Figure
1.
Schematic diagram of the RF magnetron sputtering discharge setup.
| Citation: |
Wenjin CHEN, Zhiwei MA, Haowei ZHANG, Wei ZHANG, Longwen YAN. Free-boundary plasma equilibria with toroidal plasma flows[J]. Plasma Science and Technology, 2022, 24(3): 035101. DOI: 10.1088/2058-6272/ac48de
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Magnetohydrodynamic equilibrium schemes with toroidal plasma flows and scrape-off layer are developed for the 'divertor-type' and 'limiter-type' free boundaries in the tokamak cylindrical coordinate. With a toroidal plasma flow, the flux functions are considerably different under the isentropic and isothermal assumptions. The effects of the toroidal flow on the magnetic axis shift are investigated. In a high beta plasma, the magnetic shifts due to the toroidal flow are almost the same for both the isentropic and isothermal cases and are about 0.04a0 (a0 is the minor radius) for M0=0.2 (the toroidal Alfvén Mach number on the magnetic axis). In addition, the X-point is slightly shifted upward by 0.0125a0. But the magnetic axis and the X-point shift due to the toroidal flow may be neglected because M0 is usually less than 0.05 in a real tokamak. The effects of the toroidal flow on the plasma parameters are also investigated. The high toroidal flow shifts the plasma outward due to the centrifugal effect. Temperature profiles are noticeable different because the plasma temperature is a flux function in the isothermal case.
Radio-frequency (RF) magnetron sputtering is an important tool for the deposition of thin films. Progress made in the RF magnetron sputtering system for the past several decades have led to its widespread use [1‒3]. Many works showed that the 27.12 MHz high excitation frequency magnetron sputtering had better deposition characteristics than that of commercial 13.56 MHz RF magnetron sputtering [4‒11]. For example, the sputtering rate of Li–Mn–O films deposited by the 27.12 MHz magnetron sputtering was higher than that of conventional RF magnetron sputtering without compromising on the quality of the films, and the nucleation and growth of films were significantly improved [4, 5]. The low deposition rate of LiCoO2 thin films fabricated using commercial RF magnetron sputtering was tackled by raising the excitation frequency to 27.12 MHz, and the higher deposition rate and the excellent electrochemical performance were obtained [6]. In addition, the silicon films with higher growth rate [7], the WS2–x films with highly (001) textured and a low lattice expansion as well as large grains in c axial direction [8], the Ag films with a good face-centered cubic (fcc) structure [9] and the Si-rich Si1−xCx films [10] were all prepared using the 27.12 MHz magnetron sputtering. The reasons on the higher deposition rate and the excellent crystallographic quality by the 27.12 MHz magnetron sputtering were thought to be related to the low target voltage [4, 5, 8, 11]. At the 27.12 MHz magnetron sputtering, the low target voltage led to a low particle energy onto a substrate surface, reducing the energy of argon ions bombarding the growing film, and avoiding the crystallograhic defects during film growth [4, 5, 8, 11]. However, seldom work is reported on why the low target voltage can be obtained at this driving frequency. In addition, the relationship between discharge characteristics and films deposition is of lacking. Therefore, this work investigated the discharge and plasma characteristics of 27.12 MHz magnetron sputtering with Ag target and its effect on the Ag films deposition.
The homemade magnetron sputtering system used in this experiment is shown in figure 1, which is composed of a main chamber and vacuum acquisition equipment. The main chamber was a cylindrical vacuum chamber (350 mm in diameter and 300 mm in height), in which a water-cooled circular Ag target (99.99% pure, 50 mm in diameter) was placed at the top, and the electrically floated stainless steel substrate holder (100 mm in diameter) was set at the bottom, about 70 mm away from the center of target surface. At the sidewall, the flange ports for Langmuir probe and ion energy analyzer were made. The 27.12 MHz power was applied to the Ag target through the matching box. As a comparison, the magnetron sputtering driven by 13.56 MHz power was also carried out, and its power was applied to the Ag target through the correspond matching box. The wall of the chamber was electrically grounded. The vacuum acquisition equipment included the gas inlet and vacuum unit. Argon with the flow rate around 9 mL/min was used as the discharge gas. The base pressure of the magnetron sputtering system was less than 5 × 10−4 Pa, and the operating pressure was about 4.7 Pa, evacuated with a 600 L/s turbo-molecular pump backed up with a mechanical pump.
The electric characteristics, including the discharge power (the difference between forward power and reflect power), discharge voltage, discharge current, discharge impedance and phase for the fundamental frequencies of 27.12 MHz and 13.56 MHz were measured using the Impedans Octiv Suite RF V–I probe, which was installed between the matching box and the Ag target and allowed for a real-time measurement without time delay [12‒14]. In the experiment, the forward powers of 100–400 W (at 27.12 MHz) and 110–350 W (at 13.56 MHz) were applied. However, due to the difference in the matching and the reflect power, the actual discharge powers were about 94–322 W (at both 27.12 MHz and 13.56 MHz).
The electron density ne and electron temperature Te of the bulk plasma were estimated from the current–voltage (I–V) characteristics, which were measured at about 20 mm above the center of the substrate surface (as shown in figure 1) using Hiden Analytical RF compensated cylindrical ESPion Langmuir probe. The details on probe measurement had been described in the previous work [15]. Because the intensity of the magnetic field at the position of probe tip was about 10 G, the effect of magnetic field on probe measurement can be neglected [15]. When calculating the electron density ne and electron temperature Te, the Druyvesteyn method was used because a non-Maxwellian electron energy distribution function (EEDF) was obtained. The ion energy was obtained by measuring ion velocity distribution function (IVDF) using the Semion HV-2500 retarding field energy analyzer (RFEA) at the substrate holder [16, 17].
To investigate the depositing characteristics, the Ag films were deposited using the 27.12 MHz and 13.56 MHz magnetron sputtering. The Ag target was pre-sputtered in Ar for 10 min prior to each run. The deposition time was 60 min. The n-type (100) silicon wafers and quartz crystal wafers were used as the substrates. The crystalline nature of the Ag films deposited on quartz wafer substrates was measured using the D/MAX-2000PC x-ray diffractometer (XRD) with Cu Kα radiation (λ = 0.154051 nm). The microstructure of Ag thin films grown on silicon wafers was observed using a Hitachi S-4700 FE-scanning electron microscope (SEM).
In order to understand the reason on the low target voltage at the driving frequency of 27.12 MHz, the magnetron sputtering discharge is treated using an electrical load model. For the magnetron sputtering discharge, the equivalent circuit can be simplified as the two sub-circuits in series representing the plasma body and the electrode sheath [18, 19], as shown in figure 2. The plasma impedance Z is given as follows:
| Z=(Rst+Rυ+Rsh)+j(ωL0−1ωCsh), | (1) |
where Rst and Rυ represent the plasma resistance due to the stochastic electron heating on the oscillating plasma boundaries and the electron collisions with gas atoms, L0 is the plasma inductance due to the electron inertia in the RF field, Csh and Rsh are the sheath capacitance and sheath resistance. Thus, the plasma impedance can be characterized by its impedance components Z = R + jX [12, 14], where R = Rst + Rυ + Rsh and X = ωL0−1ωCsh .
The variations of plasma impedance with the discharge power and discharge pressure have been reported in the previous work [19]. In order to clearly analyze the low target voltage behavior at the 27.12 MHz magnetron sputtering discharge, the impedance characteristics at the pressure of 4.7 Pa are further investigated here. As a comparison, the impedance characteristics of the 13.56 MHz magnetron sputtering discharge are also presented. Figure 3 shows the variations of plasma impedance Z with the discharge power. As the discharge power increases, the impedance Z at the 27.12 MHz discharge shows a transition from a decreasing trend to an increasing trend, not as the monotone decrease at the 13.56 MHz discharge. The impedance Z of the 27.12 MHz discharge is in the range of 19.8–21.6 Ω, lower than that of commercial 13.56 MHz discharge (42.5–67.6 Ω). Because of this low impedance Z, the voltage needed for the maintaining discharge can be reduced. Therefore, the low discharge voltage is obtained at the 27.12 MHz magnetron sputtering discharge.
The plasma impedance Z includes the real part R and the imaginary part X. Figure 4(a) shows the change of real part R with the discharge power. The real part R of 27.12 MHz discharge is in the range of 18.5–19.7 Ω, lower than that of 13.56 MHz discharge (39.4–42.6 Ω). Figure 4(b) shows the change of imaginary part X with the discharge power. For the 27.12 MHz discharge, with the discharge power increase, the imaginary part X decreases to 0 Ω from a negative value, and then becomes a positive value. Because the negative value of the imaginary part X means the capacitive reactance characteristic, while the positive value means the inductive reactance characteristic, this transition indicates that the plasma impedance changes from the capacitive reactance to the inductive reactance. At the discharge power about 223 W, X = ωL0−1ωCsh = 0 Ω, the sheath capacitive reactance is completely cancelled by the plasma inductive reactance, and a series LC resonance takes place [20]. This series resonance phenomenon is defined as the electron series resonance (ESR). Therefore, the 27.12 MHz magnetron sputtering is a kind of magnetron discharge operated near the electron series resonance oscillation, and the imaginary part X is the major component contributing to the low impedance Z of 27.12 MHz discharge. From the figure 4(b), for the 13.56 MHz magnetron sputtering operated at the same power range as that of 27.12 MHz, the values of the imaginary part X are all the negative values (capacitive). Thus, the 13.56 MHz magnetron sputtering is a kind of magnetron discharge operated with the capacitive reactance. No electron series resonance oscillation can take place. Therefore, the low target voltage at the 27.12 MHz magnetron sputtering is related to the impedance transition near the ESR oscillation.
The ESR oscillation is a prominent feature in the low pressure capacitive coupled plasma (CCP) [21‒31]. For the unmagnetized CCP discharges, the ESR is caused by significant oscillations in the RF current [21‒23]. During the discharge, the energetic electrons in the sheath are accelerated by the expanding sheath, and penetrate into the plasma bulk. In a voltage driven system, they can create an electric field reversal between the plasma sheath and the bulk, which attracts cold bulk electrons back towards the expanding sheath. These bulk electrons react on the timescale of the local plasma frequency and their nonlinear interaction with the sheath leads to significant oscillations in the RF current [21, 22]. However, for the magnetized CCP discharge, the ESR was thought to relate to the increase of inductive reactance in the bulk plasma due to the magnetization of electrons in the magnetic field, which balances the usually dominant capacitive reactance of the sheaths [30, 31]. In addition, the ESR in the 27.12 MHz magnetron sputtering discharge was also related to the electron confined by magnetic field, which makes the sheath thinner and the capacitive reactance smaller [19].
As the ESR takes place, the discharge behavior and heating mechanism were strongly influenced [24‒30]. For the unmagnetized CCP discharges, the electron resonance heating can be achieved by strongly enhancing the electron power absorption, which can enhance the ohmic and stochastic heating [24‒26], increase the electron density [27, 28] and the ionization [29], and reduce the excessive thermal loads on the processing substrates [30]. For the magnetized CCP discharges, however, the discharge behavior near the ESR oscillation is seldom reported. Therefore, understanding the discharge characteristics near the ESR oscillation is very important to the application of films deposition.
The discharge voltage and current are important discharge characteristic. For the commercial 13.56 MHz RF magnetron sputtering, the impedance Z (42.5–67.6 Ω) is close to the output impedance (50 Ω) of power source. When the power source operated with the voltage drive, the near-sinusoidal waveform of discharge voltage, and the non-sinusoidal waveform of discharge current due to the asymmetry electrodes were observed, as shown in figure 5(a). However, for the 27.12 MHz magnetron sputtering discharge, when the powered electrode was driven by a sinusoidal RF voltage, the measured discharge voltage and current showed a non-sinusoidal voltage while a near-sinusoidal current waveforms, as shown in figure 5(b). The discharge voltage between positive and negative cycle is asymmetry and the deformation of negative cycle occurs, while the discharge current exhibits a good symmetry, only small deviation from the sinusoids. This result is significantly different from that of 13.56 MHz magnetron sputtering discharge. The near-sinusoidal discharge current and non-sinusoidal discharge voltage are related to the low discharge impedance. With the voltage drive, the output impedance of power source is 50 Ω. But for the discharge plasma, the impedance Z is in the range of 19.8–21.6 Ω. Although the matching network has been used, to some extent, the impedance mismatch still exists. The low impedance makes the output voltage instability, leads to a non-sinusoidal discharge voltage while a near-sinusoidal discharge current. As a result, the discharge behavior is similar to the power source operated with current drive. The possible reason has been discussed in the previous work [19]. Therefore, for the magnetized CCP discharges, the low impedance near the electron series resonance oscillation can have significant influence on the output feature of power source.
The I–V characteristic of magnetron sputtering discharges is shown in figure 6. The discharge voltage of the 27.12 MHz magnetron sputtering discharge is in the range of 48.6–82.6 V, lower than that of 13.56 MHz discharge (104.8–121.8 V), while the discharge current (2.3–4.1 A) is higher than that of 13.56 MHz discharge (1.6–2.9 A). The result shows that the lower discharge voltage with higher discharge current is an important feature of magnetron discharge operated near the ESR oscillation.
The variations of electron density ne and electron temperature Te against the discharge power are shown in figure 7. For the 27.12 MHz discharge, the electron density is in the range of (1.21–6.24)×1016 m−3, slight higher than that of 13.56 MHz discharge at the discharge power below 226 W but lower than that of 13.56 MHz discharge at the discharge power range of 233–323 W. The electron temperature Te at the 27.12 MHz discharge is in the range of 1.20–1.99 eV, lower than that of 13.56 MHz discharge at the discharge power below 158 W but higher than that of 13.56 MHz discharge at the discharge power range of 174–323 W. Because the electron heating at the pressure of 4.7 Pa is achieved mainly by ohmic heating, the result shows that the higher electron density can be obtained for the magnetron sputtering operated near ESR oscillation, but cannot be further increased by the electron collisions with gas atoms. This change of electron density with the discharge power has significant influence on the imaginary part X because the L0 is inversely proportional to the electron density (L0=2dmAe2n) [12, 18] and the Csh is related to the sheath thickness influenced by the electron density. As the plasma density increased, ωL0 and 1/ωCsh decreased at different rates [29]. At a low plasma density, 1/ωCsh was larger than ωL0, and at a high plasma density, ωL0 was larger than 1/ωCsh [29]. Therefore, for the 27.12 MHz discharge, with the discharge power increase, the plasma density increases. The imaginary part X changes from the capacitive reactance to the inductive reactance, and the intersection of ωL0 and 1/ωCsh can be obtained. However, for the 13.56 MHz discharge, because of the higher plasma density, the ωL0 becomes smaller. As a result, in the power range of this work, the intersection of ωL0 and 1/ωCsh cannot be obtained.
The change of ion flux density with the discharge power is shown in figure 8(a). For the 27.12 MHz discharge, the ion flux density is in the range of 0.032–0.078 A/m2, higher than that of 13.56 MHz (0.028–0.055 A/m2). The result shows that the ionization can be effectively increased for the magnetron sputtering operated near the ESR oscillation. The change of ion energy with the discharge power is shown in figure 8(b). For the 27.12 MHz discharge, the ion energy is in the range of 47.2–53.5 eV, also higher than that of 13.56 MHz discharge (44.4–48.6 eV). Therefore, the higher ion flux density and ion energy are obtained for the magnetron discharge operated near the ESR oscillation. Compared with the ion energy and the discharge voltage, no clear evidence on that the low discharge voltage leads to low ion energy is seen because for the RF discharge the ion energy is controlled not only by the discharge voltage but also by the driving frequency [15, 32].
During depositing films using the magnetron sputtering, the ions incident on a substrate surface transfer their kinetic energy to the adatoms and improve their surface diffusivity, thus influencing the growth and properties of films [33, 34]. The high ion flux density is helpful for increasing the ion reaching on the growth surface, and moderate ion energy is helpful for the migration of ion along the surface, reducing the ions bombarding the growing film, avoiding the crystallograhic defects during film growth. Therefore, the crystalline nature of the films deposited by magnetron discharge operated near the ESR oscillation can be improved.
In order to understand the effect of ESR oscillation on the film deposition, the Ag films were deposited using magnetron sputtering at the driving frequencies of 27.12 MHz and 13.56 MHz. Figure 9 shows the x-ray diffraction (XRD) patterns of Ag films. The Miller indices (hkl) are indicated on each diffraction peak. For the 27.12 MHz discharge, the dominant Ag(111) peak and other diffraction peaks of Ag(200), Ag(220) and Ag(311) are all found. For the 13.56 MHz discharge, the XRD pattern of Ag film is similar to that of 27.12 MHz discharge, but the significant difference is the change of Ag(220) intensity, as denoted in the figure 9 with a red box. From the intensity ratios of the peaks I200/I111, I220/I111 and I311/I111 of Ag films and Ag powder listed in table 1, it can be found that the crystal structure of Ag film deposited at the 27.12 MHz discharge is very close to that of Ag powder, while deviating from that of Ag powder at the 13.56 MHz discharge. This result indicates that the Ag film deposited near the electron series resonance oscillation has a good face-centered cubic (fcc) crystal structure. Figure 10 shows the SEM surface morphologies of the Ag films. For the 27.12 MHz discharge, the film surface is composed of dense and uniform grains. For the 13.56 MHz discharge, the film surface is still composed of dense grains, but the uniformity of grains deteriorates. Therefore, the crystalline nature of the Ag films deposited by magnetron sputtering operated near the ESR oscillation can be improved significantly.
| Sputtering frequency (MHz) | Sputtering power (W) | I200/I111 | I220/I111 | I311/I111 |
| 27.12 | 216 | 0.49 | 0.34 | 0.28 |
| 13.56 | 229 | 0.46 | 0.53 | 0.32 |
| Ag powder | - | 0.40 | 0.25 | 0.26 |
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The characteristics of Ag magnetron sputtering operated near the electron series resonance oscillation, which was excited using the driving frequency of 27.12 MHz, were investigated. By analyzing the discharge impedances, the imaginary part of impedance Z was found to undergo a transition from capacitive to inductive on varying RF power, and the conditions for ESR excitation were satisfied at the 27.12 MHz magnetron sputtering. By analyzing the I–V characteristic of magnetron discharges, the lower discharge voltage with higher discharge current at the 27.12 MHz magnetron sputtering is obtained due to the small impedance Z led by the mutual compensation between the sheath capacitive reactance and the plasma inductive reactance. By analyzing the plasma characteristics, the moderate electron density and the higher electron temperature were obtained. By analyzing the ion characteristics, the higher ion flux density and ion energy were obtained. The interaction of high energy ions on growth film improved the crystallographic quality of Ag films, leading to better deposition characteristics than that of commercial RF (13.56 MHz) magnetron sputtering. Therefore, the 27.12 MHz high excitation frequency magnetron sputtering is a kind of magnetron sputtering operated near the electron series resonance oscillation. This sputtering technology has better deposition characteristics than that of commercial RF (13.56 MHz) magnetron sputtering, and plays an important role in the film deposition.
This work was supported by National Key Research and Development Program of China (Nos. 2019YFE03030004 and 2019YFE03020003), and National Natural Science Foundation of China (NSFC) (Nos. 11775188 and 11835010).
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Supported by: Beijing Renhe Information Technology Co., Ltd. 
| Sputtering frequency (MHz) | Sputtering power (W) | I200/I111 | I220/I111 | I311/I111 |
| 27.12 | 216 | 0.49 | 0.34 | 0.28 |
| 13.56 | 229 | 0.46 | 0.53 | 0.32 |
| Ag powder | - | 0.40 | 0.25 | 0.26 |
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