Impedance Monitoring of Capacitively Coupled Plasma Based on the Vacuum Variable Capacitor Positions of Impedance Matching Unit

Abstract

Plasma impedance monitoring in semiconductor manufacturing processes is performed using external sensors, such as voltage-current (VI) probes or directional couplers. Plasma chamber impedance measurements, conducted in non-50 Ω matched transmission lines, suffer from a lack of clean signals due to phase variations and the nonlinearity of plasma, thus, sensor calibration is required for each installment. In this study, we monitored plasma impedance in situ based on the position of the vacuum variable capacitor within the matching network, without employing an external VI probe. We observed changes in the matching position according to parameter variations and subsequently confirmed that the calculated plasma impedance also varied accordingly. This study demonstrates the feasibility of real-time plasma impedance monitoring under 50 Ω-matched conditions without the use of external sensors, thereby simplifying plasma diagnostics.

1. Introduction

Plasma has now become an essential element in semiconductor processes, leading to advancements in plasma diagnostic technologies to ensure process reproducibility. Plasma diagnostics have evolved not only to analyze plasma itself but also to detect equipment anomaly conditions [1,2,3,4,5,6,7,8,9,10,11,12]. Plasma diagnostic methods can be categorized into invasive techniques, such as single Langmuir probe (SLP), double Langmuir probe (DLP), cut-off probes, wafer-type sensors, and non-invasive techniques, such as optical emission spectroscopy (OES), VI probes, and directional couplers [13,14,15,16,17,18,19]. Furthermore, methods for diagnosing plasma ignition with high-speed sampling rates have also been reported [20].

Among these techniques, impedance monitoring is widely used because, unlike invasive sensors, it enables plasma diagnosis without directly interfering with the plasma. In etching processes, impedance monitoring is widely utilized for endpoint detection (EPD) to prevent over-etching [21,22]. In contrast, plasma enhanced chemical vapor deposition (PECVD) processes require stable and consistent plasma conditions, as uniform radical generation is critical for thin film deposition. Since process plasma characteristics are influenced by parameters such as pressure, power, gas ratio, and even chamber conditions, impedance monitoring is also important for detecting such variations and ensuring process stability [1,3,23].

Most impedance monitoring methods require sensors, such as VI probes or directional couplers, which are typically positioned between the matching network and the plasma reactor with a non-50 Ω transmission line. However, due to the diode-like characteristics of the plasma sheath, nonlinear behavior arises, leading to the generation of harmonics. These harmonics act as noise in sensor measurements, making it difficult to obtain clean signals [24,25]. Furthermore, the complexity of sensor calibration varies depending on the reactor used [26].

To efficiently transfer the amount of the applied power to plasma, a matching network is essential to minimize the amount of the reflected power. In RF systems, plasma generation requires power to be applied, and thus, the load impedance becomes determinable only after the plasma is ignited (it initially behaves as an unknown load impedance). Furthermore, plasma characteristics vary dynamically in real time depending on the reactor type (ICP, CCP etc.), operating conditions (pressure, power, gas etc.), and driving frequency. Consequently, the matching network topology (π-type, L-type etc.) and the configuration of internal components are designed differently to accommodate the specific plasma behavior. When RF power is applied, the variable components inside the matching network, primarily vacuum variable capacitors (VVC), dynamically adjust the impedance accordingly [27,28,29]. Numerous studies have been conducted to achieve efficient and rapid impedance matching. Shin et al. proposed a matching algorithm based on machine learning to quickly determine the optimal position of the vacuum variable capacitor (VVC) [27]. Zhang et al. proposed tuning algorithms applied to RF matching networks for CCP chambers, which improved the overall matching efficiency and automation [30]. Yu et al. implemented impedance matching using a frequency modulation technique [31]. Furthermore, recent research has explored the use of electronic variable capacitors (EVC), instead of mechanically driven VVC, to enable faster impedance matching [32].

This study aims to simplify the complexity of impedance monitoring by investigating the feasibility of plasma impedance monitoring based on real-time VVC position inside the matching network, which is located at a 50 Ω transmission line under matched conditions. We describe the experimental setup, the method for deriving plasma impedance from the matching network, and the plasma equivalent circuit in Section 2. In Section 3, we present the validation experiment, while Section 4 discusses the results. In Section 5, we provide the conclusions of this paper. The acronyms used throughout this paper are summarized in

Table 1. List of acronyms.

Acronyms	Meaning
$Z_{\mathrm{T}}$	Total impedance
$R_{\mathrm{T}}$	Total resistance
$X_{\mathrm{T}}$	Total reactance
$Z_{\mathrm{L}}$	Load impedance
$R_{\mathrm{L}}$	Load resistance
$X_{\mathrm{L}}$	Load reactance
$Z_{\mathrm{s}\mathrm{e}}$	Series impedance
$X_{\mathrm{s}\mathrm{e}}$	Series reactance
$Z_{\mathrm{s}\mathrm{h}}$	Shunt impedance
$X_{\mathrm{s}\mathrm{h}}$	Shunt reactance
${\nu }_{\mathrm{m}}$	Electron-neutral collision frequency
$m_{\mathrm{e}}$	Electron mass
$n_{\mathrm{e}}$	Electron density
${\omega }_{\mathrm{p}\mathrm{e}}$	Plasma electron frequency
${\epsilon }_0$	Permittivity of vacuum
$A$	Area of sheath (Area of electrode)
$d_{\mathrm{s}}$	Sheath thickness
${\lambda }_{\mathrm{i}}$	Ionic mean free path
$C_0$	Intrinsic capacitance of the plasma
$C_{\mathrm{s}}$	Sheath capacitance
$R_{\mathrm{p}}$	Bulk plasma resistance
$L_{\mathrm{p}}$	Bulk plasma inductance

.

2. Methods

2.1. Derivation of Load Impedance

To derive the plasma impedance using the matching network position, the matching network of a 300 mm commercial CCP system shown in Figure 1 was investigated. It forms an L-type impedance matching network, with the input sensor (VI probe) positioned at the RF IN terminal (50 Ω transmission line). The values of the components within the matching network are listed in

Table 2. Values of components in matching network.

Component	Value
L1	200 nH
L2	1.05 μH
VC1	35–500 pF
VC2	35–1000 pF

.

The circuit diagram was constructed based on the matching network, as shown in Figure 2. In Figure 2, load impedance ($Z_{\mathrm{L}}$) represents the impedance of plasma chamber, and total impedance ($Z_{\mathrm{T}}$) represents the sum of the matching network impedance and the load impedance, as viewed from the RF generator (50 Ω transmission line).

Since shunt impedance ($Z_{\mathrm{s}\mathrm{h}}$) inside the matching network is in parallel with series impedance ($Z_{\mathrm{s}\mathrm{e}}$) and $Z_{\mathrm{L}}$, the total impedance ($Z_{\mathrm{T}}$) can be expressed as follows.

$$Z_{\mathrm{T}}={\displaystyle \frac{Z_{\mathrm{s}\mathrm{h}}\left(Z_{\mathrm{s}\mathrm{e}}+Z_{\mathrm{L}}\right)}{Z_{\mathrm{s}\mathrm{h}}+Z_{\mathrm{s}\mathrm{e}}+Z_{\mathrm{L}}}}$$

(1)

Rearranging this equation for $Z_{\mathrm{L}}$ gives the following expression:

$$Z_{\mathrm{L}}={\displaystyle \frac{Z_{\mathrm{T}}{Z}_{\mathrm{s}\mathrm{h}}+Z_{\mathrm{T}}{Z}_{\mathrm{s}\mathrm{e}}-Z_{\mathrm{s}\mathrm{h}}{Z}_{\mathrm{s}\mathrm{e}}}{Z_{\mathrm{s}\mathrm{h}}-Z_{\mathrm{T}}}}$$

(2)

Since $Z_{\mathrm{s}\mathrm{h}}={jX}_{\mathrm{s}\mathrm{h}}$ and $Z_{\mathrm{s}\mathrm{e}}={jX}_{\mathrm{s}\mathrm{e}}$,

$$Z_{\mathrm{L}}={\displaystyle \frac{{jX}_{\mathrm{s}\mathrm{h}}{R}_{\mathrm{T}}-X_{\mathrm{T}}{X}_{\mathrm{s}\mathrm{e}}+{jX}_{\mathrm{s}\mathrm{e}}{R}_{\mathrm{T}}-X_{\mathrm{T}}{X}_{\mathrm{s}\mathrm{e}}+X_{\mathrm{s}\mathrm{h}}{X}_{\mathrm{s}\mathrm{e}}}{j\left(X_{\mathrm{s}\mathrm{h}}-X_{\mathrm{T}}\right)-R_{\mathrm{T}}}}$$

(3)

Substituting $X_{\mathrm{s}\mathrm{h}}-X_{\mathrm{T}}=a$ and rearranging the equation in the form of $Z=R+jX$, we obtain the following expression:

$$Z_{\mathrm{L}}={\displaystyle \frac{R_{\mathrm{T}}{X}_{\mathrm{s}\mathrm{h}}^2}{R_{\mathrm{T}}^2+a^2}}+j{\displaystyle \frac{A\left(X_{\mathrm{T}}{X}_{\mathrm{s}\mathrm{h}}+X_{\mathrm{T}}{X}_{\mathrm{s}\mathrm{e}}-X_{\mathrm{s}\mathrm{h}}{X}_{\mathrm{s}\mathrm{e}}\right)-R_{\mathrm{T}}^2(X_{\mathrm{s}\mathrm{h}}+X_{\mathrm{s}\mathrm{e}})}{R_{\mathrm{T}}^2+a^2}},\left(a=X_{\mathrm{s}\mathrm{h}}-X_{\mathrm{T}}\right)$$

(4)

At this point, since the experiment is based on the 50 Ω matched condition, $R_{\mathrm{T}}$ is set to 50 Ω.

$$Z_{\mathrm{L}}={\displaystyle \frac{{50}^2{X}_{\mathrm{s}\mathrm{h}}^2}{{50}^2+X_{\mathrm{s}\mathrm{h}}^2}}-j{\displaystyle \frac{X_{\mathrm{s}\mathrm{h}}^2{X}_{\mathrm{s}\mathrm{e}}+{50}^2\left(X_{\mathrm{s}\mathrm{h}}+X_{\mathrm{s}\mathrm{e}}\right)}{{50}^2+X_{\mathrm{s}\mathrm{h}}^2}}\Omega$$

(5)

Since $L_1=200\times {10}^{-9}$ (H) and $L_2=1.05\times {10}^{-6}$ (H), $X_{\mathrm{s}\mathrm{h}}$ and $X_{\mathrm{s}\mathrm{e}}$ can be expressed as follows.

$$X_{\mathrm{s}\mathrm{h}}=2\pi f{L}_1-{\displaystyle \frac{1}{2\pi f{C}_1}}=2\pi \times 13.56\times {10}^6\times 200\times {10}^{-9}-{\displaystyle \frac{1}{2\pi \times 13.56\times {10}^6\times C_1}}\Omega$$

(6)

$$X_{\mathrm{s}\mathrm{e}}=2\pi f{L}_2-{\displaystyle \frac{1}{2\pi f{C}_2}}=2\pi \times 13.56\times {10}^6\times 1.05\times {10}^{-6}-{\displaystyle \frac{1}{2\pi \times 13.56\times {10}^6\times C_2}}\Omega$$

(7)

Therefore, by substituting the capacitance of the VVC in the matching network into Equation (5), the plasma impedance can be derived. Equation (5) was cross validated using advanced design system (ADS), as shown in Figure 3a. When the process was not in operation, the home position (preset) of the matching network was VC₁ = 313 pF and VC₂ = 372 pF. Assuming $Z_{\mathrm{T}}=25+j30$, the calculated load impedance was $Z_{\mathrm{L}}=3.2998-j44.1101$. After inputting this value into the load of the ADS circuit and running the simulation, it was confirmed that the $Z_{\mathrm{T}}$ value was identical, as shown in Figure 3b.

2.2. Equivalent Circuit of Capacitively Coupled Plasma

To analyze the impedance of plasma, an equivalent circuit model is required. As shown in Figure 4, the equivalent circuit can be simplified as a series connection of sheath capacitance ($C_{\mathrm{s}}$), plasma inductance ($L_{\mathrm{p}}$), and plasma resistance ($R_{\mathrm{p}}$). Accordingly, the load impedance ($Z_{\mathrm{L}}$) based on the equivalent circuit is given as follows:

$$Z_{\mathrm{L}}=R_{\mathrm{L}}+j{X}_{\mathrm{L}}=R_{\mathrm{p}}+j\left(\omega L_{\mathrm{p}}+{\displaystyle \frac{1}{\omega C_{\mathrm{s}}}}\right)$$

(8)

Here, ω is the angular frequency of the RF source ($2\pi f$), and the variables for each term, shown in Figure 4, are defined as follows [33]:

$$R_{\mathrm{p}}={\nu }_m{L}_{\mathrm{p}}={\displaystyle \frac{{\epsilon }_0{m}_{\mathrm{e}}{\nu }_{\mathrm{m}}}{C_0{e}^2{n}_{\mathrm{e}}}}\propto {\displaystyle \frac{{\nu }_{\mathrm{m}}}{n_{\mathrm{e}}}}$$

(9)

$$L_{\mathrm{p}}={\omega }_{\mathrm{p}\mathrm{e}}^{-2}{C}_0^{-1}$$

(10)

$$C_{\mathrm{s}}={\epsilon }_0{\displaystyle \frac{A}{d_{\mathrm{s}}}}$$

(11)

${\nu }_m$ is the electron-neutral collision frequency, $m_{\mathrm{e}}$ is the electron mass, $n_{\mathrm{e}}$ is the electron density, ${\omega }_{\mathrm{p}\mathrm{e}}$ is the plasma electron frequency, ${\epsilon }_0$ is the permittivity of vacuum, $A$ is the area of sheath, and $d_{\mathrm{s}}$ is the sheath thickness. Since the experiments in this study were conducted under high-pressure conditions, the sheath thickness is proportional to the square root of the ionic mean free path (${\lambda }_{\mathrm{i}}$), following the collisional sheath model [3]. $C_{\mathrm{o}}$ represents the intrinsic capacitance of the plasma. The displacement current flowing through $C_{\mathrm{o}}$ is significantly smaller than the conduction current passing through the bulk plasma, making its effect on the overall reactance negligible; thus, it can be ignored [33].

Furthermore, in the case of CCP, the reactance component is predominantly capacitive, meaning that almost all the applied RF voltage appears across $C_{\mathrm{s}}$ [3,33]. Therefore, in this study, variations in $C_{\mathrm{s}}$ are further considered ($X_{\mathrm{i}\mathrm{n}\mathrm{d}.}\ll X_{\mathrm{c}\mathrm{a}\mathrm{p}.}$), as expressed in Equation (12).

$${∆X}_{\mathrm{L}}\propto -{\displaystyle \frac{1}{∆C_{\mathrm{s}}}}$$

(12)

Accordingly, the load impedance can be expressed as follows:

$${\mathit{Z}}_{\mathbf{L}}={\mathit{R}}_{\mathbf{L}}+{\mathit{j}\mathit{X}}_{\mathbf{L}}\approx {\mathit{R}}_{\mathbf{p}}+{\mathit{j}\mathit{X}}_{\mathbf{s}}\approx {\mathit{R}}_{\mathbf{p}}-\mathit{j}{\displaystyle \frac{{\mathit{d}}_{\mathbf{s}}}{\mathit{\omega }{\mathit{\epsilon }}_0\mathit{A}}}$$

(13)

3. Validation Experiment

The experiments were conducted using the 300 mm commercial CCP-type PECVD system, TES (Yongin-si, South Korea), as it is already shown in Figure 1. The VVC position data from the matching network were acquired once per second via an RS−232 communication cable. Forward and reflected power data were obtained from the generator. The most reliable method for evaluating the measured load impedance is to compare it with external sensors such as a VI probe. However, due to structural limitations of the powered electrode (showerhead) in the commercial PECVD system used in this study, it was not feasible to install such commercial sensors. Therefore, for cross-validation between plasma impedance and plasma information (PI), optical emission spectroscopy (OES, model SM−245, resolution: about 0.35 nm) from Korea Spectral Products (Seoul, Korea) was utilized, with data acquisition performed every 0.1 s. To estimate plasma variations, the spectral data of $N_2$ plasma obtained through OES were analyzed using the line ratio method, focusing on the 337.1 nm ($N_2$: C − B) and 391.4 nm ($N_2^{+}$: B − X) emission lines [1,34].

The experiments were conducted using the recipes listed in

Table 3. Recipe of N₂ plasma split test.

N2 (sccm)	RF Power (W)	Pressure (mTorr)	Electrode Gap (mm)
3000	200−500 (Increments by 50)	2250	16
	350	1500−3000 (increments by 250)

, where plasma variations were induced by splitting two parameters: power and pressure. During the experiments, no reflected power was observed due to mismatching, confirming that the system maintained a 50 Ω matched condition. Once this condition was verified, matching network data and OES data were acquired.

4. Result and Discussions

4.1. Result of Power Split Test and Discussion

As a result of the power split test conducted from 200 to 500 W, the reactance increased within the negative region (capacitive region), as shown in Figure 5 ($\Delta X_{\mathrm{L}}=4.74\Omega$), whereas the resistance remained almost constant compared to the reactance ($\Delta R_{\mathrm{L}}=0.43\Omega$). Consequently, the load impedance ($\left|Z_{\mathrm{L}}\right|$) decreased ($∆Z_{\mathrm{L}}=-4.5\Omega$). This reduction in the imaginary component of the load impedance indicates that the plasma behaves more resistively, enhancing power transfer efficiency [35].

The increase in reactance within the negative region corresponds to an increase in sheath capacitance ($C_{\mathrm{s}}$) as expressed by Equation (12), indicating a decrease in sheath thickness ($d_{\mathrm{s}}$) according to Equation (11). An increase in input power leads to an increase in electron density ($n_{\mathrm{e}}$) and a decrease in sheath thickness [33,35,36]. However, as previously described, the sheath thickness under high-pressure conditions is influenced by the ionic mean free path (${\lambda }_{\mathrm{i}}$).

Consequently, the overall emission intensity of the $N_2$ plasma measured by OES increased, as illustrated in Figure 6, and particularly, the intensity at 391.4 nm increased ($∆I_{391.4}=939[a.u.]$), indicating enhanced ionization of $N_2$ molecules within the plasma [36]. In addition, the emission line at 337.1 nm, which corresponds to the excitation of $N_2$ molecules, increased significantly ($∆I_{337.1}=\mathrm{27,064}[\mathrm{a}.\mathrm{u}.]$). These emission lines are widely used for optical diagnostics of plasmas containing $N_2$ [18,37]. Kim et al. reported the diagnosis of process plasma variations using the line ratio of these emission lines, while Paris et al. conducted a study to estimate the electric field strength (E/N) based on the line ratio of these lines [1,38]. An increase in the intensity ratio ($I_{337.1\mathrm{n}\mathrm{m}}/I_{391.4\mathrm{n}\mathrm{m}}$) between excitation and ionization lines implies a relatively stronger excitation of neutral molecules, as shown in Figure 7. The increased density of neutral species reduces the ionic mean free path, resulting in a reduction of the sheath thickness. Additionally, the elevated electron density increases the frequency of electron-neutral collisions (${\nu }_{\mathrm{m}}$), which explains why the load resistance remains relatively constant compared to the reactance, despite the increase in electron density, as described by Equation (9).

4.2. Result of Pressure Split Test and Discussion

The pressure split test conducted from 1500 to 3000 mTorr revealed that the reactance increased ($\Delta X_{\mathrm{L}}=1.86\Omega$) in the negative region, and the resistance slightly increased ($\Delta R_{\mathrm{L}}=0.75\Omega$), as illustrated in Figure 8. However, since the magnitude of the reactance increase was greater than that of the resistance, the overall load impedance decreased ($\Delta Z_{\mathrm{L}}=-1.6\Omega$). As previously described, this reduction in impedance indicates an improvement in RF power transfer efficiency.

In this case, the increase in reactance in the negative region also indicates an increase in sheath capacitance, signifying a reduction in sheath thickness. It has been generally reported that increasing pressure under high-pressure conditions leads to a reduction in sheath thickness and an increase in electron density [39,40,41].

The overall emission intensity of the $N_2$ plasma, obtained through OES, increased with pressure, as shown in Figure 9. In particular, the intensity at 391.4 nm increased ($∆I_{391.4}=1241[a.u.]$), indicating enhanced $N_2$ ionization. In addition, the emission line at 337.1 nm, which corresponds to the excitation of $N_2$ molecules, increased significantly ($∆I_{337.1}=\mathrm{53,752}[a.u.]$). The line ratio presented in Figure 10, also increased, suggesting that the excitation of neutral molecules became more dominant compared to ionization processes within the plasma. As a result, the density of neutral molecules increased, leading to a reduction in the mean free path of ions [33], which consequently contributed to the decrease in sheath thickness. On the other hand, while the electron density increased, the rise in neutral molecule density led to a higher frequency of electron-neutral collisions [42]. This is presumed to cause a slight increase in plasma resistance, differing from the power split test results. These results demonstrate the feasibility of plasma impedance monitoring solely based on the matching network and real-time VVC position data, without the need for external sensors.

5. Conclusions

In this study, a method for monitoring the load impedance in a CCP system was investigated using only the matching network, without using external sensors such as a VI probe or a directional coupler. The equation for deriving the load impedance, based on the matching network circuit, was cross verified using ADS, and the load impedance was monitored through power and pressure split experiments. As the applied power and pressure increased, the calculated load reactance increased in the negative region, which was cross validated through OES, confirming the reduction in sheath thickness. This study demonstrates that plasma impedance monitoring is feasible under a 50 Ω matched condition and suggests that it can contribute to process reproducibility and optimization not only in PECVD systems but also in other CCP-based plasma equipment such as etching and sputtering systems. Although the system used in this study operated at a frequency of 13.56 MHz, the proposed method is not limited to that frequency. It is expected that the same approach can be applied to extract the load impedance in systems operating at other RF frequencies, such as 27.12 MHz, 40.68 MHz, or other frequencies commonly used in plasma processing. Furthermore, by eliminating the need for external sensors, this approach simplifies plasma diagnostics, making it highly applicable even in constrained R&D environments. However, when an impedance matching network is specifically designed for a particular frequency of 13.56 MHz in this research, applying a power source operating at a different frequency can lead to mismatching. Consequently, the method proposed in this study may not be readily applicable under such conditions.