Fast and Automatic Control of a Frequency-Tuned Radiofrequency Plasma Source

A frequency-tuned radiofrequency (rf) plasma source is automatically controlled to minimize the rf power reflection and to maintain the constant net rf power corresponding to the forward power minus the reflected power. The experiment is performed with a power amplifier operational for the frequency of 37–43 MHz, a compact helicon source consisting of a loop antenna, a solenoid, and an insulator tube. The rf power is supplied to the rf antenna via an impedance matching circuit consisting of only fixed small ceramic capacitors. It is demonstrated that the reflection coefficient of the rf power is minimized within ~10 ms, and the net power is successfully maintained at a constant level.


INTRODUCTION
Radiofrequency (rf) plasma source operated in the frequency of 1-100 MHz has been widely used for various applications such as industrial plasmas [1,2], space propulsion devices [3,4], and fusion plasmas [5]. To transfer the rf power to a load, the load impedance has to be matched to the output impedance of the generator and the characteristic impedance of a power transmission line, being typically 50 . The impedance matching is generally performed by inserting two variable capacitors and an inductor (if necessary), where the capacitances are adjusted by mechanical motion.
Fundamental studies on and development of space propulsion devices utilizing the rf plasma sources have vigorously progressed in recent years [6][7][8][9][10][11]. Since the weight and size of the rf system mountable on the spacecraft is very limited, development of the compact rf system is required for the rf plasma thruster. Further addressing space propulsion, the time lag of the communication between the spacecraft and the ground control station would be a serious problem for the impedance matching. Therefore, automatic and fast control of the impedance tuning is useful for further development of the rf plasma thruster.
The compact, automatically controlled, and fast-controlled rf plasma system is also useful for terrestrial industrial plasma devices such as plasma sputtering and etching reactors in a recently developed new concept of the semiconductor manufacturing system, being called "Minimal Fab" [12,13]. In the traditional semiconductor manufacturing system, the diameter of the silicon wafer has been increased to yield sufficient economic benefit by low-mix high-volume production in the large-scale manufacturing system (called "Mega Fab"). On the other hand, Minimal Fab consists of various manufacturing tools in processing a half-inch wafer. Since the wafer is transferred between the processing tools in a localized clean wafer transfer system, no clean room is required for the device production; the facility and production costs can be reduced for the high-mix and lowvolume products. The frame and wafer transfer structures are strictly standardized to connect the processing tools. Therefore, all of the components required for each tool, e.g., a plasma reactor, a pumping system, an rf generator, the wafer transfer mechanics, and the programmable logic controller, and so on, have to be contained within the compact frame. Furthermore, the precise control of the pulsed plasma would also be required for some plasma processing methods, e.g., plasma etching by Bosch process [14], where gas species are alternatively switched for etching and passivation.
As described above, the available space for the rf system is strictly limited in the applications; hence, the development of the compact rf system for the plasma source is a significantly important technology. To overcome this issue, a frequencyvariable tuning has been tested in several laboratory experiments. Charles et al. has used the frequency-variable power generator operated at around 13.56 ± 0.678 MHz with the fixed small ceramic capacitors for impedance tuning [15]. One of the authors has used an amplifier operational for the broader range of the frequency to match the impedance for the industrial plasma source [16], where the frequency was manually adjusted for the initial laboratory test. These experiments have been performed with the linear rf amplifier classified as class AB, while class D or class E switching amplifiers have also been used for the frequency-tunable matching [17][18][19][20]. The traditional impedance matching technique can perform nearly perfect impedance matching by adjusting two capacitors, while it would be difficult to obtain the zero power reflection for the frequency tuning since only one control parameter (frequency) is adjustable. Since the primary parameter deciding the plasma characteristics in terms of the rf system would be the net power given by the forward power minus the reflected power, it would be favorable to maintain the constant net power during plasma production rather than the forward power when the perfect impedance matching is difficult.
The aim of the present study is to develop a compact, automatic, and fast-controlled rf system for future applications of the rf plasma source to the terrestrial plasma processing tools in "Minimal Fab" and the space propulsion device called a helicon thruster. By mounting an autonomously operational controller in the rf system, frequency tuning for the impedance matching and power control for maintaining the constant net rf power, which corresponds to the forward power minus the reflected power, are simultaneously performed. Details of the rf system providing the impedance tuning within about 10 ms is described here. Figure 1A shows the schematic diagram of the plasma reactor used for the present experiment, which is very similar to that of the previous experiment [16]. The experiment is performed with a weakly magnetized rf plasma source attached to a 114 mm 3 vacuum chamber, which is evacuated by a 70-l/s turbomolecular pump to a base pressure of about 10 −4 Pa. The source consists of a 50-mm-outer-diameter, 42-mm-inner-diameter, and 75-mmlong ceramic source tube wound by a double-turn rf loop antenna and a solenoid providing a static magnetic field. The solenoid is situated at z = −15 mm, and dc current of I B = 4.5 A is supplied to the solenoid from a dc power supply, providing a magnetic field strength of about 45 G at the solenoid center, where the open source exit is defined as z = 0. The rf loop antenna consisting of a 4-mm-diameter copper tube is wound at z = −50 ± 10 mm, where the antenna radius is about 27 mm. The upstream side of the ceramic tube is terminated at z = −75 mm by a grounded vacuum flange having a gas injection port and a small viewport. Argon gas is introduced from the gas injection port via a mass flow controller, and the gas flow rate is maintained at 10 sccm, giving the chamber pressure of about 0.65 Pa, which is measured by an ionization gauge attached to the side flange of the chamber. The rf antenna is powered by a broadband class AB rf amplifier via an impedance matching circuit consisting of only fixed ceramic capacitors (C 1 and C 2 ) as drawn in Figure 1B; the argon plasma is produced inside the source tube. R p , L p , R a , and L a in Figure 1B are the plasma resistance, plasma inductance, antenna resistance, and antenna inductance, respectively, which will be discussed for the matching network design in "Design of Matching Network." Figure 2 shows the photograph of the source, including the impedance matching circuit; the matching circuit can be made very compact as shown in the photograph of Figure 2 as it does not contain the variable capacitors. To reduce the power loss at the capacitors, high-Q and ultra-low equivalent series resistance capacitors (HQCC series of AVX Corporation) are mounted on the circuit. The plasma source structure and the matching circuit are air-cooled by using a 40-mm-diameter small fan; it is confirmed that the plasma source can be operated in steady state (at least for 20-30 min in the laboratory experiment) for 200 W rf power. It should be noted that a similar previous experiment has shown plasma density of about 10 18 m −3 for the rf power of about 100 W [16]. An optical emission intensity I opt is measured by a photodetector via an optical fiber connected to the viewport of the upstream flange to very roughly know the relative plasma density. Figure 3 shows the schematic diagram of the presently developed rf system. An rf signal from a voltage-controlled oscillator (VCO) is input into a voltage variable attenuator (VVA) and further input into a 200-W class AB rf power amplifier (AMP) operational between 37 and 43 MHz. Both the output impedance of the amplifier and the coaxial cables are 50 . It should be noted that the dc-rf conversion efficiency of the power amplifier is about 75%; the bandwidth of the amplifier is limited to 37-43 MHz to ensure the conversion efficiency. The amplified rf power is transferred to a load via a bi-directional coupler (50 ± 0.5 dB coupling and 20 dB directivity). The rf signals coupled with the forward and reflected powers are converted into dc voltages by using zero-bias schottky diode rf detectors and low-pass filters (LPFs); then, the absolute value of the reflection coefficient |Γ r | given by  the Linux Real-Time operating system (OS), field-programmable gate array (FPGA), analog-digital (AD) converters, and digitalanalog (DA) converters; it has ports of the digital input/output (DIO), analog input (AI), and analog output (AO). The voltage signal to the VCO and the VVA can be controlled by the AO channels, and the dc voltage corresponding to the forward and reflected powers are monitored by the AI channels, where the DIO channels are used to control the RF on/off and to monitor some signals from the thermal interlock. Since the CompactRIO Single-Board Controller has the OS, it can autonomously operate even if a personal computer (PC) is disconnected. The detailed procedure of the autonomous control is described in the "Results."

DESIGN OF MATCHING NETWORK
Since it is difficult to perfectly match the load impedance to the output impedance of the rf amplifier for the frequency tuning system as described in "Introduction, " it is significantly important to select proper capacitors in the matching network. Many modeling studies have been performed to characterize the electrical property of the rf plasma source over the wide range of parameters [21]. However, the very simple equivalent circuit shown in Figure 1B is used here to explore the suitable capacitances for the matching network since the detailed model strongly depends on the specification of the plasma source. The total impedance Z L of the matching circuit including the plasma in Figure 1B is given by The reflection coefficient given by Equation (1) can be rewritten as where Z 0 is the output impedance (50 ) of the amplifier being equal to the characteristic impedance of the coaxial cable connecting the amplifier and the matching network. One of the experiments measured the resistance and the reactance of the load including the rf antenna and the plasma for the inductively coupled plasma source [22], where the equivalent circuit is very similar to Figure 1B. The results showed the plasma resistance of about a few ohms, which is higher than the typical circuit resistance of an order of 10 −1 . Furthermore, the reactance is mostly unchanged or decreases a fraction with an increase in the discharge power; it can be considered that the plasma reactance is much smaller than the antenna reactance (L ∼ L a ). The inductance of the N-turn antenna having the radius a and the axial length l is generally given by where µ 0 is the vacuum permeability. K n is the Nagaoka coefficient given by [23] K n = 4 where K(k) and E(k) are the complete elliptic integrals of the first and second kind, respectively. The numerically calculated inductance for the given antenna geometry of l = 20 mm, a = 27 mm, and N = 2 is L a ∼ 0.235 µH. The two capacitors in Figure 1B are chosen so as to have a minimum value of |Γ r | within the frequency range of 37-43 MHz and nearly zero value of |Γ r | for R of a few ohms. Figure 4A shows the typical calculation of |Γ r | as a function of the frequency for various values of R, where C 1 = 390 pF, C 2 = 73 pF, and L = 0.235 µH are used. It is found that the nearly zero value of |Γ r | can be obtained for R = 2 at the frequency of ∼40 MHz. It should be noted that a slight decrease in |Γ r | at ∼ 40 MHz is still obtained for R = 0.25 case, which would be enough to ignite the discharge.
For the high frequency above 10 MHz, the reactance is significantly changed by the geometrical error of the antenna, the parasitic capacitance and inductance in the circuit. Figure 4B shows the calculated |Γ r | for the R = 2 cases with the inductances of L a and L a ± 10 %. The frequency giving the minimum |Γ r | is found to be shifted by the change of the inductance. Therefore, the measurement of the reflection coefficient by a vector network analyzer is required to be performed, whereby the values of the capacitance should be adjusted. However, the above-mentioned design procedure is useful to roughly estimate the capacitors in the matching network.

RESULTS
Before showing the automatic and fast control of the frequency tuning rf system, the basic characteristics of the loads without and with the plasma are shown. Figure 5A shows the reflection coefficient |Γ r | as a function of the rf frequency. The data plotted by crosses and filled circles are taken with no gas (no plasma) and with argon flow rate of C Ar = 10 sccm and solenoid current of I B = 4.5 A, respectively. It is noted that the voltage signals to the VVA are maintained at a constant level, and the data are taken by changing the voltage signal to the VCO, i.e., the rf frequency. The optical emission intensity I opt , forward rf power P f , and reflected rf power P r measured for C Ar = 10 sccm and I B = 4.5 A are plotted by filled circles in Figure 5B and by open circles and filled squares in Figure 5C, respectively. The net power P net is simply calculated by P net = P f -P r and plotted by crosses in Figure 5C. The optical emission intensity shows that plasma can be produced for the frequency range of 39.5-42 MHz.
For the no plasma case (C Ar = 0 sccm and I B = 0 A), the reflection coefficient |Γ r | is found to be minimized at the frequency of ∼40.8 MHz as seen by the crosses in Figure 5A, while the minimum |Γ r | is obtained at ∼41.2 MHz for the case of C Ar = 10 sccm and I B = 4.5 A. Since the frequency giving the minimum |Γ r | is changed by the presence of the plasma and the variation of the impedance is expected to be non-linear, frequency tuning is required to minimize the power reflection when using only the fixed capacitors in the impedance matching ∆f, ∆G, P set , f 0 , G 0 f = f 0 , G = G 0 RF ON? Measure P f , P r , P net , |Γ r | f = f -sign ( ) * ∆f * |Γ r | d|Γ r | df G = G -sign(P net -P set )* ∆G yes no FIGURE 6 | Flow chart of the automatic, fast, and autonomous control of the rf system. f, G, P set , f 0 , and G 0 are the variation step of the frequency, the variation step of the gain of the VVA, the target value of the net rf power, the initial frequency, and the initial gain of the VVA, respectively.
circuit. It is clearly observed that the optical emission intensity I opt increases when the power reflection is reduced (as shown in Figures 5A,B). Although the gain (attenuation) of the VVA is maintained at a constant level in Figure 5, the output power is fairly changed by the frequency due to the not constant gain of the amplifier and the impedance mismatch. Therefore, the voltage signal to the VVA has to be adjusted to control the output power from the amplifier. Furthermore, the optical emission intensity I opt seems to fit the net power P net , implying the importance of maintaining not the forward power P f but the net power P net .
In order to automatically control the frequency and the gain of the VVA to minimize the reflection coefficient |Γ r | and to adjust the net rf power P net close to the target value, the CompactRIO Single-Board Controller is controlled by a Labview program. Figure 6 shows the brief flow chart of the controller. Before turning on the rf power, the variation step of the voltage signal to the VCO (i.e., frequency step, f ), the variation step of the voltage signal to the VVA (i.e., the gain step, G), the target value of the net power P set , the initial values of the frequency f 0 , and the initial gain of the VVA G 0 are given as the external parameters. During the period of "RF ON, " the forward and reflected powers (P f , P r ) are measured, and the net power P net and the reflection coefficient |Γ r | are calculated on the CompactRIO Single-Board Controller. Based on the measurement of P net and |Γ r |, the frequency of the VCO and the gain of the VVA are changed according to the equations of By multiplying the signs of d|Γ r |/df and (P net -P set ) as in Equations (9) and (10), the voltage signals to the VCO and VVA  can be varied toward the minimum reflection coefficient and the target value of the net power, respectively. Around the frequency giving the reduced reflection coefficient, the variation step of the frequency is reduced by multiplying |Γ r | in Equation (9), providing the stable operation around the frequency giving a small value of |Γ r |. Typical temporal evolutions of the frequency f, the reflection coefficient |Γ r |, the optical emission intensity I opt , the rf powers of P f , P r , and P net are shown in Figures 7, 8, where the initial frequency is set at f 0 = 37.6 MHz in Figure 7 and 40.6 MHz in Figure 8, respectively. The target value of the net power is chosen as P set = 40 W here, and the rf power is turned on for t = 0-100 ms for both cases. As can be seen in both figures, the reflection coefficient is rapidly decreased by automatic frequency tuning; then, plasma is produced and optical emission is detected. For the case of Figure 7, longer time is required to reduce the power reflection since the initial frequency for this case is more distant from the matching point than that in the case of Figure 8. However, stable plasma production can be obtained at about t ∼ 10 ms. When choosing the initial frequency properly, stable plasma production can be obtained within a few of milliseconds as seen in Figure 8. Furthermore, it is demonstrated that the net power P net equal to the target value P set is successfully sustained during the discharge, as seen in both Figures 7, 8, providing the fairly constant optical emission intensity I opt . These data demonstrate that the automatic and fast control of the impedance and power tuning in the presently developed system can provide stable plasma production during pulse, which can provide highspeed minimization of power reflection.
One of the applications of the presently developed rf system is industrial plasma processing tool such as a plasma etcher operated in Bosch process, where etching and passivation gases are alternatively switched, e.g., as in Chang et al. [24]. Therefore, impedance tuning has to be finished for a much shorter time than the discharge pulse. Thus, high-speed impedance tuning would be an important technique to stably sustain the discharge when shortening the periods of each process. The plasma etcher utilizing the inductively coupled or helicon plasma source generally uses two rf amplifier for plasma production and substrate bias voltage [2,25]. Moreover, the available space for the rf system in the recently proposed "Minimal Fab" (see "Introduction") is significantly limited [12]. Therefore, the system having two rf generators has to be made compact to be fitted to the frame designed for Minimal Fab. Figure 9 shows the photograph of the presently developed rf system including the two rf amplifiers and the CompactRIO Single-Board Controller. It can be successfully made within the size of 220 mm in width, 135 mm in height, and 260 mm in depth and would be contained in the frame designed for Minimal Fab. The target value of the net power and the initial frequency can be set by putting the analog voltage signal, which can facilitate the initial test of the plasma source. impedance matching circuit consists of only the fixed ceramic capacitors, leading to a compact plasma source. Frequency tuning is accomplished within about 10 ms, and the net power corresponding to the forward power minus the reflected power is successfully maintained at a constant level during the pulse, which stabilizes the plasma source operation. For future application to the plasma etcher in Minimal Fab, the rf system containing the two rf generators is made compact, being contained within the size of 220 mm in width, 135 mm in height, and 260 mm in depth. The system will also be useful for space propulsion device utilizing the rf plasma source. The actual process of plasma etching and application to propulsion device remain further as challenging issues.

DATA AVAILABILITY STATEMENT
All datasets generated for this study are included in the article/supplementary material.

AUTHOR CONTRIBUTIONS
The rf generator was designed and assembled by KT. The controller program was written by KT. KH installed the generator to the plasma source designed and assembled by KT. The data were taken and analyzed by KT and KH. The results were discussed by KT, KH, and AA. KT wrote the manuscript. KH and AA reviewed the manuscript.

FUNDING
This work was partially supported by Strategic Core Technology Advancement Program (Supporting Industry Program) by Tohoku Bureau of Economy, Trade and Industry. This is also partially supported by a grant-in-aid for scientific research (18K18907, 18K18746, and 19H00663) from the Japan Society for the Promotion of Science and JAXA.