rate by employing DISH algorithm to include the effect of quantum coherence in the calculations54,55. The electron-hole recombination rate (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\uptau}$$\end{document}) for the full exponential decay process is formulated as56:3 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text{P}\left(\text{T}\right)=\text{exp}\left(\frac{-\text{T}}{{\uptau}}\right)$$\end{document}

The calculated value of electron transfer and holes transfer rate is 12.23 ps (Fig. 4 (a)) and 32.21 ps (Fig. 4 (b)), respectively. The recombination of VBM of PtSSe and CBM of ζ-phosphorene takes place in 48.16 ps as depicted in Fig. 4 (c), which is higher than CrS3/GeSe (6.24 ps) and15 copper-nickle sulphide/ g-C3N4 (36.9 ps) heterostructures57. The results of NAMD simulations suggest that electron transfer and holes transfer are much faster than electron-hole recombination, which suggests that PtSSe/ζ-phosphorene heterostructure follows traditional Type-II mechanism for water splitting12,58,59.

Fig. 4 (a) Electron transfer rate, (b) hole transfer rate and (c) recombination rate corresponding to Se-side of Janus PtSSe contacting ζ-Phosphorene in PtSSe/ζ-Phosphorene heterostructure.

Next, the charge carrier mobility is calculated to explore the migration capability of charge carriers using deformation potential theory60,61:4 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\upmu_{\text{c}}=\frac{\text{e}{{\hslash}}^{3}{\text{C}}^{2\text{D}}}{{\text{K}}_{\text{B}}\text{T}\text{m}{\text{m}}^{{*}}{\text{E}}_{\text{d}}^{2}}$$\end{document}

where µc represents the carrier mobility, m is the effective mass, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{C}}^{2\text{D}}$$\end{document} is the elastic modulus and Ed is the deformation potential. The calculated value of electrons mobility comes out to be 103 cm2V− 1s− 1. Note that the carrier mobility of ζ-Phosphorene and Janus PtSSe monolayers is calculated to be 102 cm2V− 1s− 1 (Table S1). The details of carrier mobility calculations are given in ESI (Fig. S9 and Table S1).

Further to investigate the light harvesting ability of PtSSe/ζ-Phosphorene, the optical absorbance spectra is calculated from the imaginary part of the dielectric function as62,63:5 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text{A}\left({\upomega}\right)=\frac{{\upomega}}{\text{c}}\text{L}{\varepsilon}_{imaginery}\left({\upomega}\right)$$\end{document}

Where, L is the length of unit cell in Z-direction. From the computed optical absorption spectra of heterostructure and monolayers, it is observed that the first most prominent peak lies in the visible region (Fig. S10). Also, the PtSSe/ζ-Phosphorene heterostructure possess low value of excitonic binding energy as compare to monolayers of Janus PtSSe and ζ-Phosphorene, which is favorable factor for spatial separation of charge carriers. The detailed calculation of excitonic binding energy is provided in ESI.

Next, the stability of PtSSe/ζ-Phosphorene heterostructure photocatalyst in aqueous solution is accessed by calculating thermodynamic oxidation (Фox) and reduction potential (Фre) using the method proposed by Chen and Wang64. The calculated value of reduction (oxidation) potential − 1.29 eV (3.61 eV) is higher (lower) than the reduction potential of H+/H2 (oxidation potential O2/H2O), that indicates the stability of PtSSe/ζ-Phosphorene heterostructure in the aqueous solution. The detailed discussion of calculation of oxidation and reduction potential is provided in ESI.

Furthermore, the feasibility of adsorption of water molecule on the heterostructure surfaces is accessed by calculating water adsorption energy as:\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{E}}_{\text{a}\text{d}\text{s}\text{o}\text{r}\text{p}\text{t}\text{i}\text{o}\text{n}}={\text{E}}_{{*}{\text{H}}_{2}\text{O}}-{\text{E}}_{{*}}-{\text{E}}_{{\text{H}}_{2}\text{O}}$$\end{document}. The calculated value of adsorption energy is ≈ -0.5 eV. The negative value adsorption energy indicates the feasibility of adsorption of water molecules on the surfaces of PtSSe/ζ-Phosphorene heterostructure. The atomic adsorption models of water molecule on different surfaces of heterostructure are shown in Fig. S11.

Next, to access the feasibility of the oxidation and reduction half reactions for water splitting on PtSSe/ζ-Phosphorene heterostructure surfaces, the Gibbs free energy profile are obtained using the method proposed by Nørskov et al.65 The details of the calculations of Gibbs free energy is provided in ESI (Table S2). The potential for the photogenerated electrons (holes) was obtained by the difference between the potential of CBM (VBM) and the reduction potential of water at HSE06 level of theory. The computed values of photogenerated electron potential and holes potential corresponding to Se-side contacting ζ-Phosphorene in heterostructure for Type-II scheme (Z-scheme) are 0.68 eV (0.66 eV) and 1.66 eV (1.71 eV), respectively (Figs. 5 and 6). On the other hand, the computed values of photogenerated electron potential and holes potential corresponding to S-side contacting ζ-Phosphorene in heterostructure for Type-II scheme (Z-scheme) are 0.67 eV (0.64 eV) and 1.65 eV (1.69 eV), respectively (Fig. S12).

For the spontaneous process of HER to occur on the Se-side of PtSSe contacting ζ-Phosphorene in heterostructure surface required an extra potential of 1.09 eV and 1.13 eV for Type-II and Z-scheme mechanism, respectively. Further, for spontaneous OER processes, an extra potential of 1.17 eV and 1.08 eV is required in Type-II and Z-scheme mechanism (Figs. 5 and 6), respectively. The required extra OER potential for PtSSe/ζ-Phosphorene is lower than β-PtSSe (1.27 eV)66, GaAs (1.39 eV)67 and g-C3N4 (1.45 eV)68.

Next, the STH conversion efficiency of PtSSe/ζ-Phosphorene heterostructure photocatalyst for type-II mechanism is calculated as:696 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\upeta}}_{\text{S}\text{T}\text{H}}^{{\prime}}=\frac{{\Delta}\text{G}{\int}_{\text{E}}^{{\infty}}\frac{\text{E}\left({\hslash}{\upomega}\right)}{{\hslash}{\upomega}}\text{d}\left({\hslash}{\upomega}\right)}{{\int}_{0}^{{\infty}}\text{E}\left({\hslash}{\upomega}\right)\text{d}\left({\hslash}{\upomega}\right)+{\Delta}\text{V}{\int}_{{\text{E}}_{\text{g}}}^{{\infty}}\frac{\text{E}\left({\hslash}{\upomega}\right)}{{\hslash}{\upomega}}\text{d}\left({\hslash}{\upomega}\right)}$$\end{document}

Fig. 5 The reaction pathways and Gibbs free energy profiles of HER and OER for the Z-scheme corresponding to Se-side contacting ζ-Phosphorene in PtSSe/ζ-Phosphorene heterostructure. Color code: white sphere = H-atom; red sphere = O-atom, Green sphere = Se-atom, Yellow sphere = S-atom and silver sphere = Pt atom and dark grey sphere = P-atom, respectively). The violet and sky blue lines specify the circumstances in the absence and presence of light irradiation (at the potential of photogenerated carriers), respectively, while the orange lines represent the situation with required external potentials.

Fig. 6 Gibbs free energy profiles of (a) HER and (b) OER for Se-side contacting PtSSe/ζ-Phosphorene heterostructure in Type-II scheme. Color code: white sphere = H-atom; red sphere = O-atom, Green sphere = Se-atom, Yellow sphere = S-atom and silver sphere = Pt atom and dark grey sphere = P-atom, respectively). The violet and sky blue lines specify the circumstances in the absence and presence of light irradiation (at the potential of photogenerated carriers), respectively, while the orange lines represent the situation with required external potentials.

The STH conversion efficiency of PtSSe/ζ-Phosphorene heterostructure photocatalyst for Z-scheme is calculated as:707 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\upeta}}_{\text{S}\text{T}\text{H}}^{{\prime}}=\frac{1}{2}\frac{{\Delta}\text{G}{\int}_{\text{E}}^{{\infty}}\frac{\text{E}\left({\hslash}{\upomega}\right)}{{\hslash}{\upomega}}\text{d}\left({\hslash}{\upomega}\right)}{{\int}_{0}^{{\infty}}\text{E}\left({\hslash}{\upomega}\right)\text{d}\left({\hslash}{\upomega}\right)+{\Delta}\text{V}{\int}_{{\text{E}}_{\text{g}}}^{{\infty}}\frac{\text{E}\left({\hslash}{\upomega}\right)}{{\hslash}{\upomega}}\text{d}\left({\hslash}{\upomega}\right)}$$\end{document}

Where, Eg is the larger of the bandgap of monolayer projected in heterostructure and E is the energy of photon utilized to proceed water splitting mechanism feasible. The details of the STH calculations are given in ESI. The calculated value of STH conversion efficiency for Se-side and S-side contacting ζ-Phosphorene in PtSSe/ζ-Phosphorene heterostructure for Type- II mechanism is 24.86% and 23.96%, respectively, whereas for the Z-scheme mechanism it is calculated to be 12.43% and 11.98%, respectively.

Next, we study the role of rotation of one monolayer over other in heterostructure, on the electronic band structure and band alignments. The one monolayer over other in the heterostructure is rotated at 40, 80 and 120. The top view and side view of heterostructure at different rotation is shown in Fig. S13. Further the thermodynamic stability of these heterostructures are demonstrated in the terms of AIMD simulations in NVT ensemble. The smaller fluctuation of temperature around a constant level with respect to time steps confirms their thermal stability as depicted in Fig. S14. The atomic configuration of these monolayers remains undistorted after heating systems at 300 K.

The electrostatic potential energy difference of PtSSe and ζ-Phosphorene decreases as the different angle of rotation as depicted in Fig. S15 and the 0.028 electron/atom, 0.035 electron/atom and 0.31 electron/atom charge accumulated around Se atom, respectively at 40, 80 and 120 rotations. The electronic band structure at different rotation angle is shown in Fig. S16 and Table S3. Due to change in the bandgap value, the corresponding change in the VBM and CBM of Janus PtSSe, ζ-Phosphorene and PtSSe/ζ-Phosphorene heterostructure is observed. PtSSe/ζ-Phosphorene heterostructure at different angle of rotation shows proper band alignment for water splitting as depicted in Fig. S17. The photogenerated potential for electron (Ue) and holes (Uh) at different angle of rotations illustrated in Table S4. The photogenerated potential of holes are higher than electron potential. The conduction band offsets of PtSSe and ζ-Phosphorene modifies on rotation, that results into change in the STH conversion efficiency of heterostructure.

Conclusions

In summary, we designed the thermally stable PtSSe/ζ-Phosphorene heterostructure for efficient photocatalytic water splitting. PtSSe/ζ-Phosphorene possess suitable band alignment for water splitting with high carrier mobility (≈ 103 cm2V− 1s− 1). Moreover, the most prominent peak of optical absorption spectra lies in visible region. The calculated value of recombination, electron transfer and holes transfer rate of photogenerated charge carrier is 48.16 ps, 12.23 ps and 32.21 ps, respectively. The higher value of electron-hole transfer rate as compared to the electron-transfer and hole-transfer suggested Type-II scheme mechanism more suitable for PtSSe/ζ-Phosphorene heterostructure. The STH conversion efficiency is further tunable with rotation of one layer over other in the heterostructures. Our study demonstrates that PtSSe/ζ-Phosphorene heterostructure is potential candidate for photocatalytic water splitting.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary Material 1

Acknowledgements

This work is supported by the funding from DST-SERB (EEQ/2022/000047), Government of India. The results presented in this work were obtained using the computational resources at the Department of Physics at the Central University of Punjab. Helpful discussion with Jaspreet, Gokul and Favas is highly acknowledged.

Author contributions

P.C. performed the calculations and written original draft. A.K. supervised the work and review and edit the manuscript.

Data availability

All data generated or analysed during this study are included in this published article [and its supplementary information files].

Declarations

Competing interests

The authors declare no competing interests.

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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