## 3 Results
### Sensing Properties Evaluation  
In the current state, resistance-type gas sensors have gained extensive utilization [54]. The resistance is closely linked to the band structure. When the band gap narrows, electrons are more readily excited to the conduction band, resulting in an increase in resistance. The relative conductivity can be assessed as follows [55]:  
\[\sigma\propto e^{[-E_{\text{gap}}/(2k_{B}T)]} \tag{6}\]  
where \(E_{\text{gap}}\), \(k_{B}\), and \(T\) represent the bandgap, Boltzmann's constant (\(8.62\times 10^{-5}\) eV/K), and the temperature in Kelvin (K), respectively. The Ag-WS\({}_{2}\) monolayer processes a bandgap of 1.28 eV. Following adsorption, the band gap experiences varying degrees of reduction. Consequently, the resistance diminishes for all three gas adsorptions. Furthermore, a larger adsorption energy corresponds to a greater adsorbing capacity [56]. However, despite SO\({}_{2}\) adsorption causing the most substantial decrease in the band gap, it is noteworthy that NO\({}_{2}\) exhibits the highest adsorption energy. As a result, distinguishing between the changes in resistance caused by NO\({}_{2}\) and SO\({}_{2}\) becomes challenging. To overcome this limitation, the work function of Ag-WS\({}_{2}\) was calculated. This parameter can be measured using the Kelvin probe method. Simplifying the experimental approach, the metal-insulator-semiconductor (MIS) capacitors can effectively reflect changes in the work function [57]. According to Formula (5), the results of the work function calculations are depicted in Figure 6. Before adsorption, the work function of Ag-WS\({}_{2}\) stands at 4.80 eV. After the adsorption of the three different gases, the work function undergoes distinct degrees of augmentation. The smallest change in the work function is observed after CO  
Figure 5: Electronic properties of CO, NO\({}_{2}\), and SO\({}_{2}\) on Ag-WS\({}_{2}\) monolayer: (**a**) band structure of CO on Ag-WS\({}_{2}\) monolayer; (**b**) TDOS of CO on Ag-WS\({}_{2}\) monolayer and molecular orbitals of CO before and after adsorption; (**c**) atomic orbitals of Ag 4d in Ag-WS\({}_{2}\) and C 2p in CO; (**d**) band structure of NO\({}_{2}\) on Ag-WS\({}_{2}\) monolayer; (**e**) TDOS of NO\({}_{2}\) on Ag-WS\({}_{2}\) monolayer and molecular orbitals of NO\({}_{2}\) before and after adsorption; (**f**) atomic orbitals of Ag 4d in Ag-WS\({}_{2}\) and 2p orbitals of one O atom in NO\({}_{2}\); (**g**) band structure of SO\({}_{2}\) on Ag-WS\({}_{2}\) monolayer; (**h**) TDOS of SO\({}_{2}\) on Ag-WS\({}_{2}\) monolayer and molecular orbitals of SO\({}_{2}\) before and after adsorption; (**i**) atomic orbitals of Ag 4d in Ag-WS\({}_{2}\) and 2p orbitals of the bottom O atom in SO\({}_{2}\). adsorption, leading to an increase in value to 4.88 eV. However, the work function experiences a remarkable elevation following NO\({}_{2}\) adsorption, reaching 5.50 eV. Concerning SO\({}_{2}\), this value becomes 5.19 eV. For the sensing scheme of Ag-WS\({}_{2}\), the MIS-based gas sensor is shown in Figure 7. The operating principle of hybrid suspended gate FET (HSGFET) is that the change of work function results in a shift of the gate voltage [57; 58; 59; 60]. Therefore, the maximum increase in the work function of Ag-WS\({}_{2}\) after NO\({}_{2}\) detection results in the change of the gate voltage at the greatest extent. In summary, among the three types of gases, NO\({}_{2}\) causes the most substantial enhancement in the work function, aligning with its higher adsorption energy and adsorption capacity. Consequently, if Ag-WS\({}_{2}\) operates as a work function-based gas sensor, it exhibits the most pronounced response to NO\({}_{2}\) compared to the other two gases at the same concentration. Another aspect that requires consideration is the recovery property. When a gas sensor is exposed to an atmosphere containing the target gases, these gas molecules are adsorbed onto the active sites of the sensing material, initiating subsequent surface reactions.