Density functional study on the hole doping of single-layer SnS₂ with metal element X (X = Li, Mg, and Al)

Abstract

The effects of metal element X-doping on the electronic and optical properties of single-layer SnS₂ were investigated using density functional theory. The results show that the doping is energetically more favorable under S-rich conditions than under Sn-rich conditions. For Li and Mg doping, there is the existence of ionic bonding between the dopants and adjacent S atoms, and the systems exhibit magnetic ground states. However, covalent bonding character is observed in Al-doped single-layer SnS₂, and the system exhibits non-magnetic ground states. The optical properties show that the optical absorptions are anisotropic for all doping cases. The X doping not only results in a red shift of the absorption edges, but also enhances the effective utilization in the near-infrared light region. Additionally, Li-doped single-layer SnS₂ is active for overall water splitting under visible light radiation whereas Mg and Al-doped SnS₂ are only suitable for oxygen evolution.

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1. Introduction

In recent years, graphene with a two-dimensional (2D) honeycomb structure has received particular attention because of its outstanding thermal conductivity, high charge mobility, and excellent mechanical properties.^1–5 However, its intrinsic “zero band-gap” characteristic hinders its applications in the fields of semiconductor devices and integrated circuits.³ Therefore, many researchers have focused on developing novel materials that not only have analogous graphene layered organization, but also exhibit excellent band structures, such as BN,^6,7 GaN,⁸ GaS,⁹ SnS₂,^10–12 and MoS₂.^13–15 Among them, being an earth-abundant, nontoxic, and environment-friendly semiconductor, SnS₂ has been widely reported for applications in lithium batteries, water splitting, and field effect transistors.^16–19 In particular, due to its band gap of 2.18–2.44 eV and good stability in acidic and neutral aqueous solutions,^17,18 SnS₂ is currently thought to be a fascinating candidate for use as a visible light sensitive photocatalyst.

Experimentally, SnS₂ with 2D structures, such as nanoparticles, nanoplates and nanosheets, has been synthesized.^20–23 Especially, single-layer SnS₂ exhibits more preeminent photocatalytic properties in comparison with its three-dimensional (3D) counterparts. For instance, Sun et al.²² synthesized SnS₂ single-layers with three atom thickness and observed that the visible-light conversion efficiency of 38.7% is much higher than that of 3D bulk SnS₂. Wei et al.²³ also prepared ultrathin SnS₂ nanosheets, in which the photocatalytic activity is significantly enhanced due to the 2D sheet-like nanostructure. Although the photocatalytic activity of single-layer SnS₂ is improved with respect to its bulk phase, visible optical absorption and hydrogen production from solar water splitting are restricted.²⁴ More recently, in addition to exploring the electronic and optical properties of SnS₂, the doping of foreign species into pristine single-layer SnS₂ has been carried out in order to solve the above mentioned problems. An et al.²⁵ prepared transition metal Cu-doped SnS₂ nanosheets, in which the visible-light-driven activity is 7 times higher than blank SnS₂ nanosheets. Besides that, n- and p-type anion doping was also investigated to understand the conductivity mechanism of SnS₂ nanosheets based on first principle calculations.²⁶ However, to the best of our knowledge, there have been no systematic reports about hole doping at cation sites in single-layer SnS₂ until now. And cation doping is usually easier realized than that of anion doping in experiments. It is very imperative to explore the optical mechanism of low valence metal doping in single-layer SnS₂. Besides, Peng et al.²⁷ pointed out that there was a correlation between defect-induced ferromagnetism and hole doping for semiconductors. That is to say, the influence of a cation-site doping-induced hole on the magnetism of single-layer SnS₂ also should be considered. Therefore, in the present work, metal element X (X = Li, Mg, and Al) was chosen as a dopant in single-layer SnS₂. Using density functional theory (DFT), the effects of doping X with different hole densities on the electronic structure and optical properties of single-layer SnS₂ were systematically investigated, and the magnetic and photochemical behaviors of the X-doped SnS₂ monolayer were analyzed in detail.

2. Computational methods

All the calculations were performed using DFT methods with the projector augmented wave (PAW) pseudopotentials as implemented in the Vienna Ab Initio Simulation Package (VASP) code.^28,29 The Perdew–Burke–Ernzerhof (PBE) parametrization of the generalized gradient approximation (GGA) was employed to model the exchange and correlation interactions.³⁰ The valence electron configurations considered in this work were Li (1s²2s¹), Mg (3s²), Al (3s²3p¹), Sn (4d¹⁰5s²5p²) and S (3s²3p⁴), respectively. For the supercell model, a 4 × 4 × 1 (48 atoms) single layer of a SnS₂ supercell was used, and a vacuum space of 14 Å was added to eliminate interaction between the layers. A kinetic energy cutoff of 450 eV was adopted in the plane-wave expansions, and the Monkhorst–Pack k-point grid was 3 × 3 × 1 for Brillouin zone integrations. A larger 5 × 5 × 1 (75 atoms) supercell was used to test the effects of finite size on the characteristics of a doped SnS₂ monolayer. The formation energy obtained from the larger supercell only differs by a fraction of meV from the calculation using the 4 × 4 × 1 (48 atoms) supercell and the magnetic moments are similar to the results obtained using the 4 × 4 × 1 supercell, which indicates that the supercell size adopted in our work is reasonable. To precisely reproduce the experimental band gap of SnS₂, an on-site coulomb interaction of U = 9 eV was applied only to Sn 3d orbitals, which has also been reported in other literature.^26,31 During the geometrical optimization, all atomic positions and lattice constants were relaxed until the residual forces on the atoms were less than 0.01 eV Å⁻¹, and the convergence criterion of total energy was set to be 10⁻⁵ eV per atom. In addition, for the bulk SnS₂, the van der Waals interaction was considered using Grimme's DFT-D2 method³² to better describe the non-bonding interaction between the layers of bulk SnS₂.

3. Results and discussion

3.1. Structural optimization and formation energies

The crystal structure of bulk SnS₂ was firstly optimized with the PBE and PBE+U methods to probe the accuracy and applicability of the calculated parameters adopted in this work. The calculated structural parameters, bond lengths and band gaps E_g are summarized in Table 1. Compared to the results obtained from the PBE calculations, the optimized lattice constants and the band gap from the PBE+U method are in much better agreement with the experimental values.³³ Moreover, we also performed the structural optimization of single-layer SnS₂ using the PBE+U approach. The obtained lattice parameter (a = 3.481 Å), the S–Sn bond length (d_S–Sn = 2.437 Å) and the band gap (E_g = 2.240 eV) are also close to the reference data.²² Therefore, the above calculated results indicate that the PBE+U method and the parameters adopted are reliable and believable.

Table 1 Calculated structural parameters a and c, the bond lengths d_Sn–S and band gaps E_g for SnS₂ bulk and monolayer compared to the experimental values

	Bulk (monolayer)
	PBE	PBE+U	Experiment
a (Å)	3.716 (3.645)	3.693 (3.481)	3.645 (3.700)
c (Å)	12.790 (—)	11.680 (—)	11.802 (—)
d Sn–S (Å)	2.590 (2.579)	2.460 (2.437)	2.570 (2.600)
E g (eV)	1.300 (1.574)	1.910 (2.240)	2.000 (2.230)

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Low valence metal X doping in single-layer SnS₂ was modeled by replacing the Sn site with one X atom (X = Li, Mg, and Al) (X_Sn) in the supercell. The top view and side view of the optimized SnS₂ monolayer are shown in Fig. 1. In order to explore the bonding nature in X-doped single-layer SnS₂, the difference in charge density near dopant X is simulated and plotted in Fig. 2. For pure single-layer SnS₂ (Fig. 2(d)), covalent bonding apparently exists between Sn and S atoms. For X-doped single-layer SnS₂, it is easy to find that the covalent character of a X–S bond is gradually weakened while the ionic character is enhanced with the increase in hole density (from Fig. 2(c) to (a)). Furthermore, significant ionic bonding behavior is observed between the Li and adjacent S atoms in Li-doped SnS₂. To further understand the chemical bond characteristic, the Bader charge³⁴ was calculated to analyze the charge transfer of every atom and the related X–S bond length is also presented, as summarized in Table 2. Positive and negative values indicate the loss and gain of charge, respectively. As can be seen, the valence electron on the Li atom is almost lost, which shows that an obvious ionic bond character is easy to form in Li-doped SnS₂. Besides, the charge transfer rate decreases with the decreasing hole density introduced by the dopant, indicating that the electron transfer becomes increasingly unobvious, thereby resulting in the ionicity being weakened. This is in agreement with the above analysis of the difference in charge density. In addition, the results in Table 2 show that the X–S bond length (X = Li, Mg, and Al) is larger than that of Sn–S in pristine single-layer SnS₂. It is well known that covalent bond strength is greater than ionic bond strength. Consequently, a possible reason for the above conclusion is the existence of a strong Sn–S covalent bond relative to a Li(Mg)–S ionic bond and slightly weak Al–S covalent bond. In particular, combining the results shown in Table 2 and Fig. 2, it can be seen that the ionicity of the Li–S bond is much stronger than that of the Mg–S bond, thus leading to a shorter length for the Li–S bond (2.540 Å) than the Mg–S bond (2.567 Å).

Fig. 1 The top view (a) and side view (b) of optimized X-doped single-layer SnS₂. Yellow, dark and red spheres represent the S, Sn and X (X = Li, Mg and Al) atoms, respectively.

Fig. 2 Charge density difference near the dopant X and adjacent host atoms for (a) Li-, (b) Mg-, (c) Al-doped SnS₂, and (d) pure single-layer SnS₂.

Table 2 The Bader charge on the dopant X and its adjacent host atoms, as well as the X–S bond length d_X–S (Å) are listed

Bader charge (e)
Species	Sn	S	Li	Mg	Al	d X–S (Å)
Li:SnS2	1.48	−0.67	0.84	—	—	2.540
Mg:SnS2	1.48	−0.79	—	1.58	—	2.567
Al:SnS2	1.48	−0.89	—	—	2.20	2.451
Pure	1.48	−0.74	—	—	—	2.437

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In order to check the relative stability of the doped systems, the formation energy of X substitution with charged state q is calculated according to the following formula

where E(doped) and E(pure) denote the total energies of X-doped and pure single-layer SnS₂, respectively. The n_i (i = Sn, S and X) is the number of atoms removed (n_i > 0) or added (n_i < 0) to the system, and μ_i is the chemical potential of the corresponding species. E_F is the Fermi energy level with respect to the energy position of the valence band maximum (ε_VBM) of the perfect single-layer SnS₂. Δν is the correction for the shift in average electron static potential of the 1s core level energy of a Sn atom (located far away from the defect site) between the neutral and charged states. As is well known, the formation energy depends on the growth conditions, which may be either Sn-rich or S-rich conditions. Conventionally, μ_i = μ^bulk_i +Δμ_i, where μ^bulk_i is defined as the chemical potential of the elemental bulk solid, and Δμ_i denotes the chemical potential change of defects under different growth conditions. To avoid the precipitation of SnS or Sn₂S₃ in the SnS₂ phase, we set constraints on the chemical potentials of the type mΔμ_Sn +nΔμ_S ≤ ΔH(Sn_mS_n),³⁵ in which ΔH(Sn_mS_n) is the formation enthalpy of Sn_mS_n, and we obtain −3.54 eV ≤ Δμ_Sn ≤ −0.06 eV from the constraints. The value Δμ_Sn = −0.06 eV corresponds to the Sn-rich environment, whereas Δμ_Sn = −3.54 eV characterizes the Sn-poor (S-rich) condition. Then μ_S is computed using the equilibrium condition in SnS₂: μ_Sn + 2μ_S =μ_SnS2. In addition, during the metal element X doping process, the restriction mΔμ_X + nΔμ_S ≤ ΔH(X_mS_n) is further considered to prevent the formation of phases Li₂S, MgS, and Al₂S₃ between the dopant and host atoms. According to eqn (1), the neutral formation energies of X doping in single-layer SnS₂ are calculated under different conditions, as summarized in Table 3. The results show that the formation energies are lower under S-rich conditions than those under Sn-rich conditions for all doping cases, which implies that the doping is energetically favored under S-rich conditions. In particular, there exists the lowest formation energy (E_f) when the Sn site is substituted by an Al atom, which shows that Al doping is easier to achieve compared with Li and Mg doping. Besides, the E_f shows a decreasing trend with the decreasing hole density. The values of E_f are in the order Li > Mg > Al, which is consistent with the order of ionic radius (Li > Mg > Al) but not in agreement with that of electronegativity (Li (0.98) < Mg (1.31) < Al (1.61)). This indicates that the influence of the ionic radius on the E_f exceeds the electronegativity so that suitable ion size plays a significant role in the feasibility of doping in single-layer SnS₂ in experiments. Meanwhile, to investigate the transition energy level between the neutral and charged defects, the formation energies of a X-doped SnS₂ monolayer in different charged states under S-rich growth conditions were calculated. Fig. 3 shows the formation energies as a function of the Fermi level E_F. It can be seen that the calculated (0/−1) transition energy levels are 0.61 eV, 0.60 eV and 0.68 eV above the VBM for Li, Mg and Al-doped single-layer SnS₂, respectively. These large values of transition energy level indicate that the X dopants are deep acceptor impurities.

Table 3 The total magnetic moments M (μ_B), and formation energies E_f (eV) of X-doped single-layer SnS₂ under Sn-rich and S-rich conditions

X-doped SnS2	M (μB)	E f (eV)
		Sn-rich	S-rich
Li	3.00	5.18	3.57
Mg	1.75	4.92	3.18
Al	0	1.32	0.45

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Fig. 3 The formation energies of X substitution (X_Sn) as a function of the Fermi level under S-rich conditions.

On the other hand, another issue that should be paid attention is the formation of compensating defects, which can kill the hole carriers, for instance the formation of a S vacancy (V_S). This hole killing mechanism has been already observed in the DFT+U studies of Cu-doped ZnS reported by Wang et al.³⁶ Therefore, the complex defect of X_Sn + V_S is introduced to explore whether it is more favorable or challenging to form p-type characteristics in the X-doped SnS₂ monolayer. Based on our calculations, the formation energies of the complex defect of X_Sn + V_S under S-rich conditions are 12.15 eV, 8.38 eV and 5.06 eV for Li, Mg and Al-doped SnS₂, respectively, which are much higher than that of separated neutral and charged X_Sn and V_S defects. It indicates that the V_S related defects are difficult to form in this situation. That is to say, this mechanism of hole compensation could be less pronounced in eliminating the hole carriers, thereby making the p-type doping for SnS₂ more favorable.

3.2. Electronic properties

To investigate the effects of doping on the characteristics of the electronic structure of SnS₂, we present the total density of states (TDOS) and partial density of states (PDOS) of single-layer SnS₂ with X doping in Fig. 4. For comparison, the TDOS and PDOS of a pure SnS₂ monolayer are also calculated and displayed in Fig. 4(a) and (e). As can be seen, for pristine single-layer SnS₂, the valence band (VB) mostly comprises the S 3p states, while the conduction band (CB) is mainly dominated by the hybridization of the S 3p and Sn 5s states. These results are in accordance with previous experimental and theoretical calculations,^22,26,33 which further indicates our calculated method is reasonable.

Fig. 4 Calculated TDOS (a)–(d) and PDOS (e)–(h) for pure and X-doped single-layer SnS₂. The vertical dash line indicates the E_F position.

For Li and Mg doping in single-layer SnS₂, as shown in Fig. 4(b) and (c), the Fermi level (E_F) penetrates into the VB which indicates p-type doping. The remarkable difference compared to the TDOS in Fig. 4(a) is that the incorporation of Li or Mg atoms leads to the occurrence of defect states located above the valence band maximum (VBM). In addition, the PDOS of Fig. 4(f) and (g) show that the VB is still mainly dominated by the S 3p states and the CB is composed of a mixture of the S 3p and Sn 5s states. The Li or Mg dopant has only a little contribution to the constitution of the VB and CB, but it has a major influence on the adjacent atoms and changes their density of states distribution, thereby resulting in the hybridization between most of the S 3p orbitals and a small number of the Sn 4d orbitals to form the defect states. These defect states are spin-polarized hole states, which makes the spin-up and spin-down TDOS asymmetric and causes spin splitting. This implies that the single-layer SnS₂ doped with Li or Mg atoms exhibits magnetic ground states. Fig. 4(d) and (h) present the TDOS and PDOS of Al doping in single-layer SnS₂. Similar to the Li and Mg doping cases, the components of the VB and CB show no obvious changes, and the injection of Al atoms also introduces defect states with S 3p orbital character in the band gap. However, one can see that the spin-up and spin-down TDOS are symmetric, which suggests that the Al-doped single-layer SnS₂ exhibits non-magnetic ground states.

Table 3 lists the calculated total magnetic moments of doped systems. They are 3.00 μ_B, 1.75 μ_B and 0 μ_B for Li, Mg and Al doped SnS₂, respectively. We notice that the induced magnetic moments exhibit a monotonic decreasing trend, which may be ascribed to the decrease in hole density introduced by doping. In particular, although one hole is injected when the Al substitutes a Sn atom, the system is non-spin-polarized. The reason can be explained as follows; it is well known that the hole-doped system becomes spin polarized if it satisfies the Stoner criterion D(E_F)J > 1, where D(E_F) is the density of states at the Fermi level and J denotes the strength of the exchange interaction.²⁷ As can be seen from the TDOS, the values of D(E_F) are 8.94, 7.55 and 0.79 states per eV for Li, Mg, and Al doping, respectively. This value for Al doping is relatively small compared to that for Li and Mg doping. Consequently, the relatively low D (E_F) will result in the Stoner criterion being unlikely to be satisfied and thereby there is no magnetic moment in Al-doped single-layer SnS₂. In order to more intuitively observe the distribution of magnetic moments, the spin density distributions of Li and Mg doped systems are plotted in Fig. 5. Obviously, the spin density is mainly located on the nearest-neighbor and third-neighbor S atoms. The dopant Li or Mg has no spin polarization, which differs from the results of nonmetal doping in the SnS₂ monolayer,²⁶ in which the induced spin polarizations are almost located on the defect site. The above results suggest that the only key role of the dopant is to provide S atoms with holes and the spontaneous magnetization in the system is induced by the hole with S 3p orbital character, which is consistent with the analysis of the density of states.

Fig. 5 Spin density distribution for Li-doped (a) and Mg-doped (b) single-layer SnS₂.

3.3. Optical properties and photochemical energy conversion applications

As a promising material in the fields of photovoltaic devices and photocatalysis, it is essential to explore the effects of X doping on the optical properties of single-layer SnS₂. In our calculations, the optical absorption coefficient α(ω) is obtained from the expression:where the imaginary part ε₂(ω) is directly associated with optical absorption and the real part ε₁(ω) is calculated from ε₂(ω) by the Kramer–Kronig transformation:³⁷In Fig. 6, we present the optical absorption spectra of X-doped single-layer SnS₂ as a function of photon energy. As a reference, the optical absorption coefficient of pure SnS₂ monolayer is also calculated and plotted in Fig. 6. Moreover, different optical incident light polarization directions, parallel (E∥z) and perpendicular (E⊥z) to the z-axis, are taken into account in this work for each doping case. As can be seen from Fig. 6, the characteristics of the optical absorption coefficients along the E∥z and E⊥z directions are different, which indicates that the optical absorption presents anisotropy for doped systems. This is owing to the different dielectric response caused by the hexagonal structure of doped SnS₂. The optical anisotropy is also observed in Sn_1−xTi_xS₂ ternary alloys.³¹ Besides, for all doping cases, the absorption along the E⊥z direction is stronger than that along the E∥z direction. Thus, in order to enhance the efficiency of the solar spectrum, the growth direction perpendicular to the z-axis should be chosen for the low valence metal X-doped single-layer SnS₂. In Fig. 6(a), we can see that the absorption edges of the three doped systems exhibit an obvious red shift with respect to pure SnS₂, which is associated with the decrease in band gap. It indicates that low valence metal X doping is beneficial to improve the optical absorption in the visible light range. Furthermore, a broad absorbance peak from 0 to 2 eV occurs for each doping case, which is advantageous to improve the capacity of absorption in the low energy region. From the density of states analysis in Section 3.2, the appearance of the peak is directly related to the intraband transition caused by the unoccupied S 3p states located above the E_F. That is to say, the low valence metal X doping in single-layer SnS₂ can enhance the effective utilization of the solar spectrum, especially in the near-infrared light region.

Fig. 6 The optical absorption coefficients as a function of photon energy along the directions of perpendicular (a) and parallel (b) to the z axis for X doping in single-layer SnS₂.

In order to evaluate the effects of X-doped SnS₂ on photocatalytic water splitting, the energy levels of the doped systems are calculated and compared with the standard reduction and oxidation potentials of water. In our work, the energy zero is set to the reduction potential of H⁺/H₂, and the valence and conduction band-edge positions are estimated from the calculated density of states. As a reference, the energy level diagram of pure single-layer SnS₂ is also given in Fig. 7. Apparently, the VBM of the pristine SnS₂ monolayer is below the oxidation potential of H₂O/O₂ while the CBM does not lie across the reduction potential of H⁺/H₂. This indicates that pure single-layer SnS₂ is only favorable for oxygen evolution but not for hydrogen evolution, which agrees with the theoretical results of ref. 24. For X-doped (Mg and Al) single-layer SnS₂, the values of the VBM lie more negative than the oxidation level of water and the CBM values still lie within the reduction level of water, which shows that they are active only for the photo-oxidation of water. However, for Li doping in SnS₂, the VBM lie more negative than the oxidation potential of H₂O/O₂ and the CBM is about 0.03 eV higher than the reduction potential of H⁺/H₂, which indicates that the doped system is beneficial for both the photo-reduction and photo-oxidation of water. Furthermore, the stability of semiconductors in aqueous solution is also important for the photocatalytic ability of materials, in addition to the band edge alignment. As reported by Wang et al.,³⁸ whether the semiconductor is resistant to photocorrosion depends on the alignment of thermodynamic oxidation (φ^ox) and reduction potentials (φ^re) relative to the water redox potentials. The φ^ox and φ^re should be taken into account for the choice of candidate photocatalytic materials. Therefore, in order to investigate the stability of doped systems in aqueous solution, the thermodynamic potentials were estimated with the model proposed by Wang et al., as shown in Fig. 7. As can be seen, the φ^ox is lower than the oxidation potential of H₂O/O₂ for Mg (or Al)-doped single-layer SnS₂, which shows that this material is stable with respect to hole oxidation. For Li-doped SnS₂, the φ^ox is lower than the oxidation potential of H₂O/O₂ and the φ^re is higher than the reduction potential of H⁺/H₂, indicating this doped system is stable with respect to both hole oxidation and electron reduction. Thus, Li-doped single-layer SnS₂ is expected to be a potential candidate for overall water splitting under visible light radiation.

Fig. 7 Energy level diagram of pure and X-doped single-layer SnS₂ with respect to the standard reduction and oxidation potentials of water. The red and blue solid lines indicate the thermodynamic reduction and oxidation potentials, respectively.

4. Conclusions

The first-principles calculations were performed to investigate the electronic and optical properties of low valence metal X (X = Li, Mg and Al) doping in single-layer SnS₂. The results show that the doping is energetically favored under S-rich conditions with respect to Sn-rich conditions, and Al doping is easier to realize than Li and Mg doping. There is ionic bonding character for Li–S and Mg–S bonds, and covalent bonding behavior for Al–S bonds. The defect states of S 3p character are introduced in the band gap, leading to a total magnetic moment of 3.00 μ_B and 1.75 μ_B for Li and Mg-doped SnS₂, respectively. However, the system with Al doping exhibits non-magnetic ground states, which is due to the low hole density around the Fermi level. The calculations of optical properties show that the optical absorption along the xy plane is stronger than that along the z direction, and the red shift of absorption edges is observed for all doping cases, which accordingly improves the photocatalytic ability in the visible light range. Also, the effective utilization in the near-infrared light region is enhanced because of the defect states. In addition, Li-doped single-layer SnS₂ is expected to be a potential candidate for overall water splitting whereas Mg and Al doping is suitable only for oxygen evolution.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (51074112) and (11247224), and the supercomputing resources were supported by the High Performance Computing Center of Tianjin University, China.

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