# Numerical Analysis of the Breakdown Process of CF\({}_{3}\)I at Low Pressure
## 3 Results
### Electron Kinetics  
Figure 4 gives the two-dimensional distribution of the four parameters of the electron's density, current density, energy, and heating rate in time and space. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Stage** & **Before Breakdown** & **Breakdown** & **After Breakdown** \\ \hline \(\mathrm{t}\) (\(\mathrm{\mu s}\)) & \(0\to 6.4\) & \(6.4\to 15\) & \(15\to 150\) \\ \(\overline{n}_{e}\) (\(\mathrm{m}^{-3}\)) & \(10^{10}\to 10^{8}\to 7\times 10^{11}\) & \(7\times 10^{1  
During the time period of 0-6.4 us, which constitutes the before-breakdown stage, the electric field permeates the entire polar plate region. A parallel electric field points from the anode to the cathode within the 0-2 cm polar plate space, generated by the negative voltage source. As electrons are attracted to the anode and accelerated in the electric field, their energy increases closer to the anode. As depicted in Figure 4c, electrons near the negative plate possess energies of approximately 10 eV, while those close to the positive plate reach energies of about 70 eV due to electric field acceleration. As shown by the collision cross-section in Figure 1, at higher electron energies, the ionization reaction predominates due to the larger cross-section, whereas the adsorption reaction rate remains small. Thus, ionization reactions become dominant in regions with higher electron energy, while the rate of adsorption reactions is low. The collision of higher energy electrons with CF\({}_{3}\)I molecules initiates the ionization reaction, leading to the generation of more electrons and a significant increase in electron density near the anode region. However, electron energy near the cathode is only about 10 eV, insufficient to trigger enough ionization reactions to replenish electron density losses. During the before-breakdown stage, electron density at 2 cm (i.e., at the anode plate) rises to \(5\times 10^{12}\) m\({}^{-3}\), while density at 0 cm (i.e., at the cathode plate) is only \(10^{9}\) m\({}^{-3}\), with an average density of \(7\times 10^{11}\) m\({}^{-3}\). This indicates a tenfold increase in electron density relative to the initial density during the before-breakdown stage. Electron current density is consistently negative because electron motion is from the cathode to the anode. The absolute value of electron current density remains below 1 Am\({}^{-2}\) during the before-breakdown stage, indicating very low electron current due to insufficient electron density. Additionally, as depicted in Figure 4d, the heating rate of electrons remains below 10 kWm\({}^{-3}\). These parameters indicate that reactions during the before-breakdown stage are considerably less vigorous than during the breakdown stage. Notably, the overall electron density experiences a slight decrease before rising during the  
Figure 4: Spatiotemporal distribution of (**a**) electron density, (**b**) electron current density, (**c**) average electron energy and (**d**) electron heating rate. before-breakdown stage. This decrease is attributed to the small mass and high mobility of electrons, causing initial electrons near the anode to be rapidly lost under the influence of the electric field. However, as electrons from other locations migrate toward the anode after being accelerated by the electric field, ionization reactions are triggered, leading to a rapid rebound in electron density near the anode. The breakdown stage ranges from 6.4 us to 15 us. During this stage, the formation of the cathode sheath begins at 6.4 us and is complete at 15 us. The electron density increases dramatically at this stage because of the electron avalanche. The bulk region's range begins to expand while electron density within the bulk region rises. The electron density within the bulk region reaches approximately 10\({}^{13}\) m\({}^{-3}\). In the gradually forming cathode sheath, the electron density ranges between 10\({}^{11}\) m\({}^{-3}\) and 10\({}^{12}\) m\({}^{-3}\).