Effect of radiofrequency bias power on transmission spectrum of flat-cutoff sensor in inductively coupled plasma Open Access

Plasma diagnostics and monitoring are becoming increasingly important in industrial semiconductors and display processing, particularly in etching and deposition, owing to the increasing demand for precise feedback control of plasma,^1–5 which occurs due to the continual reduction in the linewidths of semiconductor devices.⁶ Among the various plasma parameters, electron density is the most critical because it significantly affects the state of the processing plasma, including the plasma potential and the abundance of radical species as well as ions that contribute to etching or deposition.^7–10 The electron density directly affects the processing throughput and quality. Consequently, achieving real-time and accurate measurements of plasma density has become the priority in plasma-equipment and device-manufacturing industries.

Among the various plasma diagnostic methods, microwave plasma diagnostics are suitable for real-time process plasma diagnosis because they enable plasma measurements even when a deposition film, owing to the processing gas, is formed on the plasma diagnostic tool.^11,12 Such measurements encompass various microwave diagnostic methodologies, including cutoff,^11–13 plasma absorption,^14,15 multipole resonance,^16,17 impedance,¹⁸ and hairpin probes.^19,20 Nonetheless, inserting a probe into the plasma inevitably causes plasma perturbation and chamber contamination due to probe intrusion, which is unacceptable in an industrial mass-production environment.²¹ Moreover, the assessment of plasma parameters on a wafer surface is subject to constraints arising from the inherent physical attributes of the probe structure. Thus, noninvasive sensors that can measure plasma parameters in real time and with exceptional precision during industrial processing operations are highly demanded.

Noninvasive microwave diagnostic techniques for electron density measurements include flat cutoff,^22–24 curling,^25,26 noninvasive impedance,²⁷ and planar multipole resonance^28,29 sensors. Among these, a flat-cutoff sensor can be used to measure the electron density at a real-time plasma sheath boundary even in the presence of dielectric, conductive, doped, or patterned wafers on its surface.^23,30,31 However, to measure the electron density at the wafer plane in environments where radio frequency (RF) bias power is applied to the electrode, such as in semiconductor etching processes, a flat-type plasma diagnostic sensor should be embedded in the electrode. Furthermore, the effect of RF bias power on flat-type plasma diagnostic sensors must be analyzed. Nonetheless, current investigations pertaining to flat-type plasma diagnostic sensors have primarily focused on the characteristics of sensor measurements in environments devoid of bias power, as exemplified by cases such as inductively coupled plasma. Consequently, analyzing the quantities measured using flat plasma diagnostic sensors in environments where bias power is applied and the sheath becomes thicker is crucial for the real-time diagnostics of process plasmas. This technology is essential for ensuring accurate plasma parameter measurements under the above-mentioned conditions.

In this study, we investigate the transmission spectrum of an electrode-embedded flat-cutoff sensor in low-pressure plasma using an RF-biased system. Results of electromagnetic (EM) simulation indicate that under sheath widths of 1 mm or less, the flat-cutoff sensor accurately measures the electron density, which is equal to the input electron density. However, in a thicker-sheath environment, the cutoff frequency measured by the flat-cutoff sensor may be lower than the input plasma frequency, and the cutoff frequency becomes difficult to observe. Plasma diagnostics using a flat-cutoff sensor in thick-sheath environments can be achieved by optimizing the flat-cutoff sensor structure. The results obtained can contribute significantly to plasma diagnostics on wafer surfaces, even in environments where RF bias power is applied to the electrode, such as in the semiconductor etching process.

To analyze the characteristics of plasma measured using a flat-cutoff sensor under bias power, we performed an EM simulation. A commercial EM wave simulation tool, CST Microwave Studio, was adopted owing to its effective time-domain solver for three-dimensional full Maxwellian equations.^32,33 To analyze the sensor characteristics, an open-boundary condition that excluded reflected waves, cavity resonance, and other effects was applied. All conductors in the simulation were considered perfect electric conductors, and the material for the sensor dielectric was Teflon. Figure 1(b) shows the top view of the flat-cutoff sensor. The structure of the flat-cutoff sensor was utilized from previous studies.^30,31 In detail, the flat-cutoff sensor consisted of an antenna with a width of 3 mm and a length of 20 mm, along with a 1-mm-thick insulator. Additionally, the distance between the radiating and detecting antennas (d) was 5 mm. The plasma was assumed to be spatially uniform, and its permittivity was set based on the Drude model,^19,24 i.e., $ϵp=1−ωpe2ωω−iνm.$ Meanwhile, $ωpe$ is the electron plasma frequency, which is expressed as $e2ne/ϵ0me$⁠, $ne$ is the electron density, $me$ is the electron mass, $e$ is the elementary charge, $ω$ is the driving frequency, and $νm$ is the electron-neutral collision frequency. In the EM simulation, we set $ωpe=2πfp=2π×1 GHz$ as the input and a gas pressure of 10 mTorr. The width of the sheath (s) formed on top of the flat-cutoff sensor varied depending on the RF bias voltage. Therefore, the EM simulation calculations were performed based on the variations in the sheath width. In the simulation, the sheath width was set between 0.2 and 10 mm. In the EM simulation, the sheath is set as a vacuum layer with a dielectric constant of 1.

This experiment was performed in a planar inductively coupled plasma (ICP) with an RF-biased electrode, as illustrated in Fig. 1. The chamber was cylindrical with an inner radius and height of 300 and 230 mm, respectively. The electrode was positioned 80 mm from the bottom of the chamber. RF powers of 13.56 and 12.56 MHz were applied to the one-turn planar coil and electrode, respectively, via an auto-matching network. The power from the 13.56 MHz frequency applied to the ICP coil was maintained at 500–1000 W, whereas that of the 12.56 MHz frequency applied to the electrode was 0–400 W. The base pressure in the vacuum chamber was less than $2×10−6$ Torr, as measured using an ion gauge. The experimental pressure was 10 mTorr, which was measured using a capacitance diaphragm gauge calibrated with a standard pressure gauge at the Korea Research Institute of Standards and Science. The Ar gas supply was maintained at 30 sccm using a mass-flow controller. A flat-cutoff sensor was inserted into the electrode. A single Langmuir probe was installed 65 mm from the ICP antenna to measure the electron density, electron temperature, and sheath thickness. To obtain the transmission spectrum, the flat-cutoff sensor was connected to a vector network analyzer (National Instruments, PXIe-S5090) using 50  $Ω$ coaxial cables. To ensure that the RF bias power applied to the electrode did not affect the vector network analyzer, we installed a high-pass filter (Crystek, 549-CHPFL-0100) between the vector network analyzer and sensor. The cutoff frequency of the high-pass filter was 100 MHz. Figure 1(c) shows the peak-to-peak voltage measured using a high-voltage probe (Tektronix, P6015A) and an oscilloscope (Tektronix, TDS3052), with respect to the RF bias power. The peak-to-peak voltage was measured at positions 1–3 in Fig. 1(a), which correspond to the electrode, flat-cutoff sensor, and high-pass filter, respectively. Under a bias power of 400 W, the peak-to-peak voltage measured at the bottom of the electrode was 982 V, whereas those measured at the flat-cutoff sensor and high-pass filter were 70.1 and 0.55 V, respectively, which were approximately 1785 times lower. The maximum voltage measured by a vector network analyzer is typically 5 V. Therefore, a high-pass filter can be used to measure the electron density without damaging the vector network analyzer, even in an environment with bias power.

Figure 2(a) shows the transmission (S₂₁) spectra for both vacuum and plasma media. For the plasma media, the plasma frequency was fixed at 1 GHz, and the sheath width was varied from 0.2 to 10 mm. In vacuum, the transmission spectrum of the flat-cutoff sensor showed an increase in transmittance with increasing frequency. This spectral shape is interpreted as being due to the capacitive coupling between the radiating and detecting antennas. In the plasma medium with $s≤1 mm$⁠, the flat-cutoff sensor showed a cutoff frequency (⁠ $fc$⁠) that is equal to the input plasma frequency. However, when $s>1 mm$⁠, the cutoff frequency shifted to lower frequencies compared with the input plasma frequency as the sheath thickness increased. Furthermore, at a sheath thickness of 10 mm, the cutoff frequency could not be identified easily. In Fig. 2(b), the blue line and symbols represent the cutoff frequency as a function of the sheath width. As the sheath thickness increased, the cutoff frequency reduced to 23.3% lower than the input plasma frequency. This shift in the cutoff frequency with increasing sheath width can be explained using the circuit model of the flat-cutoff sensor. Figure 2(c) illustrates a cross-sectional view of the flat-cutoff sensor, including the lumped circuit element. In the circuit model, the plasma is assumed to be a capacitor containing a dielectric material with permittivity $ϵp$⁠, and based on the plasma equivalent circuit model, it is represented by plasma inductance (⁠ $Lp=ωpe−2C0−1)$⁠, plasma resistance (⁠ $Rp=νmLp$⁠), and a vacuum capacitor (⁠ $C0$⁠).^24,38 The sheath is represented as a vacuum layer, assumed to be a capacitor with vacuum permittivity (⁠ $Cs$⁠). Consequently, the plasma and sheath are represented as a parallel connection, and the cutoff frequency is expressed as follows: $ωc=1/Lp(C0+Cs)$⁠. An increase in the sheath width increases the sheath capacitance, thus decreasing the parallel resonant frequency.²⁴ Furthermore, increasing the sheath thickness decreased the peak intensity and shifted the minimum transmission peak (cutoff frequency). The black line in Fig. 2(b) represents the transmission intensity in vacuum minus the transmission intensity at the cutoff frequency. Depending on the sheath width, the intensity of the minimum transmission peak decreased, with a significant decrease in approximately 4 dB at a sheath width of 5 mm. This occurred because as the sheath width increased, the sheath capacitance increased, and the sheath impedance decreased accordingly. Therefore, under bias power levels where the sheath thickness is 5 mm or greater, measuring the cutoff frequency and electron density using a flat-cutoff sensor may be difficult.

The shift to lower cutoff frequencies and the decrease in intensity with increasing sheath thickness are the effects of increased sheath capacitance. This can be improved by optimizing the geometry of the flat-cutoff sensor, such as the antenna distance. Figure 4 shows the transmission spectrum calculated via EM simulation under various d values. In this calculation, the input plasma frequency was 1 GHz and the sheath width was 10 mm. The cutoff frequency was not observed in the transmission spectrum up to a distance of d = 10 mm; however, as d increased to 40 mm, the cutoff frequency became visible. Additionally, the peak intensity improved as d increased. In the circuit model, a previous study confirmed that increasing the distance between the radiating and detecting antennas (d) decreases the sheath capacitance.²⁴ The reduction in sheath capacitance due to the increased antenna distance results in an increase in the resonant frequency, and under sufficiently large antenna distance conditions, the resonant frequency matches the electron plasma frequency, $limCs→01Lp(C0+Cs)=1LpC0=ωpe$⁠. Therefore, increasing the antenna distance enables plasma measurements, even in environments with thicker sheaths. Thus, to perform electron density measurements in plasma environments with thicker sheaths owing to high bias power, establishing an appropriate antenna distance may serve as an effective method.

In conclusion, the transmission-spectrum and measured plasma-density characteristics of an electrode-embedded flat-cutoff sensor were analyzed via EM simulation and experimental validation under applied bias power. The results indicated that when the sheath width was less than 1 mm, the flat-cutoff sensor accurately measured a cutoff frequency, which was equal to the input plasma density. Conversely, when the sheath width increased to 5 mm, the flat-cutoff sensor measured a cutoff frequency that was 23.3% lower than the input plasma frequency, which was due to increased sheath capacitance. Moreover, when the sheath thickness was 10 mm, identifying the cutoff frequency in the transmission spectrum measured using the flat-cutoff sensor became challenging. The disappearance of the cutoff frequency under a thick-sheath environment can be addressed by modifying the structure of the flat-cutoff sensor to reduce the sheath capacitance. The findings of this study can enhance the analysis of plasma parameters on wafer surfaces in processing environments with applied bias power.

This study was supported by the Material Innovation Program (Grant No. 2020M3H4A3106004) of the National Research Foundation (NRF) of Korea and funded by (i) the Ministry of Science and ICT and the R&D Convergence Program (Grant No. CRC-20–01-NFRI) of the National Research Council of Science and Technology (NST) of the Republic of Korea, (ii) the Korea Evaluation Institute of Industrial Technology (Grant No. 1415181740), (iii) the Korea Research Institute of Standards and Science (Grant No. KRISS GP2024-0012-04), and (iv) the Technology Innovation Program (public–private joint investment semiconductor R&D program (K–CHIPS) to foster high-quality human resources) (Nos. RS-2023-00237058, 1415187722, 1415188153, and 1415187709) funded by the Ministry of Trade, Industry & Energy (MOTIE, Korea) and KSRC (Korea Semiconductor Research Consortium) (Grant Nos. 00235950 and 00237058).

The authors have no conflicts to disclose.

Hee-Jung Yeom and Gwang-Seok Chae contributed equally to this work.

Hee-Jung Yeom: Conceptualization (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – original draft (equal). Gwang-Seok Chae: Conceptualization (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – original draft (equal). Min Young Yoon: Formal analysis (equal); Investigation (equal); Methodology (equal). Wooram Kim: Formal analysis (equal); Investigation (equal); Methodology (equal). Jae Heon Lee: Formal analysis (equal); Investigation (equal); Methodology (equal). Jun Hyung Park: Formal analysis (equal); Investigation (equal); Methodology (equal). Chan-Woo Park: Formal analysis (equal); Investigation (equal); Methodology (equal). Jung-Hyung Kim: Conceptualization (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Supervision (equal); Validation (equal); Writing – review & editing (equal). Hyo-Chang Lee: Conceptualization (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Supervision (equal); Validation (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.