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. 2026 Sep 28;16(45):58084–58096. doi: 10.1039/d6ra07394h

Multifunctional Janus XHfPH (X = S, Se, Te) semiconductors for solar water splitting: a first-principles analysis

Thinh D Tran a,b, Huynh V Phuc c, Le T N Tu c, A A Lavrentyev d, A I Kartamyshev e,f, Tuan V Vu e,f,✉
PMCID: PMC13618333  PMID: 42807954

Abstract

Using first-principles density functional theory, we design and systematically investigate a family of highly stable Janus XHfPH (X = S, Se, Te) monolayers. Comprehensive stability and Raman spectra calculations indicate that these monolayers are theoretically stable and may warrant further investigation toward potential experimental realization. Notably, these monolayers exhibit robust in-plane and out-of-plane piezoelectricity, with SHfPH and TeHfPH showing exceptional promise for nanoscale electromechanical devices. Our calculated results indicate that XHfPH monolayers are semiconductors with moderate indirect bandgaps from 1.07 to 1.57 eV. Furthermore, their intrinsic structural asymmetry generates a built-in electric field that drives efficient spatial separation of photogenerated carriers, enabling favorable band-edge alignment for photocatalytic water splitting. Consequently, SHfPH and SeHfPH achieve impressive theoretical solar-to-hydrogen conversion efficiencies of 10.03% and 9.97%, respectively. These findings establish Janus XHfPH monolayers as highly promising, multifunctional 2D materials for next-generation optoelectronic, piezoelectric, and solar-energy conversion applications.

Using first-principles density functional theory, we design and systematically investigate a family of highly stable Janus XHfPH (X = S, Se, Te) monolayers.graphic file with name d6ra07394h-ga.webp

1. Introduction

Recent advances in 2D materials have opened new opportunities for developing multifunctional devices in nanoelectronics, piezoelectric technologies, optoelectronics, and renewable energy conversion.1–4 Beyond graphene, a wide variety of 2D materials, including transition-metal oxides/chalcogenides,5–7 bismusthene,8 black phosphorous,9 MXenes,10 and antinonene,11 have been discovered both theoretically and experimentally. Among the rapidly expanding family of 2D materials, Janus monolayers have emerged as a particularly attractive class because of their intrinsically asymmetric atomic structures. From centrosymmetric monolayers, Janus materials are formed by replacing one atomic layer with a different chemical species, thereby breaking the out-of-plane mirror symmetry. This structural asymmetry generates an intrinsic electric dipole moment perpendicular to the monolayer plane, producing a built-in electric field that profoundly modifies the electronic structure, charge distribution, optical response, and carrier dynamics.12,13

One of the most appealing consequences of the broken inversion symmetry in Janus materials is the emergence of piezoelectricity in both in-plane and out-of-plane directions, unlike conventional non-Janus monolayers that typically exhibit only in-plane responses. Considerable efforts have been devoted to the exploration of Janus 2D piezoelectric semiconductors for electromechanical applications. Xu et al. theoretically proposed Janus MXY (M = Sb/As, X = Te/Se, and Y = Br/I) monolayers through density functional theory (DFT) simulations, and demonstrated that these materials were indirect-bandgap semiconductors suitable for visible-light absorption. They also exhibited large optical absorption coefficients of approximately 105 cm−1 and strong in-plane/vertical piezoelectric responses, highlighting their promise in piezotronic, photovoltaic, and optoelectronic systems.14 Janus FeGeN3 was reported to be a multifunctional semiconductor with a bandgap of 1.99 eV, intrinsic ferromagnetism, and an out-of-plane piezoelectric coefficient of −0.31 pm V−1. Its strain-enhanced ferromagnetic behavior suggested strong potential for spintronic and magnetoelectric applications.15 Based on first-principles investigations, Guo et al. predicted a family of Janus group-III monochalcogenide monolayers with semiconducting bandgaps of 0.89–2.03 eV and excellent piezoelectric performance. The calculated in-plane piezoelectric coefficient reached 8.47 pm V−1, while out-of-plane coefficients ranged from 0.07 to 0.46 pm V−1. These combined electronic and piezoelectric properties made the proposed monolayers promising candidates for piezotronic and nanoelectromechanical applications.16–19

In addition to the piezoelectric properties, the Janus monolayers have attracted considerable interest as photocatalysts for solar-driven water splitting. The intrinsic built-in electric field induced by structural asymmetry offers a natural mechanism for spatially separating electrons and holes, thereby suppressing carrier recombination and improving photocatalytic efficiency. Many Janus 2D materials have been predicted to exhibit superior photocatalytic activity compared with their symmetric counterparts. For instance, first-principles DFT studies showed that Janus MXY (M = Mo/W; X/Y = S, Se, or Te) transition-metal dichalcogenide monolayers possessed moderate bandgaps of 1.37–1.96 eV, favorable band-edge alignments for water redox reactions, and type-II heterostructures that facilitated efficient charge separation. Besides, their highly anisotropic carrier mobilities indicated excellent charge transport capability, making these MXY Janus materials attractive candidates for photocatalytic, optoelectronic, and nanoelectronic applications.20 MM′XX′ (M, M′ = Ga or In; X, X′ = S, Se, or Te) group-III chalcogenide family proposed by Wang et al. through comprehensive first-principles calculations was another representative example of high-performance Janus photocatalysts.21 These monolayers were found to possess excellent dynamical stability together with moderate semiconducting bandgaps ranging from 0.89 to 2.03 eV. Their band-edge positions satisfied the energetic requirements for overall water splitting, while strong visible-light absorption ensured efficient solar-energy harvesting. In addition, carrier mobilities exceeding 103 cm2 V s−1 indicated outstanding charge transport capability and reduced carrier recombination. As a result of these synergistic properties, the Janus MM′XX′ monolayers achieved a theoretical solar-to-hydrogen conversion efficiency as high as 18.51%, making them attractive candidates for next-generation photocatalytic and solar-energy conversion technologies.21 Using DFT simulations, Peng et al. proposed Janus PtSSe as a stable 2D photocatalyst with excellent thermodynamic, dynamical, and mechanical stability. The monolayer exhibited an indirect bandgap of 2.19 eV, favorable band-edge alignment, efficient carrier separation, and strong visible-light absorption, all of which were beneficial for photocatalytic water splitting. Furthermore, different stacking configurations of PtSSe bilayers were predicted to sustain photocatalytic activity under both visible and infrared-light irradiation, demonstrating their significant potential for solar-energy conversion.22

Inspired by the exceptional multifunctional properties of Janus 2D materials and the growing demand for sustainable hydrogen production, we conduct a comprehensive first-principles investigation on Janus XHfPH (X = S, Se, Te) monolayers to evaluate their potential for photocatalytic water splitting, while simultaneously exploring their mechanical, electronic, piezoelectric, and transport properties. The structural stability of XHfPH is examined through cohesive-energy calculations, phonon dispersion analysis, ab initio molecular dynamics (AIMD), and elastic-constant evaluation. Raman spectra are further calculated. The electronic structures are analyzed using hybrid density functional calculations, while carrier transport properties are evaluated using the AMSET (Ab initio Model for Mobility and Seebeck Coefficient using the Boltzmann Transport equation) formalism by considering multiple carrier-scattering mechanisms. Furthermore, the piezoelectric responses, electrostatic potential, and photocatalytic performance are systematically explored to assess their suitability for renewable-energy applications.

2. Computational methods

First-principles investigations were performed using the framework of DFT implemented in the Vienna Ab Initio Simulation Package (VASP).23,24 The interaction between electrons and ions was described by the projector augmented-wave (PAW) approach.25,26 During structural optimization, atomic coordinates were relaxed until the maximum residual force on each atom was less than 10−3 eV Å−1, and the total energy variation between successive electronic steps was constrained to less than 10−6 eV. The wave functions were expanded using a plane-wave basis with an energy cutoff of 650 eV, and reciprocal-space integration was carried out on a 12 × 12 × 1 Monkhorst–Pack mesh. To accurately model isolated monolayers, a vacuum thickness of 30 Å was applied along the surface-normal direction. Vibrational properties were analyzed by calculating phonon spectra through the finite-displacement technique implemented in PHONOPY27 using a 5 × 5 × 1 supercell. The thermal stability of the optimized XHfPH monolayers was further assessed through ab initio molecular dynamics (AIMD) simulations performed at 300 K for 10 ps using a 5 × 5 × 1 supercell within the NVT ensemble. A time step of 1 fs was employed, and the temperature was maintained at 300 K using a Nosé–Hoover thermostat. Electronic structures were calculated using the Perdew–Burke–Ernzerhof (PBE) generalized gradient approximation28 and the Heyd–Scuseria–Ernzerhof (HSE06) screened hybrid functional.29 Spin–orbit coupling (SOC) was explicitly included self-consistently in the PBE calculations to account for relativistic effects,30 while the HSE06 calculations were performed without SOC. Raman intensities were evaluated from the frequency-dependent macroscopic dielectric tensor.31 The second-order elastic constants together with the piezoelectric response were obtained using density functional perturbation theory (DFPT). Finally, carrier transport was investigated with the AMSET formalism.32 which explicitly considers several intrinsic scattering mechanisms and combines their individual scattering rates through Matthiessen's rule within the relaxation-time approximation.33

3. Results and discussion

3.1. Structural parameters, stability, and vibrational properties

The crystal structures of the SHfPH, SeHfPH, and TeHfPH monolayers are first established and optimized as illustrated in Fig. 1(a). The three XHfPH monolayers crystallize in a hexagonal honeycomb lattice formed by interconnected Hf–X bonds. The side-view configuration reveals a layered sandwich geometry, where two central P and Hf bilayers are enclosed by H and X layers on each side, forming a non-centrosymmetric structure. After full structural relaxation, the lattice constant (a), characteristic bond lengths (dX–Hf, dHf–P and dP–H), and monolayer thickness (Δh) are extracted and tabulated in Table 1. Among the investigated systems, SHfPH possesses the smallest a of 3.66 Å, whereas larger values of 3.71 and 3.87 Å are obtained for SeHfPH and TeHfPH, respectively. A similar increasing trend is observed for the X–Hf bond length (dX–Hf), accompanied by a gradual increase in the monolayer thickness from 4.36 Å for SHfPH to 4.50 Å for SeHfPH and 4.64 Å for TeHfPH. These structural changes originate from the progressively larger atomic radius of the chalcogen site element, increasing from 1.84 Å to 1.98 Å and 2.21 Å, respectively, for S, Se, and Te.34,35

Fig. 1. (a) Top and side views of the atomic structure and (b) charge density difference rendered at an isosurface value of 0.007 e Å−3 for Janus XHfPH (X = S, Se, Te) configurations.

Fig. 1

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Table 1. Lattice constant a (Å), different bond lengths of dX–Hf, dHf–P and dP–H (Å), and thickness of monolayer Δh (Å) of Janus XHfPH monolayers.

a d X–Hf d Hf–P d P–H Δh E coh
SHfPH 3.66 2.53 2.61 1.42 4.36 −5.90
SeHfPH 3.71 2.67 2.60 1.42 4.50 −5.66
TeHfPH 3.87 2.91 2.61 1.43 4.64 −5.39
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The redistribution of electrons in the XHfPH monolayers is examined through charge-density difference calculations. Fig. 1(b) clearly shows that electrons preferentially accumulate around the Hf and P atoms, while depletion regions are concentrated near the H and X atoms. Such charge redistribution reflects the electron-transfer pathway between different atomic species and provides insight into the nature of chemical bonding in these Janus XHfPH monolayers. The asymmetric redistribution of electrons across the two surfaces generates an intrinsic out-of-plane dipole moment, which is expected to play an important role in the piezoelectric and optoelectronic properties of the Janus XHfPH monolayers.

Next, the cohesive energy (Ecoh) is calculated to evaluate the energetic stability of the proposed Janus XHfPH monolayers. A relatively large cohesive energy indicates strong chemical bonding of the constituent atoms and suggests that the structure is energetically favorable. The Ecoh values are typically calculated as follows:

3.1. 1

Here the total energy of the XHfPH configurations is defined as Etot. The energies of the individual atom of X, Hf, P, and H are indicated by EX, EHf, EP, and EH with NX, NHf, NP, and NH representing the exact number of each atom in a single unit cell.

According to the obtained cohesive energies presented in Table 1, the absolute Ecoh value decreases from SHfPH to TeHfPH. Specifically, SHfPH possesses the most negative cohesive energy of −5.90 eV per atom, followed by SeHfPH (−5.66 eV per atom) and TeHfPH (−5.39 eV per atom). These attained results indicate that SHfPH is the energetically most favorable among the three Janus monolayers, which can be related to its shorter X–Hf bond length, leading to stronger chemical bonding. Furthermore, the absolute cohesive energy values of all XHfPH monolayers are considerably larger than those reported for Janus Sb2SeTe2 (−2.93 eV per atom),36 Pd4S3Se3 (4.32 eV per atom),37 and BGaS2 (−5.02 eV per atom),12 suggesting their strong energetic stability and support their potential experimental feasibility.

To verify the structural stability of the XHfPH systems, both dynamical and thermal stability analyses are conducted. The phonon dispersions shown in Fig. 2(a) reveal twelve vibrational branches for each monolayer, corresponding to three acoustic and nine optical modes arising from the four atoms in the primitive cell. The complete absence of imaginary phonon frequencies throughout the Brillouin zone indicates that the proposed SHfPH, SeHfPH, and TeHfPH structures are dynamically stable. Their thermal stability is further evaluated by performing AIMD simulations at 300 K over a period of 10 ps. As depicted in Fig. 2(b), the total energies remain nearly unchanged except for small thermal fluctuations. The final configurations obtained after the AIMD simulations show that the atomic arrangements are well preserved, without any evidence of bond dissociation or noticeable structural deformation. These results demonstrate the excellent thermal robustness of the Janus XHfPH monolayers. From a synthetic perspective, the successful fabrication of similar asymmetric 2D materials, such as Janus MoSSe6,38 and MoSH,39via plasma-assisted atom substitution, and surface hydrogenation provides a realistic experimental roadmap. Consequently, XHfPH could be synthesized by growing XHfP-based precursor sheets via chemical vapor peposition (CVD) followed by controlled hydrogen plasma treatment to selectively passivate the phosphorus layer while preserving the opposing chalcogen face.

Fig. 2. (a) Calculated phonon dispersion curves and (b) evolution of the total energy during AIMD simulations at 300 K for the XHfPH structures.

Fig. 2

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Additionally, the Raman spectra of the XHfPH monolayers are calculated to investigate their vibrational characteristics. As Raman spectroscopy is directly associated with lattice vibrations, it provides important information about phonon behavior, chemical bonding, and interatomic interactions. The Raman-active modes, including both in-plane and out-of-plane vibrations, are closely related to the mechanical, thermal, and electronic properties of the monolayers. Besides, the Raman peak frequencies and relative intensities serve as characteristic signatures of the materials. The symmetry analysis predicts that the optical phonons at the Γ point of XHfPH monolayers are composed of four non-degenerate (A1) modes and four doubly degenerate (E) modes. Consequently, the irreducible representation of the Raman active optical modes is:

Γoptical = 4E + 4A1. 2

The attained Raman spectra are displayed in Fig. 3. Although all three monolayers share the same symmetry-allowed Raman-active modes, TeHfPH exhibits a greater number of clearly resolved peaks due to larger mode separation and distinct intensities. In all three monolayer, the most intense Raman peak corresponds to the A1 mode, appearing at approximately 350 cm−1 in SHfPH, 327 cm−1 in SeHfPH, and 178 cm−1 in TeHfPH. As the X atom changes from S to Te, this A1 mode gradually shifts toward lower frequencies. Besides, TeHfPH exhibits high intensity peaks corresponding to the E and A1 modes located near 545 and 2297 cm−1, respectively.

Fig. 3. Raman spectra of Janus XHfPH monolayers.

Fig. 3

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3.2. Mechanical and piezoelectric properties

The elastic properties of the XHfPH monolayers are examined to understand their mechanical behavior under external strain. Elastic constants are determined by fitting the total energy variations obtained from applied in-plane strains between −1.5% and 1.5%.40 Owing to the hexagonal symmetry of the XHfPH monolayers, the elastic constants satisfy the relations C22 Created by potrace 1.16, written by Peter Selinger 2001-2019 C11 and C66 = (C11 − C12)/2, leaving only C11 and C12 as independent parameters. The calculated elastic constants, summarized in Table 2, are all positive. Among the three systems, SHfPH exhibits the highest in-plane stiffness with C11, C12, and C66 values of 73.50, 30.19, and 21.65 N m−1, respectively. These values decrease to 68.57, 28.57, and 20.00 N m−1 for SeHfPH, and further to 61.93, 26.50, and 17.72 N m−1 for TeHfPH. This trend is also attributed to the progressive weakening of the X–Hf bond associated with the increasing atomic radius from S to Te. Moreover, all SHfPH, SeHfPH, and TeHfPH monolayers satisfy the Born–Huang mechanical stability criterion (C11 > |C12| and C66 > 0),41,42 confirming their mechanical stability.

Table 2. Elastic coefficient Cij, Young's modulus Y2D, Poisson's ratio ν2D, and piezoelectric stress/strain coefficients e11, e31, d11, d31 of Janus XHfPH configurations.

C 11 (N m−1) C 12 (N m−1) C 66 (N m−1) Y 2D (N m−1) ν e 11 10−10 C m−1 e 31 10−10 C m−1 d 11 (pm V−1) d 31 (pm V−1)
SHfPH 73.50 30.19 21.65 61.10 0.41 −0.95 −0.10 −2.18 −0.10
SeHfPH 68.57 28.57 20.00 56.67 0.42 −0.29 −0.02 −0.73 −0.03
TeHfPH 61.93 26.50 17.72 50.59 0.43 0.38 0.10 1.07 0.11
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The in-plane stiffness of the XHfPH monolayers is evaluated by calculating the 2D Young's modulus (Y2D) from the elastic constants according to:

3.2. 3

The resulting Young's moduli are 61.10, 56.67, and 50.59 N m−1 for SHfPH, SeHfPH, and TeHfPH, respectively, as summarized in Table 2. Due to the hexagonal crystal symmetry, all three XHfPH monolayers exhibit isotropic in-plane elastic behavior. A gradual decrease in Y2D value is observed from SHfPH to TeHfPH, which can be referred to the increase in dX–Hf bond length and the corresponding reduction in bond stiffness. As a result, SeHfPH and TeHfPH materials exhibit lower in-plane stiffness than SHfPH. Although, the Young's modulus values of the proposed XHfPH configurations are lower than that of conventional 2D nanostructures, including graphene (336 N m−1),43 MoS2 (180 N m−1),44 and MoSi2P4 (203 N m−1),45 they remain comparable to those of several 2D materials reported in the literature such as Al2TeSe (59.38 N m−1), Pb2PAs (43.21 N m−1),46 SnSeNH (68.27 N m−1),47 and Pd4S3Se3 (36.20 N m−1).37 The relatively low in-plane stiffness suggests mechanical flexibility, making these XHfPH materials promising candidates for wearable and flexible devices.

The transverse mechanical response of the XHfPH monolayers is quantified by evaluating the 2D Poisson's ratio, defined as:

3.2. 4

The calculated Poisson's ratios are 0.41 for SHfPH, 0.42 for SeHfPH, and 0.43 for TeHfPH as listed in Table 2. These values are relatively large compared with those of reported 2D MoS2 (ν2D = 0.25),48 ZrSeTe (ν2D = 0.26),49 and Al2SO (ν2D = 0.25)46 materials. This implies that the XHfPH monolayers exhibit considerable transverse deformation when subjected to uniaxial tensile loading. These characteristics are advantageous for flexible nanoelectronics and strain-tunable devices.

Moreover, the piezoelectric performance of the XHfPH monolayers is subsequently investigated to assess their suitability for nanoscale electromechanical applications. In non-centrosymmetric crystals, an applied mechanical strain breaks the equilibrium charge distribution, leading to the generation of spontaneous electric polarization. This strain-induced polarization underlies the piezoelectric effect, which enables reversible conversion between mechanical and electrical energy. Following the first-principles approach proposed by Duerloo et al.,40 the piezoelectric response of the XHfPH monolayers is evaluated by calculating the piezoelectric stress (eijk) and strain (dijk) tensors. These coefficients are obtained from the polarization variation induced by external strain according to the following expressions:16

3.2. 5
3.2. 6

In these equations, σjk and εjk denote the components of the stress and strain tensors, respectively, while the indices (i, j, k) identify the Cartesian directions (x, y, z). It should be noted that in the DFT calculations, the 2D materials are modeled using a three-dimensional supercell with a vacuum layer. To obtain the intrinsic piezoelectric response of the isolated XHfPH monolayers, the three-dimensional piezoelectric coefficients are rescaled according to e2Dij = z × e3Dij where z is the out-of-plane lattice parameter of the supercell. This conversion removes the vacuum contribution and enable direct comparison with other 2D materials.

After obtaining the piezoelectric stress coefficients (eij), the corresponding piezoelectric strain coefficients (dij) are determined through the relationship between piezoelectric and elastic tensors as follows:16

3.2. 7
3.2. 8

The calculated piezoelectric coefficients, summarized in Table 2, demonstrate that the XHfPH monolayers possess high electromechanical properties. The in-plane piezoelectric strain coefficients (d11) are predicted to be −2.18 pm V−1 for SHfPH, −0.73 pm V−1 for SeHfPH, and 1.07 pm V−1 for TeHfPH. These values are higher than those reported of 2D piezoelectric materials, including GaO (d11 = 0.41 pm V−1),50 CrSI (d11 = 0.28 pm V−1),51 and h-BN (d11 = 0.60 pm V−1).40 Another important feature is the presence of out-of-plane piezoelectricity. The calculated d31 coefficient reaches 0.11 pm V−1 in the TeHfPH system, which is considerably larger than those reported for 2D Ga2SSe (0.07 pm V−1)16 and MoSiGeN4 (−0.014 pm V−1)52 materials. The coexistence of in-plane and out-of-plane piezoelectric responses makes the XHfPH monolayers promising candidates for piezoelectric sensors and mechanical energy-harvesting technologies.

3.3. Electronic properties

The electronic properties of the XHfPH monolayers are systematically investigated using the PBE framework. The corresponding band structures are presented in Fig. 4. The calculation results reveal that all three XHfPH monolayers are indirect bandgap semiconductors. At the PBE level, SHfPH exhibits a bandgap energy of 0.87 eV with the valence band maximum (VBM) located at the Γ point and the conduction band minimum (CBM) at the M point. The SeHfPH and TeHfPH show lower bandgaps of 0.86 and 0.46 eV, respectively, as listed in Table 3. To obtain more reliable electronic bandgaps, the HSE06 hybrid functional is further employed. Although the overall band dispersions remain nearly identical to those predicted by PBE, the bandgap values increase, as expected from the improved description of exchange interactions. Importantly, the indirect bandgap semiconductor behavior of the three XHfPH monolayers is preserved. The calculated HSE06 bandgaps are 1.55, 1.57, and 1.07 eV for SHfPH, SeHfPH, and TeHfPH, respectively. These HSE06 bandgaps indicate that the proposed XHfPH monolayers are moderate-bandgap semiconductors for next-generation nanoelectronic and optoelectronic devices.

Fig. 4. Electronic band structures of the XHfPH systems calculated using (a) the PBE/HSE06 functionals and (b) the PBE approach including SOC.

Fig. 4

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Table 3. Band-gap energies Eg computed using the PBE, HSE06, and PBE + SOC approaches, along with the valence-band spin splitting λv at the K point, work functions for the H/X surfaces ΦH/ΦX and vacuum level difference ΔΦ of XHfPH monolayers. All values are in eV.

E PBE E PBE+SOC E HSE06 λ v Φ H Φ X ΔΦ
SHfPH 0.87 0.85 1.55 0.29 4.78 5.58 0.80
SeHfPH 0.86 0.78 1.57 0.31 4.78 5.56 0.78
TeHfPH 0.46 0.28 1.07 0.33 4.42 5.19 0.77
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Moreover, spin–orbit coupling is incorporated into the band structure calculations. SOC plays a crucial role in 2D materials containing heavy elements because it lifts spin degeneracy and modifies the band dispersion through relativistic spin–orbital interactions. The PBE + SOC electronic band structures of the XHfPH monolayers are displayed in Fig. 4(b). It can be observed that the overall band curves remain nearly unchanged, SOC influences the electronic states near the band-edges. In particular, the bandgap decreases after including SOC, giving values of 0.85 eV for SHfPH, 0.78 eV for SeHfPH, and 0.28 eV for TeHfPH, respectively (Table 3). The reduction becomes more significant with increasing atomic number of the chalcogen atoms, reflecting the enhanced relativistic effects associated with heavier elements. An important effect of SOC is the removal of spin degeneracy, which produces spin splitting in the valence bands of all three XHfPH monolayers. The calculated valence-band spin splitting energies (λv) around the K point are 0.29, 0.31, and 0.33 eV for SHfPH, SeHfPH, and TeHfPH, respectively.

To gain insight into the electronic band formation, the weighted band structures of the SHfPH, SeHfPH, and TeHfPH monolayers are calculated using the PBE functional. The results, presented in Fig. 5, show that the XHfPH monolayers possess very similar orbital distributions throughout their electronic bands. The valence band is dominantly composed of the Hf-d, X-p and P-p orbitals. At higher energies, the p orbital of X and P atoms also slightly contribute to the conduction bands. In contrast, the CBM is mainly derived from the Hf-d orbital. Meanwhile, the remaining Hf-s, Hf-p, X-s, P-s, and H-s orbitals give only a small contribution to the electronic band structures.

Fig. 5. Weighted band structures of Janus (a) SHfPH, (b) SeHfPH and (c) TeHfPH systems.

Fig. 5

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3.4. Transport properties

Furthermore, the carrier transport properties of the XHfPH systems are explored to evaluate their potential for high-performance nanoelectronic devices. The carrier mobility (µ), which quantifies the ability of charge carriers to move through a crystal under an applied electric field, serves as a key indicator of transport efficiency. The carrier mobility calculations are performed using the AMSET package.32 Compared with the widely used deformation-potential model, AMSET provides a more realistic description of carrier transport by accounting for multiple scattering mechanisms. In particular, polar optical phonon (POP), acoustic deformation potential (ADP), piezoelectric (PIE), and ionized impurity (IMP) scatterings are considered simultaneously, enabling a comprehensive evaluation of the factors governing carrier relaxation in the XHfPH monolayers. The individual scattering rates are subsequently combined through Matthiessen's rule33 to determine the overall carrier mobility according to:

3.4. 9

where µADP, µIMP, µPIE, and µPOP denote the carrier mobilities associated with the four dominant scattering mechanisms of ADP, IMP, PIE, and POP scatterings, respectively.

In this work, carrier concentrations of 1 × 1016 and 1 × 1020 cm−3 are selected to represent the low and high doping limits, respectively. The calculated electron (µe) and hole (µh) mobilities of the Janus XHfPH, together with the individual contribution from different scatterings, are presented in Fig. 6 and 7. At the lower carrier concentration of 1 × 1016 cm−3, the electron and hole transports are found to be governed primarily by ADP scattering for all three XHfPH monolayers (Fig. 6). This effect indicates a strong interaction between carrier charges and acoustic deformation potential in these Janus XHfPH systems. In comparison, the contributions from POP and PIE scatterings are smaller and the IMP scattering exhibits only a weak temperature dependence, especially at high temperatures. As summarized in Table 4, among the investigated structures, TeHfPH exhibits the highest room-temperature µe of 2.61 cm2 V s−1 at a carrier concentration of 1 × 1016 cm−3. The corresponding electron mobilities of SHfPH and SeHfPH are calculated to be 0.39 and 0.89 cm2 V s−1, respectively. This low electron mobility is in good agreement with the flat band feature at the conduction band minimum, as illustrated in Fig. 4. A similar trend is observed for the hole transport; the µh value of TeHfPH (0.84 cm2 V s−1) is higher than that of SHfPH (0.51 cm2 V s−1) and SeHfPH (0.59 cm2 V s−1) monolayers.

Fig. 6. Electron (a) and hole (b) mobilities versus temperature in Janus XHfPH monolayers at a carrier concentration of 1 × 1016 cm−3, accounting for multiple scattering mechanisms.

Fig. 6

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Fig. 7. Electron (a) and hole (b) mobilities versus temperature in Janus XHfPH monolayers at a carrier concentration of 1 × 1020 cm−3, accounting for multiple scattering mechanisms.

Fig. 7

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Table 4. Room-temperature carrier mobilities of the Janus XHfPH systems, including contributions from individual phonon scattering mechanisms and the corresponding total mobilities.

Carrier concentration (cm−3) Compound µ ADP (cm2 V s−1) µ IMP (cm2 V s−1) µ PIE (cm2 V s−1) µ POP (cm2 V s−1) µ total (cm2 V s−1)
Electron n c = 1 × 1016 SHfPH 0.40 829.00 19.80 23.20 0.39
SeHfPH 0.95 995.00 39.90 23.10 0.89
TeHfPH 2.89 2320.00 82.20 39.90 2.61
n c = 1 × 1020 SHfPH 0.40 17.30 22.40 17.60 0.38
SeHfPH 0.97 23.70 46.50 17.20 0.87
TeHfPH 3.01 33.80 105.00 29.90 2.47
Hole n c = 1 × 1016 SHfPH 0.54 322.00 18.70 21.70 0.51
SeHfPH 0.62 398.00 41.50 17.30 0.59
TeHfPH 0.86 898.00 295.00 31.30 0.84
n c = 1 × 1020 SHfPH 0.59 12.00 22.50 13.50 0.52
SeHfPH 0.71 14.40 59.00 11.60 0.63
TeHfPH 1.02 20.20 759.00 20.50 0.93
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The carrier transport behavior at a high carrier concentration of 1 × 1020 cm−3 is presented in Fig. 7. Similar to the low-concentration case, both electron and hole mobilities decrease progressively with increasing temperature because enhanced lattice vibrations intensify carrier scattering. However, the relative importance of the individual scattering mechanisms changes slightly with carrier concentration. In particular, the POP and PIE scatterings give weaker contributions to the overall carrier mobility, whereas IMP scattering contributes more significantly. The ADP scattering remains an important mobility-limiting mechanism throughout the investigated temperature range. Consequently, the carrier transport at high doping levels of 1 × 1020 cm−3 is still mainly governed by the effect of ADP scattering. At 300 K, the calculated electron mobilities are 0.38 cm2 V s−1 for SHfPH, 0.87 cm2 V s−1 for SeHfPH, and 2.47 cm2 V s−1 for TeHfPH. Among the XHfPH materials, TeHfPH also exhibits the highest hole mobility of 0.93 cm2 V s−1. The µh values of SHfPH and SeHfPH are lower of 0.52 and 0.63 cm2 V s−1, respectively. The consistently higher electron mobility for both low and high carrier concentrations in SeHfPH and TeHfPH suggests that electron transport is energetically more favorable than hole transport in these systems. Overall, the carrier mobilities of the XHfPH monolayers are lower than those reported for 2D semiconductors such as MoTe2, T-SnS2, and GeS.33,53 This relatively modest transport performance can be attributed to the strong carrier scattering inherent to the Janus structures. The broken out-of-plane mirror symmetry enhances electron–phonon interactions and introduces additional piezoelectric scattering channels. These competing scattering mechanisms collectively limit carrier transport despite the favorable electronic structure of the XHfPH monolayers.54

3.5. Photocatalytic properties

Finally, the photocatalytic potential of the XHfPH Janus monolayers for overall water splitting is evaluated by analyzing their electronic band structures and band-edge alignments. Photocatalytic water splitting involves two half-reactions, namely the hydrogen evolution reaction (HER), 2H+ + 2e− → H2, and the oxygen evolution reaction (OER), expressed as Inline graphic. For a semiconductor to function as an efficient photocatalyst, two fundamental requirements must be fulfilled. First, its bandgap should exceed the thermodynamic minimum of 1.23 eV while remaining sufficiently narrow to harvest a significant fraction of visible sunlight. Second, the conduction and valence band-edges must appropriately straddle the redox potentials of water so that photogenerated electrons and holes possess enough driving force to promote the HER and OER simultaneously. At pH = 0, this requires the CBM to be higher than the H+/H2 reduction potential (−4.44 eV) and the VBM to be lower than the O2/H2O oxidation potential (−5.67 eV).

Owing to the asymmetric atomic configuration of the Janus XHfPH monolayers, the two opposite surfaces possess distinct chemical environments and electronegativities, resulting in different vacuum levels on the two sides of the monolayers. To characterize the surface electronic properties of the Janus XHfPH monolayers, their work functions Φ, which represent the minimum energy required to remove an electron from the Fermi level (EF) to the vacuum level (Evac), are calculated. This Φ value is an important parameter for evaluating electron emission, interfacial charge transfer, and contact formation in electronic systems. Based on the planar-averaged electrostatic potential, the work function is determined as: Φ = Evac − EF. The calculated electrostatic potential profiles, including dipole correction, are presented in Fig. 8(a). It is easy to observe that the ΦX on the X surface is consistently higher than that of the H surface (ΦH), implying that electron emission is energetically less favorable from the X terminated surface. As summarized in Table 3, ΦH value ranges from 4.42 to 4.78 eV, whereas ΦX varies between 5.19 and 5.58 eV. The work-function difference ΔΦ provides a quantitative measure of the intrinsic surface potential asymmetry. As the chalcogen X element changes from S to Te, ΔΦ decreases slightly from 0.80 eV for SHfPH to 0.78 eV for SeHfPH and further to 0.77 eV for TeHfPH. This trend originates from the gradual reduction in electronegativity difference between the two surfaces, which weakens the built-in electric field. Accordingly, SHfPH exhibits the largest surface potential difference because sulfur possesses the highest electronegativity among these three considered chalcogen elements. The same evolution of the work-function difference has also been reported for the Janus MoSiX3H and WBAsX2 monolayers.55,56 The pronounced work-function asymmetry predicted for the XHfPH monolayers is expected to facilitate directional charge separation and carrier transfer across the two surfaces.

Fig. 8. Electrostatic potentials of XHfPH monolayers (a), optical absorption coefficients of XHfPH monolayers (b), and band alignments with standard oxidation/reduction potentials at pH = 0 of SHfPH and SeHfPH for water splitting.

Fig. 8

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Because light absorption plays a crucial role in driving photocatalytic reactions, the optical absorption spectra were first calculated to assess the light-harvesting capability of the materials, followed by a systematic investigation of their photocatalytic properties. The optical absorption coefficients can be calculated as57,58

3.5. 10

where ε2(ω) represents the imaginary part of the dielectric function and ε1(ω) is the real part which is derived from ε2(ω) using the Kramers–Kronig relation.59

The calculated optical absorption coefficients along the xx-direction of Janus XHfPH monolayers are shown in Fig. 8(b). It can be seen that the Janus XHfPH monolayers demonstrate strong optical absorption within the visible and ultraviolet light regions. The firsr absorption peak of these monolayers appears at around 1.8 eV in the visible light region. It suggests that these materials can efficiently utilize solar energy, making them highly promising candidates for visible-light-driven photocatalytic applications.

Improving energy-conversion efficiency is a primary objective in the development of solar-driven photocatalytic water splitting. The theoretical solar-to-hydrogen (STH) efficiency can be determined through the light-absorption efficiency ηabs and the carrier utilization efficiency ηcu. We assume a 100% absorption efficiency for incident photons with energies equal to or greater than the band gap. The total uncorrected STH efficiency ηSTH is defined as:60

ηSTH = ηabs × ηcu. 11

Here, the light-absorption efficiency ηabs can be written as60

3.5. 12

where Eg is the band gap of the photocatalyst, P(hω) is the photon energy flux of the standard AM1.5 G solar spectrum, and hω is the incident photon energy.

The efficiency of carrier utilization is given by:60

3.5. 13

where ΔG denotes the Gibbs free-energy change of 1.23 eV required for water splitting, and E represents the photon energy that can be effectively utilized to drive the water-splitting reaction.

During photocatalytic water splitting, the intrinsic electric field performs positive work to facilitate electron–hole separation. Consequently, this energetic contribution must be incorporated into the total energy. The corrected STH efficiency Inline graphic for 2D Janus materials featuring a vertical intrinsic electric field is thus calculated as:60

3.5. 14

where ΔΦ is the vacuum level difference on the two surfaces of the studied Janus materials.

As presented in Table 3, TeHfPH possesses a relatively narrow bandgap of 1.07 eV, which is insufficient to satisfy the thermodynamic energy requirement for overall water splitting, as the minimum bandgap must exceed 1.23 eV to provide adequate free energy for both the HER and OER. Therefore, only the photocatalytic performance of SHfPH and SeHfPH is further evaluated by aligning their absolute band-edge positions with the water redox potentials under pH = 0. The band-edge energies are referenced to the vacuum level based on the calculated electrostatic potentials of the two nonequivalent surfaces. As shown in Fig. 8(b), the two opposite surfaces exhibit distinct photocatalytic behaviors owing to the intrinsic structural asymmetry of the Janus SHfPH and SeHfPH configurations. For SHfPH monolayer, the band-edges referenced to the H surface satisfy the reduction requirement, as its CBM at −4.04 eV is sufficiently negative to drive the HER. Meanwhile, the VBM on the S surface at −6.40 eV is favorably positioned for the OER. It is similar for SeHfPH, where the H surface exhibits suitable band-edge alignment for HER, while the VBM on Se surface satisfies the OER requirement. Consequently, the CBM on H side and the VBM on S/Se sides of SHfPH and SeHfPH, respectively, together meet the thermodynamic requirements for overall water splitting at pH = 0. Therefore, SHfPH and SeHfPH are predicted to be promising bifunctional photocatalysts for overall water splitting. These findings demonstrate that the intrinsic polarity of Janus monolayers offers an effective strategy for designing high-performance photocatalysts that utilize visible solar energy.

Efficient photocatalytic water splitting requires not only strong absorption of solar radiation but also effective utilization of the generated charge carriers. The calculated electronic structures show that SHfPH and SeHfPH possess moderate HSE06 bandgaps of 1.55 and 1.57 eV, making them capable of absorbing a significant fraction of visible light. Accordingly, these two materials exhibit high carrier utilization efficiencies of more than 44% as listed in Table 5. Such strong carrier utilization is comparable to that of 2D photocatalytic materials, including In2S3 and Al2Se3.60 Thus, the high solar-to-hydrogen (STH) efficiencies of 10.03 and 9.97% are obtained for SHfPH and SeHfPH systems, respectively. Overall, the combination of broad-spectrum light harvesting, efficient intrinsic charge separation, and high predicted STH efficiency highlights the Janus SHfPH and SeHfPH monolayers as promising candidates for next-generation photocatalytic water splitting as well as optoelectronic and solar-energy conversion devices.

Table 5. Overpotentials χ(H2) and χ(O2), light absorption efficiency ηabs, carrier utilization ηcu, STH efficiency ηSTH and corrected STH efficiency Inline graphic.

χ(H2) χ(O2) η abs (%) η cu (%) η STH (%) graphic file with name d6ra07394h-t16.jpg
SHfPH 1.20 0.73 22.66 44.24 10.03 9.41
SeHfPH 1.14 0.77 22.55 44.21 9.97 9.37
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4. Conclusion

In conclusion, we have designed and systematically characterized a family of Janus XHfPH monolayers using first-principles DFT. Comprehensive stability analyses demonstrate that the XHfPH systems are energetically, dynamically, thermally, and mechanically stable for experimental synthesis. Their Raman spectra further provide distinct vibrational signatures that may facilitate future experimental identification. The coexistence of strong in-plane and out-of-plane piezoelectricity, particularly in SHfPH and TeHfPH, highlights the potential of these monolayers for piezoelectric and electromechanical devices. The calculated electronic structures reveal indirect-bandgap semiconducting behavior with bandgap energies ranging from 1.07 to 1.57 eV. In particular, SHfPH and SeHfPH possess a suitable bandgap for efficient visible-light harvesting while maintaining the thermodynamic driving force required for photocatalytic water splitting. Carrier mobility calculations indicate that electron transport is considerably more efficient than hole transport in the SeHfPH and TeHfPH systems. Finally, the intrinsic out-of-plane polarization associated with the Janus structure creates a substantial surface potential difference that promotes favorable band-edge alignment and facilitates charge separation. Consequently, SHfPH and SeHfPH achieve impressive theoretical solar-to-hydrogen conversion efficiencies of 10.03 and 9.97%, respectively. Combined with their suitable electronic structures, these features make SHfPH and SeHfPH attractive candidates for highly efficient solar-driven hydrogen evolution, while also offering considerable promise for future optoelectronic and renewable-energy conversion systems.

Conflicts of interest

There are no conflicts of interest to declare.

Data availability

The data that support the findings of this study are available from the authors upon reasonable request.

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Data Availability Statement

The data that support the findings of this study are available from the authors upon reasonable request.

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