Semiconductor devices recently have been developed with increased integration density to meet the demands of various applications that require high performance and low power characteristics, resulting in a reduction of node sizes [1–3]. Consequently, the number of process steps required to produce a single device has significantly increased, leading to longer manufacturing times. Therefore, reducing the manufacturing time, in addition to device miniaturization, has become a key factor in semiconductor processing. To reduce the production time of semiconductor devices, high-productivity equipment capable of processing multiple wafers in a single process, such as dual and quad chambers, is being introduced. Furthermore, as these high-productivity systems have larger volumes, high pumping speed and high-performance vacuum pumps are required to rapidly establish the process environment [4–6].

In addition, miniaturized devices are susceptible to defects caused by even small impurities. As new processes, such as high-density plasma and ultra-high vacuum chemical vapor deposition, are introduced to achieve an ultra-high vacuum, research on the development and scaling of high vacuum pumps has been actively conducted [7,8]. Turbo molecular pumps (TMP_s) are the most commonly used equipment for achieving high vacuum environments, and high pumping speed and ultimate pressure are the most important characteristics for reducing process time and achieving a high vacuum. Therefore, evaluating the pumping performance of TMP_s, including pumping speed and ultimate pressure, is crucial, as it indicates both process time and impurity removal efficiency in semiconductor manufacturing equipment. In line with this, performance indicators for TMP_s have been established based on international standards, such as international organization for standardization (ISO) 21360, which provides general procedures for test chamber design, vacuum gauge placement, and evaluation methods [9,10].

However, although a standardized evaluation procedure has been established through general evaluation procedures, research has not been reported on the impact of pressure gauge corrections and local outliers on pumping performance. In the present study, a test chamber and evaluation platform were constructed to evaluate the pumping performance of a 4,000 L/s class commercial TMP, including pumping speed and ultimate pressure, according to ISO 21360. Furthermore, a method of correcting the vacuum gauges used in the evaluation and data processing methods was proposed, and the impact of these methods on performance evaluation results was analyzed.

2.1. Development of evaluation platform

The TMP pumping performance evaluation platform was designed based on the international standard ISO 21360, and Fig. 1 shows a schematic diagram of the chamber specifications and instrument positions. The chamber is a single-dome chamber, which is the most commonly used for evaluating vacuum pump performance, allowing assessment across all pressure ranges. The height of the chamber is determined according to the size of the vacuum pump inlet, and each height is set to 1.5 and 0.5 times the size of the inlet. In addition, gases for pumping speed evaluation can be introduced through a mass flow controller (MFC), and a temperature sensor is installed to measure the temperature of the gas. Since TMP_s cannot perform standalone exhaust, a backing pump is required, and a vacuum gauge is installed between the two pumps.

Figure 1. Schematic of the TMP performance evaluation platform based on ISO 21360.

For pressure measurements, the evaluation platform uses four types of gauges, a full range gauge (hot cathode gauge + Pirani gauge), a spinning rotor gauge (SRG), and two types of capacitive diaphragm gauges (CDG), to measure precise vacuum pressures ranging from 1,000 to 5 × 10⁻¹⁰ mbar. Additionally, MFCs with maximum flow rates of 0.7, 20.0, 400.0, and 5,000.0 sccm are used to control the pressure and gas flow, allowing for the evaluation of N₂ gas.

2.2. Measurement method of ultimate pressure and pumping speed

Ultimate pressure, a critical factor in determining the base pressure in the process and the cleanliness of the chamber, is defined as the lowest pressure that can be achieved by the pump in the absence of gas injection. To evaluate the ultimate pressure, the pump is operated without gas injection, and pressure changes are monitored over time to measure the lowest pressure. However, in high-vacuum pumps such as TMP_s, virtual leaks caused by outgassing from components can affect the evaluation process [9]. According to the ISO standard procedure, a bake-out must be performed at a temperature between 180 and 300 °C for 48 h. Pumping must subsequently be maintained for an additional 48 h, and then the ultimate pressure (P_b) is determined by measuring 100 times. In this study, the bake-out was performed at 180 °C, considering the operating temperature of the vacuum gauge attached to the chamber.

Pumping speed (S) represents the volume of gas that can be expelled per unit time, and it directly impacts process pressure, flow rate, and impurity removal time. To evaluate this, the pumping speed can be calculated using Eq. (1) based on the flow rate and pressure values measured in a chamber that maintains a constant pressure or flow rate:

Here, P represents the pressure measured during gas injection, and Q denotes the flow rate introduced into the chamber. High-purity gases with a purity of 99.999 % or higher should be used for evaluation, and the gas should be maintained for at least 60 s after injection to ensure pressure stabilization. The resulting value is then defined as the pumping speed at that pressure. To eliminate the effect of virtual leaks, the ultimate pressure is subtracted from the measured pressure. In this study, a constant flow rate was introduced into the chamber for 100 s using an MFC, and pressure measurements were taken while gradually increasing the flow rate for the pumping speed evaluation.

2.3. Measurement gauge correction and anomaly detection method

Since the measurement range and accuracy of vacuum gauges vary depending on their range and mechanism, it is common to use a combination of several gauges to measure across a wide pressure range. However, due to differences in accuracy between gauges, errors may occur in the measurement results, making it essential to verify the accuracy and reliability of the gauges [9]. In this study, the pressuredependent errors of the gauges used were verified according to the standard procedure of the Korea Research Institute of Standards and Science (KRISS) (Calibration procedure of vacuum gauges using a comparison method, C-09-2-1002), and a correction formula was established based on these results.

During the measurement process, outliers may occur due to various factors such as external electromagnetic interference, communication errors, and power noise, which can degrade the consistency of the measurement data and lead to incorrect pumping performance calculations. Especially in TMP evaluation platforms, which involve very low pressure measurements, even small discrepancies in the data can lead to significant errors, making outlier detection and removal essential. Various statistical methods are used for outlier detection, such as standard deviation, median absolute deviation, and interquartile range (IQR). Among these, the IQR method is efficient in terms of time and cost-effectiveness compared to other outlier detection methods, due to ease of calculation and low sensitivity to distortion caused by outliers. However, if the number of data points is too small, it may provide incorrect information about outliers, and thus it is appropriate to use this method when at least 50 data points are available. IQR represents the range between the value at the lower 25 % (Q₁) and the value at the lower 75 % (Q₃) of a sorted dataset; that is, it represents the difference between these two points. Using this, the lower and upper bounds for detecting outliers are determined, with the lower bound defined as Q₁ − (1.5 × IQR) and the upper bound as Q₃ + (1.5 × IQR). Values outside of these bounds are considered outliers. Using 1.5 × IQR, the range encompasses about 99.3 % of the data in a normal distribution [11–13]. In this study, approximately 70 data points were secured for the TMP performance evaluation, and the IQR method was used to detect and remove outliers to reduce sensitivity to data distortion.

3.1. Vacuum gauge correction

The vacuum gauges used in the evaluation were compared with the KRISS standard gauge (P_s) to determine the measurement error by calculating the ratio between the test gauge (P_t) and the P_s, as shown in Fig. 2(a). A ratio closer to 1 indicates a smaller error relative to the P_s. The full range gauge is designed to measure a wide pressure range by switching between an ion gauge and a Pirani gauge, depending on the pressure range. Between these, the Pirani gauge, which operates based on thermal conductivity, showed lower accuracy compared to other gauges, resulting in an average error rate of 18.55 % for the full range gauge, which was higher than the other gauges. The SRG and CDGs showed relatively higher accuracy, with error rates of 5.92, 1.50, and 1.25 %, respectively. The varying error rates among the gauges indicate the necessity of corrections to ensure the consistency of pressure measurements.

Figure 2. Correction by comparison to a standard gauge (a) Correction factors for the standard gauge and the measuring gauge. (b)−(e) Before and after correction for each gauge.

A correction formula was established to align the pressure values of the P_t with those of the P_s, based on the measured errors. The correction formula was determined using a fitting analysis, and either a linear or polynomial fitting was selected based on the R² value being close to 1. The R² value, known as the coefficient of determination, indicates the correlation between two values, with values closer to 1 indicating a higher correlation. Table I shows the correction functions used for each gauge. For the CDG, the correction formula was represented as a linear function due to its high linearity, and the post-correction errors were 0.15 and 0.14 %, demonstrating high consistency. Figures 2(d) and 2(e) show the differences in measurement values before and after correction for the CDG, confirming high linearity. For the full range gauge and SRG, due to the wide measurement range, the errors were non-linear, resulting in a polynomial correction function; however, the R² value remained close to 1, indicating a strong correlation. Figures 2(b) and 2(c) show the results before and after correction, with errors of 0.92 and 0.02 %, respectively. Although all gauges showed an error rate of less than 1 %, it is important to note that more complex correction formulas may introduce additional errors during the correction process.

Table I. Vacuum gauge correction range and function result..

Gauge	Function	Error compared to the ref. gauge		R2
		Before	After
Full range	y = a[1−e−bx ]	18.55 %	0.92 %	1.0000
SRG	y = (a+bx)/(1+cx+dx2)	5.92 %	0.02 %	1.0000
CDG1	y = a+bx	1.50 %	0.15 %	0.9999
CDG2	y = a+bx	1.25 %	0.14 %	1.0000

a, b: constant, x: P_t, and y: ref. gauge.

3.2. Pumping performance evaluation of TMP

Using a 4,000 L/s class TMP and a 25 L/s backing pump, the ultimate pressure and pumping speed were measured to assess the effect of vacuum gauge correction. In this experiment, the ultimate pressure was determined by calculating the average pressure over 120 s after a total of 96 h. Figure 3(a) shows the pressure graph during the ultimate pressure measurement, with periodic vertical peaks resulting from the outgassing function used to remove adsorbed gases from the ion gauge. After 96 h, the measured pressure before gauge correction was 1.83 × 10⁻⁹ mbar, while the corrected pressure was 2.19 × 10⁻⁹ mbar. This difference is attributed to the correction results of the full range gauge, which is capable of high vacuum measurements. Figures 3(b) and 3(c) show the pressure distribution before and after correction, confirming that there was no change in distribution even after correction.

Figure 3. (a) Ultimate pressure measurement process and pressure measurement results before and after vacuum correction after 96 h. Distribution of ultimate pressure results (b) before and (c) after vacuum gauge correction.

For the pumping speed evaluation, nitrogen (N₂), which is commonly used in such assessments, was used, and the flow rate was measured up to 2,500 sccm, which is the maximum flow rate of the target TMP. Using an MFC, the flow rate was increased by 5 % increments up to the maximum, and gas was injected for 100 s at each flow rate. After gas injection, a stabilization period of 40 s was followed by averaging the pressure measured over 60 s, which was then used to calculate the pumping speed using Eq. (1). Figures 4(a) and 4(b) show the pumping speed and distribution of the measurement results at each pressure. A rapid drop in pumping speed was observed in the low vacuum range above 1 × 10⁻² mbar. This phenomenon is due to the operating characteristics of the TMP, which imparts directionality to gas molecules through the blades; at high flow rates, gas molecules lose directionality and cause backflow. Therefore, a rapid decrease in the pumping speed of the TMP indicates performance degradation and is not a normal state. The point at which the TMP performance degrades varies depending on factors such as the TMP blade design, rotor speed, and backing pump performance. Therefore, it is difficult to set a single standard. In this study, performance degradation was considered to occur when the overall average pumping speed of the TMP decreased by 20 % or more, which occurred at 1E-2 mbar. The average pumping speed was calculated only for pressures below 1 × 10⁻² mbar, which is considered the normal state, and the resulting value was 4,392 L/s. Figure 4(b) shows a wide distribution of the results, with the full width at half maximum (FWHM) calculated as 894 L/s. This indicates a mismatch in consistency between gauges.

Figure 4. Pumping speed calculation results (a) before and (c) after vacuum gauge correction. Distribution of pumping speed calculation results (b) before and (d) after vacuum gauge correction.

To compare changes in pumping speed after applying the correction formula, the previously established gauge correction formula was applied, and the results are shown in Figs. 4(c) and 4(d). The average pumping speed was calculated to be 3,934 L/s, representing a 10 % decrease, and the distribution appeared to improve; however, the FWHM remained broad at 894 L/s. As shown in Figs. 4(a) and 4(c), the measurements are inconsistent, with localized decreases resembling outliers.

3.3. Outlier removal

Despite correcting the vacuum gauge, it was confirmed that the distribution of the pumping speed measurement results remained broad. This is believed to be due to local pressure anomalies or minor discrepancies between the gauges, rather than a deterioration in the performance of the vacuum pump. The ideal solution would be to eliminate local pressure anomalies through an extensive evaluation or replace the vacuum gauge and achieve perfect linearity through a new correction, but this requires significant time and cost. Additionally, practical constraints, such as the number of installed vacuum gauges, must be considered, making this approach challenging.

Therefore, in this experiment, a statistical analysis was used to remove outliers and improve measurement reliability. After correction, outlier detection was performed on the pumping speed results using the IQR method. The results of the IQR analysis are shown in Fig. 5(a), where Q₁ was 3,839.89 L/s, Q₃ was 4,056.38 L/s, and the IQR was calculated as 216.49 L/s. The upper limit was calculated as 3,533.59 L/s and the lower limit as 431.05 L/s, as presented in Table II. Based on the IQR analysis, the results and distribution of the pumping speed after removing the outliers are shown in Figs. 5(b) and 5(c). The average pumping speed was calculated to be 3,903 L/s and the FWHM was reduced to 371 L/s. Compared to the pre-outlier removal value of 3,934 L/s, the average pumping speed decreased by 1 %, but the FWHM decreased by 41 %, resulting in a much sharper distribution. Additionally, it showed a 12 % difference from the uncorrected pumping speed, confirming the significant impact of data processing on TMP pumping performance indicators. The differences are summarized in Table III. For ultimate pressure, no outliers were detected, as the TMP was operated in an idle state without gas injection.

Figure 5. (a) Pumping speed IQR analysis results after vacuum gauge correction. (b) Pumping speed results of data processing such as vacuum gauge and remove outliers. (c) Pumping speed distribution results of data processing such as vacuum gauge and remove outliers.

Table II. Pumping speed IQR analysis results..

	Value (L/s)
Q3	4,056.38
Q1	3,839.89
Q3 + (1.5 × IQR)	4,373.29
Q1 − (1.5 × IQR)	3,520.36

Table III. Gauge correction and the effect of outlier on pumping speed..

	Value (L/s)	FWHM (L/s)
Origin	4,392	894
Gauge correction	3,934	894
Gauge correction + remove outlier	3,903	371

In this study, the performance of a commercial 4,000 L/s class TMP was evaluated using an evaluation platform based on the international standard ISO 21360, and the impact of vacuum gauge correction and outlier detection on data processing was analyzed. A correction formula was established through a comparison with a P_s, which reduced the measurement error rate from up to 18.55 to below 1.00 %. Due to gauge correction, the pumping speed was calculated to be 3,934 L/s from an initial speed of 4,392 L/s, and the ultimate pressure was determined to be 2.19 × 10⁻⁹ mbar from an initial 1.83 × 10⁻⁹ mbar. Although the reduction in error rates led to changes in pumping performance indicators, it was confirmed that anomalies such as localized pressure irregularities still existed. Therefore, an exploratory data analysis was performed using the IQR method, and detected outliers were removed. As a result, the pumping speed decreased to 3,903 L/s, and the FWHM of the pumping speed distribution decreased by 41 %, showing a clearer distribution. In conclusion, vacuum gauge errors and outliers can significantly affect TMP performance indicators during a performance evaluation, and pressure correction and outlier detection methods are critical factors for enhancing the accuracy and reliability of the evaluation.

This research was supported by Korea Evaluation Institute of Industrial Technology - Grant funded by the Korean Government (KEIT-2022-20011567), This work was funded by the Ministry of Trade, Industry and Energy (MOTIE) under the project of development of monitoring and analysis technologies for greenhouse gases in the semiconductor manufacturing etching process (RS-2023-00265582), and This work was supported by K-CHIPS (Korea Collaborative & High-tech Initiative for Prospective Semiconductor Research) (NTIS-1415187510, KEIT – 2023 – RS-2023-00235156, 23013-45FC) funded by the Ministry of Trade, Industry & Energy (MOTIE, Korea).

The authors declare no conflicts of interest.