**4.1. Multi-hollow electrode**

gas inelastic collision, this SEE energy of *E*SEE = 200 eV has the maximum ionization cross section [20]. Thus, for *V*RF > 400 Vpp, the ionization of Ne gas is effectively enhanced by the high SEE coefficient of MgO [21], which leads to the marked increase of plasma density. In fact, the RF power input to the plasma for MgO was higher than that for Al at a fixed applied voltage. Unfortunately, the power efficiency of the reactor could not be estimated because it was not

The reason why the plasma density for MgO becomes constant for *V*RF > 800 Vpp is considered as follows. The ionization cross section starts to decrease with increasing *E*SEE for *E*SEE > 400 eV

**Figure 4** shows optical emission intensity of the Ne I line (588.1 nm) as a function of *V*RF. Here, the optical emission intensity was measured with a spectrometer and a digital oscilloscope. The intensity increases markedly with increasing *V*RF, in the same manner as plasma density. Therefore, the high-density plasma production is realized by using MgO with a high SEE coefficient in CCP. The effect of high secondary electron emission is one candidate to produce high-density plasma.

In this section, it is described that structured electrodes can produce the high-density capacitively coupled plasma. One of the structured electrodes is a hollow cathode. The hollow cathode discharge [24] is applied into a production mechanism of CCP to attain high-density plasma.

easy to directly monitor current and phase difference between voltage and current.

[20]. Thus, the plasma density decreases with increasing *V*RF for *V*RF > 800 Vpp.

**Figure 4.** Optical emission intensity of He I line (588.1 nm) as a function of *V*RF.

214 Plasma Science and Technology - Basic Fundamentals and Modern Applications

**4. Effect of structured electrodes on high-density capacitively** 

**coupled plasma production**

The effects of a multi-hollow cathode discharge and a high SEE are applied to capacitively coupled plasma to produce high-density plasma [25, 26]. **Figure 5(a)** and **(b)** shows the experimental apparatus and construction of the multi-hollow electrode, respectively. As shown in **Figure 5(b)**, one plate has 35 holes with 5-mm diameter and 15-mm length, and these holes lay on a concentric circle. In order to emit secondary electron emission from the electrode facing the multi-hollow electrode, the other electrode is biased by the voltage of low frequency of 1 MHz. The plate is called as the substrate electrode.

**Figure 6** shows plasma density and electron-neutral mean free path as a function of Ar gas pressure. Here, plasma density was estimated by ion saturation current density of a negatively biased probe because plasma density is proportional to ion saturation current [27]. The electron-neutral mean free path *λ*en was also calculated by the following equation:

$$
\lambda\_{\rm on} = \text{ (}\sigma n\text{)}^{-1}\text{.}\tag{4}
$$

where *σ* and *n* are electro-neutral cross section and Ar gas density, respectively. In **Figure 6**, as a reference value, an absolute value of the plasma density for Ar gas pressure 37.5 mTorr was estimated from electron saturation current density of probe and is approximately 8 × 1010 cm−3. The plasma density drastically increases with an increasing gas pressure from 7.5 to 22.6 mTorr Pa and then varies by order, although the electron-neutral mean free path is inversely proportional to the gas pressure and reaches the hole size of 5 mm at the gas pressure of 113 mTorr. It is confirmed that the hollow cathode effect is achieved at the pressure range of 22.6–112.5 mTorr where the mean free path is comparable to the hole size of 5 mm.

The effect of SEE to attain high-density plasma production was examined by biasing the substrate electrode. **Figure 7** shows plasma density as a function of substrate biasing voltage *V*<sup>b</sup> for axial position *z* = 5 mm and radial position *r* = 0 where the origins of *z* and *r* are the surface and the center of the powered electrode, respectively. The dashed line denotes the absolute value of plasma density for *V*<sup>b</sup> = 0, which was estimated to be approximately 1010 cm−3 from probe characteristics. It is seen that plasma density increases with the substrate-biased voltage *V*b and approached approximately 1011 cm−3 at *V*<sup>b</sup> = −800 V. This suggests that the increase in *V*<sup>b</sup> performs to ionize neutral atoms by inelastic collisions of secondary high-energy electrons. The film preparation is tried by using methane gas. **Figure 8** shows the deposition rate as a function of substrate biased voltage *V*<sup>b</sup> . It is found that the deposition rate exponentially increases with increasing *V*<sup>b</sup> in the range of 100 < *V*<sup>b</sup> < 500 V and then saturates. This is because the hybrid discharge combines the hollow cathode discharge and the secondary electron emission. Therefore, the drastic increase in the deposition rate is ascribed by realizing this hybrid discharge. For *V*<sup>b</sup> > 300 V, the deposition rate exceeds the previous reported maximum value which is approximately 30 nm/min [28]. The deposition rate of 200 nm/min is attained at *V*<sup>b</sup> > 500 V.

#### **4.2. Ring-shaped hollow electrode**

In the previous subsection, the effect of multi-hollow electrode on high-density capacitively coupled plasma was described [29]. In this subsection, the ring-shaped hollow electrode was tried to produce high-density capacitively coupled plasma. The high-density plasma in the

**Figure 5.** (a) Experimental apparatus and (b) construction of multi-hollow electrode.

trench diffuses toward the downstream region, and then the radial profile of plasma density becomes uniform at a certain axial position. The influence of trench width and gas pressure on plasma density and its profile is examined, comparing the case of a conventional flat electrode. It is very important to accelerate electrons in the trench by moving RF cathode sheath for producing the high-density plasma with a hollow cathode effect. To satisfy the hollow cathode effect, it is required that the hollow trench width *W* be twice as long as the sheath thickness

as shown in **Figure 9(a)**. The depth of the hollow trench must be larger than the sheath

2 *eV* \_\_\_*\_\_sh Te* )

\_\_3 4

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\_\_ \_\_2 <sup>3</sup> *λ<sup>D</sup>* ( can be estimated

, (5)

thickness. In order to determine the trench width *W*, the sheath thickness *d*<sup>s</sup>

**Figure 8.** Deposition rate of thin films and plasma density as a function of RF-biased voltage.

*d*s

by the following equation:

*ds* <sup>=</sup> <sup>√</sup>

**Figure 7.** Plasma density as a function of RF-biased voltage.

**Figure 6.** Plasma density and electron-neutral mean free path as a function of Ar gas pressure.

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**Figure 7.** Plasma density as a function of RF-biased voltage.

**Figure 6.** Plasma density and electron-neutral mean free path as a function of Ar gas pressure.

**Figure 5.** (a) Experimental apparatus and (b) construction of multi-hollow electrode.

216 Plasma Science and Technology - Basic Fundamentals and Modern Applications

**Figure 8.** Deposition rate of thin films and plasma density as a function of RF-biased voltage.

trench diffuses toward the downstream region, and then the radial profile of plasma density becomes uniform at a certain axial position. The influence of trench width and gas pressure on plasma density and its profile is examined, comparing the case of a conventional flat electrode.

It is very important to accelerate electrons in the trench by moving RF cathode sheath for producing the high-density plasma with a hollow cathode effect. To satisfy the hollow cathode effect, it is required that the hollow trench width *W* be twice as long as the sheath thickness *d*s as shown in **Figure 9(a)**. The depth of the hollow trench must be larger than the sheath thickness. In order to determine the trench width *W*, the sheath thickness *d*<sup>s</sup> can be estimated by the following equation:

$$d\_s = \frac{\sqrt{2}}{3} \lambda\_D \left(\frac{2 \, eV\_{sh}}{T\_e}\right)^{\frac{3}{4}},\tag{5}$$

**Figure 9.** (a) Cross section near the ring-shaped trench and (b) structure of the RF hollow powered electrode.

where *λ*D, *T*e, and *V*sh denote the Debye length, the electron temperature, and the time-averaged sheath voltage of the RF electrode which was used as the typical self-biased voltage, respectively. Eq. (1) is derived from the Child-Langmuir Law [1, 11]. The sheath thickness *d*s can be estimated to be approximately 2 mm by Eq. (4) using *T*<sup>e</sup> = 4 eV, *n*<sup>e</sup> = 1010 cm−3 and *V*sh = 200 V. In this experiment, *D* is set at 5 and 10 mm. **Figure 9(b)** shows the cross section of the ring-shaped hollow electrode with 100-mm diameter and 20-mm thickness.

**Figure 10(a)** and **(b)** show typical images of plasma emission near the RF electrode for the ring-shaped hollow electrode and the flat electrode, respectively. As shown in **Figure 10(a)**, a high intensity of plasma emission is observed near the ring-shaped hollow trench for the ring-shaped hollow electrode. The hollow cathode effect is attained in the trench. On the other hand, the conventional flat electrode shows a uniform glow plasma on the whole electrode.

**Figure 11** shows plasma density *n*<sup>e</sup> as a function of Ar gas pressure *p* for the hollow and the flat electrodes. The position is fixed at *z* = 8 mm and *r* = 38 mm. For the hollow electrode, the plasma density raises rapidly with raising Ar gas pressure *p* and has a peak at *p* = 180 mTorr and then remains almost constant. At *p* = 350 mTorr, the plasma density decreases discontinuously, and then at *p* > 350 mTorr, the plasma density is independent of the gas pressure. The electron-neutral mean free path *λ*en decreases with increasing gas pressure. *λ*en at *p* = 350 mTorr is approximately 1 mm which is of the order of the magnitude of the hollow trench size. The maximum plasma density is approximately 2 × 1011 cm−3. It is seen that the high-density plasma with the order of magnitude of 1011 cm−3 is achieved in a wide range of gas pressure from 100 to 300 mTorr. In the flat electrode, the plasma density shows a similar tendency with the hollow electrode. The maximum value of the plasma density is one order of magnitude lower than that of the hollow electrode.

**Figure 12** shows plasma density as a function of Ar gas pressure for *W* = 5 and 10 mm. Here, the measured position is at *z* = 12 mm and *r* = 38 mm. It is seen that the critical pressure when the plasma density attained 10<sup>11</sup> cm−3 decreases with increasing the trench width. In fact, the critical values are 140 and 100 mTorr at *W* = 5 and 10 mm, respectively. The sheath thickness

**Figure 11.** Plasma densities as a function of Ar gas pressure for the hollow (solid circles) and the flat electrodes (squares).

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was calculated to be approximately 1.7 mm at *n*<sup>e</sup> = 1011 cm−3 at the critical gas pressures. The

is satisfied at the critical gas pressure.

**Figure 10.** Typical images of plasma structure for (a) the hollow and (b) the flat electrodes.

*d*s

condition of *W* > 2*d*<sup>s</sup>

Here, the ring-shaped trench width is *W* = 5 mm.

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**Figure 10.** Typical images of plasma structure for (a) the hollow and (b) the flat electrodes.

where *λ*D, *T*e, and *V*sh denote the Debye length, the electron temperature, and the time-averaged sheath voltage of the RF electrode which was used as the typical self-biased voltage, respectively. Eq. (1) is derived from the Child-Langmuir Law [1, 11]. The sheath thickness

**Figure 9.** (a) Cross section near the ring-shaped trench and (b) structure of the RF hollow powered electrode.

218 Plasma Science and Technology - Basic Fundamentals and Modern Applications

 can be estimated to be approximately 2 mm by Eq. (4) using *T*<sup>e</sup> = 4 eV, *n*<sup>e</sup> = 1010 cm−3 and *V*sh = 200 V. In this experiment, *D* is set at 5 and 10 mm. **Figure 9(b)** shows the cross section of

**Figure 10(a)** and **(b)** show typical images of plasma emission near the RF electrode for the ring-shaped hollow electrode and the flat electrode, respectively. As shown in **Figure 10(a)**, a high intensity of plasma emission is observed near the ring-shaped hollow trench for the ring-shaped hollow electrode. The hollow cathode effect is attained in the trench. On the other hand, the conventional flat electrode shows a uniform glow plasma on the whole electrode.

flat electrodes. The position is fixed at *z* = 8 mm and *r* = 38 mm. For the hollow electrode, the plasma density raises rapidly with raising Ar gas pressure *p* and has a peak at *p* = 180 mTorr and then remains almost constant. At *p* = 350 mTorr, the plasma density decreases discontinuously, and then at *p* > 350 mTorr, the plasma density is independent of the gas pressure. The electron-neutral mean free path *λ*en decreases with increasing gas pressure. *λ*en at *p* = 350 mTorr is approximately 1 mm which is of the order of the magnitude of the hollow trench size. The maximum plasma density is approximately 2 × 1011 cm−3. It is seen that the high-density plasma with the order of magnitude of 1011 cm−3 is achieved in a wide range of gas pressure from 100 to 300 mTorr. In the flat electrode, the plasma density shows a similar tendency with the hollow electrode. The maximum value of the plasma density is one order

as a function of Ar gas pressure *p* for the hollow and the

the ring-shaped hollow electrode with 100-mm diameter and 20-mm thickness.

*d*s

**Figure 11** shows plasma density *n*<sup>e</sup>

of magnitude lower than that of the hollow electrode.

**Figure 11.** Plasma densities as a function of Ar gas pressure for the hollow (solid circles) and the flat electrodes (squares). Here, the ring-shaped trench width is *W* = 5 mm.

**Figure 12** shows plasma density as a function of Ar gas pressure for *W* = 5 and 10 mm. Here, the measured position is at *z* = 12 mm and *r* = 38 mm. It is seen that the critical pressure when the plasma density attained 10<sup>11</sup> cm−3 decreases with increasing the trench width. In fact, the critical values are 140 and 100 mTorr at *W* = 5 and 10 mm, respectively. The sheath thickness *d*s was calculated to be approximately 1.7 mm at *n*<sup>e</sup> = 1011 cm−3 at the critical gas pressures. The condition of *W* > 2*d*<sup>s</sup> is satisfied at the critical gas pressure.

**Figure 12.** Plasma density as a function of Ar gas pressure at the hollow electrode for *W* = 5 and 10 mm under lower pressure conditions.

#### **4.3. Magnetized ring-shaped hollow cathode discharge**

In a low pressure of 1 Pa, it is difficult to produce plasma using only hollow cathode discharge [30]. In this subsection, in order to attain high-density plasma in the low-gas pressure, the combination of hollow cathode discharge and magnetic confinement with magnets is proposed. The addition of a magnetic field is one candidate for performing discharge in the lowgas pressure. It is easy to magnetize electrons under the low-gas pressure.

**Figure 13** shows the construction of a ring-shaped hollow cathode for (a) the NS-NS arrangement, (b) the NS-SN arrangement, and (c) the NS arrangement of permanent magnets. The neodymium magnets were used. Three arrangements of permanent magnets were investigated. The NS-Ns arrangement is that two NS magnets with 7 × 10 mm<sup>2</sup> in cross section and 10 mm in length are positioned at both walls of a hollow trench and six couples of the NS-NS magnets are used as shown in **Figure 13(a)**. In the NS-SN arrangement, NS and SM magnets are mounted as shown in **Figure 13(b)**. As shown in **Figure 13(c)**, six NS magnets with 10 × 15 mm2 in cross section and 6 mm in length are set at the bottom of a hollow trench for the NS arrangement. The outside of magnets is covered by iron yokes with 1 mm in thickness as shown in **Figure 13**.

**Figure 14** shows two-dimensional distributions of magnetic field lines at (a) NS-NS, (b) NS-SN, and (c) NS arrangements of permanent magnets, respectively. Here, the area enclosed by dashed lines is the hollow trench. As shown in **Figure 14(b)**, for the NS-SN arrangement, it is clear that the profile of the magnetic field lines is quite different from the other arrangement. The magnetic field lines show a cusp profile in the trench. The NS-SN arrangement is

**Figure 15.** Plasma density as a function of Ar gas pressure at *r* = 29 mm and *z* = 23 mm at various magnet arrangements.

**Figure 14.** Two-dimensional distributions of magnetic field lines near the hollow cathode for (a) the NS-NS arrangement,

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(b) the NS-SN arrangement, and (c) the NS arrangement of the permanent magnets.

**Figure 15** shows plasma density as a function of gas pressure at *r* = 29 mm and *z* = 23 mm at various arrangements. For the case without magnet, it is found that plasma density decreases from approximately 1011 cm−3 to 8 × 109 cm−3 with a decreasing gas pressure less than 80 mTorr and saturates for a gas pressure region of 80–200 mTorr. It is difficult to sustain high-density plasma without magnet at a low-gas pressure. It is noticeable that the addition of magnets with hollow cathode discharge is effective for producing high-density plasma under the low-gas pressure. For the case of NS-SN arrangement, high-density plasma over 10<sup>11</sup> cm−3 is achieved at all gas pressures.

the best profile for magnetic confinement of electrons.

Here, the data without magnetic field are also included for the comparison.

**Figure 13.** Constructions of a ring-shaped hollow cathode for (a) the NS-NS arrangement, (b) the NS-SN arrangement, and (c) the NS arrangement of permanent magnets. The neodymium magnets were used.

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**Figure 14.** Two-dimensional distributions of magnetic field lines near the hollow cathode for (a) the NS-NS arrangement, (b) the NS-SN arrangement, and (c) the NS arrangement of the permanent magnets.

**4.3. Magnetized ring-shaped hollow cathode discharge**

220 Plasma Science and Technology - Basic Fundamentals and Modern Applications

15 mm2

shown in **Figure 13**.

pressure conditions.

In a low pressure of 1 Pa, it is difficult to produce plasma using only hollow cathode discharge [30]. In this subsection, in order to attain high-density plasma in the low-gas pressure, the combination of hollow cathode discharge and magnetic confinement with magnets is proposed. The addition of a magnetic field is one candidate for performing discharge in the low-

**Figure 12.** Plasma density as a function of Ar gas pressure at the hollow electrode for *W* = 5 and 10 mm under lower

**Figure 13** shows the construction of a ring-shaped hollow cathode for (a) the NS-NS arrangement, (b) the NS-SN arrangement, and (c) the NS arrangement of permanent magnets. The neodymium magnets were used. Three arrangements of permanent magnets were investi-

10 mm in length are positioned at both walls of a hollow trench and six couples of the NS-NS magnets are used as shown in **Figure 13(a)**. In the NS-SN arrangement, NS and SM magnets are mounted as shown in **Figure 13(b)**. As shown in **Figure 13(c)**, six NS magnets with 10 ×

NS arrangement. The outside of magnets is covered by iron yokes with 1 mm in thickness as

**Figure 13.** Constructions of a ring-shaped hollow cathode for (a) the NS-NS arrangement, (b) the NS-SN arrangement,

and (c) the NS arrangement of permanent magnets. The neodymium magnets were used.

in cross section and 6 mm in length are set at the bottom of a hollow trench for the

in cross section and

gas pressure. It is easy to magnetize electrons under the low-gas pressure.

gated. The NS-Ns arrangement is that two NS magnets with 7 × 10 mm<sup>2</sup>

**Figure 15.** Plasma density as a function of Ar gas pressure at *r* = 29 mm and *z* = 23 mm at various magnet arrangements. Here, the data without magnetic field are also included for the comparison.

**Figure 14** shows two-dimensional distributions of magnetic field lines at (a) NS-NS, (b) NS-SN, and (c) NS arrangements of permanent magnets, respectively. Here, the area enclosed by dashed lines is the hollow trench. As shown in **Figure 14(b)**, for the NS-SN arrangement, it is clear that the profile of the magnetic field lines is quite different from the other arrangement. The magnetic field lines show a cusp profile in the trench. The NS-SN arrangement is the best profile for magnetic confinement of electrons.

**Figure 15** shows plasma density as a function of gas pressure at *r* = 29 mm and *z* = 23 mm at various arrangements. For the case without magnet, it is found that plasma density decreases from approximately 1011 cm−3 to 8 × 109 cm−3 with a decreasing gas pressure less than 80 mTorr and saturates for a gas pressure region of 80–200 mTorr. It is difficult to sustain high-density plasma without magnet at a low-gas pressure. It is noticeable that the addition of magnets with hollow cathode discharge is effective for producing high-density plasma under the low-gas pressure. For the case of NS-SN arrangement, high-density plasma over 10<sup>11</sup> cm−3 is achieved at all gas pressures.

In these chapters, in order to improve the plasma density in CCP, various typed CCP discharges have been presented. In Section 3, it is indicated that RF electrode with a high secondary electron emission oxide of MgO is effective to produce high-density capacitively coupled plasma. The plasma density for MgO electrode increases drastically with increasing RF voltage compared with the metal electrode of Al. In Section 4, it is described that the structured electrode plays an important role to improve the plasma density. This mechanism is ascribed by the hollow cathode effect.

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