# Numerical Analysis of the Breakdown Process of CF\({}_{3}\)I at Low Pressure
## 2 Models
### Physics Models
#### 2.1.1 Electron-Molecule and Ion-Molecule Collision  
Our models include electrons, one negative ion (I\({}^{-}\)), and four positive ions (I\({}^{+}\), CF\({}_{3}^{+}\), CF\({}_{3}\)I\({}^{+}\), CF\({}_{2}\)I\({}^{+}\)), with CF3I as the background gas. The reactions considered include an attachment, an elastic collision, a vibration, five excitations, and four ionizations. Figure 1 presents the reaction cross-sections, focusing only on key reactions that significantly influence the discharge process.  
It should be noted that in the study conducted by [PERSON] et al. [23], the ionization reactions considered include seven positive ions, three more ions than our data (namely CF\({}_{2}^{+}\), CF\({}^{+}\), and CI\({}^{+}\)). However, the original cross-section data are not provided in the paper, making them impossible to use. Furthermore, the generation of CF\({}_{2}^{+}\), CF\({}^{+}\), and CI\({}^{+}\) requires the breaking of multiple chemical bonds, resulting in higher reaction thresholds and smaller cross-sections. By comparing the cross-sections, it can be observed that the ionization cross-sections for generating CF\({}_{2}^{+}\), CF\({}^{+}\), and CI\({}^{+}\) are one to two orders of magnitude smaller than those for generating I\({}^{+}\), CF\({}_{3}^{+}\), CF\({}_{3}\)I\({}^{+}\), and CF\({}_{2}\)I\({}^{+}\), thus rendering them negligible. The dataset used in this study comes from the Troitsk Institute of Innovation and Fusion Research(TRINITI) in Russia, available at [[https://us.lxcat.net/cache/635b483e31117/](https://us.lxcat.net/cache/635b483e31117/)]([https://us.lxcat.net/cache/635b483e31117/](https://us.lxcat.net/cache/635b483e31117/)) (accessed on 14 June 2024) [24]. We consider TRINITI's simplification of ionization cross-sections acceptable.  
Regarding the choice of the ions I\({}^{-}\) over F\({}^{-}\): The bond energy of the C-F bond in CF\({}_{3}\)I is 5.044 eV, while the bond energy of the C-I bond is 2.496 eV. The nearly two-fold difference in bond energies indicates that the C-I bond is more susceptible to breaking during collisions, resulting in more I\({}^{-}\) ions from electron attachment reactions. In the study by [PERSON] et al., the cross-section for the formation of F\({}^{-}\) ions is lower than that for I\({}^{-}\) ions by about two orders [25]. Therefore, we only consider the I\({}^{-}\) ions.  
Fluorine atoms, I\({}_{2}\), and C\({}_{2}\)F\({}_{6}\) may also be produced during the reaction, but their densities are too low to be significant and can therefore be ignored.  
This paper utilizes the method proposed by [PERSON] [26; 27] to construct a standard MCC model. The reaction rate is determined by the Rice-Ramsperger-Kassel (RRK) theory [28]. The probability of ion collision is calculated by (1):  
\[P_{c}=\left(\frac{\pi\alpha_{p}e^{2}}{\varepsilon_{0}\mu}\right)^{1/2}\beta_{ \infty}^{2}n_{g}\Delta t \tag{1}\]  
where \(\alpha_{p}\) represents the molecular polarizability of CF\({}_{3}\)I, which is equal to \(20.0\alpha_{0}^{3}\)[29; 30], \(a_{0}\) denotes the Bohr radius, \(e\) is the electron charge, \(\varepsilon_{0}\) is the vacuum dielectric constant, \(\mu=m_{i}m_{n}/(m_{i}+m_{n})\) is the reduced mass, and \(m_{i}\) and \(m_{n}\) are the ion and neutral mass, respectively. The parameter \(\beta_{\infty}\) is the cutoff value of the dimensionless shock parameter \(\beta\), generally chosen as 3, and \(n_{g}\) is the density of CF\({}_{3}\)I gas.  
Appendix A provides the reaction formulas and threshold energies for ion-molecule collisions. Detailed calculation formulas can be found in the study by [PERSON] et al. [22].