Simulation of mode transitions in capacitively coupled Ar/O₂ plasmas

1.   Introduction

Capacitively coupled plasma discharge has attracted significant attention due to its simple structure and ability to produce high-density and uniform plasma [1–22]. As an inert gas, argon can provide a large number of high-energy ions during the discharge process, so it has become a commonly used gas in various industries. Adding a certain amount of oxygen to argon to form an Ar/O₂ hybrid gas can produce a high throughput of active particles such as oxygen atoms (O) and ozone molecules (O₃) [23–27]. These active particles can play an important role in plasma cleaning, etching, semiconductor manufacturing, and other applications.

There are three common discharge modes in capacitively coupled plasma Ar/O₂ discharge: α, drift-ambipolar (DA), and γ. The α mode involves electron power absorption resulting from the interactions between free electrons and the expanded plasma sheath. When there is secondary-electron emission on the surface of the plate, the newly emitted secondary electrons will be heated to high energy by the sheath’s electric field, and they will collide with neutral particles; this is referred to as the γ mode [28]. The DA mode mainly exists in electronegative gas discharge, in which the drift electric field in the plasma region is very strong. The maximum ionization rate is presented at the collapsing sheath edges, which is caused by a high average electron energy (ambipolar field), and a strong gradient of the electron density. Transitions between different discharge modes will significantly affect the plasma characteristics and thus the process characteristics, they have therefore attracted a great deal of interest from researchers.

In recent years, a large amount of research has been conducted to examine discharge modes. The existence of different regimes (α and γ) in capacitively coupled radio-frequency (RF) discharge was first reported by Levitskii [29]. Through experiments, Godyak and Khanneh [30] observed an abrupt transition from the α mode to the γ mode in helium RF discharge at moderate pressure when the voltage was increased from 100 to 2000 V. To give a clear qualitative and quantitative description of this transition, Belenguer and Boeuf [31] developed a self-consistent fluid model to analyze the existence of the α and γ modes. By measuring the current-voltage characteristics of oxygen plasma, Lisovskiy and Yegorenkov [32] also found a transition between the α and γ modes, and they pointed out that pressure plays an important role in this mode transition.

Recently, Schulze et al [33] found that the drift electric field induced by low plasma conductivity and the ambipolar electric field induced by a strong electron density gradient play important roles in electron power absorption in electronegative discharges, this is referred to as the DA mode. In the DA mode, ionization mainly occurs in the bulk plasma and near the collapsing sheath edge. Liu et al [34] observed a transition between the α and DA modes in CF₄ discharge induced by the RF power (15–100 W), pressure (20–90 Pa), and driving frequency (13.56–60 MHz). Furthermore, they concluded that this mode transition is more sensitive to the working pressure than to the RF power. A specific electron heating mode (the magnetized DA mode) was identified and characterized by particle-in-cell/Monte Carlo simulations, and the structural transitions of the discharge plasma were studied and reported in reference [35]. Proshina et al [36] observed a typical electron heating mode transition from the bulk heating mode into classical electron heating by increasing the driving voltage or decreasing the pressure in CF₄ capacitive discharge. In summary, most relevant studies have focused on transitions between the α and γ modes or the α and DA modes in RF discharges, while few have examined the mutual transitions among the α/DA, γ/DA, γ, DA, and α modes in low-frequency (LF) discharges.

In an LF plasma, ions have the possibility of obtaining higher energies within a long discharge cycle, and a small plasma volume will give rise to high power densities [37]. Thus, LF plasma is widely used in surface treatment and the modification of materials [38]. In this work, we mainly focused on comparisons between the discharge modes in the high-frequency (HF) and LF regions and the effects of process parameters on the mode transitions. The remainder of this article is structured as follows. A detailed description of the fluid model is given in section 2, and discussions of mode transitions in Ar/O₂ discharge are presented in section 3. Conclusions are drawn in section 4.

2.   Theoretical model

2.1   Fluid model

An overview of the 15 different species (molecules, radicals, electrons, and ions) considered in our model is shown in table 1, and the electron chemical reactions and the reaction coefficients between particles are listed in table 2.

Table  1.  Various particles incorporated in this model.

Neutrals	Charged particles
${\text{A}}{{\text{r}}_{}}$, ${\text{A}}{{\text{r}}_{\text{m}}}$	${\text{O}}_{\text{2}}^ -$, ${{\text{O}}^ - }$
${\text{A}}{{\text{r}}_{\text{r}}}$, ${\text{A}}{{\text{r}}^ * }$	e
${{\text{O}}_{\text{2}}}$, ${{\text{O}}_{\text{3}}}$, ${\text{O}}$	${\text{O}}_2^+$
${\text{O}}{(^1}{\text{D}})$, ${{\text{O}}_{\text{2}}}{(^1}\Delta {\text{g)}}$	$\text{O}^+,\ $ ${\text{A}}{{\text{r}}^{\text{ + }}}$

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Table  2.  The electron collisions and the reaction coefficients used in the model [39–44].

No.	Reaction equation	Rate coefficient (cm3 s−1)
01	${\text{Ar}} + {\text{e}} \to {\text{A}}{{\text{r}}^ + } + 2{\text{e}}$	$2.3\times10^{-8}T_{\text{e}}^{0.68}\exp\left(-15.76/T_{\text{e}}\right)$
02	${\text{Ar}} + {\text{e}} \to {\text{A}}{{\text{r}}_{\text{m}}} + {\text{e}}$	$2.5\times10^{-9}T_{\text{e}}^{0.74}\exp\left(-11.56/T_{\text{e}}\right)$
03	${\text{Ar}} + {\text{e}} \to {\text{A}}{{\text{r}}_{\text{r}}} + {\text{e}}$	$2.5\times10^{-9}T_{\text{e}}^{0.74}\exp\left(-11.56/T_{\text{e}}\right)$
04	${\text{Ar}} + {\text{e}} \to {\text{A}}{{\text{r}}^ * } + {\text{e}}$	$1.4\times10^{-8}T_{\text{e}}^{0.71}\exp\left(-13.2/T_{\text{e}}\right)$
05	${\text{A}}{{\text{r}}_{\text{r}}} + {\text{e}} \to {\text{A}}{{\text{r}}^ + } + 2{\text{e}}$	$6.8\times10^{-9}T_{\text{e}}^{0.67}\exp\left(-4.2/T_{\text{e}}\right)$
06	${\text{A}}{{\text{r}}_{\text{r}}} + {\text{e}} \to {\text{Ar}} + {\text{e}}$	$4.3 \times {10^{ - 10}}{T_{\text{e}}}^{0.74}$
07	${\text{A}}{{\text{r}}_{\text{r}}} + {\text{e}} \to {\text{A}}{{\text{r}}_{\text{m}}} + {\text{e}}$	$3 \times {10^{ - 7}}$
08	${\text{A}}{{\text{r}}_{\text{r}}} + {\text{e}} \to {\text{A}}{{\text{r}}^ * } + {\text{e}}$	$8.9\times10^{-7}T_{\text{e}}^{0.51}\exp\left(-1.59/T_{\text{e}}\right)$
09	${\text{A}}{{\text{r}}_{\text{m}}} + {\text{e}} \to {\text{A}}{{\text{r}}^ + } + 2{\text{e}}$	$6.8\times10^{-9}T_{\text{e}}^{0.67}\exp\left(-4.2/T_{\text{e}}\right)$
10	${\text{A}}{{\text{r}}_{\text{m}}} + {\text{e}} \to {\text{Ar}} + {\text{e}}$	$4.3 \times {10^{ - 10}}{T_{\text{e}}}^{0.74}$
11	${\text{A}}{{\text{r}}_{\text{m}}} + {\text{e}} \to {\text{A}}{{\text{r}}_{\text{r}}} + {\text{e}}$	$2 \times {10^{ - 7}}$
12	${\text{A}}{{\text{r}}_{\text{m}}} + {\text{e}} \to {\text{A}}{{\text{r}}^ * } + {\text{e}}$	$8.9\times10^{-7}T_{\text{e}}^{0.51}\exp\left(-1.59/T_{\text{e}}\right)$
13	${\text{A}}{{\text{r}}^ * } + {\text{e}} \to {\text{A}}{{\text{r}}^ + } + 2{\text{e}}$	$1.8\times10^{-7}T_{\text{e}}^{0.61}\exp\left(-2.61/T_{\text{e}}\right)$
14	${\text{A}}{{\text{r}}^ * } + {\text{e}} \to {\text{Ar}} + {\text{e}}$	$3.9 \times {10^{ - 10}}{T_{\text{e}}}^{{\text{0}}{\text{.71}}}$
15	${\text{A}}{{\text{r}}^ * } + {\text{e}} \to {\text{A}}{{\text{r}}_{\text{r}}} + {\text{e}}$	$1.5 \times {10^{ - 7}}{T_{\text{e}}}^{{\text{0}}{\text{.51}}}$
16	${\text{A}}{{\text{r}}^ * } + {\text{e}} \to {\text{A}}{{\text{r}}_{\text{m}}} + {\text{e}}$	$1.5 \times {10^{ - 7}}{T_{\text{e}}}^{{\text{0}}{\text{.51}}}$
17	${\text{A}}{{\text{r}}_{\text{r}}} \to {\text{Ar + }}h\nu$	$2\times10^6\ \text{s}^{-1}$
18	${\text{A}}{{\text{r}}_{\text{m}}} \to {\text{Ar + }}h\nu$	$2\times10^6\ \text{s}^{-1}$
19	${\text{A}}{{\text{r}}^ * } \to {\text{A}}{{\text{r}}_{\text{r}}}{\text{ + }}h\nu$	$3\times10^7\ \text{s}^{-1}$
20	${\text{A}}{{\text{r}}^ * } \to {\text{A}}{{\text{r}}_{\text{m}}}{\text{ + }}h\nu$	$3\times10^7\ \text{s}^{-1}$
21	${\text{A}}{{\text{r}}^ + } + {\text{e}} \to {\text{A}}{{\text{r}}_{\text{r}}}{\text{ + }}h\nu$	$1 \times {10^{ - 11}}$
22	${\text{A}}{{\text{r}}^ + } + {\text{e}} \to {\text{A}}{{\text{r}}_{\text{m}}}{\text{ + }}h\nu$	$1 \times {10^{ - 11}}$
23	${\text{A}}{{\text{r}}^ + } + {\text{e}} \to {\text{A}}{{\text{r}}^ * }{\text{ + }}h\nu$	$1 \times {10^{ - 11}}$
24	${\text{e + }}{{\text{O}}_{\text{2}}} \to {{\text{O}}_{\text{2}}}{(^1}\Delta {\text{g) + e}}$	$1.7\times10^{-9}\exp\left(-3.1/T_{\text{e}}\right)$
25	${\text{e + }}{{\text{O}}_{\text{2}}} \to {\text{O}} + {\text{O}}{(^1}{\text{D}}) + {\text{e}}$	$5\times10^{-8}\exp\left(-8.4/T_{\text{e}}\right)$
26	${\text{e + }}{{\text{O}}_{\text{2}}} \to 2{\text{O}} + {\text{e}}$	$4.2\times10^{-9}\exp\left(-5.6/T_{\text{e}}\right)$
27	${\text{e + }}{{\text{O}}_{\text{2}}} \to {{\text{O}}^ - } + {\text{O}}$	$8.8\times10^{-11}T_{\text{e}}^{0.51}\exp\left(-4.4/T_{\text{e}}\right)$
28	${\text{e + }}{{\text{O}}_{\text{2}}} \to {\text{O}}_2^ + + {\text{2e}}$	$9\times10^{-10}T_{\text{e}}^{0.5}\exp\left(-12.6/T_{\text{e}}\right)$
29	$\text{e + }\text{O}_{\text{2}}\to\text{O}^-+\text{O}^{\text{+}}+\text{e}$	$7.1\times10^{-11}T_{\text{e}}^{0.5}\exp\left(-17/T_{\text{e}}\right)$
30	$\text{e + }\text{O}_2\to\text{O}+\text{O}^{\text{+}}+2\text{e}$	$5.3\times10^{-10}T_{\text{e}}^{0.9}\exp\left(-20/T_{\text{e}}\right)$
31	${\text{e + }}{{\text{O}}_2}{{\text{(}}^1}\Delta {\text{g)}} \to {{\text{O}}_2} + {\text{e}}$	$5.6\times10^{-9}T_{\text{e}}^{0.9}\exp\left(-2.2/T_{\text{e}}\right)$
32	${\text{e + O}} \to {\text{O}}{(^1}{\text{D}}) + {\text{e}}$	$4.2\times10^{-9}T_{\text{e}}^{0.9}\exp\left(-2.25/T_{\text{e}}\right)$
33	${\text{e + O}}{(^1}{\text{D}}) \to {\text{O}} + {\text{e}}$	$8 \times {10^{ - 9}}$
34	$\text{e + O}(^1\text{D})\to\text{O}^{\text{+}}+2\text{e}$	$9\times10^{-9}T_{\text{e}}^{0.7}\exp\left(-11.6/T_{\text{e}}\right)$
35	${\text{e + O}} \to {{\text{O}}^ + } + 2{\text{e}}$	$9\times10^{-9}T_{\text{e}}^{0.7}\exp\left(-13.6/T_{\text{e}}\right)$
36	${\text{e + }}{{\text{O}}_{\text{3}}} \to {\text{O}}_2^ - + {\text{O}}$	$1 \times {10^{ - 9}}$
37	${\text{e + }}{{\text{O}}^ - } \to {\text{O}} + 2{\text{e}}$	$2\times10^{-7}\exp\left(-5.5/T_{\text{e}}\right)$
38	${\text{e + O}}_2^ + \to 2{\text{O}}$	$2.2 \times {10^{ - 8}}T_{\text{e}}^{ - 0.5}$
39	${{\text{O}}_2} + {{\text{O}}_2}{\text{ + O}} \to {{\text{O}}_3} + {{\text{O}}_{\text{2}}}$	$6.9\times10^{-34}\exp(300/T\mathrm{_g})^{1.25}\ \text{c}\text{m}^6\ \text{s}^{-1}$
40	${{\text{O}}^{{ - }}} + {{\text{O}}_2} \to {{\text{O}}_{\text{3}}} + {\text{e}}$	$5 \times {10^{ - 15}}$
41	${\text{O}}{{\text{(}}^{\text{1}}}{\text{D) + }}{{\text{O}}_3} \to 2{{\text{O}}_{\text{2}}}$	$1.2 \times {10^{ - 10}}$
42	$\text{O}^-+\text{O}_3\to\text{O}_3^-+\text{O}$	$8 \times {10^{ - 10}}$
43	${\text{e}} + {{\text{O}}_2} + {{\text{O}}_2} \to {\text{O}}_2^ - + {{\text{O}}_{\text{2}}}$	$1.4 \times {10^{ - 29}}(0.026/{T_{\text{e}}}) \times$ $\exp(100/T\mathrm{_g}-0.061/T_{\text{e}})\ \text{c}\text{m}^6\ \text{s}^{-1}$

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The fluid model is composed of the continuity, momentum, electron energy, and Poisson equations. The continuity equation of the electrons is

where ${n_{\text{e}}}$ is electron density and R_e is the electron source term, the electron flux Г_e is obtained from the drift-diffusion approximation,

in which µ_e and D_e are the mobility and diffusion coefficients of electrons, respectively. To facilitate the solution, the flux of ions is also solved by the drift-diffusion approximation:

where µ_i and D_i are the mobility and diffusion coefficient of ions, respectively; R_i is the source term of ions; and n_i and Г_i are the ion density and flux, respectively. However, because the ion mass is much larger than the electron mass, ions cannot respond instantaneously to the electric field; thus, an effective electric field E_eff,i is introduced to replace the electric field E in equation (4). The effective electric field is described by

where v_m,i = e/m_iµ_i is the momentum transport frequency of ions, m_i is the ion mass, and µ_i is the ion mobility.

The neutral particle equation is

where n_n is the density of neutral particles, D_n is the diffusion coefficient of neutral particles, and R_n is the source terms of neutral particles (such as O, O₃, O(¹D)).

The electric field E and the potential V can be obtained from the Poisson equation

where ${\varepsilon _0}$ is the dielectric constant in vacuum, n₊ is the density of positive ions, and n₋ is the density of negative ions.

Finally, the electron energy equation is

where T_e is the electron temperature, R_w is the energy-loss term due to collisions, and the electron energy flux density Г_w is calculated by

The ion temperature and neutral-gas temperature are both assumed to be 300 K; thus, no energy equations are taken into account.

2.2   Boundary condition

The simulation model comprises a capacitively coupled reactor with two separated electrodes, the lower of which is grounded and the upper of which is driven with the voltage V = V₀sin(ωt). The electron flux at the upper and lower electrodes can be described by

where Θ = 0.25 is the electron reflection coefficient on the wall, ${u_{{\text{th}}}} = \sqrt {8{k_{\text{B}}}{T_{\text{e}}}/{\text{π}}{m_{\text{e}}}}$ is the electron average thermal velocity, and γ_se is the secondary-electron emission coefficient. The electron energy flux at the upper and lower electrodes is described by

The positive ion flux is considered to be continuous at the boundary, while the negative ion flux is 0 at the boundary:

The neutral particle flow at the boundary is given by

where s_n is the sticking probability of a neutral particle and $u_{\text{th,n}}=\sqrt{8k_{\text{B}}T_{\text{n}}/\text{π}m_{\text{n}}}$ is the thermal velocity of the neutral particles. The gas molecules will be reflected to the original gas when they touch the wall, so the sticking probability is considered to be 0. The excited gas will become de-excited at the wall, its sticking probability is thus set to 1.

3.   Results and discussion

In this section, we present an analysis of the influence of the process parameters especially the frequency on the discharge mode. Since oxygen is an electronegative gas, the DA mode always exists in Ar/O₂ discharges, while the α and γ modes are closely related to the choice of process parameters. The plate separation was fixed at 3.0 cm, and the voltage amplitude V₀ was 200 V. The frequency varies from 100 kHz to 40 MHz, the pressure varies from 300 to 800 mTorr, the secondary electron emission coefficient varies from 0.05 to 0.2, and the gas composition varies from Ar/O₂ = 9:1 to 1:9. The following discussions are based on a stable fluid model, typically after 1 ms, which ensures that the relative change of discharge parameters in two continuous cycles is less than 10⁻⁶ [45].

3.1   Effect of frequency

The temporal and spatial variations of the ionization rate at different frequencies are shown in figure 1. It is known that when the frequency is low and the voltage is high, secondaries play a more important role in sustaining the plasma [46]. Thus, when f = 100 kHz, the discharge is in the γ-DA hybrid mode, which can be seen from figure 1. As the frequency is increased, the sheath collapses, and the extreme ionization rate moves through the plasma region from one sheath edge to the other sheath edge; that is, the γ mode gradually weakens (the ionization rate percentage decreases from 79% to 67%) and the DA mode gradually increases (the ionization rate percentage increases from 21% to 33%). We can also see that in the LF region (100 kHz to 2 MHz), the ionization rate decreases with increasing frequency. This is because the sheath thickness decreases as the frequency is increased; the energy obtained from the secondary electrons then also decreases, which reduces the ionization rate. However, when the frequency is increased to 13.56 MHz, the discharge is converted from the γ-DA mode dominated by the γ mode, to the DA-α mode dominated by the DA mode. As the frequency continues to increase, the ionization rate increases, and both the DA mode and the α mode are enhanced. In the DA mode, due to the strong drift and ambipolar electric field, the electrons obtain energy from the electric field and collide with neutral gas. As the frequency is increased, these collisions become more frequent, which in turn increases the ionization rate. It should be emphasized that f = 2 MHz is not only the critical value for the mode transition from γ-DA to DA-α, but it is also the critical value for the mode transition from a γ-dominated to a DA-dominated mode.

Figure  1.  Spatiotemporal distributions of ionization rate at different frequencies, with γ_se = 0.2, Ar:O₂ = 8:2, and P = 300 mTorr.

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To give the change of ionization rate more clearly, figure 2 shows the spatial distributions of ionization rate at different times (corresponding to the peak value of ionization rate) within a cycle for different frequencies. It can be seen that the ionization rate in DA mode is less than that of γ mode in the LF region while it is larger than that of α mode in the HF region, which is consistent with the discussion results in figure 1.

Figure  2.  The spatial distributions of ionization rate at different times within a cycle for different frequencies, with γ_se = 0.2, Ar:O₂ = 8:2, and P = 300 mTorr.

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To verify that there is a mode transition from γ to α when the frequency is increased from 2 to 13.56 MHz, the dependence of the electron density on the secondary-electron emission coefficient is shown in figure 3. It can be seen that when the frequency is 2 MHz, the electron density increases with the secondary-electron emission coefficient. This means that the discharge is sustained by the secondary electrons. When f = 13.56 MHz, the secondary-electron emission coefficient has little effect on the electron density, which suggests that the γ mode has been converted to the α mode.

Figure  3.  The spatial distributions of electron density at different secondary electron emission coefficients with (a) f = 2 MHz and (b) f = 13.56 MHz, γ_se = 0.2, Ar:O₂ = 8:2, and P = 300 mTorr.

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Figure 4 shows the spatiotemporal distributions of electron temperature at different frequencies. It can be seen that the electron temperature is higher in the sheath region and lower in the plasma region. When the frequency is low, the peak value of electron temperature in the first half-cycle is near the lower electrode plate, and the peak value of electron temperature in the second half-cycle is near the upper electrode plate, which shows that the discharge characteristics are dominated by the γ mode. As the frequency is increased, the peak of the electron temperature in the sheath region becomes wider, and it then gradually diffuses to the entire sheath, showing the discharge characteristics of the DA-α mode [47]. It can also be seen from figure 4 that the electron temperature decreases with increasing frequency. This is because in the LF region (100 kHz to 2 MHz), the discharge is mainly maintained by secondary-electron emission. As the frequency is increased, the sheath thickness decreases, and the energy obtained by the secondary electrons from the sheath decreases, and the electron temperature therefore decreases. In the HF region (f > 2 MHz), the discharge is dominated by the DA mode. Under the action of the ambipolar electric field, electrons move to the sheath region and collide with oxygen. The higher the frequency, the more intense these collisions and the greater the energy loss; thus, the electron temperature decreases with increasing frequency.

Figure  4.  Spatiotemporal distributions of electron temperature at different frequencies, with γ_se = 0.2, Ar:O₂ = 8:2, and P = 300 mTorr.

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Figure 5 shows the dependence of the main particles’ density on the frequency, concerning those particles with relatively high density in the discharge. The particle densities plotted in this figure are all those in the center of the discharge. It can be seen from figure 5 that the electron density decreases in the LF region and increases in the HF region, and the lowest point is at f = 2 MHz. In the LF region, as the frequency is increased, the sheath thickness decreases, and the energy obtained by the secondary electrons from the sheath decreases, which means that the oxygen cannot be easily ionized; thus, the electron density decreases with increasing frequency. In the HF region, as the frequency is increased, the electrons obtain more energy from the drift-diffusion field, and more collisions between the electron and the gas take place; thus, more electrons are ionized. The collisions between electrons and oxygen will produce O, O⁺, ${\mathrm{O}}^+ _2$, ${\mathrm{O}}^- _2$, and O⁻, and increasing the electron density will aggravate these collisions; thus, the densities of O, O⁺, ${\mathrm{O}}^+ _2$, ${\mathrm{O}}^- _2$, and O⁻ exhibit the same variation trend as the electron density.

Figure  5.  The dependence of main particle density on frequency, with γ_se = 0.2, Ar:O₂ = 8:2, and P = 300 mTorr.

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3.2   Effect of pressure

The spatiotemporal distributions of the ionization rate for different frequencies are given in figure 6 for a pressure of 500 mTorr. It can be seen that the ionization rate increases with pressure, such as the maximum ionization rate at f = 100 kHz increases from 1.1×10¹⁷ cm⁻³ s⁻¹ at P = 300 mTorr to 7.3×10¹⁷ cm⁻³ s⁻¹ at P = 500 mTorr. This is because as the pressure is increased, the number of collisions between electrons and gas molecules increases, resulting in an increase in the ionization rate. In contrast to figure 1, however, there is almost no DA mode at the frequencies of 100 and 400 kHz; this is mainly because the ionization rate in the γ mode greatly increases with the pressure, while the ionization rate in the DA mode changes little with the pressure. When f = 2 MHz, the discharge is in the γ-DA hybrid mode dominated by the γ mode, and the maximum ionization rate in the DA mode is almost 2.2×10¹⁶ cm⁻³ s⁻¹, which is larger than 5.8×10¹⁵ cm⁻³ s⁻¹ at a pressure of 300 mTorr. As the frequency is increased further, the discharge moves to the DA-α mode dominated by the DA mode; this is similar to the situation seen in figure 1. Note that the ionization rate in the HF region increases by about three times when the pressure is increased from 300 to 500 mTorr. This suggests that the electronegativity increases with gas pressure, which correlates with the phenomenon observed by Schulze et al in CF₄ discharge [33].

Figure  6.  The spatiotemporal distributions of ionization rate at different frequencies, with γ_se = 0.2, Ar:O₂ = 8:2, and P = 500 mTorr.

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To further explain the influence of pressure on the discharge mode, figure 7 shows the spatial distributions of ionization rate at different times within a cycle for different frequencies. It is observed that the ionization rate in DA mode is less than that of γ mode in the LF region, and it is larger than that of α mode in the HF region.

Figure  7.  The spatial distributions of ionization rate at different times within a cycle for different frequencies, with γ_se = 0.2, Ar:O₂ = 8:2, and P = 500 mTorr.

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To further explore the influence of pressure, the dependence of the electron density on the frequency at different pressures is shown in figure 8. It can be observed that the electron density decreases exponentially with increasing frequency in the LF region, while it increases linearly with frequency in the HF region, the data fitting curve and the corresponding equations can be seen in figure 9. We can also see that the electron density increases with pressure due to more collisions occurring between electrons and neutral particles. The large increase of electron density in the LF region causes the electronegativity to become weaker; thus, no DA mode appears at the frequencies of 100 and 400 kHz. We can also see that the lowest point of electron density at different pressures appears at f = 2 MHz, which indicates that pressure has little effect on the mode transition from γ to α.

Figure  8.  Variations of the electron densities as a function of frequency for different pressures, with γ_se = 0.2, Ar:O₂ = 8:2, and P = 500 mTorr.

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Figure  9.  The fitting function of the dependence of electron density on frequency under different pressures.

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3.3   Effect of secondary-electron emission coefficient

The influence of the secondary-electron emission coefficient on the discharge mode conversion was also considered, at a pressure of 500 mTorr. Figure 10 shows the spatiotemporal distributions of the ionization rate, with γ_se = 0.05. It can be observed that the DA mode exists across the whole frequency range, which is different from figure 6 when γ_se = 0.20. This is because the large secondary-electron emission coefficient and the strong γ mode cause the DA mode to not appear. In figure 10, when f = 100 kHz, the discharge is in the γ-DA mode dominated by the γ mode. As the frequency is increased, the electronegativity increases, and the discharge is converted to the γ-DA mode dominated by the DA mode when f = 400 kHz. As the frequency is increased to 2 MHz, there is still some γ mode, but it is very weak. In the HF region (13.56–40 MHz), the γ mode has been converted to the α mode, and the discharge is in the DA-α mode dominated by the DA mode, which is the same as that in figure 6. That is to say, the frequency for the mode transition from γ to DA is reduced from 2 MHz at γ_se = 0.20 to 400 kHz at γ_se = 0.05, while the frequency for the mode transition from γ to α at γ_se = 0.05 is the same as that at γ_se = 0.20. Through our calculations, it was found that when the secondary-electron emission coefficient is less than 0.06, the frequency for the mode transition from γ to DA decreases.

Figure  10.  The spatiotemporal distributions of ionization rate at different frequencies, with γ_se = 0.05, Ar:O₂ = 8:2, and P = 500 mTorr.

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Figure 11 shows the spatial distributions of ionization rate at different times within a cycle for different frequencies. It can be seen from figure 11 that the DA mode is slightly lower than the γ mode at f = 100 kHz, while at f = 400 kHz, the DA mode is already higher than the γ mode and increases as the frequency increases. It is further confirmed that when f $\geqslant$ 400 kHz, the discharge is dominated by DA mode.

Figure  11.  The spatial distributions of ionization rate at different times within a cycle for different frequencies, with γ_se = 0.05, Ar:O₂ = 8:2, and P = 500 mTorr.

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To further verify the above results, figure 12 shows the dependence of the electron density on the frequency at different secondary-electron emission coefficients when P = 500 mTorr. It can be observed that the lowest electron density is found at the frequency of 400 kHz when γ_se = 0.05; thus, the electronegativity is strong, and a mode transition from γ to DA takes place, which is consistent with the discussion of the results in figure 10. As the secondary-electron emission coefficient is increased to 0.1, the γ mode is enhanced, and the frequency for the mode transition from γ to DA is then increased to 2 MHz. It can also be observed from figure 11 that in the HF region, the electron densities are almost unaffected by the secondary-electron emission coefficients, such as when f = 13.56 MHz, the electron density remains 4×10¹⁰ cm⁻³. This further demonstrates that f = 2 MHz is the value for the mode transition from γ to α.

Figure  12.  Variations of the electron density as a function of frequency for different secondary electron emission coefficients, with Ar:O₂ = 8:2, and P = 500 mTorr.

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3.4   Effect of gas composition

It was found from the above results that f = 2 MHz is the mode-transition point; it is therefore necessary to explore the plasma-discharge characteristics at f = 2 MHz. The spatiotemporal distributions of ionization rates at different gas compositions are shown in figure 13, with f = 2 MHz and γ_se = 0.20. It can be seen from the above results that the discharge is in the hybrid γ and DA mode when f = 2 MHz. As noted above, oxygen is an electronegative gas; as such, when the proportion of oxygen is increased, the electronegativity increases, which causes the DA mode to be enhanced (the ionization rate percentage increases from 14% to 89%) and the γ mode to be weakened (the ionization rate percentage decreases from 86% to 11%). From figure 13, we can observe that when Ar:O₂ = 4:6, the discharge mode is transformed from DA-γ dominated by γ to DA-γ dominated by DA. As the proportion of oxygen continues to increase to Ar:O₂ = 1:9, the γ mode becomes very weak and almost disappears; that is to say, the effect of secondary-electron heating on the discharge is almost negligible. Since the threshold energy of oxygen (13.61 eV) is lower than that of argon (15.76 eV), the former is more easily ionized than the latter; thus, the ionization rate increases with increasing oxygen content.

Figure  13.  The spatiotemporal distributions of ionization rate at different gas compositions, with γ_se = 0.2, f = 2 MHz, and P = 300 mTorr.

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To further explore the influence of gas composition on the discharge mode, we give the spatial distributions of ionization rate at different times within a cycle for different frequencies in figure 14. From figure 14, we can see that as the oxygen ratio increases, both the DA mode and the γ mode increase, but the increase of the γ mode is small. When Ar:O₂ = 4:6, the γ mode is weaker than the DA mode, which is consistent with the discussion results in figure 13.

Figure  14.  The spatial distributions of ionization rate at different times within a cycle for different frequencies, with γ_se = 0.2, f = 2 MHz, and P = 300 mTorr.

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Figure 15 shows spatiotemporal distributions of the electric field at different gas compositions, corresponding to two different discharge modes. It can be seen that when Ar:O₂ = 9:1, the electric field in the bulk region is very small, and it is mainly distributed in the sheath region. This indicates that the DA mode is weak when Ar:O₂ = 9:1, verifying the result of figure 13. However, when Ar:O₂ = 1:9, there is an obvious drift electric field in the bulk plasma, which reflects the distribution characteristics of the electric field of the DA mode. This indicates that the DA mode is very strong when Ar:O₂ = 1:9, which is consistent with the results of figure 13.

Figure  15.  The spatiotemporal distributions of the electric field at different oxygen content, with γ_se = 0.2, f = 2 MHz, and P = 300 mTorr.

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Figure 16 shows the spatial distributions of electron density and electron temperature averaged over a cycle under different gas compositions. It can be seen that the electron density increases with the oxygen content, which is because oxygen is more easily ionized than argon. When the oxygen content is low, it is dominated by the γ mode, and the electron density in the plasma region is high. As the oxygen content is increased, the action of the ambipolar electric field accelerates the electrons to the plate, resulting in a rapid increase in the electron density in the sheath region and a small increase in the electron density in the bulk region. It can be seen from figure 16 that the electron temperature decreases with increasing oxygen content. As the oxygen content is increased, the DA mode is enhanced, and the electrons are accelerated by the electric field to collide with oxygen, increasing the energy loss and decreasing the electron temperature.

Figure  16.  The spatial distributions of electron density and electron temperature averaged over a cycle under different gas compositions, with γ_se = 0.2, f = 2 MHz, and P = 300 mTorr.

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The spatial distributions of oxygen atoms and ozone densities averaged over a cycle at different oxygen contents are shown in figure 17. It can be seen that the oxygen-atom and ozone densities increase rapidly with the oxygen content. Oxygen atoms are produced by the dissociation of oxygen molecules, and the electron density increases with the oxygen content; thus, the number of oxygen atoms increases with the oxygen content. O₃ is produced by the recombination of an oxygen atom and an oxygen molecule; thus, the O₃ density also increases with the oxygen content, but the O₃ density is much lower than the O density. It is worth mentioning that the concentration of O₃ increases by nearly two orders of magnitude with the oxygen content, which is much faster than the increase in atomic oxygen. This can be explained by the fact that O₃ is mainly produced by the reaction (39) in table 2 and the density of O₃ is proportional to the square of the oxygen density. In practical applications, we can therefore obtain more O₃ by increasing the proportion of oxygen in Ar/O₂ discharges. O₃ has strong oxidizing properties and thus has applications in sewage treatment and the food and medicine industries [48–51].

Figure  17.  The spatial distributions of oxygen atom density and ozone density averaged over a cycle under different oxygen ratios with γ_se = 0.2, f = 2 MHz, and P = 300 mTorr.

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4.   Conclusions

In this work, using a one-dimensional fluid model, we studied the effects of the driving frequency, secondary-electron emission coefficient, gas composition, and pressure on the discharge mode in capacitively coupled Ar/O₂ plasmas. Transitions among the α, γ, and DA discharge modes were observed. The simulation results can be summarized as follows.

As the driving frequency is increased, the discharge experiences a transition from the γ-DA mode dominated by the γ mode to the DA-α mode dominated by the DA mode at a frequency of 2 MHz. In addition, in the LF region, the plasma density and electron temperature decrease with increasing frequency. In the HF region, as the frequency is increased, the plasma density increases while the electron temperature decreases.

If the pressure is changed from 300 to 800 mTorr, there is no alteration in the mode transition from γ to α caused by varying the frequency. Note that by increasing the pressure, the electronegativity in the LF region increases little, inducing a mode transition from γ-DA into a pure γ mode. However, the electronegativity in the HF region increases as a function of pressure.

When the secondary-electron emission coefficient is less than 0.06, the DA mode is enhanced and the γ mode is weakened in the LF region. This results in a decrease in the frequency for the mode transition from γ to DA, and the frequency corresponding to the lowest electron density also decreases.

When oxygen content is increased, the γ mode is weakened and the DA mode is enhanced. Once the proportion of oxygen reaches 90%, a transition from the γ-DA mode into the pure DA mode is induced. More importantly, the O₃ density increases by dozens of times as the proportion of oxygen is increased, which is important for practical applications.

In summary, the ranges of discharge parameters corresponding to the mode transition have been presented in this article. It is expected that our research results can provide a basis for parameter selection for actual plasma processes.