**3. Effect of high secondary electron emission oxide on high-density capacitively coupled plasma production**

In general, plasma is generated by electrons with an energy higher than an ionization potential of target neutral gas [19]. According to the ionization cross section [20] for noble gases of He, Ne, Ar, and Xe, their ionization energy ranges from 10 to 30 eV, while the energy is a few 100 electron volts when the ionization cross section becomes maximum. These electrons are effectively possible to ionize neutral gases through inelastic collisions. Then, it is expected to produce high-density plasma. In CCP discharge, it is also easy to generate a high voltage of a few hundred volts between the powered and grounded electrodes, that is, CCP can generate secondary electron emission (SEE) from the powered electrode. It was reported that magnesium oxide (MgO) electrodes have a high SEE coefficient which are a few 10 times higher than that of conventional metal electrodes such as aluminum [21].

In this section, the effect of SEE as the acceleration mechanism of electrons is proposed to solve the serious problem of CCP density. The RF breakdown voltage and plasma density are studied experimentally. As show in **Figure 1(a)**, an RF power of 13.56 MHz was supplied to generate CCP between two electrodes of 20-mm diameter with a gap *d*gap of 10 mm, which were mounted into the center of a cylindrical vessel of 160-mm diameter and 200-mm length. The back of the RF electrode is covered by a grounded metal enclosure to avoid additional discharge between the RF electrode and the grounded vessel. An MgO disk of 20-mm diameter and 2-mm thickness was connected to the Al metal electrode, as shown in **Figure 1(b)**. As a working gas, Ne or Ar gas was introduced in the vessel at 133 Pa.

**Figure 2** shows RF breakdown voltage *V*Brf characteristics. *V*Brf is expressed as a peak-to-peak value measured by a high voltage probe and a digital oscilloscope. *V*Brf characteristics exhibit a roughly U-shaped distribution like Paschen's curve of Townsend discharge [22] for both Ne

that *V*Brf for Ar gas is lower than that for Ne gas because the ionization potential of Ar gas is

trode and the grounded vessel. The plasma density was estimated from an ion saturation cur-

by the probe. This is because the electron temperature was almost constant as a function of

mentioned in **Figure 3**, the breakdown voltage *V*Brf for Ne gas at both MgO and Al electrodes ranged from 500 to 1750 Vpp. For Al electrode, it is found that plasma density increases roughly proportionally to *V*RF. The plasma density is only of the order of 109 cm−3 at even *V*RF = 1 kVpp. According to the scaling law under the assumption that the stochastic heating without the SEE effect in the main discharge mechanism in CCP [17], the plasma density can be

*ne* ∝ *ω*<sup>2</sup> *VRF* /*ε*, (3)

where *ω*, *V*RF, and *ε* are the angular driving frequency, the RF voltage, and the energy needed

under the experiment that *ω* and *ε* are fixed. In the case of Al electrode, the experimental data almost correspond to the line of *n*<sup>e</sup> ∝ *ω*. That is, the plasma production without SEE effect is predominant by stochastic heating where electrons accelerated by the oscillating RF sheath

For MgO electrode, the plasma density is one order of magnitude higher than that for Al electrode. It is found that plasma density increases obviously with increasing *V*RF for *V*RF > 400 Vpp, and then attained over 10<sup>10</sup> cm−3 for *V*RF > 800 Vpp and then saturates. The SEE energy emitted from the MgO electrode corresponds to approximately 200 eV at *V*RF = 400 Vpp. For electron-Ne

is as a function of *V*RF for Al and MgO electrodes. The solid line is the line of *n*<sup>e</sup> ∝ *ω*.

the RF voltage. The solid line shown in **Figure 3** corresponds to *j*

to generate electrons and ions, respectively. Eq. (3) expresses that *n*<sup>e</sup>

is = 8 × 10−3 A/cm2

is [23] measured by a tiny Langmuir probe to avoid the disturbance of the plasma

Physics of High-Density Radio Frequency Capacitively Coupled Plasma with Various Electrodes…

is as a function of RF voltage *V*RF applied between the RF elec-

is almost an electron density of approximately 1010 cm−3. As

is when it is proportional to

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213

is proportional to *V*RF

lower than that of Ne gas [20]. **Figure 3** shows plasma density *j*

rent density *j*

expressed as

ionize neutral particles.

**Figure 3.** Plasma density *j*

*V*RF. The value of *j*

**Figure 1.** (a) Experimental apparatus and (b) electrode construction.

**Figure 2.** Breakdown voltage *V*RF as a function of *pd*gap. Here, *p* and *d*gap denote gas pressure and gap distance, respectively.

and Ar gases. It is found that *V*Brf for MgO electrode is higher than that for Al electrode for both Ne and Ar gases, whereas it is reported [21] that the coefficient of SEE for MgO is higher than that for Al. This is ascribed by the effect of voltage drop across MgO. It is also observed that *V*Brf for Ar gas is lower than that for Ne gas because the ionization potential of Ar gas is lower than that of Ne gas [20].

**Figure 3** shows plasma density *j* is as a function of RF voltage *V*RF applied between the RF electrode and the grounded vessel. The plasma density was estimated from an ion saturation current density *j* is [23] measured by a tiny Langmuir probe to avoid the disturbance of the plasma by the probe. This is because the electron temperature was almost constant as a function of the RF voltage. The solid line shown in **Figure 3** corresponds to *j* is when it is proportional to *V*RF. The value of *j* is = 8 × 10−3 A/cm2 is almost an electron density of approximately 1010 cm−3. As mentioned in **Figure 3**, the breakdown voltage *V*Brf for Ne gas at both MgO and Al electrodes ranged from 500 to 1750 Vpp. For Al electrode, it is found that plasma density increases roughly proportionally to *V*RF. The plasma density is only of the order of 109 cm−3 at even *V*RF = 1 kVpp.

According to the scaling law under the assumption that the stochastic heating without the SEE effect in the main discharge mechanism in CCP [17], the plasma density can be expressed as

$$
\mathfrak{n}\_{\iota} \ll \omega^2 V\_{R^{\sharp}} / \varepsilon\_{\iota} \tag{3}
$$

where *ω*, *V*RF, and *ε* are the angular driving frequency, the RF voltage, and the energy needed to generate electrons and ions, respectively. Eq. (3) expresses that *n*<sup>e</sup> is proportional to *V*RF under the experiment that *ω* and *ε* are fixed. In the case of Al electrode, the experimental data almost correspond to the line of *n*<sup>e</sup> ∝ *ω*. That is, the plasma production without SEE effect is predominant by stochastic heating where electrons accelerated by the oscillating RF sheath ionize neutral particles.

For MgO electrode, the plasma density is one order of magnitude higher than that for Al electrode. It is found that plasma density increases obviously with increasing *V*RF for *V*RF > 400 Vpp, and then attained over 10<sup>10</sup> cm−3 for *V*RF > 800 Vpp and then saturates. The SEE energy emitted from the MgO electrode corresponds to approximately 200 eV at *V*RF = 400 Vpp. For electron-Ne

**Figure 3.** Plasma density *j* is as a function of *V*RF for Al and MgO electrodes. The solid line is the line of *n*<sup>e</sup> ∝ *ω*.

and Ar gases. It is found that *V*Brf for MgO electrode is higher than that for Al electrode for both Ne and Ar gases, whereas it is reported [21] that the coefficient of SEE for MgO is higher than that for Al. This is ascribed by the effect of voltage drop across MgO. It is also observed

**Figure 2.** Breakdown voltage *V*RF as a function of *pd*gap. Here, *p* and *d*gap denote gas pressure and gap distance, respectively.

**Figure 1.** (a) Experimental apparatus and (b) electrode construction.

212 Plasma Science and Technology - Basic Fundamentals and Modern Applications

**4.1. Multi-hollow electrode**

*V*b

increasing *V*<sup>b</sup>

1 MHz. The plate is called as the substrate electrode.

*λ*en = (*n*)−<sup>1</sup>

and approached approximately 1011 cm−3 at *V*<sup>b</sup>

of substrate biased voltage *V*<sup>b</sup>

**4.2. Ring-shaped hollow electrode**

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

Physics of High-Density Radio Frequency Capacitively Coupled Plasma with Various Electrodes…

**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

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

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

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

charge 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 approxi-

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

mately 30 nm/min [28]. The deposition rate of 200 nm/min is attained at *V*<sup>b</sup> > 500 V.

in the range of 100 < *V*<sup>b</sup> < 500 V and then saturates. This is because the hybrid dis-

, (4)

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215

= −800 V. This suggests that the increase in *V*<sup>b</sup>

. It is found that the deposition rate exponentially increases with

electron-neutral mean free path *λ*en was also calculated by the following equation:

22.6–112.5 mTorr where the mean free path is comparable to the hole size of 5 mm.

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

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

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

**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.
