## 4 Experimental Data
### Summary Statistics
This indicates a weak negative linear relationship between the two variables, suggesting almost no correlation. There was a strong positive correlation between the concentration and volume flow rates of gases existing in the system, particularly a correlation of 0.906 between the concentration of gases out (\"conc out\") and 1-Ui, and 0.899 between the volume flow rate out and 1-Ui. These results suggest that the concentration and volume of gas existing in the system significantly determine the remaining gas rate (1-Ui). Given the definition of 1-Ui, which reflects the proportion of unused gas, it is expected that \"conc out\" and \"volume flow rate out\" would exhibit a natural and robust correlation with 1-Ui. In the case of \"Concentration Dependence\", higher \"conc out\" implies that a more significant fraction of the input gas remains unreacted or unused, directly contributing to an increased value of 1-Ui. Conversely, lower \"conc out\" indicates higher gas utilization, reducing the 1-Ui rate. In the case of volume flow dependence, \"volume flow rate out\" captures the overall movement of gases existing in the chamber. When combined with substantial residual concentration (\"conc out\"), a higher flow rate reinforces the inefficiency in gas utilization, thereby correlating positively with 1-Ui. The robust correlation aligns with the measurement methodology, where these output variables are key determinants in calculating the unused gas rate (1-Ui). Therefore, the natural and strong linkage between these variables highlights their role as critical process efficiency indicators. This confirms that 1-Ui can be considered a key target for understanding the effects of plasma intensity on gas output. The results of the correlation analysis indicated no direct relationship between plasma intensity and 1-Ui when specific gas types were not considered. To address this, gases were grouped according to plasma intensity levels to more thoroughly investigate the potential \begin{table}
\begin{tabular}{c c c c c c} \hline  & **Plasma** & **Flow Late Out** & **Con Cut** & **Volume Flow Rate Out** & **1-Ui** \\ \hline Plasma & 1.000 & \(-\)0.261 & \(-\)0.052 & \(-\)0.107 & \(-\)0.016 \\ Flow late out & \(-\)0.261 & 1.000 & 0.235 & 0.330 & 0.241 \\ Conc out & \(-\)0.052 & 0.235 & 1.000 & 0.993 & 0.906 \\ Volume flow & \(-\)0.107 & 0.330 & 0.993 & 1.000 & 0.899 \\ Rate out & \(-\)0.016 & 0.241 & 0.906 & 0.899 & 1.0 \\ \hline \end{tabular}
\end{table} 
Table 5: Correlation between columns with 1-Ui. relationships and impacts of plasma intensity on 1-Ui. Plasma intensity was divided into the following three groups for analysis:  
Group 1: Plasma intensities less than 100, including NF\({}_{3}\) and SF\({}_{6}\). Group 2: Plasma intensities of 500, 600, and 700, including CH\({}_{2}\)F\({}_{2}\) and CHF\({}_{3}\). Group 3: Plasma intensities of 1000, 2000, and 3000, including the gases C\({}_{4}\)F\({}_{6}\), C\({}_{4}\)F\({}_{8}\), and CF\({}_{4}\). This categorization allows for a more detailed exploration of the influence of plasma intensity on 1-Ui across different gas types and intensity levels. Table 6 summarizes the frequency distribution of plasma intensity levels by gas type. The gases C4F6, C4F8, and CF4 were subjected to experimental measurements across three distinct plasma intensity levels, with the number of recorded data points corresponding to the values shown in the table. Similarly, experimental data for CH2F2 and CHF3 were collected at the same plasma intensity levels. For NF3 and SF6, data were collected at varying intensities, reflecting that these gases are utilized in different processes within semiconductor manufacturing. This variation in plasma intensity reflects each gas's distinct operational requirements and applications at different stages of the production process. The missing data points for certain plasma intensity levels can be attributed to the experimental design and the operational requirements for each gas.