Tunable electronic structures in MPX₃ (M = Zn, Cd; X = S, Se) monolayers by strain engineering

Abstract

By density functional theory calculations, we systematically investigate the strain effect on electronic structures of MPX₃ (M = Zn, Cd; X = S, Se) monolayers. An indirect–direct band gap transition occurs under compressive strains in ZnPS₃, ZnPSe₃, and CdPSe₃, but CdPS₃ always remains in an indirect band gap phase. The band gaps of MPX₃ monolayers increase firstly and then decrease under compressive strain, while they only decrease in the case of tensile strain. In addition, we find that MPX₃ monolayers are perfect substitutes for the unachievable two-dimensional MX (M = Zn, Cd; X = S, Se), due to their quite comparable electronic structures, such as their band gaps and effective masses. This indicates that MPX₃ monolayers should be promising candidates in optoelectronic applications for tunable electronic structures by strain engineering.

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1. Introduction

Since two-dimensional (2D) graphene was exfoliated by Novoselov et al.¹ in 2004, a number of atomically thin 2D layered materials have attracted considerable attention for their potential applications in the next-generational optoelectronic devices, due to their particular physical and chemical properties in nanoscale electronics and optoelectronics.^2–6 In recent years, 2D artificial heterostructures based on these few-layered materials have provided alternative choices for applications in solar cells and photocatalysis, for their high performances in electronic–hole separation, charge transfer and spectrum response range.^7,8 In particular, transition metal dichalcogenide (TMD) AX₂ (A = W, Mo; X = S, Se, Te) heterostructures have been widely studied, because of their relatively simplified preparation process and controllable stacking orientations.^9,10 However, their narrow range of band gaps limits their light response range at visible and ultraviolet (UV) wavelengths.^11–13

Group-IIB chalcogenides MX (M = Zn, Cd; X = S, Se, Te), with wurtzite and zinc-blende structures, have been extensively investigated for their broad applications in electronic, photonic, and optoelectronic devices, due to their large range of band gaps (2.0–3.9 eV).^14–17 With the technology revolution, heterostructures composed from these compounds, including core/shell quantum dots,¹⁸ nanocrystals,¹⁹ nanowires,²⁰ nanoribbons²¹ and nanobelts,²² have been studied as functional parts in UV-light sensors, photocatalysts and photovoltaic devices. The 2D MX nanostructures have also attracted considerable attention; however, only a few theoretical calculations have reported the mono-atomic-layer graphene-like MX,^23,24 which mainly attributes to the unavailability of MX monolayers in ambient conditions. Therefore, to develop stable and high performance 2D heterostructures for a wide range of wavelengths, it is important to find a family of compounds to substitute for these MX monolayers.

Since layered transition metal phosphorus trichalcogenides MPX₃ were synthesized by Hahn and Klingen in 1965,²⁵ they have been extensively studied for particular electronic, optoelectronic and magnetic properties.^26–30 In recent years, attention has mostly focused on exploring the properties of atomically thin MPX₃.^31–35 For example, Liu et al.³² studied theoretical electronic structures of MPX₃ (M = Zn, Cd, Mg; X = S, Se) monolayers, and predicted their potential for photocatalytic water splitting. Du et al.³⁵ successfully fabricated single layered MPS₃ (M = Fe, Mn, Ni, Cd and Zn) by micromechanical exfoliation, and demonstrated the stability of these compounds by cleavage energy calculations. The electronic structures of MPX₃ monolayers are quite similar to those of bulk MX structures, implying that they could substitute for 2D MX monolayers. Of particular interest to us are the 2D group-IIB MPX₃ (M = Zn, Cd; X = S, Se) monolayers, which have shown significant advantages in optoelectronics due to their wide range of band gaps (2.2–3.5 eV), and thus they could be considered as the optimal candidates for the building of 2D MPX₃-based heterostructures.

As electronic structures around the Fermi level are highly sensitive to orbit coupling and interactions with neighboring atoms, strain engineering is an effective method for tuning electronic structures, especially in 2D materials, due to their extraordinary break strength and structural stability.^36–39 For example, it has been previously indicated that strain can open up a band gap in graphene,⁴⁰ and local strain on NbS₂ and NbSe₂ can induce a ferromagnetic characteristic.⁴¹ Moreover, for semiconducting devices, 2D materials are often supported on substrates, which could lead to a lattice mismatch and consequently result in an external strain.⁴² However, there is scarcely any research about the strain effect on the electronic structures of MPX₃ monolayers. Therefore, by first principle calculations, we mainly focus on the tunable electronic structures of MPX₃ (M = Zn, Cd; X = S, Se) monolayers produced by strain engineering.

2. Computational details

Density functional theory (DFT) calculations were performed using the Projector-Augmented Wave (PAW) pseudopotential implementation of the Vienna Ab initio Simulation Package (VASP).^43–45 Electron exchange and correlation effects were described by employing both the Heyd–Scuseria–Ernzerhof hybrid functional (HSE06)⁴⁶ and the Perdew–Burke–Ernzerhof (PBE) functional of generalized gradient approximation (GGA).⁴⁷ The exchange screening parameter in HSE06 was set to be 0.2. The energy cutoff for the plane-wave basis was set to be 450 eV on the 9 × 9 × 1 Monkhorst–Pack k-point grid. An energy cutoff of 1 × 10⁻⁵ eV was set as the convergence criteria for the electronic self-consistent field iterations. The atomic positions were optimized until the maximum Hellmann–Feynman forces on each atom were less than 10⁻² eV Å⁻¹. Vacuum regions with thicknesses larger than 20 Å were placed to avoid interactions between the monolayers and their periodic images.

3. Results and discussion

The stacked MPX₃ (M = Zn, Cd; X = S, Se) structures are weakly bonded with van der Waals interactions between X and X atoms. For regular bulk MPX₃, the crystal structure of MPS₃ is monoclinic with space group C2/m while MPSe₃ is rhombohedral with space group R̄3.^28,30 Reducing the film thickness of either MPS₃ or MPSe₃ from bulk to a monolayer, results in the same M₂P₂X₆ unit cell, as shown in Fig. 1. For each intralayer of MPX₃, there are two layers of chalcogen atoms, between which are located octahedrally coordinated transition metal atoms and phosphorus pairs. A hexagonal unit cell was used for all calculations, as marked in Fig. 1. Before studying the electronic structures, we optimized the structures by DFT calculations. The optimized geometries, including the lattice constants, monolayer chalcogenide heights, and the nearest atomic distances of M–X, M–P, and P–P, are summarized in Table 1. The detailed crystal structures including lattice vectors and atomic coordinates are shown in Table S1 of the ESI.† It is obvious that the parameters of MPSe₃ are larger than those of MPS₃, and that the parameters of CdPX₃ are larger than those of ZnPX₃, differences which can be attributed to the various elements. Moreover, the results are consistent with the previous calculations by Liu et al.³² but slightly larger than those of bulks obtained by experiments or calculations.

Fig. 1 The top view (a) and side view (b) of monolayer MPX₃, where the gray, yellow and purple balls represent the M (Zn or Cd), X (S or Se) and P atoms, respectively.

Table 1 The optimized geometries of monolayer MPX₃, including the lattice constants (a₀), monolayer chalcogenide heights (h), and the nearest atomic distances (d) of M–X, P–P, and X–P. All values are in units of angstroms

Material	a0 calc.	Bulk a0	h calc.	dM–X	dP–P	dX–P
a Boucher et al.^28b Jörgens and Mewis.^30
ZnPS3	6.011	5.971^a	3.234	2.584	2.211	2.042
ZnPSe3	6.357	6.290^b	3.393	2.705	2.241	2.218
CdPS3	6.3	6.218^a	3.411	2.761	2.257	2.042
CdPSe3	6.618		3.584	2.877	2.284	2.214

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Next, we studied detailed band structures for unstrained MPX₃ (M = Zn, Cd; X = S, Se) monolayers. The exchange–correlation functional by GGA typically underestimates band gaps. Hybrid functionals, such as HSE06, which contain part of the exact Hartree–Fock exchange, generally tend to be more accurate. Thus we employed the HSE06 functional to obtain the band structures, and we also give the results by PBE for comparison. Fig. 2 shows the band structures calculated with both the HSE06 and PBE functionals. It is clear that the valence band maximum (VBM) is at the K point and the conduction band minimum (CBM) is located at the Γ point, indicating indirect band gaps for MPX₃ monolayers. The family of MPX₃ (M = Zn, Cd; X = S, Se) monolayers exhibits a large range of band gaps from 2.24 to 3.30 eV by HSE06, which is greater than that obtained by PBE (1.29–2.13 eV). The values of the band gaps are listed in Table 2, and are in good agreement with the previous calculations and the experimental results for the bulk compounds.^29,32,35,48 Moreover, the band gaps of wurtzite MX structures were calculated with HSE06 and are shown in Table 2 together with the theoretical and experimental values obtained in previous reports.^17,49–53 When the results of MPX₃ monolayers and MX are compared, it can be seen that the band gaps of ZnPS₃ (ZnPSe₃) and the corresponding ZnS (ZnSe) are quite similar, but that the value of CdPS₃ (CdPSe₃) is a bit larger than that of CdS (CdSe).

Fig. 2 Band structures of (a) ZnPS₃, (b) ZnPSe₃, (c) CdPS₃, and (d) CdPSe₃. The red and black lines represent the HSE06 and PBE functionals, respectively. The Fermi level is set to zero.

Table 2 Band gaps of MPX₃ and wurtzite MX (M = Z, Cd; X = S, Se) calculated by HSE06 and PBE functionals. Experimental values of the bulk materials are also listed

Materials	E^HSEg (eV)	E^PBEg (eV)	Eg (bulk in experiment) (eV)
a Liu et al.^32b Du et al.^35c Brec et al.^48d Calareso et al.^29e Yadav et al.^52f Fang et al.^17g Zhang et al.^50h Schröer et al.^53i Hayashi et al.^49j Kale and Lokhande.^51
ZnPS3	3.30 (3.30^a)	2.13 (2.14^a)	3.5^b, 3.4^c
ZnPSe3	2.32 (2.31^a)	1.31 (1.32^a)
CdPS3	3.03 (3.03^a)	1.92 (1.93^a)	3.4^b, 3.3^c, 3.06^d
CdPSe3	2.24 (2.25^a)	1.29 (1.29^a)	2.29^d
ZnS	3.29	2.14^e	3.77^f
ZnSe	2.42	1.20^e	2.67^g
CdS	2.19	1.3 (LDA)^h	2.42^i
CdSe	1.57	0.6 (LDA)^h	1.7^j

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Subsequently, we considered the partial density of states (PDOS) of MPX₃ monolayers including the s, p, and d orbitals of Zn (Cd), S (Se) and P atoms, and compared them to those of the corresponding MX (Fig. 3). As expected, the PDOS near the VBM and CBM of MPX₃ is very close to that of the corresponding MX. The VBM is mainly dominated by p orbitals of the S or Se atoms, and the CBM is mainly comprised of the s orbital of the Zn or Cd atoms, but the P atoms do not contribute to the CBM or VBM. Therefore, MPX₃ monolayers would have potential for optoelectronic devices, due to their comparable and wide range of band gaps.

Fig. 3 PDOS of (a) ZnPS₃ and ZnS, (b) ZnPSe₃ and ZnSe, (c) CdPS₃ and CdS, and (d) CdPSe₃ and CdSe calculated with the PBE functional, where the contributions of s, p, and d orbitals of Zn (Cd), S (Se) and P atoms are plotted. Inset in (a): the detailed PDOS of ZnPS₃ around the CBM. The Fermi level is set to zero.

We also examined the effective masses of electrons and holes of MPX₃ monolayers. The effective masses of electrons and holes is calculated by , where ℏ is the reduced Planck constant, and can be obtained by parabolic fitting near the VBM or CBM.^54,55 Table 3 summarizes the variations of effective masses of electrons and holes for MPX₃ monolayers in different directions. Small effective masses of electrons remain in all MPX₃ compounds, with 0.29, 0.18, 0.29 and 0.21m_e for ZnPS₃, ZnPSe₃, CdPS₃ and CdPSe₃, respectively, which are nearly half of the hole effective masses, implying n-type semiconductors. Moreover, in order to compare carrier transport properties, the effective masses of the corresponding MX-wurtzite structure and single layered group-VIB dichalcogenides are listed as well.^50,56,57 It is obvious that the effective masses of MPX₃ are very close to those of the corresponding MX, whereas they are much smaller than those of MoS₂ and WS₂. As effective masses of carriers generally indicate carrier transport, the smaller in MPX₃ provide a meaningful insight into the carrier transport performance of these materials in optoelectronic devices.

Table 3 Effective masses of electrons and holes for the unstrained MPX₃ (M = Zn, Cd; X = S, Se) monolayers stated in units of the electron rest mass (m₀). Effective masses of the wurtzite MX, 2H-MoS₂ and WS₂ are also summarized

	ZnPS3	ZnPSe3	CdPS3	CdPSe3	ZnS^a	ZnSe^b	CdS^a	CdSe^b	MoS2^c	WS2^c
a Lippens and Lannoo.^56b Zhang et al.^50c Wickramaratne et al.^57 The values of 0.30/0.29 (ZnPS3) mean along Γ–K and Γ–M directions, respectively, and values of 0.51/0.60 (ZnPS3) mean along K–Γ and K–M directions, respectively.
	0.30/0.29	0.19/0.18	0.30/0.29	0.22/0.21	0.42	0.16	0.18	0.11	0.50	0.35
	0.51/0.60	0.44/0.47	0.61/0.79	0.51/0.62	0.61	0.58	0.53	0.44	0.54	0.34

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Based on the above comparisons, it is clear that the electronic structures of MPX₃ monolayers are quite comparable with those of MX structures, with both having a wide range of band gaps, similar contributions to the VBM by X-p orbitals and to the CBM by M-s orbitals, and similar electron effective masses, which can be explained by the limited contribution of P atoms to the VBM and CBM. These results suggest that MPX₃ monolayers could be the perfect candidates to substitute for the unachievable MX monolayers and to provide further potential in optoelectronic applications.

It is well known that the manipulation of band structures can enhance the performance of electronic and optoelectronic devices, for their remarkable modulation of phase transitions, band gaps and so on.^40,58 Therefore, we studied strain effects on the electronic characteristics of MPX₃ monolayers. Calculations of electronic properties for the strained MPX₃ monolayers were carried out, starting with the relaxed structures. Fig. 4 shows the evolution of band structures calculated by HSE06 under biaxial compressive and tensile strains from −10% to 10%. It is clear that all MPX₃ compounds are semiconductors with large tunable band structures under the strain. An indirect–direct band gap transition occurs under compressive strains for ZnPS₃, ZnPSe₃, and CdPSe₃, but CdPS₃ always remains in an indirect band gap phase. In the case of tensile strain for the above four compounds, the VBM is located at the K point and the CBM is located at the Γ point, so a phase transition does not exist.

Fig. 4 The evolution of band structures of MPX₃ calculated by the HSE06 functional under biaxial strains of −8%, −4%, 0, 4%, and 8%, for (a) ZnPS₃, (b) ZnPSe₃, (c) CdPS₃ and (d) CdPSe₃. Red arrows represent the direction of the band gap from the VBM to the CBM. The Fermi level is set to zero.

To precisely investigate the strain effect on the band gaps, we plotted the band gaps from the VB to the CB, including Γ → Γ, K → K, K → Γ, and Γ → K, as shown in Fig. 5. The plots are divided into three regions to distinguish the distinct band gaps under the applied strains. It is noted that band gaps increase initially and then decrease under compressive strain, while they decrease steadily in the case of tensile strain. The band gap maxima are at about 3.67 eV, 2.54 eV, 3.50 eV and 2.60 eV for ZnPS₃, ZnPSe₃, CdPS₃ and CdPSe₃, respectively. These values are about 12 percent larger than those of the unstrained states, and located at the boundary of the indirect (I) and direct (II) states for ZnPS₃, ZnPSe₃ and CdPSe₃. The transition from the indirect (I) to direct (II) band gap occurs when the monolayers suffer strains of about −4%, −2% and −4% for ZnPS₃, ZnPSe₃ and CdPSe₃, respectively. With an increase in compression, ZnPSe₃ and CdPSe₃ revert back to indirect (III) states when the compressive strength exceeds the value of −8%. The origin of the indirect–direct transitions is mainly the orbit coupling and interactions with neighboring atoms, due to the changes in the lattice parameters and the atomic coordinates under the strain. In order to visually analyze the contribution of the CBM, we compare the spatial distributions of wave functions of CdPSe₃ in the unstrained and strained (−8%) state in Fig. S1 (ESI†). It is obvious that the CBM is mainly comprised of the s orbital of the Cd atom in Fig. S1(a)† and the p orbital of the Se atom in Fig. S1(b),† which can be attributed to the increase of the monolayer chalcogenide heights and the decrease of the nearest atomic distances of Cd–Cd under the compressive strain. Therefore, the CBM of MPX₃ monolayers is determined by the competition between the p orbitals of X atoms and the s orbital of M atoms.

Fig. 5 The change in the energy gaps of (a) ZnPS₃, (b) ZnPSe₃, (c) CdPS₃ and (d) CdPSe₃, including Γ → Γ (black), K → K (red), K → Γ (blue), and Γ → K (green) transitions, where the regions of I, II, and III represent the indirect, direct, and indirect band gaps, respectively.

In addition, we depict the evolution of the band structures and the change of band gaps calculated by the PBE functional (in Fig. S2 and S3 of the ESI†). Despite the underestimated band gaps by PBE, the general trends of the strain effects on the band structures are consistent with those obtained by HSE06. Therefore, strain has remarkable effects on the modulation of the band structures of MPX₃ compounds, which suggests their potential applications in the design of novel MPX₃-based 2D heterostructures in photodetectors, as well as photocatalysts, solar cells and hydrogen storage, due to the fact that they offer tunable band gaps over a large range.

4. Conclusions

In conclusion, by employing DFT, we provide a detailed investigation of the electronic properties of MPX₃ (M = Zn, Cd; X = S, Se) monolayers. We find that the electronic structures of MPX₃ monolayers are quite comparable with those of MX structures, which indicates that MPX₃ monolayers would be perfect substitutes for the unachievable 2D MX (M = Zn, Cd; X = S, Se). Moreover, we demonstrate that electronic structures can be modulated by a wide range of strain. Transitions between indirect and direct band gaps are observed using compressive strain engineering for ZnPS₃, ZnPSe₃ and CdPSe₃, but not for CdPS₃. Furthermore, the electron effective masses of MPX₃ monolayers indicate that they offer outstanding carrier transport in devices. These observations indicate that MPX₃ monolayers are promising candidates for electronic and optoelectronic applications.

Acknowledgements

This work was supported by the Fundamental Research Funds for the Central Universities, a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD). We are grateful for the support of NSFC (51672126). The calculations were performed on parallel computers at the High Performance Computing Center (HPCC) of Nanjing University.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ra14101c

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