Vibrational behaviors, piezoelectricity, spin-splitting, and carrier mobility in Janus HWSZ (Z = N, P, As) monolayers

Abstract

Janus two-dimensional (2D) materials provide a versatile platform for symmetry-driven physics. However, the influence of surface functionalization on their intrinsic properties remains an open question. In this Letter, we propose and systematically investigate a class of Janus materials formed by the one-side hydrogenation of the Janus WSZ (Z = N, P, As) or HWSZ monolayers using first-principles density functional theory. Asymmetric hydrogenation acts as an additional symmetry-breaking mechanism, markedly reshaping the band structure and strengthening spin–orbit coupling. This transition yields a robust spin splitting up to 0.46 eV, highlighting the role of surface functionalization in engineering giant spin-dependent characteristics. Furthermore, the intrinsic vertical dipole induces a significant out-of-plane piezoelectric response, with the d₃₁ coefficient reaching 0.31 pm V⁻¹. In particular, we evaluate the electron mobility by explicitly incorporating multiple phonon scattering mechanisms to identify the fundamental transport limits.

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1 Introduction

The emergence of two-dimensional (2D) Janus materials has revolutionized the field of low-dimensional physics by breaking out-of-plane structural symmetry.^1,2 This intrinsic asymmetry produces a built-in dipole moment that enhances piezoelectric responses, enables sizable spin splitting, and accelerates carrier separation.^3,4 As a result, Janus systems exhibit properties that are fundamentally inaccessible in their centrosymmetric counterparts, making them attractive for next-generation nanoelectronic and optoelectronic devices.^5–7 Beyond their intrinsic characteristics, external modification strategies further expand the tunability of these materials. Among them, surface functionalization, particularly hydrogenation, has emerged as a powerful approach for modulating electronic phases, tailoring band structures, and even inducing magnetic behavior in 2D lattices.^8,9

Although surface hydrogenation has been extensively investigated in symmetric monolayers such as graphene¹⁰ and goldene,⁶ its application to inherently asymmetric Janus structures introduces an additional and highly versatile degree of control. In symmetric systems, hydrogenation primarily modifies local bonding and opens band gaps; however, in Janus monolayers, it also interacts with the pre-existing intrinsic dipole field. By selectively hydrogenating one surface of a Janus structure, one can effectively tune the magnitude and direction of the internal electric field, thereby altering charge redistribution and interlayer potential gradients. This selective functionalization can significantly influence spin–orbit coupling (SOC), leading to enhanced Rashba-type spin splitting and enabling precise control over spin textures. Furthermore, hydrogen-induced modifications may stabilize new electronic or magnetic phases that are otherwise absent in pristine Janus materials. The coupling between chemical functionalization and structural asymmetry thus provides a rich platform for engineering material responses at the atomic scale. Consequently, the interplay between intrinsic Janus asymmetry and hydrogenation offers a highly flexible and controllable pathway for designing multifunctional materials with tailored electronic, transport, and spintronic properties, paving the way for innovative applications in quantum devices and energy technologies.

This study proposes and systematically investigates a class of functionalized 2D Janus systems, namely one-side hydrogenated Janus WSZ (Z = N, P, As) or HWSZ monolayers. Hydrogenation of an existing Janus material to create a new Janus structure represents a promising approach for exploring novel physical properties. Using density functional theory (DFT), we explore how the precise introduction of hydrogen on a specific Janus surface acts as a secondary symmetry-breaking mechanism. Beyond simple surface passivization, this asymmetric hydrogenation modulates the intrinsic dipole moment of the WSZ template, providing a unique pathway to engineer its electronic band alignment. Our analysis focuses on the resulting modification of the electronic structure, vibrational behaviors, spin-dependent properties, and transport characteristics that arise from the interplay between the Janus-intrinsic field and hydrogen-induced perturbations. We primarily investigate the electronic properties of these monolayers, focusing on SOC-induced spin splitting and the emergence of out-of-plane piezoelectricity. A key aspect of this study is the rigorous evaluation of carrier mobility, carried out by explicitly incorporating multiple scattering mechanisms in order to elucidate the intrinsic limits of charge transport.

2 Computational details

First-principles calculations were carried out using the Vienna Ab initio Simulation Package (VASP). The projector augmented-wave (PAW) method^11,12 was employed to describe the core–valence interaction, and an energy cutoff of 650 eV was adopted for the plane-wave expansion. Electronic structures were evaluated using the Perdew–Burke–Ernzerhof (PBE)¹³ and the hybrid Heyd–Scuseria–Ernzerhof (HSE06)¹⁴ functionals. Further, spin–orbit coupling (SOC) was taken into consideration throughout the self-consistent electronic structure calculations.¹⁵ Brillouin zone sampling employed a 12 × 12 × 1 Γ-centered k-mesh, with convergence thresholds of 10⁻⁶ eV for energy and 10⁻³ eV Å⁻¹ for forces. A 25 Å vacuum layer and dipole-layer corrections were applied to eliminate periodic image interactions in the asymmetric Janus monolayers. Structural and thermal stabilities were verified via PHONOPY¹⁶ with 5 × 5 × 1 supercell and AIMD simulations at 300 K. Elastic and piezoelectric constants were derived using density functional perturbation theory (DFPT), while Raman spectra were calculated from the macroscopic dielectric tensor.¹⁷ Carrier transport was modeled using AMSET package,¹⁸ which accounts for multiple scattering mechanisms under the relaxation time approximation and integrates them via Matthiessen's rule.¹⁹

3 Results and discussion

The crystal structures of the proposed Janus HWSZ (Z = N, P, As) monolayers are shown in Fig. 1. The unit cell of HWSZ contains four atoms, consisting of one H, one W, one S, and one Z atom. Due to inherent vertical structural asymmetry, HWSZ crystallizes in the P3m1 space group. Structural optimization reveals that the in-plane lattice constants increase from 3.04 to 3.31 Å as the pnictogen elements changing from N to As. The calculated lattice constants and other structural parameters of the proposed Janus materials are summarized in Table 1.

Fig. 1 Crystal structures (a and b) and electron localization function (c) of 2D Janus HWSZ (Z = N, P, As) monolayers. In the electron localization function maps, blue and red are used to represent charge depletion and charge accumulation, respectively.

Table 1 Lattice constants a (Å), bond lengths d (Å), monolayer thicknesses Δh (Å), cohesive energies E_coh (eV per atom), and Bader charge analysis results q(e), vacuum level difference ΔΦ (eV), and work functions Φ_H,S (eV) of Janus HWSZ (Z = N, P, As) monolayers

	a	dS–W	dW–Z	dZ–H	Δh	Ecoh	qW	qH	qS	qZ	ΔΦ	ΦH	ΦS
HWSN	3.04	2.38	2.10	1.03	3.78	−7.38	−1.217	0.024	0.370	0.823	2.70	2.70	5.40
HWSP	3.26	2.43	2.39	1.42	4.43	−6.57	−0.812	0.519	0.473	−0.180	2.20	2.99	5.19
HWSAs	3.31	2.44	2.48	1.52	4.60	−6.18	−0.586	0.485	0.466	−0.365	2.29	3.03	5.32

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To assess the structural stability of Janus HWSZ monolayers, the cohesive energy E_coh was calculated first. This analysis is crucial for identifying viable candidates for experimental synthesis. The cohesive energy is defined by the following expression:

where E_tot represents the total energy of the Janus WHSZ monolayer, while E_i and N_i (i = H, W, S, Z) denote the energies of the isolated constituent atoms and their corresponding counts within the unit cell, respectively.

It is demonstrated that the obtained values of the cohesive energy for HWSN, HWSP, and HWSAs monolayers are −7.38, −6.57, and −6.18 eV, respectively. As a primary indicator of atomic bonding strength, a more negative cohesive energy signifies enhanced thermodynamic stability and stronger chemical bonds. Such significantly negative values indicate that these Janus monolayers are not only energetically favorable but also characterized by strong chemical bonds, ensuring their structural and thermodynamic stability. Further, to elucidate the chemical bonding in the Janus HWSZ monolayers, we also performed a Bader charge analysis to quantify charge transfer among atoms. Owing to the structural asymmetry and electronegativity differences, this analysis is crucial for understanding the origin of the internal dipole moment. The Bader charge analysis results for all three Janus structures are presented in Table 1. It is evident that the W atoms lose a significant amount of charge across all three structures. This is attributed to the fact that the electronegativity of W is considerably lower than that of S and N, and only marginally higher than that of P and As (W bonded to S and Z = N, P, As). In the case of Z = N, namely HWSN monolayer, charge strongly accumulates around the N atoms due to its high electronegativity. In contrast, the pnictogen elements P and As act as charge donors in the cases of HWSP and HWSAs owing to their lower electronegativity relative to the surrounding atoms. The calculated electron localization function of the studied structures are also provided in Fig. 1. The asymmetric charge transfer inherent in Janus configurations induces an intrinsic dipole moment across the layer, creating a shift in vacuum levels within the electrostatic potential. To gain deeper insight, we analyzed the planar-averaged electrostatic potential, as shown in Fig. 2, to evaluate the difference between the vacuum levels and determine the corresponding work functions of the Janus monolayers. A pronounced difference in vacuum levels exists between the two surfaces, with values of 2.70, 2.20, and 2.29 eV for HWSN, HWSP, and HWSAs monolayers, respectively,as listed in Table 1. The work function Φ, defined from the Fermi level E_F and the vacuum level E_vac according to Φ = E_vac − E_F, varies across the two surfaces. As shown in Table 1, the work function at the S-terminated surface Φ_S is significantly larger than at the H-terminated surface Φ_H, indicating that electrons can be more easily extracted from the H-terminated face.

Fig. 2 Planar-averaged electrostatic potentials of 2D Janus HWSN (a), HWSP (b), and HWSAs (c) monolayers.

To thoroughly evaluate the dynamic behavior and thermal stability of the investigated structures, AIMD simulations were executed at a constant room temperature over a trajectory of 10 ps. As illustrated in Fig. 3, the evolution of the total energy displays merely marginal variations, confined to a narrow energetic window of around 0.5 eV over the entire simulated timeframe. This steady energetic profile strongly implies that the atomic configurations continuously oscillate around their local thermodynamic minima without escaping the equilibrium state. Crucially, a detailed examination of the final atomic coordinates demonstrates that the proposed structures perfectly maintain their intrinsic lattice integrity. Also, there are no observable indications of critical failures such as bond breaking, surface reconstruction, or spontaneous transition into alternate structural phases. Ultimately, this combination of conserved atomic topology and steady thermodynamic parameters unequivocally confirms the excellent thermal durability of these materials under ambient environmental conditions, highlighting their potential for room-temperature device integration.

Fig. 3 Time-dependent total energy variations during room-temperature AIMD simulations of HWSZ (Z = N, P, As) monolayers. The insets within panels illustrate the final snapshots of the crystal structures at the end of the simulation.

Next, we calculate the phonon dispersion spectra of the materials to evaluate their vibrational behaviors and, specifically, to assess their dynamical stability. Fig. 4(a) displays the phonon spectra of HWSZ, which consists of 12 phonon branches: three acoustic branches in the low-frequency region and nine optical branches at higher frequencies. A significant gap is observed within the optical vibration region, which can be attributed to the contrast in atomic sizes between the constituent elements (specifically between H and the other components). Most importantly, the absence of imaginary modes throughout the Brillouin zone confirms the dynamical stability of the proposed crystal structures.

Fig. 4 (a) Phonon dispersions and (b) Raman activities of Janus HWSZ (Z = N, P, As) monolayers.

While our structural analyses confirm the theoretical stability of the proposed HWSZ (Z = N, P, As) monolayers, establishing their experimental feasibility is equally crucial for future applications. Drawing inspiration from the successful synthesis of Janus transition metal dichalcogenides¹ and Janus graphene with one-side functionalization,¹⁰ we propose a highly plausible two-step fabrication strategy. First, the foundational WSZ Janus structure can be synthesized via chemical vapor deposition (CVD) coupled with selective atomic substitution. Subsequently, asymmetric hydrogenation can be achieved using a controlled hydrogen plasma treatment, a technique widely proven to be effective for the surface functionalization of other 2D materials.²⁰ Together, these steps provide a robust and viable pathway for experimental realization.

To further investigate the vibrational properties and provide a reference for experimental characterization, we calculated the Raman active modes of the Janus monolayer. For the structure crystallizing in the P3m1 space group with a four-atom unit cell, group theory analysis predicts a specific set of Raman-active vibrations. At the Brillouin zone center (Γ), the total representation of the optical phonon modes can be decomposed into irreducible representation as 3A₁ + 3E, where both the A₁ (non-degenerate) and E (doubly degenerate) modes are Raman active. The A₁ modes correspond to out-of-plane vibrations, while the E modes represent in-plane displacements. For crystals belonging to the P3m1 space group, both A₁ and E modes exhibit Raman activity. The distinct peaks observed in the calculated Raman spectrum serve as a fingerprint for identifying the structural integrity and the broken inversion symmetry of the Janus lattice. The Raman spectra presented in Fig. 4(b) show that the Raman peak corresponding to the A₁ mode at the highest optical vibrational frequency exhibits a remarkably strong intensity, substantially exceeding that of all other Raman features. Other Raman-active modes are also clearly resolved, with particularly pronounced contributions from the high-frequency E modes, such as the E peak at 720 cm⁻¹ in the HWSN monolayer and the E peak at 633 cm⁻¹ in the HWSP monolayer.

Beyond dynamical stability, we evaluated the mechanical integrity of the monolayers through their elastic constants. Due to their hexagonal symmetry, the mechanical response of Janus HWSZ is fully defined by the in-plane constants C₁₁, C₁₂, and C₆₆, where C₆₆ = (C₁₁ − C₁₂)/2. These parameters determine the mechanical stability criteria and also in-plane stiffness. From these values, the Young's modulus and Poisson's ratio were calculated to comprehensively characterize the mechanical strength and flexibility of the studied 2D structures. The calculated results for the in-plane elastic constants of HWSZ monolayers are summarized in Table 2. It is demonstrated that the calculated C₁₁ elastic constants are relatively high, varying from 109.92 to 188.95 N m⁻¹, while the corresponding C₁₂ values are considerably lower, in the range of from 23.75 to 41.57 N m⁻¹. The positive values of C₆₆ across all three proposed structures signify robust shear rigidity, a prerequisite for maintaining structural integrity under tangential stress. These calculated values satisfy the Born criteria, specifically C₁₁ > 0 and C₁₁ > |C₁₂|,^21,22 thereby confirming that all three structures are mechanically stable and resistant to spontaneous deformation. The calculated Young's modulus values Y_2D exhibit a systematic decline as the atomic size of the pnictogen species increases, shifting from 179.80 N m⁻¹ for HWSN to 104.79 N m⁻¹ for HWSAs. This downward trajectory indicates a pronounced mechanical softening trend, where the substitution of nitrogen with heavier pnictogens like phosphorus and arsenic weakens the interatomic resistance to elastic deformation. This phenomenon is likely driven by the increase in bond lengths and the corresponding reduction in orbital overlap associated with larger atomic radii. The stiffness values of the HWSZ monolayers are comparable to those of several similar structures, such as WSiAs₃H (124.80 N m⁻¹)²³ or WBAsS₂ (195.93 N m⁻¹).²⁴ However, these values are still significantly lower than that of graphene (336 N m⁻¹).²⁵ The Janus HWSZ monolayers exhibit a consistent Poisson's ratio (ν_2D ≈ 0.2 as listed in Table 2), indicating relatively low lateral contraction under uniaxial tensile strain. This stability across the series suggests that the fundamental bonding nature and elastic anisotropy are preserved, even as in-plane stiffness decreases with larger pnictogen atomic sizes. Ultimately, a Poisson's ratio of 0.2 reflects an ideal balance between mechanical rigidity and flexibility, ensuring structural integrity and a low risk of instability under moderate strain.

Table 2 Calculated elastic constants C_ij, Young's modulus Y_2D, Poisson's ratio ν_2D, piezoelectric coefficients e_ij and d_ij, PBE/HSE06/PBE + SOC band gaps E_g, and spin splitting energy at K point in the valence band λ_v of Janus HWSZ monolayers

	C11 (N m^−1)	C12 (N m^−1)	C66 (N m^−1)	Y2D (N m^−1)	ν2D	e11 (10^−10 C m^−1)	e31 (10^−10 C m^−1)	d11 (pm V^−1)	d31 (pm V^−1)	E^PBEg (eV)	E^HSE06g (eV)	E^PBE+SOCg (eV)	λv (eV)
HWSN	188.95	41.57	73.69	179.80	0.22	2.59	0.71	1.76	0.31	2.17	2.67	1.93	0.43
HWSP	120.70	24.30	48.20	115.81	0.20	3.96	−0.23	4.11	0.16	1.38	1.80	1.13	0.45
HWSAs	109.92	23.75	43.09	104.79	0.22	4.41	−0.41	5.12	−0.31	1.30	1.72	1.03	0.46

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Having established the mechanical behavior of these monolayers through their elastic constants, we now shift our focus to the piezoelectric coefficients to evaluate their electromechanical coupling and response. The intrinsic lack of inversion symmetry in 2D Janus materials gives rise to pronounced structural anisotropy, thereby enabling both in-plane and out-of-plane piezoelectric responses. Here, we employ a DFT-based approach to calculate the piezoelectric coefficients, as proposed previously by Duerloo and co-workers.²⁶ The piezoelectric tensors e_ijk and d_ijk are defined according to the following relations:^26,27

where P_i denotes the polarization component, ε_jk and σ_jk represent the strain and stress tensors, respectively. The indices (i, j, k = 1, 2, 3) correspond to the Cartesian directions, with 1, 2, and 3 indicating the x, y, and z axes, respectively. In the case of 2D Janus monolayers, the piezoelectric coefficients e₁₁ and e₃₁ can be directly calculated using the DFT method, while the corresponding d_ij coefficients can be obtained from the following relations:²⁷

The calculated results for the piezoelectric coefficients of Janus HWSZ monolayers are summarized in Table 2. The values of e₁₁ for Janus HWSZ are found to range from 2.59 × 10⁻¹⁰ to 4.41 × 10⁻¹⁰ C m⁻¹, while the absolute values of e₃₁ lie between 0.23 × 10⁻¹⁰ to 0.71 × 10⁻¹⁰ C m⁻¹. Meanwhile, Janus WHSAs exhibits the highest in-plane piezoelectric response, exhibits the highest in-plane piezoelectric response, with a d₁₁ value of 5.12 pm V⁻¹. The corresponding d₁₁ values for Janus HWSN and HWSP are calculated to be 1.76 and 4.11 pm V⁻¹, respectively. These obtained values are significantly higher than those reported for several similar structures, such as MSi₂N₄ (0.778 pm V⁻¹),²⁸ MoSiN₃H (1.622 pm V⁻¹),²⁹ and WSiN₃H (0.99 pm V⁻¹).²³ The large d₁₁ value of WHSAs is comparable to that of several structures exhibiting strong in-plane piezoelectric effects, such as In₂SeTe (4.73 pm V⁻¹)²⁷ and NiClI (5.12 pm V⁻¹).³⁰ Notably, the Janus HWSZ monolayers exhibit remarkable out-of-plane piezoelectric coefficient d₃₁, reaching up to 0.31 pm V⁻¹ (in absolute value) for both HWSN and HWSAs monolayers. The out-of-plane piezoelectric response of these HWSZ monolayers is comparable to that of several other 2D materials with pronounced piezoelectric properties, such as Janus GaInS₂ (d₃₁ = 0.38 pm V⁻¹).²⁷ This substantial vertical response, characteristic of Janus structures, confers multifunctional potential upon the monolayers, making them promising candidates for integration into advanced electromechanical and sensing applications.

We next explore the electronic properties of the proposed Janus HWSZ monolayers, which are crucial for understanding their fundamental physics and evaluating their potential for technological applications. The calculated band structures of HWSZ materials are presented in Fig. 5. Obtained results are indicated that all three Janus structures are semiconductors with direct band gaps at K point in the Brillouin zone. At the PBE theoretical level, the band gaps of HWSN, HWSP, and HWSAs are found to be 2.17, 1.38, and 1.30 eV, respectively. The correction of the band structures using the HSE06 hybrid functional leads to a significant increase in the band gaps compared to the PBE results, as shown in Fig. 5(a). Accordingly, the corrected band gap energies of the Janus HWSZ monolayers are found to range from 1.72 to 2.67 eV, as summarized in Table 2. Further, we also evaluate the influence of SOC on the electronic bands of the proposed Janus structures. It is indicated that SOC is essential for an accurate description of electronic properties, particularly in systems containing heavy elements like tungsten. In such materials, these relativistic effects significantly modify the band structure by lifting degeneracies and shifting energy levels, which in turn alters the fundamental electronic characteristics of materials. The calculated band structures by PBE + SOC method for Janus HWSZ monolayers are shown in Fig. 5(b). The inclusion of SOC slightly reduces the band gap energies of the proposed Janus materials, as detailed in Table 2. Notably, SOC lifts the spin degeneracy, resulting in distinct spin-split energy levels throughout the band structure. A pronounced spin splitting occurs within the valence band at the K-point, where the splitting energy λ_v reaches a significant magnitude of 0.46 eV (HWSAs).

Fig. 5 Band structures of 2D Janus HWSZ (Z = N, P, As) monolayers at the PBE/HSE06 (a) and PBE + SOC (b) theoretical levels.

Finally, we evaluate the carrier mobility of the proposed Janus HWSZ structures. Various scattering mechanisms have been taken into account, including acoustic-deformation-potential (ADP), ionized-impurity (IMP), piezoelectric (PIE), and polar-optical-phonon (POP) scattering. The total mobility µ_total is determined via Matthiessen's rule, including the contributions of these individual mechanisms:¹⁹

where µ_ADP, µ_IMP, µ_PIE, and µ_POP refer to the carrier mobilities limited by ADP, IMP, PIE, and POP scattering, respectively.

The temperature dependence of the electron mobility in the Janus HWSZ monolayers is illustrated in Fig. 6. The two representative carrier concentrations n_c of 1 × 10¹⁶ and 1 × 10²⁰ cm⁻³, correspond to the low and high carrier concentration regimes, respectively. When evaluating the volumetric carrier concentrations, the slab thickness of the HWSZ monolayers was defined as Δh as listed in Table 1. This ensures the carrier concentration strictly reflects the volume of the 2D slab rather than the entire vacuum-padded simulation box. In both the low and high carrier concentration regimes, ADP scattering consistently acts as the primary mechanism governing the total electron mobility. This dominance is particularly evident in the HWSP and HWSAs monolayers, where the electron mobility limited by ADP scattering closely follows the trend of the total electron mobility over the entire temperature range, indicating that other scattering channels play only a minor role. In the meantime, for the Janus HWSN monolayer, the calculated results presented in Fig. 6 reveal a more complex interplay between scattering mechanisms. Although ADP scattering still provides a major contribution, PIE scattering also plays a non-negligible role in determining the overall magnitude of the total electron mobility, particularly in the low-temperature region. The comparable strength of these two mechanisms suggests that the intrinsic piezoelectric response of the HWSN monolayer enhances electron–phonon coupling through long-range polarization fields, thereby further limiting carrier transport. The dominant contribution of ADP scattering in the Janus HWSZ monolayers is consistent with that observed in the WBAsS²⁴ and MoS₂ or WS₂ monolayers.¹⁹ Nevertheless, in the most 2D transition metal dichalcogenide materials, electron mobility is predominantly governed by longitudinal optical phonon scattering.¹⁹ Even in HfSiZ₃H monolayers,⁴ which are structurally and chemically analogous to the materials studied in this study, POP scattering remains the governing factor. This highlights that scattering mechanisms in 2D materials are not easily predicted. A comprehensive analysis of all relevant scattering channels is therefore essential to accurately determine mobility limits.

Fig. 6 Temperature dependence of individual and total electron mobilities in Janus HWSZ (Z = N, P, As) materials at carrier concentrations of 1 × 10¹⁶ cm⁻³ (a) and 1 × 10²⁰ cm⁻³ (b).

Fig. 7 depicts the temperature dependence of hole mobility in the proposed Janus materials. Consistent with the behavior of electrons, APD scattering is the dominant mechanism governing total hole mobility, except for Janus HWSP monolayer, where PIE scattering becomes the dominant mechanism in the high-temperature regime. Furthermore, at high carrier concentration of 1 × 10²⁰ cm⁻³, IMP scattering also plays a significant role in determining hole mobility within the HWSN monolayer, as depicted in Fig. 7(b). The competition between the IMP and PIE scattering mechanisms is similarly observable for electrons at high carrier concentration in this material, as shown in Fig. 6(b).

Fig. 7 Temperature dependence of individual and total hole mobilities in Janus HWSZ (Z = N, P, As) materials at carrier concentrations of 1 × 10¹⁶ cm⁻³ (a) and 1 × 10²⁰ cm⁻³ (b).

Table 3 presents a comprehensive summary of the carrier mobility in the Janus HWSZ monolayers at room temperature, including the individual contributions from different scattering mechanisms as well as the total mobility. The calculated results reveal that the electron mobility of the Janus HWSZ monolayers is relatively low. At a carrier concentration of 1 × 10¹⁶ cm⁻³, the room-temperature total electron mobilities µ_tot of HWSN, HWSP, and HWSAs are 10.45, 10.61, and 8.93 cm² V⁻¹ s⁻¹, respectively. As the carrier concentration increases, the mobility decreases markedly, indicating enhanced carrier scattering at higher doping levels. In the case of n_c = 1 × 10²⁰ cm⁻³, the room-temperature total electron mobilities of HWSN, HWSP, and HWSAs are reduced to 5.35, 3.19, and 2.58 cm² V⁻¹ s⁻¹, respectively. This same trend is clearly observable in the case of hole mobility, as detailed in Table 3. These results suggest that carrier transport in the Janus HWSZ monolayers is highly sensitive to doping levels, and optimizing carrier concentration will be essential for improving their electronic transport performance in practical device applications.

Table 3 Room-temperature individual and total carrier mobilities (µ, cm² V⁻¹ s⁻¹) of Janus HWSZ (Z = N, P, As) at various carrier concentrations (n_c, cm⁻³)

Carrier type	Compound	nc	µADP	µIMP	µPIE	µPOP	µtotal
Electron	HWSN	1 × 10^16	18.70	5.63 × 10^8	23.70	3.82 × 10^5	10.45
	HWSP		11.30	776.00	223.00	3.71 × 10^5	10.61
	HWSAs		9.45	581.00	226.00	9.33 × 10^4	8.93
	HWSN	1 × 10^20	9.14	37.90	19.50	2.41 × 10^5	5.35
	HWSP		4.24	29.60	22.90	2.33 × 10^4	3.19
	HWSAs		2.95	23.30	173.00	7.21 × 10^3	2.58
Hole	HWSN	1 × 10^16	7.16	111.00	18.20	2.12 × 10^3	4.90
	HWSP		1.86	547.00	8.49	924.00	1.52
	HWSAs		2.17	471.00	93.20	421.00	2.10
	HWSN	1 × 10^20	6.40	8.19	22.60	1.07 × 10^3	3.90
	HWSP		2.65	24.40	2.19	248.00	1.14
	HWSAs		1.30	21.00	29.20	143.00	1.17

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4 Conclusion

In summary, DFT calculations confirm that Janus HWSZ (Z = N, P, As) monolayers are stable, direct-gap semiconductors with high experimental viability. Their broken inversion symmetry, combined with strong spin–orbit coupling (SOC), induces massive spin splitting, positioning these materials as premier candidates for spintronic devices. However, transport analysis indicates that electron mobility in HWSZ is relatively low and fundamentally limited by ADP scattering. Despite these transport limitations, the pronounced out-of-plane piezoelectric response offers a viable route toward multifunctional electromechanical integration. Ultimately, the combination of sizable band gaps, strong spin splitting, and robust piezoelectricity establishes HWSZ monolayers as a versatile platform for next-generation nanoelectronic applications, provided that their intrinsic scattering mechanisms are carefully controlled.

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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