# Numerical Analysis of the Breakdown Process of CF\({}_{3}\)I at Low Pressure
## 4 Discussions
### Particle Kinetics
Both negative ions and electrons migrate from the cathode toward the anode, causing a reduction in the density of negative ions and electrons near the cathode. As positive ions collide with the cathode, producing secondary electrons that replenish some of the quantity lost by electron drift toward the anode, the density of negative ions at the cathode is consequently lower than that of electrons. With an increase in particle density, the current density experiences a significant surge. Comparing Figure 13a with Figure 13b, the absolute value of the electron current density near the positive plate increases significantly, from approximately 0.01 Am\({}^{-2}\) to 0.45 Am\({}^{-2}\). In Figure 14b, the potential near the plate changes from \(-\)1000 V to \(-\)990 V. This change is attributed to the progressive increase in current between plates with the onset of the breakdown process, resulting in a higher current in the external circuit. Figure 12: Energy snapshots at (**a**) 1 us (before breakdown), (**b**) 6.4 us (breakdown), (**c**) 10 us (breakdown), (**d**) 15 us (breakdown), (**e**) 25 us (anode sheath formation phase of after breakdown), and (**f**) 150 μs (stable phase of after breakdown). Consequently, this causes the partial voltage across the external resistor to increase, leading to a reduction in the absolute value of the voltage between the pole plates to less than 1000 V.  
At 10 us, the breakdown process enters an intermediate stage, during which the cathode sheath gradually forms, as illustrated in Figures 11c-14c. The density of positive ions near the cathode surpasses that of electrons and negative ions, resulting in a positive net charge near the cathode. This uneven distribution of space charge generates an electric field directed toward the anode, which shields the applied electric field. Consequently, the strength of the electric field diminishes in the anode region, causing electrons to  
Figure 14: Potential snapshots at (**a**) 1 μs, (**b**) 6.4 μs, (**c**) 10 μs, (**d**) 15 μs, (**e**) 25 μs, and (**f**) 150 μs. decelerate and rapidly lose energy. Simultaneously, this phenomenon leads to an escalation in the electric field near the cathode, resulting in an increased energy of electrons within the cathode sheath. As depicted in Figure 11(c), the electron energy in the anode region measures approximately 15 eV, while high-energy electrons of around 350 eV emerge in the cathode sheath. When comparing Figures 11(c) and 11(c), it is evident that while the electron density in the anode region exceeds that of the cathode region by two orders of magnitude, the electron energy in the anode region is significantly lower than that in the cathode region. The combination of high-density, low-energy electrons in the anode region results in a more vigorous adsorption reaction in comparison to ionization reactions. Consequently, this leads to the generation of a substantial number of negative ions in the anode region. In contrast, the cathode region lacks replenishment of negative ions, with its negative ion density nearing zero. Consequently, the electric field generated by the uneven distribution of the charge continues to intensify, gradually expanding the cathode sheath. In Figure 14(c), the potential near the anode approaches zero due to the shielding effect of the electric field, while the potential of the cathode plate measures \(-930\) V. It should be noted that the absolute voltage value between the plates is lower than that at 6.4 us, due to the ongoing increase in current between the plates. This observation is further supported by comparing the current densities in Figure 13(b) with Figure 13(c), revealing a significant increase in the current density. At 15 us, the breakdown stage is complete and a stable cathode sheath has been formed, as evidenced by the images in Figures 11(d) and 14(d). As shown in Figure 11(d), the positive ion density curve in the bulk region coincides with the negative ion density curve.