First-Principle Insight into Ga-Doped MoS₂ for Sensing SO₂, SOF₂ and SO₂F₂

Abstract

First-principle calculations were carried out to simulate the three decomposition gases (SO₂, SOF₂, and SO₂F₂) of sulfur hexafluoride (SF₆) on Ga-doped MoS₂ (Ga-MoS₂) monolayer. Based on density functional theory (DFT), pure MoS₂ and multiple gas molecules (SF₆, SO₂, SOF₂, and SO₂F₂) were built and optimized to the most stable structure. Four types of Ga-doped positions were considered and it was found that Ga dopant preferred to be adsorbed by the top of Mo atom (T_Mo). For the best adsorption effect, two ways of SO₂, SOF₂, and SO₂F₂ to approach the doping model were compared and the most favorable mode was selected. The adsorption parameters of Ga-MoS₂ and intrinsic MoS₂ were calculated to analyze adsorption properties of Ga-MoS₂ towards three gases. These analyses suggested that Ga-MoS₂ could be a good gas-sensing material for SO₂ and SO₂F₂, while it was not suitable for SOF₂ sensing due to its weak adsorption. This work provides a theoretical basis for the development of Ga-MoS₂ materials with the hope that it can be used as a good gas-sensing material for electrical equipment.

1. Introduction

SF₆ is known as a colorless, odorless, non-toxic, and incombustible inert gas [1]. It has an octahedral molecular structure and high chemical stability with short bond length and high bond energy [2]. SF₆ is used for the insulation of Gas-Insulated-Switchgear (GIS) installations and arc extinguishing dielectric due to its extraordinary arc extinguishing property, insulation performance, and adequate chemical steadiness [3]. During the long running times, GIS installations may get some insulation defects such as metal particle defects, metal protrusion defects, air gap defects, etc. [4]. Insulating defects will initiate partial discharge and lead to the disintegration components of SF₆, such as SO₂, SOF₂, and SO₂F₂, etc. [5]. On the one hand, some decomposition products are corrosive, which may cause certain damages to the equipment [6,7]. On the other hand, the stability and insulation of the decomposition gases are far inferior than that of SF₆ [8]. In order to ensure the stable and safe operation of GIS equipment, the specific types and degree of equipment defects could be evaluated by measuring the types and concentrations of SF₆ disintegration components [9]. At present, one of the main methods to detect SF₆ disintegration products is the gas sensor detection method [10]. MoS₂ monolayer is a new member of two-dimensional materials like graphene, which has unique physical, chemical, and electrical characters [11]. According to previous papers, MoS₂ monolayers have a bandgap of 2.06 eV, suitable carrier fluidity, and high thermal stability [12,13]. In general, its unique structure makes it exhibit good gas sensitivity and adsorption characteristics [14]. Furthermore, published literature already proved that some metal or non-metal doping on MoS₂ monolayers could further enhance their sensitivity to gas molecules [15,16]. The reason was the fit doped atoms regulate the electrons on the surface of MoS₂ monolayers and improve the electron density of the doping points to realize the orbital interaction between the doped atoms and some atoms of the gas molecules [17]. Wang J.X. et al. developed a hydrothermal synthesis of Au-MoS₂ microspheres, whose conductivities were better than that of the intrinsic MoS₂ material [18]. Abbas H.G. et al. modified MoS₂ with non-metallic atoms N and P, and tested the adsorption of O₂ and NO. They found that the adsorption effects of modified N-MoS₂ and P-MoS₂ were stronger than that of intrinsic MoS₂ [19]. Ga is a common semiconductor dopant, which is used as the dopant of nitrogen, arsenic, phosphorus, and other elements. However, as far as we know, the Ga-MoS₂ monolayer has not been reported for its application in SF₆ decomposition products detection.

In this paper, Ga-MoS₂ was selected as sensitive material for adsorption of three typical SF₆ disintegration components (SO₂, SOF₂, and SO₂F₂). We performed density functional theory (DFT) method and simulated the adsorption of three gas molecules onto the intrinsic MoS₂ and Ga-MoS₂, aiming to shed light on its adsorption ability [20,21]. The optimal configuration of each structure, adsorption energy, charge conversion, density of states (DOS), and band structure were calculated through the DFT method [22]. Furthermore, the simulation results were compared, and the conclusions of material adsorption performance were obtained.

2. Computational Details

Our calculations were designed to qualitatively analyze the effects of Ga doping on sensing properties of MoS₂ at the atomic level. The calculation method was basically consistent with the previous research, so that the results were comparable. The adsorption between MoS₂-based materials and gas molecules were studied with the DFT method, which is one of the most effective ways to predict the performance of materials by calculating their electronic structures [23]. The molecular spin-polarized algorithms were achieved using DMol³ package of Material Studio (MS). The generalized gradient approximation (GGA), which is the Perdew–Burke–Ernzerhof (PBE) functional, was chosen to figure out the doping and hybridization between electrons [24,25]. Within the function of MS software, the double numerical plus polarization (DNP) was utilized as the atomic orbital base install. Meanwhile, the DFT semi-core pseudopotential (DSSP) method was selected to deal with the influence of core electron relativity [26,27,28].

The Brillouin zone of MoS₂ monolayer systems was sampled with k-point of 5 × 5 × 1, and Self-Consistent Field (SCF) convergence criterion was set to 1 × 10⁻⁶ Ha [29]. The convergence criteria of geometry optimizations were set to 5 × 10⁻³ A for displacement, 2 × 10⁻³ Ha/Å for force, and 10⁻⁵ Ha for energy [30]. A 4 × 4 × 1 MoS₂ monolayer supercell was built, including 16 Mo and 32 S atoms with a vacuum zone of 15 Å [31].

In this paper, the difficulty of doping could be judged by analyzing the energy of formation, adsorption energy, and charge transfer capacity.

We obtained the energy of formation ($E_{form}$) through the calculation:

$$E_{form}=E_{Ga-Mo{S}_2}-E_{Mo{S}_2}-E_{Ga}$$

(1)

$E_{Ga-Mo{S}_2}$ is the energy of the system after Ga doping. $E_{Mo{S}_2}$ and $E_{Ga}$ denote the energy of pure MoS₂ and Ga atom, respectively [32,33].

The adsorption energy ($E_{ad}$) of each gas molecules on Ga-MoS₂ monolayer were calculated by the following equation:

$$E_{ad}=E_{Ga-Mo{S}_2/gas}-E_{Ga-Mo{S}_2}-E_{gas}$$

(2)

$E_{Ga-Mo{S}_2/gas}$ is the total energy of gas-adsorbed Ga-MoS₂ monolayers and $E_{gas}$ represents the energy of gas molecules before adsorption [34,35].

Mulliken charge characterized the number of electrons carried by gas molecules adsorbed. It was utilized to calculate the charge transfer between Ga-MoS₂ and gas molecules. The definition of charge transfer ($Q_t$) used in this paper is:

$$Q_t=Q_{adsorbed\left(gas\right)}-Q_{isolated\left(gas\right)}$$

(3)

$Q_{adsorbed\left(gas\right)}$ and $Q_{isolated\left(gas\right)}$ mean the number of charges carried by gas molecules before and after adsorption. Normally, the figure of $Q_{adsorbed\left(gas\right)}$ is zero. If electrons are shifted from gas molecules to Ga-MoS₂ monolayers, $Q_t$ is positive [36,37,38].

3. Results and Discussion

3.1. Geometric Structure of Gas Molecules, MoS₂, and Ga-MoS₂ Monolayer

First, the geometric structures of SF₆, SO₂, SOF₂, and SO₂F₂ were optimized to their steadiest configuration before studying their adsorption. Figure 1 displays the four structures and the information of bond lengths and angles are shown in

Table 1. Structural parameters of gas molecules.

Gas Molecule	Bond Length (Å)		Bond Angle (°)
SF6	S-F	1.64	F-S-F	90.3
SO2	S-O	1.48	O-S-O	119.94
SOF2	S-F	1.67	O-S-F	107.14
	S-O	1.46	F-S-F	93.039
SO2F2	S-F	1.61	O-S-O	126.73
	S-O	1.44	O-S-F	107.74
	-		F-S-F	94.44

.

A SF₆ molecule has a regular octahedral structure with six F atoms arranged symmetrically around an S atom. It is difficult to accumulate enough energy for collision ionization because of the large molecular diameter of SF₆. When electrons attach and collide with SF₆ molecules, energy loss will increase and further weaken its ionization ability. Form Figure 1b, the SO₂ molecule had structure presenting a highly symmetrical “V” shape. SOF₂ molecule presented a tetrahedral structure, as shown in Figure 1c. SO₂F₂ molecule had a similar structure to SOF₂. Figure 1d indicates that SO₂F₂ was symmetrical about the plane where the mid-perpendicular line of two F atoms or two O atoms were connected. The bond length and bond angle of the optimized structure of these gases were consistent with the previous reference [39]. The optimized pure MoS2 monolayer is shown in Figure 2a. The bandgap of the optimized structure is displayed in Figure 3a. The energy gap was 2.06 eV, which was less than the experimental value (3.2 eV) and consistent with the simulation value (2.06 eV) [40]. It indicates that the energy required for the electrons to jump between the valence band and conduction band was large and the electrons were difficult to be excited.

Four types of Ga-doped positions on pure MoS₂ monolayers were considered, which were T_S (at the top of the S atom) in Figure 2b, B_S-S (the bridge site between two S atoms) in Figure 2c, T_Mo (at the top of the Mo atom) in Figure 2d, and T_H (above the hexagonal ring center of MoS₂) in Figure 2e, respectively [41].

As shown in

Table 2. Formation energy of the four Ga-doping models.

Doping Sites	TS	BS-S	TMo	TH
$E_{form}$(eV)	−1.70	−1.74	−1.75	−1.60

, we calculated $E_{form}$ for the four Ga doping models. It was evident that the most favorable doping position had the lowest formation energy, which means that the reaction occurred most easily [42,43]. The T_Mo site had the smallest formation energy of −1.75 eV. Therefore, for the optimization model obtained by the four ways Ga can be doped on MoS₂, the optimization model of T_Mo position was the best. From the bond-forming parameters, Ga atoms preferred to approach MoS₂ monolayers from the top of Mo atoms. Three of Ga-S bonds were formed between Ga and MoS₂ monolayers, all of which were closed to 2.70 Å in length, indicating the strong interaction between Ga and S atoms. The results show that the surface structure of MoS₂ did not change much with the doping of Ga. The bond angles of Mo-S-Mo and S-Mo-S were 81.225° and 82.445°, respectively, which had little change from 81.962° before doping. Simultaneously, the distance between the Ga atom and Mo atom was a bit long (3.55 Å), showing the inferior attractive force between them. In conclusion, Figure 2d displays the most stable structure, which is the optimal model used for subsequent adsorption calculations.

Figure 3 displays the bandgap structures comparison before and after the Ga doping of MoS₂. Besides, to compare more intuitively the similarities or differences of electronic structures before and after Ga doping, the DOS contrast was carried out as displayed in Figure 4. In Figure 3, the bandgap between the valence band and conduction band decreased to 1.90 eV. The separation distance corresponds to the width between the two peaks near the Fermi level of DOS. Figure 4 shows that the total density of states (TDOS) shifted to the lower energy direction compared with that before Ga doping. From the Fermi level, it can be seen that the distance between the valence band and the conduction band shortened. It shows that the conductivity of Ga-MoS₂ ameliorated due to the doping of Ga.

3.2. Adsorption Analysis of Ga-MoS₂ Monolayer to Gas Molecules

3.2.1. Adsorption Analysis of MoS₂ Monolayer to Gas Molecules

As Figure 5 shows, the optimized pure MoS₂ model was used to adsorb the three target gases. The adsorption parameters of three gas adsorption systems listed in

Table 3. Parameters of adsorption of the target gases on MoS₂ surface.

Gas Molecules	D (Å)	${\mathit{E}}_{\mathit{a}\mathit{d}}\left(\mathbf{eV}\right)$	${\mathit{Q}}_{\mathit{t}}\left(\mathbf{e}\right)$	Structure
SO2	3.50	22.34	−0.04	∠ O-S-O	112.64
SOF2	3.58	22.41	−0.04	∠ O-S-F ∠ F-S-F	104.10 95.73
SO2F2	1.69	25.03	−0.68	∠ O-S-O ∠ O-S-F ∠ F-S-F	100.17 95.38 94.08

, including adsorption distance (D), $E_{ad}$, and $Q_t$ [44]. The adsorption distance between gas molecules and MoS₂ was large in the adsorption model, which indicates that intrinsic MoS₂ had weak adsorption capacity for the three gases. It also can see the adsorption of SO₂, SOF₂ by MoS₂ tended to be close to S atom in SO₂ and SOF₂ molecules, while SO₂F₂ molecule was close to O atom. The S-F bond was slightly elongated in SO₂F₂ molecule. As seen in Table 3, the adsorption energies of the three target gases were all positive, indicating that the reaction was endothermic and could not be spontaneous. It proves that the intrinsic MoS₂ had low adsorption effect on the target gases. The bond angles of SO₂, SOF₂, and SO₂F₂ were reduced to a certain extent after being adsorbed. The charge transfer values of SO₂, SOF₂, and SO₂F₂ were negative, and mean that electrons shifted from MoS₂ surface to gas molecules during the adsorption process. However, the electrons were not active during the adsorption process due to the micro charge transfer in the three adsorption systems. In summary, the intrinsic MoS₂ had a weak adsorption capacity for the target gases. The improved adsorption performance of MoS₂ required doping of metal or non-metal atoms.

The band structures of the adsorption systems corresponding to the three gases were analyzed, as shown in Figure 6. The bandgap of the intrinsic MoS₂ was 2.06 eV according to the previous calculation. It can be seen from Figure 6a, the bandgap decreased to 0.57 eV after adsorption of SO₂ molecule, indicating that electrons more easily transited from the valence band to the conduction band, and the conductivity of system significantly improved after adsorption [45]. Figure 6b displays that the bandgap of the SOF₂ molecule adsorption system reduced by 0.67 eV, illustrating that the conductivity of the system was raised. Figure 6c demonstrates that the bandgap of the SO₂F₂ molecule adsorption system diminished by 0.33 eV, the bandgap changed less than the other two gases, and the system’s conductivity did not change evidently. Overall, the bandgap of MoS₂ decreased most obviously after SO₂ molecule adsorption.

3.2.2. Selection of Adsorption Modes for Gas Molecules in Ga-MoS₂ Monolayer

For the best adsorption effect, two ways for SO₂, SOF₂, and SO₂F₂ to approach the doping model were compared [46], as shown in Figure 7. The parameters of gas adsorption on Ga-MoS₂ in different approaches are listed in

Table 4. Parameters of gas adsorption on Ga-MoS2 in different approaches.

Parameters	SO2		SOF2		SO2F2
Approach	Mode 1	Mode 2	Mode 1	Mode 2	Mode 1	Mode 2
D (Å)	Ga-O:1.95	Ga-S:2.86	Ga-F:3.57	Ga-O:3.21	Ga-O:2.24	Ga-F:1.91
$E_{ad}$(eV)	−0.61	−0.67	0.36	0.27	−0.15	−0.63
$Q_t$(e)	−0.40	−0.42	−0.01	0.01	−0.59	−0.60

.

As Figure 7(a1,a2) shows, two types of SO₂ adsorption models were built: O atom or S atom near the Ga atom. It can be seen that in the adsorption system obtained after optimization by mode 2, approach mode had changed, while the approach mode 1 had not changed, basically. In the two modes, SO₂ lost electrons and the Ga-MoS₂ doping model gained electrons. After calculation, the numerical value of the $E_{ad}$ of the adsorption model constructed in mode 2 was more significant than that constructed in mode 1. At the same time, the absolute value of $Q_t$ of the former was larger than that of the latter, and both are negative. It shows that the adsorption process approached in mode 2 was more intense. It also displays that Ga-MoS₂ was more inclined to mode 2 for the adsorption of SO₂. Therefore, the adsorption structure obtained by mode 2 was selected as the best structure to facilitate follow-up analysis.

It could be obtained from the above analysis that the adsorption process in the way that S atoms approach the doping model was difficult to occur. This paper adopts two gas approach modes for the adsorption of SOF₂. The one was mode 1 that approaches F atoms’ doped structure. The other was mode 2, which was approaching the doped structure with O atoms as Figure 7(b1,b2) shows. After optimization calculations, the two adsorption modes were basically unchanged, but the adsorption distance was relatively long. The doping model had a weaker adsorption effect on SOF₂ for both the approach methods. Both of their adsorption energies were positive, and the amount of charge transfer was very small and close to zero. It proved the adsorption effect of Ga-MoS₂ on SOF₂ was not ideal. However, considering the completeness of the analysis and comparison, mode 2, which has lower adsorption energy, was selected in this paper for the subsequent calculation.

Similarly, for the adsorption of SO₂F₂, two adsorption methods were selected in this paper. One was to use O atoms to approach the doped structure in Figure 7(c1) and the other was to use F atoms to approach the doped model in Figure 7(c2). It can be seen that the two adsorption methods had not changed to a large extent after optimization calculation. In addition, both SO₂F₂ and Ga-MoS₂ had a certain degree of deformation in mode 2. Among them, an S-F bond of the SO₂F₂ was elongated, and the bond between Ga and MoS₂ was also elongated, which shows that the adsorption process was relatively strong. In comparison, mode 2 had larger adsorption energy and charge transfer amount than mode 1, which also proved that the adsorption process was stronger. In summary, the adsorption model obtained by mode 2 was better for Ga-MoS₂ adsorption of SO₂F₂, so it was selected as the subsequent energy band and DOS analysis.

In order to show the varieties of structural parameters before and after adsorption, D, $E_{ad}$, $Q_t$ and some structural parameters of mode 2 are listed in

Table 5. The parameters for the target gases on the Ga-MoS₂ surface.

Gas Molecule	D (Å)	${\mathit{E}}_{\mathit{a}\mathit{d}}\left(\mathbf{eV}\right)$	${\mathit{Q}}_{\mathit{t}}\left(\mathbf{e}\right)$	Gas Structure		dGa-S (Å)	∠ S-Ga-S (°)
SO2	2.30	−0.67	−0.42	∠ O-S-O	105.53	3.32	52.80
SOF2	3.21	0.27	0.01	∠ O-S-F	106.76	2.66	71.19
				∠ F-S-F	93.543
SO2F2	1.91	−0.63	−0.60	∠ O-S-O	121.60	2.94	48.62
				∠ O-S-F	105.25
				∠ F-S-F	88.32

. Among all the adsorption models of Ga-MoS₂, the $E_{ad}$ of SO₂ and SO₂F₂ were both negative, indicating that Ga-MoS₂ could adsorb the above two gases more stably. At the same time, the $E_{ad}$ of SOF₂ was positive, which suggests that Ga-MoS₂ had some difficulty in adsorption of SOF₂.

3.2.3. Energy Band and DOS Analysis

For the sake of further discussions about electronic characteristics of the model obtained by adsorption, the energy band structure and DOS of the three adsorption models were analyzed [47,48]. Figure 8 shows the band structure diagram of the adsorption system obtained by pure MoS₂ and Ga-MoS₂ adsorbing SO₂, SOF₂, and SO₂F₂.

It can be seen from the above description that the bandgap of Ga-MoS₂ without adsorbed gas was 1.90 eV. Figure 8a displays the energy band structure diagram of the adsorption system after Ga-MoS₂ adsorbed SO₂. The energy bandgap of the system reduced to 0.60 eV, which shows that the adsorption of SO₂ could make the electrical conductivity of the material promoted to a certain extent. From Figure 8b, it can be seen that after SOF₂ adsorption, the bandgap of the adsorbed system dropped to 1.76 eV. This indicates that electrons could more likely transition from the valence band to the conduction band than the unabsorbed system. As a result, the conductivity of the material had been improved. Figure 8c displays that after the doped structure adsorbs SO₂F₂, the bandgap of the adsorption system becomes 1.93 eV, which is an increase of 0.03 eV compared to the bandgap of the system without gas adsorption. The energy minimum band distance increases slightly. The conductivity of the entire system decreases, but the decrease in the conductivity of the system was very limited due to the small bandgap increase. Thus, the adsorption of SO₂F₂ hardly influences the conductivity of Ga-MoS₂ monolayer.

To sum up, the conductivity of the material could be improved to varying degrees by adsorbing SO₂ and SOF₂. At the same time, adsorption of SO₂F₂ reduced slightly the conductivity of the material.

Figure 9, Figure 10 and Figure 11 show the DOS of Ga-MoS₂ for SO₂, SOF₂, and SO₂F₂ adsorption structures, divided into TDOS and partial density of states (PDOS).

Figure 9a represents the comparison of the TDOS of the system before and after the adsorption of SO₂. As shown, the TDOS of Ga-MoS₂ had eight peaks before adsorption of SO₂. After the adsorption of SO₂, the adsorption system added a new peak near −10 eV, which indicates that the electron orbit of the adsorption system had changed during the adsorption process. At the same time, the TDOS of the system after adsorption was slightly shifted to the right compared with that before the adsorption. After the adsorption of SO₂, the peak value of TDOS near 1 eV had increased, and electrons gathered at the bottom of the conduction band. So, the conductivity of the material had been improved to a certain extent. According to the PDOS of Ga-MoS₂ for SO₂ adsorption displayed in Figure 9b, the DOS of the listed atoms were mainly distributed in the range of −7.5~0 eV. The hybridization primarily occurred between the 4p orbital of Ga and the 2p orbital of O, and the PDOS of −7.5~−5 eV and −2.5~2.5 eV regions with varying degrees of overlap. At the same time, the 3p orbital of S had the most DOS distribution at the Fermi level. It can be inferred that S had the greatest influence on the electrical conductivity of the entire material in this adsorption system.

Figure 10a displays the TDOS changes of the system before and after SOF₂ adsorption. The TDOS of the Ga-MoS₂ system after adsorption had three new peaks. Additionally, the TDOS after adsorption was slightly moved to the left compared to the system before adsorption. The TDOS at the Fermi level had the obvious increase, meaning that the electrical conductivity of the entire system had been improved after being gas adsorbed. The electrons were more likely to jump to the conduction band. The PDOS of the system could be obtained in Figure 10b. The S-3p, F-2p, and Ga-4p orbitals mainly distributed in the range of −12.5~−5 eV. The hybridization of the system was mostly between the 4p orbital of Ga and the 2p orbital of F. At the same time, it can be seen that in this adsorption system, the 3p orbital of S has the most DOS distribution at the Fermi level. It be concluded that, in this system, S had the strongest influence on the electrical conductivity of the material.

From Figure 11a, the TDOS of the entire system had a more obvious shift to the right after SO₂F₂ was adsorbed. Focusing on the Fermi level, it is found that the DOS at the Fermi level does not change much before and after adsorption, which indicates that the conductivity of the entire system changed slightly after adsorption of SO₂F₂. Figure 11b shows the PDOS of the adsorption system. The DOS of each atom was mainly distributed in the range of −7.5~0 eV. The 4s orbital of Ga and the 2p orbital of F overlap obviously, suggesting that the hybridization of the above-mentioned two orbitals was mainly during the adsorption process. At the same time, it can be seen that in this adsorption system, at the Fermi level, the 4s orbital state density distribution of Ga is the largest, which means that in this adsorption system, the electrical conductivity of the material is mainly affected by Ga atom.

4. Conclusions

In this work, theoretical calculations were carried out to study the adsorption properties of Ga-MoS₂ for SO₂, SOF₂, and SO₂F₂. The positions of Ga doping were considered. The two ways of gas molecules to approach the doping model were compared. The adsorption parameters, energy bands, and DOS were calculated and analyzed. The main conclusions are as follows:

• Ga dopant was most likely to be adsorbed onto the MoS₂ monolayer through T_Mo site.
• The intrinsic MoS₂ had a weak adsorption capacity for the target gases.
• SO₂ molecule tends to approach the doped model with S atoms. SOF₂ molecule prefers to approach the doped model with O atoms. SO₂F₂ molecule is likely to approach the doped model with F atoms.
• The conductivity of the material could be improved to varying degrees by adsorbing SO₂, SOF₂, while adsorption of SO₂F₂ had little effect on the conductivity of the material. The $E_{ad}$ of SO₂ and SO₂F₂ were both negative, indicating that Ga-MoS₂ could adsorb the above two gases more stably. The $E_{ad}$ of SOF₂ is positive, which proves that Ga-MoS₂ had some difficulty in adsorption of SOF₂. The Ga-MoS₂ can be used as an excellent gas-sensing material for SO₂ and SO₂F₂ molecules.