Sensing Properties of Vacancy and Pd-Doped Graphene Layer: A First-Principles Study

: In this paper, the effect of SO 2 adsorption on graphene (intrinsic, vacancy, and doped) is investigated for structural and electronic properties to exploit their potential applications as a gas sensor. The adsorption energy, charge transfer, magnetic moment, density of states, as well as band structure of the SO 2 molecule on the vacancy and doped graphene systems are thoroughly discussed. The most stable adsorption site for SO 2 on various graphene sheets is also identified and reported. It is found that SO 2 molecule is weakly adsorbed on intrinsic graphene (IG) with low adsorption energy. In contrast, vacancy defect and Pd doping significantly enhance the strength of interaction between SO 2 molecule and the modified substrates. The dramatic increase in adsorption energy and charge transfer of these systems are expected to induce significant changes in the electrical conductivity of the vacancy graphene (VG) and Pd-doped graphene (PdG) sheets. Furthermore, the results present the potential of Pd-doped vacancy graphene (Pd-VG) for molecular sensor application.


Introduction
As industrialization advances rapidly, combating air pollution has become a global challenge. Gas sensor plays an irreplaceable role in numerous applications, including environmental monitoring, agricultural production, medical diagnosis, and aerospace [1][2][3]. Its value derives from the capacity to detect gas molecules in the environment at low concentrations, especially for toxic and harmful gases. Sulfur dioxide (SO2) is the most common, simple and irritating sulfur oxide. It is one of the major air pollutants resulting primarily from the combustion of coal, oil and other sulfur-containing minerals [4]. SO2 is readily soluble in water and has a powerful stimulating effect on the eyes and breathing organs. Furthermore, SO2 is the major cause of acid rain, which causes severe environmental damage. Meanwhile, SO2 is one of the main decay products of gaseous SF6 gas decomposition [5]. To control environmental acidification and ensure better GIS insulation, detecting residual SO2 gases has become a priority for environmental surveillance. In recent years, numerous types of gas sensors have been designed for this purpose to accurately monitor SO2 concentration levels and lay the foundation for environmental governance [6][7][8][9][10].
Graphene has generated considerable interest in the field of gas detection due to its extraordinary structural and electronic properties, such as ultra-high specific surface area, high electron mobility, and low electrical noise [11,12]. Certain graphene-based sensors depend on changes in conductivity of graphene sheets due to changes in localized carrier density caused by surface adsorption, which acts as an electron donor or acceptor [13][14][15]. Compared to other nanoscale gas sensors, graphene is more appropriate for highly sensitive marked chemical sensors because every exposed carbon atom can provide information from the surrounding environment [16]. However, many studies have revealed that pristine graphene with the sp 2 -hybridized carbon is almost insensitive to most gas molecules due to the insert π-electron conjugation, which limits its application as gas sensors [17][18][19]. To overcome this limitation, researchers attempted to construct sensitive graphene substrates by fabricating defective or doped atoms. The results showed that the dopants and defects could enhance the adsorption between graphene and gas molecules [20][21][22]. For example, Rezvan et al. have reported a low-cost and simple-to-fabricate methane (CH4) sensor by using graphene decorated with silver (Ag) nanoparticles [23]. Especially, this gas sensor can exhibit a higher response with the CH4 gas concentrations less than 2000 ppm. Moreover, due to its mechanical flexibility, durability and high gas response, this sensor exhibits far better efficiency than previously reported ones. Highly sensitive boron-doped few-layer graphene sensor (BFLGs) was synthesized recently and used successfully for the detection of ammonia (NH3) [24]. The authors also demonstrated that the BFLGs shows higher response and faster recovery compared to the pristine graphene sensor. Another study was that Shukri et al. explored the adsorption of CO and NO on pristine, vacancy, and Pd-doped graphene for structural and electronic properties [25]. The findings show that Pd-doping and vacancy can significantly improve the adsorption capacity of the modified graphene substrate on target gas molecules. Many studies have demonstrated by theoretical analysis and experiments that graphene can be employed as a gas sensor with doping extraneous atoms, introducing defect structure, and applying an electric field to possess appropriate band gap [26][27][28]. Hence, doping and defects have opened up numerous graphene-based applications, such as electronics and detection, due to the distinct nature of each dopant and defects.
In this paper, chapter 1 simulates the sensing applications of different graphene sheets for SO2 molecule from first principles, including intrinsic graphene (IG), vacancy graphene (VG), Pd-doped graphene (PdG) and Pd-doped vacancy graphene (Pd-VG). The adsorption models are carefully constructed to systematically address several fundamental issues. Chapter 2 provides details of the calculation. Chapter 3 analyzes and examines the most favorable adsorption configurations, adsorption energy, charge transfer, density of states (DOS), partial density of states (PDOS), and band structures of the systems. Chapter 4 concentrates on conclusions.

Computational details
All the theoretical calculations in our work were performed with the firstprinciples method based on DFT by using the Vienna ab-initio simulation package (VASP) with projector augmented wave (PAW) potentials [29][30][31][32]. To treat electron exchange and correlation, we chose the Perdew-Burke-Ernzerhof (PBE) [33] formulation of the generalized gradient approximation (GGA), which yields the correct ground-state structure of the combined systems. Plane-Wave basis function was set with a kinetic cut-off energy of 550 eV. A Monkhorst-Pack meshes [34] with the size of 5 × 5 × 1 were employed to the sample bulk Brillouin zone for the electronic properties.
The distance between adjacent graphene layers was kept as 20 Å, which avoids the interactions between periodic images. The ground-state atomic geometries were optimized by relaxing the force below 0.02 eV/Å and the convergence criteria for energy was set with the value of 1.0 × 10 -5 eV/cell. Tetrahedron method with Blöchl corrections [35] was employed for the electronic structures and total energy of our models while the Gaussian smearing was for stress/force relaxations. In order to better describe the interactions between molecules, van der Waals (vdW) interactions are included describing by the DFT-D3 method of Grimme [36]. The adsorption energy, , is defined as where ℎ , 2 , and represent the energy of the substrate, SO2 molecule and each adsorption system, respectively. Considering the different molecular orientations and adsorption sites, the most stable adsorption configuration with the lowest total energy and the highest adsorption energy was obtained by calculation.

Properties of adsorption configurations
To ensure the precision and reliability of the calculation, we constructed a stable adsorption substrate and a model of SO2 molecule. Firstly, the geometric structures of IG and VG were optimized, then the doping behaviour of Pd atoms on the two relaxed structures was studied separately. The top and side views of the optimized geometries and the detailed parameters are presented in Fig. 1. The length of C-C bond on the optimized IG was 1.420 Å, corresponding to the experimental data, as shown in Fig. 1(a). A central carbon atom is eliminated from IG to form VG, as shown in Fig. 1(b). Unlike the IG structure, due to the strain caused by the loss of the central carbon atom, three carbon atoms break out of the graphene plane and the C-C bond near the vacancy is shortened in the range of 0.005 Å to 0.028 Å.
Additionally, the PdG substrate was achieved by replacing the central C atom with Pd atom, as shown in Fig. 1(c). It can be seen that the Pd atom protrudes from the graphene sheet with a protruding height of 0.763 Å. In addition, the doping site of the graphene sheet is deformed, and the Pd-C bond length is between 1.850 Å and 1.999 Å. The measurement parameters of the Pd-VG relaxation structure are illustrated in Fig. 1

(d).
It has been observed that introducing Pd dopant in VG changes its geometry. Relative to the VG, when a Pd atom is substituted for a carbon atom in VG, the Pd atom moves toward the defect center and form new Pd-C bonds with other hanging C atoms.
Similarly, the Pd atom protrudes from the graphene sheet with a protrusion height of 0.636 Å. Pd atom prominence occurs because its radius is much larger than that of C atom. Meanwhile, Pd-VG shows the bond length between Pd to the nearest C atoms is 2.026 Å and the C-C bond length is 1.433 Å. The structural properties of Pd-VG change dramatically once the optimization has been carried out.  Table 1.  Table 1 SO2 adsorbed on IG, VG, PdG, and Pd-VG: adsorption energy ( ), adsorption length ( ), bond length of SO2 molecule after adsorption ( ), band gap of the adsorption complex ( ), charge transfer from the substrate to SO2 molecule (∆ ) and magnetic moment of the total system before adsorption ( ) and after adsorption ( ′ ).

Adsorption performance of intrinsic graphene layer
We first discussed the adsorption behaviors of IG monolayer upon SO2 molecule.
Considering several possible initial positions (i.e. top site, bridge site, and hollow site) to obtain the best adsorption configuration. The optimal position is shown in Fig. 2(a) and the corresponding adsorption parameters are summarized in Table 1. After the adsorbing SO2 molecule, the C-C bond in the interaction region is slightly elongated from 1.420 Å to 1.422 Å, and the S-O bond lengths of SO2 are found to be 1.453 Å, which is also slightly elongated compared to the individual SO2 molecule reported in the previous study [38]. From Table 1, the of SO2 molecule on IG is 0.295 eV, and the adsorption distance is 3.057 Å. The lower and longer adsorption distance indicate typically physical adsorption. Bader charge analysis showed that 0.105e charge was transferred from IG to SO2 molecule, revealing that the SO2 molecule acted as an acceptor in the adsorption phase.
To demonstrate the response of the SO2 molecule to the electronic properties of IG layer, the total density of the polarized spin states of IG without and with adsorption of SO2 has been calculated, as shown in Fig. 4(a). It can be inferred that there is no spin polarization before and after IG adsorption, and the contribution of SO2 molecule in the valence band is mainly between -4 eV and -3 eV, and in the conduction band around 0.5 eV. The DOS at Fermi level has no distinct change and the change in conductivity and magnetism is hardly noticeable. As shown in Fig. 4(b), there is no hybridization between S-3p and O-2p orbitals of SO2 molecule and C-2p orbitals around the Fermi level. The band structures of the adsorption system (before and after SO2 adsorption) was calculated. It was observed that the band gap of IG layer was zero (see Fig. 4(c)), while a small band gap ( ) about 0.02 eV, appeared after the adsorption of SO2 molecule (see Fig. 4(d)). All calculated results indicate that IG is unsuitable for detecting SO2 molecules.

Adsorption performance of vacancy graphene layer
Studies have demonstrated that vacancy defects can enhance the gas sensitivity and adsorption stability of graphene [39,40]. In this part, the adsorption performance of SO2 molecule on VG is examined. Fig. 2(b) presents the most favorable state of SO2 on VG. The optimal adsorption site is that an O atom of SO2 molecule is close to the VG to form an O-C bond, which is consistent with previous researches [41]. After adsorption, as shown in Table 1, the VG adsorption system with the of 2.522 eV and the adsorption distance is 1.425 Å. The charge transfer is 0.325e from VG to SO2 molecule, which is higher than that of IG adsorption system. Moreover, the VG has a magnetic moment of 1.7 μB in our calculations because of the loss of a C atom in VG, which can cause unpaired electrons to be generated around the defect, and then result in asymmetry in the spin-up and spin-down energy level, and thereby generate magnetism. After adsorbing SO2 molecule, the substrate becomes non-magnetic. The adsorption of SO2 molecule pair unpaired electrons with the electrons in SO2, forming chemical adsorption. After the spin-up and spin-down electrons are coordinated, the formation of the bond orbital makes the magnetism disappear. The results suggest that mono-vacancy defect improves the adsorption activity of graphene for SO2 molecules.
As presented in Fig. 5(a), the DOS curve at the Fermi level changes significantly.

Analysis of the electronic properties revealed that hybridization between the O-2p
orbital and the C-2p orbital is existed, which is responsible for the enhancement of adsorption energy for SO2-VG adsorption systems, as shown in Fig. 5(b). Furthermore, the results of the band structures of VG showed that there is an energy band crossing the Fermi level (see Fig. 5(c)), which is equivalent to a Fermi surface drop, similar to typical p-type doping. Fig. 5(d)

Adsorption performance of Pd-doped graphene layer
In this part, we substituted a C atom on the surface of graphene with a Pd atom to achieve the PdG adsorption configuration. There are obvious differences between the relaxed IG and PdG in terms of geometric structure, lattice constant and bond length.
This confirms that doping palladium and other impurities in graphene will cause 6MR deformation near the doping site due to different atomic radiation. The most stable configuration and various geometric parameters of the optimized PdG adsorption system are shown in Fig. 2(c) and Table 1. The of the SO2-PdG system is 5.650 eV and the adsorption distance is 2.281 Å. The larger adsorption energy and shorter adsorption distance suggest that chemical adsorption between SO2 and PdG is enhanced.
Moreover, there is an obvious charge transfer between SO2 and PdG, and the amount of charge transfer is 0.524e. Compared with VG adsorption system, Pd-doping disrupts the original stable structure of pure graphene and enhances behavior for SO2 adsorption.
Besides, the enhancement is also demonstrated by the slight activation of the S-O bond in the SO2 molecule after adsorption, which extends to 1.525 Å.
The DOS of PdG with and without adsorption of SO2 molecule is depicted in Fig.   6(a). It can be observed that PdG has two sharp peaks at the Fermi level after adsorbed

Adsorption performance of Pd-doped vacancy graphene layer
To investigate the adsorption mechanism of the defect-dopant combination, the adsorption behavior of the coexistence of vacancy defect and Pd dopant was discussed.
After the complete relaxation of the structure, it is observed that Pd atom in vacancy defect tends to directly occupy the position of the rotation bond, which forms two fivering and two six-ring structures. The structural parameters of Pd-VG sample are presented in Fig. 1(d), and it shows the bond length from Pd to the nearest C atom is 2.026 Å. The C-C bond length of Pd-VG ranges from 1.392 Å to 1.395 Å. Pd atom protruding from the plane caused large deformities in the area around the defect, and the structural properties of Pd-VG have changed considerably following optimization.
The most favorable configuration is that an O atom of SO2 points to the graphene plane by molecular relaxation, as shown in Fig. 2(d). Versus the PdG adsorption system, the of SO2-Pd-VG system is reduced to 0.734 eV. Meanwhile, the adsorption distance is slightly increased to 2.290 Å. These results show that the adsorption of SO2 on Pd-VG is weaker than that on PdG. The tetra-coordination system (four Pd-C bonds) formed by Pd-VG structure tends to be stable, and the number of unpaired electrons within the system is reduced compared with the tri-coordination system of PdG, which leads to its weak adsorption capacity.
To further understand the electronic properties of the Pd-VG adsorption system, the DOS and band structures are depicted in Fig. 7. As can be seen from Fig. 7(a) eV, which confirms the hybridization between orbitals, as shown in Fig. 7(b).
Consequently, Pd-VG may also detect SO2 molecules based on the change in conductivity before and after adsorption. As can be seen from Fig. 7(c), Pd-VG is semimetallic and has a direct band gap of 0.5 eV. After adsorbing SO2 molecule, the (0.25 eV) was slightly decreased as shown in Fig. 7(d)

Conclusions
Based on DFT calculations, the adsorption behavior of SO2 gas molecule on IG, VG, PdG, and Pd-VG has been systematically studied and discussed. The adsorption mechanism is revealed from the perspectives of adsorption energy, adsorption distance, charge transfer, band structure, DOS and PDOS. The results show that SO2 exhibits extremely weak interaction on IG, which is typical physical adsorption. On the other hand, doping Pd atom or introducing vacancy defect can significantly strengthen the interaction between SO2 molecule and graphene substrate and the adsorption energy is approximately 19 times and 8 times from IG, respectively, exhibiting strong chemical adsorption. Consequently, the VG and PdG could be the ideal choices for SO2 gas sensor.
Furthermore, modifying graphene with Pd dopant and vacancy defect is beneficial for detecting SO2 gas. However, the coexistence of the two methods results in a decrease in unmatched electrons and a significant reduction in the adsorption capacity of SO2.
Compared to PdG, the adsorption energy of Pd-VG is decreased by approximately 87%.
However, due to its obvious electronic structure characteristics, Pd-VG may be used as a candidate material for detecting SO2 gas molecules.

Conflicts of interest
There are no conflicts to declare.

Availability of data and material
The data used to support the findings of this study are available from the corresponding author upon request.

Code availability
Vienna ab-initio simulation package program.