The Impact of Plasma Intensity on the Unused Rate in Semiconductor Manufacturing: Comparative Analysis Across Intensity Ranges from 30 to 3000

Abstract

This study examines the impact of plasma intensity on the process unused rate, expressed as 1-Ui, within semiconductor manufacturing. Since the influence of plasma level on 1-Ui is inconsistent without considering gas, the experimental data were analyzed after grouping plasma levels by intensity. Plasma intensity is classified into three categories: low (<100), medium (500–700), and high (>1000). The dataset includes seven columns and 8324 entries representing seven gases—NF3, SF6, CH2F2, CHF3, C4F6, C4F8, and CF4. To analyze the relationship between plasma intensity and 1-Ui, we conducted a series of ANOVA tests followed by post hoc analyses to identify statistically significant differences in 1-Ui across the defined plasma intensity levels.

1. Introduction

In semiconductor manufacturing, plasma etching is a key process in material removal and surface modification. The efficiency of these plasma-based processes significantly influences production yield and the quality of semiconductor devices [1,2,3,4]. Plasma intensity, a vital parameter in these processes, substantially affects the rate of unused gas, quantified as 1-Ui (the process unused rate). Understanding the precise impact of plasma intensity on 1-Ui is a critical step in minimizing the amount of exhausted gas, thereby enhancing process efficiency and reducing environmental impacts [5,6,7,8].

Previous studies have examined the effects of plasma on the 1-Ui rate of unused gas, though only to a limited extent. For example, Yoon et al. [9] examined the role of plasma discharge characteristics, particularly in an Ar/C4F6 mixture, and its influence on etching precision and unused gas rates. Hao et al. [10] monitored atomic layer etching in Cl2/Ar plasmas, emphasizing the significance of plasma conditions, such as gas flow and plasma intensity, in determining etching rates and unused gas outcomes.

Further studies, such as Song et al. [11], analyzed CF4/O2/N2 plasma mixtures in Si₃N₄ dry etching, highlighting how gas composition variations impact etching precision and gas utilization. Choi et al. [12] investigated SF6/O2/Ar plasma conditions for silicon trench etching, focusing on how plasma uniformity affects unused gas rates. Additionally, Lee et al. [13] explored the effects of plasma intensity and chemical composition on high-aspect-ratio SiO₂ etching, offering insights into unused gas rates under different plasma intensities and gas combinations. Markku et al. [14] comprehensively reviewed deep reactive ion etching techniques, emphasizing how plasma intensity influences unused gas rates and etch uniformity in advanced semiconductor manufacturing. However, these studies have fallen short on plasma intensity and process unused rates across varying plasma levels and gas types.

We aim to contribute to this body of knowledge and reduce the identified research gaps by investigating the effects of varying plasma intensities on 1-Ui across seven gases (NF3, SF6, CH2F2, CHF3, C4F6, C4F8, and CF4). By categorizing plasma intensities into low (<100), medium (500–700), and high (>1000) groups, this research seeks to quantify how plasma intensity specifically influences 1-Ui and offer insights into optimal plasma settings to improve efficiency and minimize exhausted gases in semiconductor manufacturing processes.

2. Processes of Semiconductor Manufacturing and Measurement Methods

2.1. Processes of Semiconductor Manufacturing

In semiconductor manufacturing, the Fabrication Line (FAB) refers to the facility where wafers undergo various processes to create integrated circuits [15,16,17,18], as shown in Figure 1. The FAB processes are essential in transforming high-purity silicon wafers into functional microchips, which requires a highly controlled environment to ensure precision and minimize contamination. Each step within the FAB contributes to the environmental emissions associated with the semiconductor industry, notably involving fluorinated compounds (FCs), which are known for their stability and potential contribution to global warming [19,20,21].

2.1.1. Wafer Fabrication and Photolithography

The initial wafer fabrication step involves producing high-purity silicon wafers from raw materials. This includes extracting and purifying silicon to create a single-crystal silicon ingot and then sliced into thin wafers. These wafers serve as substrates upon which semiconductor devices are built. Following this, the photolithography process applies a light-sensitive photoresist to the wafer’s surface, and precise masking techniques, combined with exposure to light, define the circuit patterns to be formed [22,23,24]. This process determines where subsequent material deposition or removal occurs.

2.1.2. Etching, Ion Implantation, and Deposition

In the etching stage, the material is selectively removed from the exposed areas of the wafer to create the circuit patterns. Plasma etching, which utilizes gases such as CF4 and SF6, is a common technique. Following etching, the ion implantation process introduces dopants into the silicon wafer to modify its electrical properties, essential for creating p-type or n-type regions that define the semiconductor’s function [25,26].

Deposition processes then involve adding layers of material, such as silicon dioxide or metal films, onto the wafer. Chemical Vapor Deposition (CVD) is frequently employed, wherein reactive gases form thin films on the wafer’s surface. These layers are critical for insulation and creating conductive pathways within the integrated circuits.

2.1.3. Electrical Die Sorting and Packaging

Once the fabrication steps are complete, wafers undergo rigorous testing and inspection to identify any defects that could impact the performance of the final semiconductor devices [27,28]. Individual chips are then cut from the wafer and encapsulated in protective packaging, which includes attaching the die to a lead frame and connecting it to external pins for integration with other electronic components.

2.2. Measurement Methods

Measuring Ui in semiconductor manufacturing requires real-time monitoring of gas concentrations and reaction byproducts during production. Commonly used tools for this purpose include the quadrupole mass spectrometer (QMS) and Fourier-transform infrared spectrometer (FTIR).

The Ui of semiconductor manufacturing used in our analysis was measured in accordance with the Korean Industrial Standard KS I 0587 (Measurement Method for Volumetric Flow Rate of Non-CO2 Greenhouse Gases (CF4, NF3, SF6, N2O) Used in Semiconductor and Display Processes) and ES 13501 (N2O, HFCs, PFCs, SF6, NF3 of Greenhouse Gas in Industrial Process) [29,30]. Figure 2 shows that the volumetric flow rate of process exhaust gases was measured using a QMS (isepa-S, EL, Daejeon, Republic of Korea) while the concentration of F-gases was determined using a FTIR (DX4000, Gasmet, Vantaa, Finland) to calculate the Ui of the semiconductor manufacturing. The FTIR and QMS were operated following the procedures provided in the equipment manual, and data were collected by continuous measurement for one hour. In this study, the QMS operates within a mass range of 0 to 200 amu, utilizing a Faraday cup and 70 eV voltage Secondary Electron Multiplier detector. The FTIR device operates in the range of 4200–900 cm⁻¹, with a DLATGS (Deuterated L-alanine-doped Triglycine Sulfate) detector and a ZnSe (Zinc Selenide) beamsplitter.

The specifications of the FTIR used in this study are summarized in

Table 1. Genaral parameters of FTIR.

Response time, T90	Typically less than 120 s, depending on the gas flow and measurement time
Wavelength Range	- Full Range: 200~1050 nm - UV Range: 200~450 nm - VIS Range: 380~760 nm - NIR Range: 550~1050 nm
Optical Resolution	0.3–10 nm FWHM
Min. Exposure Time	1 msec

. As shown in Table 1, the response time (T90) is typically less than 120 s, depending on the gas flow and measurement conditions. The wavelength range includes the full spectrum (200–1050 nm), the UV range (200–450 nm), the visible range (380–760 nm), and the near-infrared range (550–1050 nm). The optical resolution is 0.3–10 nm FWHM, and the minimum exposure time is 1 millisecond.

Table 2. Spectrometer of FTIR.

Resolution	8 cm−1
Scan Frequency	10 scans/s
Source	SiC, 1550 K
Beamsplitter	ZnSe
Window material	ZnSe
Wave number range	900–4200 cm−1

presents the key characteristics of the FTIR spectrometer used in our data collection. The resolution is 8 cm⁻¹, and the scan frequency is 10 scans per second. The light source is a 1550 K SiC, with ZnSe used for both the beamsplitter and the window material. The wavenumber range extends from 900 to 4200 cm⁻¹.

The digitized infrared spectrum of the sample in the FTIR gas cell is measured and stored on a computer. The quantitative analysis of FTIR spectra utilizes Beer’s law, as shown in Equation (1), which serves as the fundamental principle of spectroscopic quantitative analysis. This law illustrates how the absorbance measured in the sample spectrum is related to the concentration of the sample gas.

$$\log \left({\displaystyle \frac{I_0}{I}}\right)=\log \left({\displaystyle \frac{1}{T}}\right)=A=abc$$

(1)

In the formula, I₀ represents the intensity of infrared radiation entering the sample, I represents intensity of the infrared radiation that has passed through the sample, A represents absorbance, T represents transmittance, a represents absorptivity (depends on wavelength), b represents optical path length, and c represents sample concentration.

The volumetric flow rate of F-gases is determined by injecting an inert tracer gas (such as helium or krypton) into the pipeline through which the process exhaust gas flows, using an MFC. The concentration of the tracer gas is then measured using a QMS. The volumetric flow rate of the process exhaust gas is calculated using Equation (2) as follows:

$$F={\displaystyle \frac{S_f}{C_{Kr}\times {10}^{-6}}}$$

(2)

In the formula, F represents the volumetric flow rate of the process exhaust gas for single concentration data (L/min), S_f represents the volumetric flow rate of the tracer gas injected through the gas inlet (L/min), and C_Kr represents the measured concentration of the tracer gas (μmol/mol).

The average volumetric flow rate of the tracer gas is calculated using Equation (3), and the relative standard deviation of the volumetric flow rate of the process exhaust gas is calculated using Equation (4).

$$F_m=\sum _1^n{\displaystyle \frac{F_i}{n}}$$

(3)

$${\sigma }_{F_m}=\sqrt{{\displaystyle \frac{1}{n}}{\sum }_1^n{(F_i-F_m)}^2}$$

(4)

In the formula, F_m represents the average volumetric flow rate of the process exhaust gas from the n measured data points (L/min), F_i represents the volumetric flow rate of the process exhaust gas for the i-th measurement (L/min), n represents the number of measurements, and σ_Fm represents the relative standard deviation.

The volume flow rate of F-gas is calculated from the estimated inlet volume flow rate, using Equation (5).

$$V=C\times F\times 1000$$

(5)

In the formula, V represents volume flow rate of F-gas, C represents the measured concentration of F-gas, F represents the volumetric flow rate of F-gas.

As described in Equation (6), the proportion of gas consumed during the semiconductor manufacturing process(Ui) is calcurated based on the inlet and outlet volume flow rate (V_in and V_out, respectively, in L/min), and the measured inlet and outlet concentration of F-gas using the QMS at plasma (C_in and C_out, respectively, in µmol/mol). The formula is given as follows:

$$U_i=1-{\displaystyle \frac{{(V}_{in}\times C_{in})-{(V}_{out}\times C_{out})}{{(V}_{in}\times C_{in})}}$$

(6)

The FTIR spectra for the F-gases are shown in Figure 3. The absorbance of each gas was measured using reference files with spectra similar to the one shown in Figure 3.

To accurately measure the flow rate of process gases using a QMS and FTIR, it is essential to determine calibration points using standard gases and establish a calibration curve. This calibration method is applied in the UNFCCC LCD industry’s SF6 emission reduction CDM methodology, specifically AM0078 (Point-of-Use Abatement Device to Reduce SF6 Emissions in LCD Manufacturing Operations). The QMS calibration is performed on-site before measurement, targeting the specific gas to be analyzed. Using a standard gas (1% Kr), five calibration points were measured, and the calibration curve was established, as shown in Figure 4. Each calibration point was determined by averaging at least 20 measurement data points, confirming a coefficient of determination (R²) of 0.98 or higher. Additionally, the relative error for five repeated measurements of each concentration used in the calibration curve was verified to be within ±5%.

The results of the experiment conducted to confirm the linearity of the FTIR (Fourier-transform infrared spectroscopy) using C4F6 as the target gas are shown in Figure 5. Measurements were performed over five concentration ranges, achieving a coefficient of determination (R²) of 0.9999.

Additionally, for each gas concentration, experiments were repeated for more than five cycles, and the average values were used, as depicted in Figure 6.

3. Methodology

3.1. Data Overview

The experimental dataset we use in our analysis contains measurements of the unused gas ratio 1-Ui across different plasma intensities from 30 to 3000 with a 300 mm wafer size. The measurements were obtained from a controlled experimental setup in which the plasma intensity was systematically varied, and the unused gas rate was recorded for each intensity level. This setup ensured consistency in the conditions under which the data were gathered, providing a robust basis for the subsequent analyses.

3.2. Correlation Analysis

A Pearson linear and rank correlation analysis was conducted between plasma intensity and 1-Ui for each gas. This approach provides insights into whether an increase or decrease in plasma intensity correlates with changes in 1-Ui and the intensity of this relationship. The correlation analysis used the Python v3.13, and correlation coefficients were computed to quantify the strength between the variables. This analysis helps determine if there is a predictable pattern between plasma intensity and 1-Ui and optimize plasma levels to reduce the exhausting gas.

3.3. ANOVA and Post Hoc Testing

A one-way Analysis of Variance (ANOVA) was conducted to determine if significant differences exist in 1-Ui across the different plasma intensities for each gas type. Tukey’s Honest Significant Difference (HSD) post hoc test was subsequently used to identify which specific plasma levels exhibited significant differences in 1-Ui. The ANOVA test was chosen because it allows for the comparison of means across multiple groups, and Tukey’s HSD was employed to pinpoint the specific differences between intensity levels [31,32,33,34]. These tests are effective in determining whether changes in plasma intensity have a statistically significant effect on the unused rate and in identifying which intensity levels are most impactful.

4. Experimental Data

4.1. Explanation of Collected Data

All collected data names ending with “in” in the dataset are categorical values, while those ending with “out” are continuous values. Plasma values are also categorical. Descriptions of the collected data are provided in

Table 3. Descriptions of collected data.

Collected Data	Description
plasma	Plasma intensity levels
Flow rate in/out:	The flow rate of gases entering and leaving the system.
Conc in/out	Concentration of gases entering and leaving the system.
Volume flow rate in/out	In and out of the system.
Ui	the proportion of gas consumed during the semiconductor manufacturing process
1-Ui	$\mathrm{The} \mathrm{proportion} \mathrm{of} {\mathrm{g}\mathrm{a}\mathrm{s}}_{\mathrm{i}}$ not utilized in the process, $\mathrm{representing} \mathrm{the} \mathrm{fraction} \mathrm{of} \mathrm{total} {\mathrm{g}\mathrm{a}\mathrm{s}}_{\mathrm{i}}$ that is either unconsumed, lost, or left over at the end of the manufacturing process

.

4.2. Summary Statistics

The summary statistics of the collected data are presented in

Table 4. Summary statistics.

	Plasma (W)	Flow Late in (LPM)	Flow Late Out (LPM)	Conc In (ppm)	Conc Out (ppm)	Volume Flow Rate In	Volume Flow Rate Out	1-Ui
count	8324	8324	8324	8324	8324	8324	8324	8324
mean	1209.55	62.69	61.88	979.90	295.42	61,810.41	18,657.99	0.30
std	974.72	2.33	6.43	367.56	248.87	23,674.80	16,640.30	0.23
min	40.00	57.04	45.07	478.07	0.00	27,270.65	0.00	0.00
Q1	500	62.48	55.65	608.07	143.27	37,991.50	8833.04	0.11
Q2	1000	63.62	63.96	820.78	223.07	52,841.82	14,102.37	0.32
Q3	2000	64.38	65.70	1324.66	379.91	84,269.48	24,444.16	0.47
max	3000	64.38	89.76	1525.78	1129.21	95,407.02	76,205.57	1.04

.

Figure 7 shows the distributions of the variables presented in Table 2, including plasma intensity measurements and 1-Ui. The standard deviations in Table 2 help assess the measurement precision of each variable. For instance, the standard deviation of 1-Ui is 0.23, indicating moderate variability relative to its mean value of 0.30.

Among the continuous columns, the “conc out” and “volume flow out” are skewed right, but the “flow late out” is skewed left.

Plasma intensity values were found to be widely spread, ranging from 40 to 3000. In this experiment, seven gases that had undergone various semiconductor production processes were used. Since plasma levels vary depending on the process, the range was substantial, from 40 to 3000.

The flow rates of gases entering and leaving the system (flow rates (in/out)) were relatively consistent, as indicated by the marginal differences between the flow rates in and out (mean inflow rate: 62.69; mean outflow rate: 61.88). The standard deviation in flow rates, especially “flow late out” (6.43), suggests some variability but not extreme.

The concentration values (concentration (in/out)) exhibited a wide range, particularly “conc out”, with a mean of 295.42 and a high standard deviation of 248.87. This variability reflects differences in gas behavior after processing under varying plasma intensities.

The distribution of 1-Ui (remaining gas rate) showed moderate variability with a mean of 0.3045 and a standard deviation of 0.2259. The distribution may be right-skewed, reflecting cases with higher remaining gas values.

Definition of 1-Ui is given in Equation (7):

$$1-{\mathrm{U}}_{\mathrm{i}}=1-{\displaystyle \frac{volume out}{volume in}}$$

(7)

In the formula, volume in represents the volumetric flow rate entering the system, calculated as the product of the input flow rate and the input concentration, and volume out represents the volumetric flow rate leaving the system, calculated as the product of the output flow rate and the output concentration.

In

Table 5. Correlation between columns with 1-Ui.

	Plasma	Flow Late Out	Conc Out	Volume Flow Rate Out	1-Ui
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 Rate out	−0.107	0.330	0.993	1.000	0.899
1-Ui	−0.016	0.241	0.906	0.899	1.0

, the correlation coefficient between the “plasma” and “1-Ui” columns in the dataset was approximately −0.016. 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 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 NF₃ and SF₆.
• Group 2: Plasma intensities of 500, 600, and 700, including CH₂F₂ and CHF₃.
• Group 3: Plasma intensities of 1000, 2000, and 3000, including the gases C₄F₆, C₄F₈, and CF₄.

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. Frequency of plasma level by gas.

	40	50	60	70	80	90	500	600	700	1000	2000	3000	Total
C4F6	-	-	-	-	-	-	-	-	-	302	302	302	906
C4F8	-	-	-	-	-	-	-	-	-	1033	855	609	2577
CF4	-	-	-	-	-	-	-	-	-	305	304	305	914
CH2F2	-	-	-	-	-	-	441	442	429	-	-	-	1312
CHF3	-	-	-	-	-	-	409	410	411	-	-	-	1230
NF3	96	-	98	-	96	-	-	-	-	-	-	-	290
SF6	-	363	-	366	-	366	-	-	-	-	-	-	1095

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. Each gas type was utilized within particular plasma intensity ranges based on its role and efficiency in semiconductor processes. In the case of distinct operational ranges for each gas, some gases like NF3 and SF6 are employed at lower plasma intensities (<100) due to their specific reactivity profiles and application requirements, such as surface treatment or cleaning processes. Other gases, such as CH2F2 and CHF3, are typically used at medium plasma intensity levels (500–700) for processes requiring moderate energy inputs, while high-intensity plasma levels (>1000) are reserved for gases like C4F6, C4F8, and CF4, which are better suited for etching applications that demand higher energy levels to achieve desired material removal.

In the case of process-specific limitations, certain gases are incompatible with plasma conditions outside their designated ranges due to stability issues or inefficiencies in reaction kinetics. For example, using NF3 and SF6 at higher plasma intensities could lead to undesirable side reactions or inefficiencies whereas gases like C4F6, C4F8, and CF4 are optimized for higher intensities and may not exhibit effective performance at lower intensities. These constraints ensure that each gas operates within its optimal range, maintaining both process stability and efficiency during semiconductor manufacturing.

In the case of experimental constraints, the distribution of plasma intensity levels across gases reflects practical limitations in conducting measurements and ensuring reliable data acquisition. Some intensity levels were excluded for specific gases to avoid redundancy or irrelevance to the research objectives. This selective approach was necessary to focus on collecting data that would provide meaningful insights while adhering to the operational requirements of each gas. By tailoring the intensity ranges to the most relevant conditions, the study ensured a robust and accurate analysis of the relationship between plasma intensity and 1-Ui.

5. Analysis of Group 1 Performance

5.1. Data Overview: Group 1

The experimental data classified into in this group consist of measurements of the process destruction rate (1-Ui) across plasma intensity levels below 100 for two gases, NF3 and SF6, with 300 mm wafer size. For each gas, 1-Ui values were recorded at different plasma levels, allowing for a statistical analysis of the relationship between plasma intensity and 1-Ui.

5.2. Correlation Analysis Between Plasma Intensity and 1-Ui

The correlation analysis revealed different behaviors for the two gases analyzed. For NF₃, the correlation between plasma intensity and 1-Ui was moderately negative, with a Pearson linear correlation coefficient of −0.3154 and a rank coefficient of −0.24. This indicates that as plasma intensity increases, 1-Ui tends to decrease, as shown in

Table 7. Correlation between plasma intensity and 1-Ui for NF3 and SF6.

Gas	Linear Correlation Coefficient	Rank Correlation Coefficient	p-Value
NF3	−0.315	−0.240	0.000
SF6	0.000	−0.011	0.886

. In contrast, the correlation for SF₆ was almost non-existent, with a Pearson correlation coefficient of −0.0008, suggesting no significant relationship between plasma intensity and 1-Ui.

5.3. Analysis of the Mean of Group 1 by Plasma for Each Gas

The ANOVA test showed a statistically significant difference in 1-Ui across plasma levels for NF₃, with an F-statistic of 19.26 and a p-value of 0.00. This suggests that plasma intensity significantly affects the unused rate for this gas. However, no significant difference was found for SF6, with an F-statistic of 0.010 and a p-value of 0.991, indicating that plasma intensity has no notable impact on 1-Ui for this gas.

5.4. Analysis of Pairwise Mean Test Between Plasma Level: Group 1

Tukey’s post hoc test was used to identify significant differences between plasma levels for NF₃. The results showed significant differences between plasma levels 40 and 60, 40 and 80, and 60 and 80, as indicated in

Table 8. Pairwise comparison of mean differences between plasma levels for NF3.

Comparison	Mean Difference	p-Value
Plasma 40 vs. 60	−0.180	<0.001
Plasma 40 vs. 80	−0.206	<0.01
Plasma 60 vs. 80	−0.026	<0.106

, which presents the pairwise test of Ui between groups.

5.5. 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 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.

6. Analysis of Group 2 Performance

6.1. Data Overview: Group 2

The experimental dataset for this group contains measurements of the unused gas rate 1-Ui across the plasma intensities 500, 600, and 700 for two gases: CH2F2 and CHF3 with 300 mm wafer size. The measurements were obtained from a controlled experimental setup where the plasma intensity was systematically varied, and the unused gas rate was recorded for each intensity level. This setup ensured consistency in the conditions under which the data were gathered, providing a robust basis for the subsequent analyses.

6.2. Correlation Analysis Between Plasma Intensity and 1-Ui

A Pearson and Spearman correlation analysis was performed to investigate the relationship between plasma intensity and 1-Ui, with the findings presented in

Table 9. Correlation between plasma intensity and 1-Ui for CH2F2 and CHF3.

Gas	Correlation Type	Correlation Coefficient	p-Value
CH2F2	Pearson (Linear)	−0.124	0.000
CH2F2	Spearman (Rank)	−0.360	0.000
CHF3	Pearson (Linear)	−0.172	0.000
CHF3	Spearman (Rank)	−0.379	0.000

. The Pearson correlation analysis demonstrated weak negative correlations between plasma intensity and 1-Ui for CH2F2 and CHF3. Specifically, the linear correlation coefficients were −0.124 for CH2F2 and −0.172 for CHF3, while the rank coefficients were −0.360 and −0.379, respectively. These results indicate that 1-Ui tends to decrease slightly as plasma intensity increases, although the relationship is relatively weak and non-linear. This suggests that plasma intensity alone does not fully explain the variations in 1-Ui, and other factors may need to be considered to capture the complexity of the process.

6.3. Analysis of the Mean of Group 2 by Plasma for Each Gas

To determine whether the means of the three plasma intensity groups were equal, an ANOVA test was conducted. The results, presented in

Table 10. ANOVA results for plasma intensity on CH2F2 and CHF3.

Gas	F-Statistics	p-Value
CH2F2	10.18	0.00
CHF3	19.15	0.00

, indicated statistically significant differences in 1-Ui across plasma intensity levels for both gases, with p-values below 0.05. These results suggest that plasma intensity significantly affects 1-Ui, although the relationship is not strictly linear. The F-statistic values further indicate that a portion of the variability in 1-Ui can be explained by differences in plasma intensity, supporting the hypothesis that plasma intensity levels differentially influence the reduction in unused gas in the process.

6.4. Analysis of Pairwise Mean Test Between Plasma Level: Group 2

Tukey’s post hoc analysis in

Table 11. Pairwise test of mean in plasma intensity levels for CH2F2 and CHF3.

Gas	Comparison	Mean Difference	p-Value
CH2F2	700 vs. 500	0.028	<0.001
CH2F2	600 vs. 500	0.015	0.046
CHF3	700 vs. 500	0.105	<0.001
CHF3	700 vs. 600	0.066	0.000

revealed significant differences in 1-Ui between high and low plasma intensity levels. For CH2F2, an important difference was observed between plasma intensities of 500 and 700, with a mean difference of 0.0284 (p < 0.001). In the case of CHF₃, significant differences were identified between high and low plasma intensity levels (700 vs. 500) and between high and medium levels (700 vs. 600), indicating a more substantial effect. These results suggest that the impact of plasma intensity on 1-Ui is more pronounced at extreme plasma levels, implying that the process may be more sensitive to large variations in plasma intensity compared to more minor, incremental changes.

6.5. General Trends: Group 2

As shown in Figure 8, the moderate negative correlation between plasma intensity and 1-Ui for both CH2F2 and CHF3 suggests that while higher intensities tend to reduce the unused rate, plasma intensity alone is not a strong predictor. Other factors, such as gas composition, chamber conditions, and temperature, may also impact 1-Ui, warranting further investigation to understand these influences better.

Extreme plasma levels reveal potential non-linear relationships with 1-Ui, where minor intensity shifts have limited effects, but more significant changes produce notable impacts. Future research can consider incorporating non-linear regression or machine learning models to capture these patterns, offering a more detailed understanding of plasma intensity’s role.

These findings can help optimize semiconductor plasma processes, particularly for CHF₃, where higher intensities significantly affect 1-Ui. Carefully calibrating plasma levels with attention to this tendency can improve control over the unused ratio, enhancing the efficiency of reducing exhaust gas.

7. Analysis of Group 3 Performance

7.1. Data Overview: Group 3

The experimental data used in this group consists of measurements of the process unused ratio (1-Ui) across plasma intensity levels over 1000 for three gases: C4F6, C4F8, and CF4. For each gas, 1-Ui values were recorded at plasma levels of 1000, 2000, and 3000 with a 300 mm wafer, allowing for statistical analysis of the relationship between plasma intensity and 1-Ui unused gas ratio. Summary statistics of 1-Ui by gas and plasma are shown in

Table 12. Summary statistics of 1-Ui by gas and plasma.

Gas	Plasma	Count	Mean	Std	Min	25%	50%	75%	Max
C4F6	1000	302	0.11	0.03	0.06	0.11	0.11	0.11	0.29
C4F6	2000	302	0.12	0.03	0.06	0.11	0.12	0.12	0.30
C4F6	3000	302	0.05	0.03	0.00	0.03	0.04	0.05	0.21
C4F8	1000	1033	0.48	0.14	0.01	0.50	0.51	0.52	0.90
C4F8	2000	855	0.35	0.10	0.01	0.36	0.37	0.37	0.69
C4F8	3000	689	0.34	0.10	0.02	0.35	0.36	0.36	0.70
CF4	1000	305	0.37	0.04	0.25	0.35	0.36	0.36	0.55
CF4	2000	304	0.33	0.04	0.20	0.31	0.32	0.32	0.56
CF4	3000	305	0.26	0.04	0.19	0.24	0.25	0.25	0.50

.

To assess the effect of plasma intensity on 1-Ui, box plots of 1-Ui were constructed for each gas at varying plasma levels. This visualization provides insight into the influence of plasma intensity, allowing for comparative analysis across gases and plasma levels.

As shown in the box plot of the C4F8 in Figure 9, at a plasma intensity level of 1000, the distribution of 1-Ui values is centered around 0.5, with some instances as low as 0.2, indicating a relatively high unused gas ratio. At a plasma intensity level of 2000, the distribution narrows significantly, centering more precisely around 0.37, suggesting increased consistency and a modest reduction in the unused gas ratio compared to 1000. At a plasma intensity of 3000, the distribution remains similar to that observed at 2000, with an even greater concentration of 0.3 to 0.4, further demonstrating performance stability at higher plasma intensities. These findings indicate that as plasma intensity increases, the distribution of 1-Ui for C4F8 becomes more stable and predictable, with a moderate reduction in the unused gas ratio.

As presented in Figure 10, 1-Ui values for CF₄ are primarily concentrated around 0.35 at a plasma level of 1000, indicating stable performance at this intensity. At a plasma level of 2000, the distribution shifts slightly, centering between 0.30 and 0.35, demonstrating sustained stability but with a marginally lower unused rate than at level 1000. By plasma level 3000, the distribution narrows around 0.25, signifying a continued reduction in unused rates as plasma intensity increases. These findings suggest that CF4 exhibits consistent unused gas rates across plasma levels, gradually decreasing 1-Ui as plasma intensity rises. Thus, plasma intensity is crucial in reducing the unused rate for CF4.

As shown in Figure 11, for C4F6, the distribution of 1-Ui Values at a plasma level of 1000 is centered around 0.10 to 0.15, with a considerable spread toward lower values, indicating low unused rates and less stability than other gases at this level. At plasma level 2000, the unused rate remains centered around 0.10 but with reduced variability toward lower values, suggesting a modest improvement in stability. By plasma level 3000, the distribution shifts further, with most values concentrated below 0.10, reflecting lower unused rates but increased instability at higher plasma intensities. These results show that although C4F6 consistently achieves lower unused rates as plasma intensity than other gases, its performance becomes less stable as plasma levels rise, indicating reduced overall efficiency at higher intensities.

7.2. Correlation Analysis Between Plasma and 1-Ui by Gas

The correlation results provide insights into the relationship between plasma levels and 1-Ui, the unused rate for each gas type.

Table 13. Correlation between plasma level and 1-Ui.

Gas	Pearson Correlation	Spearman Correlation	p Value
C4F8	−0.443	−0.677	0.00
CF4	−0.705	−0.809	0.00
C4F6	−0.608	−0.538	0.00

and Figure 12 present detailed information.

7.2.1. C4F8

Based on the Pearson correlation, which measures linear relationships, a moderate negative correlation between plasma and 1-Ui was observed. The Spearman rank correlation was −0.667, indicating a strong relationship where 1-Ui tends to decrease in rank as plasma levels increase, with a highly significant result. Since the relationship between plasma level and 1-Ui is not linear, the rank correlation coefficient is higher than the linear one.

7.2.2. CF4

For CF4, the Pearson correlation coefficient was −0.705 with a p-value of 0.00, indicating a strong and statistically significant negative correlation between plasma levels and the unused rate 1-Ui. This suggests that increased plasma intensity is associated with substantially reducing the unused rate for this gas. Furthermore, the Spearman correlation coefficient of −0.809, with a p-value of 0.00, reveals an even stronger negative rank correlation, affirming a significant inverse relationship between plasma intensity rank and 1-Ui rank. Both tests confirm the robustness of this inverse relationship, highlighting the impact of plasma levels on the unused rate for CF₄.

7.2.3. C4F6

For C4F6, the Pearson correlation coefficient was −0.608 with a p-value of 0.00, indicating a strong and statistically significant negative correlation between plasma levels and the unused rate 1-Ui. These results suggest that the unused rate for C4F6 decreases as plasma levels increase. The Spearman correlation coefficient of −0.528, with a similarly low p-value, reflects a moderate negative rank correlation, pointing to a significant but somewhat weaker inverse relationship between plasma intensity rank and 1-Ui rank. These findings confirm that increased plasma intensity reduces the unused rate for C4F6, and the correlation strength varies.

To summarize, the negative correlations across all gases indicate that the unused rate 1-Ui consistently decreases as plasma intensity increases. The strength of this inverse relationship varies among the gases, with some exhibiting stronger correlations than others. The uniformly low p-values across all gases affirm that these correlations are statistically significant. These results align with the general tendency that increased plasma intensities enhance the availability of reactive radicals by promoting the dissociation of input gases, which are the primary agents in etching or cleaning processes. As plasma intensity rises, the abundance of these radicals increases, leading to more effective interactions with the target surfaces or substrates. This, in turn, reduces the proportion of unused gas, reflected as a decrease in 1-Ui. In addition, higher plasma intensities accelerate reaction rates by providing the activation energy necessary for chemical reactions to proceed, ensuring that a larger fraction of the gas is consumed in desired reactions, thereby lowering the unused gas rate. Together, these mechanisms explain why increased plasma intensity correlates with a lower unused gas rate across all gases, emphasizing the importance of optimizing plasma conditions to maximize process efficiency.

7.3. Analysis of the Mean of Group 3 by Plasma for Each Gas

The ANOVA test compared the group mean of 1-Ui by plasma level for each gas, as shown in

Table 14. ANOVA 1-Ui by plasma and gas.

	Sum_sq	df	F	PR (>F)	Gas
C (plasma)	11.57651	2	406.069	0.000	C4F8
Residual	36.69079	2574			C4F8
C (plasma)	1.72091	2	472.451	0.000	CF4
Residual	1.65916	911			CF4
C (plasma)	0.92371	2	517.930	0.000	C4F6
Residual	0.80523	903			C4F6

.

The ANOVA results reveal that plasma level has a statistically significant impact on the unused rate 1-Ui across all gas types, as evidenced by the extremely low p-values, confirming the robustness of the findings. The F-statistics highlight the differential effects of plasma levels on 1-Ui depending on the gas. Specifically, C4F8 exhibits a notable F-value of 406.07, CF4 demonstrates an even more substantial impact with an F-value of 472.45, and C4F6 shows the highest impact, with an F-value of 517.93. These results suggest that while plasma intensity significantly influences the unused rate for all gases, the magnitude of this effect varies by gas type.

7.4. Analysis of Pairwise Mean Test Between Plasma Level: Group 3

Pairwise comparisons between plasma levels provide additional insights into the effect of plasma intensity on the unused rate of 1-Ui for each gas.

Table 15. Pairwise comparison of the mean of 1-Ui by plasma level.

Gas	Plasma Level 1	Plasma Level 2	T-Statistic	p-Value
C4F8	1000	2000	23.023	0.000
C4F8	1000	3000	22.820	0.000
C4F8	2000	3000	1.782	0.075
CF4	1000	2000	11.423	0.000
CF4	1000	3000	31.095	0.000
CF4	2000	3000	18.360	0.000
C4F6	1000	2000	−2.189	0.029
C4F6	1000	3000	26.614	0.000
C4F6	2000	3000	27.923	0.000

presents detailed information.

For C4F8, significant differences were observed between plasma levels 1000 and 2000 (T = 23.023, p = 0.000) and between 1000 and 3000 (T = 22.820, p = 0.000), whereas the difference between levels 2000 and 3000 is less pronounced (T = 1.782, p = 0.07). For CF4, all pairwise comparisons between plasma levels were highly significant, with p-values of 0.000, indicating marked differences in unused rate between levels 1000 vs. 2000 (T = 11.423), 1000 vs. 3000 (T = 31.095), and 2000 vs. 3000 (T = 18.360). For C4F6, pairwise comparisons revealed significant differences in 1-Ui between plasma levels 1000 and 3000 (T = 26.614, p = 0.000) and between levels 2000 and 3000 (T = 27.923, p = 0.00). Though statistically significant, the comparison between plasma levels 1000 and 2000 indicates a weaker effect (T = −2.189, p = 0.02). These findings emphasize that plasma intensity substantially impacts 1-Ui across all gases, with the effect strength varying by gas type. Furthermore, the pairwise comparisons underscore notable differences in unused rates between plasma levels, particularly in CF4 and C4F6, suggesting that the influence of plasma intensity on 1-Ui is dependent on both gas type and plasma level. These results reveal that plasma intensity significantly affects 1-Ui across all gases, with varying degrees of impact by gas type. The pairwise comparisons further highlight the differences in unused rates between specific plasma levels, particularly in CF4 and C4F6.

7.5. General Trends: Group 3

Referencing Figure 13, for C4F8, the 1-Ui value decreases with increasing plasma intensity, with the optimal plasma level being around 2000 for minimizing 1-Ui. For CF4, the trend indicates that higher plasma intensities result in lower 1-Ui values, suggesting that optimal performance can be achieved when plasma intensities are higher than 3000. In the case of C4F6, the 1-Ui distribution initially increases slightly before sharply decreasing beyond a plasma intensity of 2000, implying that the optimal plasma intensity for minimizing 1-Ui is beyond 3000.

8. Conclusions

Using experimental data collected in South Korea, this study has demonstrated that the relationship between plasma intensity and the unused gas rate (1-Ui) in semiconductor processes varies by gas type and intensity level, revealing unique trends across three plasma groups. In Group 1 (plasma intensities below 100), a weak relationship was observed for most gases, indicating that lower intensities minimally affect 1-Ui.

In Group 2 (moderate intensities of 500 to 700), an inverse relationship emerged, where increases in plasma intensity moderately decreased 1-Ui for gases such as CH2F2 and CHF3, suggesting that moderate intensities are more effective in reducing unused rates.

In Group 3 (high intensities above 1000), non-linear behavior was evident. There were significant reductions in 1-Ui for gases such as CF4 and C4F6. These results together show that high plasma intensities significantly impact 1-Ui, but accurately capturing the complex effects requires non-linear models. This distinction among groups highlights that while moderate intensities can reduce unused rates predictably, optimizing plasma conditions at higher intensities requires a nuanced, non-linear approach. Tailoring intensity settings by gas type and leveraging advanced models for Group 3 intensities can enhance efficiency, minimizing the unused gas ratio.

This study highlights the potential for industrial application by identifying optimal plasma intensity settings tailored to specific gases, such as CF4 and C4F6, to maximize efficiency while reducing waste. Furthermore, by optimizing gas utilization rates, the findings contribute to enhancing energy efficiency, lowering operational costs, and minimizing environmental impacts in semiconductor manufacturing.