## 5 Analysis of Group 1 Performance
### General Trends: Group 1  
The significant differences observed in NF3 between plasma levels of 40 and higher levels suggest a non-linear relationship. While increases in plasma intensity between 60 and 80 do not significantly affect the unused rate, the jump from 40 to 60 or 80 results in substantial changes in 1-Ui. This indicates that increasing plasma intensity within specific  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Gas** & **Linear Correlation** & **Rank Correlation** & \(p\)**-Value** \\  & **Coefficient** & **Coefficient** & \(p\)**-Value** \\ \hline NF3 & \(-\)0.315 & \(-\)0.240 & 0.000 \\ SF6 & 0.000 & \(-\)0.011 & 0.886 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Correlation between plasma intensity and 1-Ui for NF3 and SF6.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Comparison** & **Mean Difference** & \(p\)**-Value** \\ \hline Plasma 40 vs. 60 & \(-\)0.180 & \(<\)0.001 \\ Plasma 40 vs. 80 & \(-\)0.206 & \(<\)0.01 \\ Plasma 60 vs. 80 & \(-\)0.026 & \(<\)0.106 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Pairwise comparison of mean differences between plasma levels for NF3.  
ranges can significantly improve the unused rate, particularly when moving from low plasma levels (e.g., 40) to higher levels (e.g., 60 or 80). This non-linear trend highlights the need to calibrate plasma intensity carefully in NF3 processes to optimize performance. By doing so, it can help achieve more efficient etching and material removal in semiconductor manufacturing processes.  
For SF6, the lack of a significant relationship between plasma intensity and 1-Ui indicates that other factors, such as gas composition or equipment parameters, may need to be adjusted to control the destruction rate. Plasma intensity alone does not appear helpful for optimizing the process destruction rate in SF6-based processes.  
These differing trends for NF3 and SF6 in relation to 1-Ui under varying plasma intensities can be attributed to their distinct chemical properties and the key reactions that govern their behavior in plasma processes. For NF3, it readily dissociates under plasma, releasing reactive fluorine atoms. These fluorine radicals participate in highly efficient etching and surface cleaning reactions, significantly reducing 1-Ui as plasma intensity increases. The strong negative correlation observed for NF3 suggests that higher plasma intensities enhance the dissociation of NF3 and the subsequent utilization of the gas. NF3 exhibits a more straightforward dissociation mechanism compared to SF6. Its primary reaction involves breaking the nitrogen-fluorine bonds to release fluorine radicals without significant byproduct formation. NF3 dissociation is more effective at moderate electron energies commonly found in plasma processes, allowing for efficient utilization under various intensities.  
For SF6, while it also dissociates to produce fluorine radicals, the reaction pathway is more complex, often involving recombination and the formation of stable intermediates such as SFx species (x = 4 or 5). These intermediates can reduce the availability of free fluorine radicals, thereby limiting the overall gas utilization. This makes SF6 less responsive to changes in plasma intensity. As such, SF6 requires higher electron energy to achieve complete dissociation. However, under typical plasma conditions, only partial dissociation occurs, leading to less variation in 1-Ui even with increasing plasma intensity.