# The Influence of Secondary Electron Emission and Electron Reflection on a Capacitively Coupled Oxygen Discharge

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## Abstract

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`oopd1`is applied to explore the role of secondary electron emission and electron reflection on the properties of the capacitively-coupled oxygen discharge. At low pressure (10 mTorr), drift-ambipolar heating of the electrons dominates within the plasma bulk, while at higher pressure (50 mTorr), stochastic electron heating in the sheath region dominates. Electron reflection has negligible influence on the electron energy probability function and only a slight influence on the electron heating profile and electron density. Including ion-induced secondary electron emission in the discharge model introduces a high energy tail to the electron energy probability function, enhances the electron density, lowers the electronegativity, and increases the effective electron temperature in the plasma bulk.

## 1. Introduction

`xpdp1`PIC/MCC code. Since then, a number of PIC/MCC studies have been reported on oxygen and Ar/O${}_{2}$ discharges using the

`xpdx1`series of codes, in both symmetrical and asymmetrical geometry, performed over a range of pressures and compared to experimental findings [8] and to analytical density profiles [9], showing good agreement, to explore the formation of the ion energy distribution function in an O${}_{2}$/Ar mixture in an asymmetric capacitively-coupled discharge [10], and the influence of the secondary electron emission on the density profiles and the electron energy distribution function (EEDF) [11]. Other 1D PIC/MCC codes have been developed to explore the oxygen discharge. A 1D PIC/MCC model developed in Greifswald, that includes the metastable oxygen molecule O${}_{2}\left({a}^{1}{\Delta}_{g}\right)$ as a fraction of the ground state molecule, was used to determine the ion energy distribution function (IEDF) in oxygen CCP [12,13]. Furthermore, they found by comparison with experiments that one sixth of the oxygen molecules are in the metastable singlet delta state. A 1D PIC/MCC code, developed in Dalian [14,15], was applied to explore the electrical asymmetry effect in a dual-frequency capacitively-coupled oxygen discharge. Similar to Bronold et al. [12], this work assumed a constant density for the singlet metastable molecule O${}_{2}\left({a}^{1}{\Delta}_{g}\right)$. More recently, a 1D PIC/MCC code that was developed in Budapest was used to explore the heating mechanism in a capacitively-coupled oxygen discharge driven by tailored waveforms (composed of N harmonics in addition to a fundamental frequency ${f}_{1}$) [16,17]. Furthermore, a PIC/MCC fluid hybrid model was applied to explore the electron power absorption and the influence of pressure on the energetics and particle densities [18,19]. In all of these works, only electrons, the positive ion O${}_{2}^{+}$, and the negative ion O${}^{-}$ were treated kinetically, and the positive ion O${}^{+}$ was neglected. Furthermore, none of the metastable states were treated kinetically. The one-dimensional object-oriented plasma device one (

`oopd1`) code allows having the simulated particles of different weights, which allows for tracking both charged and neutral particles in the simulation. Earlier, we benchmarked the basic reaction set for the oxygen discharge in

`oopd1`to the

`xpdp1`code [20].

`oopd1`code was improved significantly [20,21,22]. Using this improved discharge model, we showed that the singlet metastable molecular states have a significant influence on the electron heating mechanism in the capacitively-coupled oxygen discharge [21,22,23,24] as well as the ion energy distribution [25]. We demonstrated that, when operating at low pressure (10 mTorr), the electron heating is mainly located within the plasma bulk (the electronegative core), while, when operating at higher pressures (50–500 mTorr), the electron heating appears almost solely within the sheath regions [22,23]. Furthermore, when operating at low pressure, the electron heating within the discharge is due to a hybrid drift-ambipolar-mode (DA-mode) and $\alpha $-mode, and while operating at higher pressures, the discharge is operated in a pure $\alpha $-mode [26,27]. We have also shown that detachment by the singlet molecular metastable states is the process that has the most influence on the electron heating process in the higher pressure regime, while it has almost negligible influence at lower pressures [22,23,24].

## 2. The Simulation

`oopd1`[34,35] is herein applied to a capacitively-coupled oxygen discharge. The

`oopd1`code, like the well-known

`xpdp1`code [7], is a general plasma device simulation tool capable of simulating various types of plasmas, including breakdown, accelerators, beams, as well as processing discharges [20].

`oopd1`code is rather extensive. Like

`xpdp1`, it includes the ground state oxygen molecule O${}_{2}\left({\mathrm{X}}^{3}{\mathsf{\Sigma}}_{\mathrm{g}}^{-}\right)$, the negative ion O${}^{-}$, the positive ion O${}_{2}^{+}$, and electrons [7,20]. In addition, oxygen atoms in the ground state O${(}^{3}$P) and ions of the oxygen atom O${}^{+}$ [20], the singlet metastable molecule O${}_{2}$(a${}^{1}{\Delta}_{\mathrm{g}}$), and the metastable oxygen atom O${(}^{1}$D) [21], and the singlet metastable molecule O${}_{2}$(b${}^{1}{\mathsf{\Sigma}}_{\mathrm{g}}^{+}$) [22] were added along with the relevant reactions and cross-sections. The full oxygen reaction set was discussed in our earlier works where the cross-sections used were also given [20,21,22]. Furthermore,

`oopd1`has energy-dependent secondary electron emission coefficients for oxygen ions and neutrals as they bombard both clean and dirty metal electrodes [22]. Thus, for this current work, the discharge model contains nine species: electrons, the ground state neutrals O(${}^{3}$P) and O${}_{2}\left({\mathrm{X}}^{3}{\mathsf{\Sigma}}_{\mathrm{g}}^{-}\right)$, the negative ions O${}^{-}$, the positive ions O${}^{+}$ and O${}_{2}^{+}$, and the metastables O(${}^{1}$D), O${}_{2}\left({\mathrm{a}}^{1}{\Delta}_{\mathrm{g}}\right)$, and O${}_{2}$(b${}^{1}{\mathsf{\Sigma}}_{\mathrm{g}}^{+})$. We herein use the secondary electron emission yield for a dirty surface as given in our earlier work [22].

`oopd1`[20,21,22,24,27] and in the work of Lichtenberg et al. [9] using the

`xpdp1`code. The discharge electrode separation is assumed to be small compared to the electrode diameter so that the discharge can be treated as one dimensional. We assume the electrode diameter to be 10.25 cm, which is needed in order to determine the absorbed power, and set the discharge volume for the global model calculations applied to determine the partial pressure of the neutral species. The time step $\Delta t$ and the grid spacing $\Delta x$ are set to resolve the electron plasma frequency and the electron Debye length of the low-energy electrons, respectively, according to ${\omega}_{\mathrm{pe}}\Delta t<0.2$, where ${\omega}_{\mathrm{pe}}$ is the electron plasma frequency, and the simulation grid is taken to be uniform and consists of 1000 cells. The electron time step is set to $3.68\times {10}^{-11}$ s. The simulation was run for $5.5\times {10}^{6}$ time steps, which corresponds to 2750 rf cycles. It takes roughly 1700 rf cycles to reach equilibrium for all particles, and the time averaged plasma parameters shown, such as the densities, the electron heating rate, and the effective electron temperature, are averages over 1000 rf cycles. All particle interactions are treated by the Monte Carlo method with a null-collision scheme [4]. For the heavy particles, we use sub-cycling, and the heavy particles are advanced every 16 electron time steps [36]. Furthermore, we assume that the initial density profiles are parabolic [36].

## 3. Results and Discussion

## 4. Conclusions

`oopd1`was applied to explore the evolution of the EEPF and of the electron heating mechanism in a capacitively-coupled oxygen discharge while including and excluding the ion-induced secondary electron emission and electron reflection. Adding secondary electron emission enhances the EEPF with a high energy tail for all the pressures. At 10 mTorr, the EEPF curves outwards. The electron heating at 10 mTorr is a hybrid DA- and $\alpha $-mode heating, and no significant difference is observed including and excluding secondary electron emission from the electrodes. Averaged over one rf cycle, a predominance of the electron heating in the plasma bulk was observed for all the cases. At 25 mTorr, the shape of the EEPF starts to develop an inward curving behavior and a hybrid DA- and $\alpha $-mode heating is observed. The role of sheath heating increases when secondary electron emission from the electrodes is included in the simulation. At 50 mTorr, the transition, which had already started at 25 mTorr, is fully accomplished, and the shape of the EEPF is now bi-Maxwellian, while no electron heating is observed in the plasma bulk.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**The electron energy probability function (EEPF) in the discharge center for a parallel plate capacitively-coupled oxygen discharge at (

**a**) 10 mTorr, (

**b**) 25 mTorr, and (

**c**) 50 mTorr with a surface quenching coefficient for the singlet metastable molecule ${\mathrm{O}}_{2}\left({\mathrm{a}}^{1}{\Delta}_{\mathrm{g}}\right)$ as ${\gamma}_{\mathrm{wqa}}=0.0001$ and a gap separation of 4.5 cm driven by a 222 V voltage source at a driving frequency of 13.56 MHz.

**Figure 2.**The time averaged electron heating profile for a parallel plate capacitively-coupled oxygen discharge at (

**a**) 10 mTorr, (

**b**) 25 mTorr, and (

**c**) 50 mTorr with a surface quenching coefficient for the singlet metastable molecule ${\mathrm{O}}_{2}\left({\mathrm{a}}^{1}{\Delta}_{\mathrm{g}}\right)$ as ${\gamma}_{\mathrm{wqa}}=0.0001$ and a gap separation of 4.5 cm driven by a 222 V voltage source at a driving frequency of 13.56 MHz.

**Figure 3.**The (

**a**) electron density and the (

**b**) electronegativity in the discharge center as a function of pressure for a parallel plate capacitively-coupled oxygen discharge with a surface quenching coefficient for the singlet metastable molecule ${\mathrm{O}}_{2}\left({\mathrm{a}}^{1}{\Delta}_{\mathrm{g}}\right)$ as ${\gamma}_{\mathrm{wqa}}=0.0001$ and a gap separation of 4.5 cm driven by a 222 V voltage source at a driving frequency of 13.56 MHz.

**Figure 4.**The spatio-temporal behavior of the electron power absorption for a parallel plate capacitively-coupled oxygen discharge at 10 mTorr for (

**a**) ${\gamma}_{\mathrm{see}}\left(\mathcal{E}\right)$ and (

**b**) ${\gamma}_{\mathrm{see}}=0.0$, (

**c**) the difference between ${\gamma}_{\mathrm{see}}\left(\mathcal{E}\right)$ and ${\gamma}_{\mathrm{see}}=0.0$, at 25 mTorr, for (

**d**) ${\gamma}_{\mathrm{see}}\left(\mathcal{E}\right)$ and (

**e**) ${\gamma}_{\mathrm{see}}=0.0$, (

**f**) the difference between ${\gamma}_{\mathrm{see}}\left(\mathcal{E}\right)$ and ${\gamma}_{\mathrm{see}}=0.0$, at 50 mTorr for, (

**g**) ${\gamma}_{\mathrm{see}}\left(\mathcal{E}\right)$ and (

**h**) ${\gamma}_{\mathrm{see}}=0.0$, and (

**i**) the difference between ${\gamma}_{\mathrm{see}}\left(\mathcal{E}\right)$ and ${\gamma}_{\mathrm{see}}=0.0$ with a surface quenching coefficient for the singlet metastable molecule ${\mathrm{O}}_{2}\left({\mathrm{a}}^{1}{\Delta}_{\mathrm{g}}\right)$ as ${\gamma}_{\mathrm{wqa}}=0.0001$, $r=0.0$, and a gap separation of 4.5 cm driven by a 222 V voltage source at a driving frequency of 13.56 MHz.

**Figure 5.**The spatio-temporal behavior of the effective electron temperature for a parallel plate capacitively-coupled oxygen discharge at 10 mTorr for (

**a**) ${\gamma}_{\mathrm{see}}\left(\mathcal{E}\right)$ and (

**b**) ${\gamma}_{\mathrm{see}}=0.0$, (

**c**) the difference between ${\gamma}_{\mathrm{see}}=0.0$ and ${\gamma}_{\mathrm{see}}\left(\mathcal{E}\right)$, at 25 mTorr, for (

**d**) ${\gamma}_{\mathrm{see}}\left(\mathcal{E}\right)$, and (

**e**) ${\gamma}_{\mathrm{see}}=0.0$, (

**f**) the difference between ${\gamma}_{\mathrm{see}}=0.0$ and ${\gamma}_{\mathrm{see}}\left(\mathcal{E}\right)$, at 50 mTorr for, (

**g**) ${\gamma}_{\mathrm{see}}\left(\mathcal{E}\right)$ and (

**h**) ${\gamma}_{\mathrm{see}}=0.0$, and (

**i**) the difference between ${\gamma}_{\mathrm{see}}=0.0$ and ${\gamma}_{\mathrm{see}}\left(\mathcal{E}\right)$ with a surface quenching coefficient for the singlet metastable molecule ${\mathrm{O}}_{2}\left({\mathrm{a}}^{1}{\Delta}_{\mathrm{g}}\right)$ as ${\gamma}_{\mathrm{wqa}}=0.0001$, $r=0.0$, and a gap separation of 4.5 cm driven by a 222 V voltage source at a driving frequency of 13.56 MHz.

**Table 1.**The parameters of the simulation, the particle weight, and the energy threshold above which kinetics of the neutral particles are followed.

Species | Particle Weight | Energy Threshold (meV) |
---|---|---|

O${}_{2}\left({\mathrm{X}}^{3}{\mathsf{\Sigma}}_{\mathrm{g}}^{-}\right)$ | $5\times {10}^{7}$ | 500 |

O${}_{2}$(${\mathrm{a}}^{1}{\Delta}_{\mathrm{g}}$) | $5\times {10}^{6}$ | 100 |

O${}_{2}$(${\mathrm{b}}^{1}{\mathsf{\Sigma}}_{\mathrm{g}}$) | $5\times {10}^{6}$ | 100 |

O(${}^{3}$P) | $5\times {10}^{7}$ | 500 |

O(${}^{1}$D) | $5\times {10}^{7}$ | 50 |

O${}_{2}^{+}$ | ${10}^{7}$ | - |

O${}^{+}$ | ${10}^{6}$ | - |

O${}^{-}$ | $5\times {10}^{7}$ | - |

e | $1\times {10}^{7}$ | - |

**Table 2.**The partial pressures of the thermal neutrals at 10, 25, and 50 mTorr for the wall quenching coefficient for the singlet metastable molecule O${}_{2}$(a${}^{1}{\Delta}_{\mathrm{g}})$ of ${\gamma}_{\mathrm{wqa}}=0.0001$ calculated by a global (volume averaged) model.

Pressure | O${}_{2}$$\left({\mathbf{X}}^{3}{\mathsf{\Sigma}}_{\mathbf{g}}^{-}\right)$ | O${}_{2}($a${}^{1}{\Delta}_{\mathbf{g}})$ | O${}_{2}($b${}^{1}{\mathsf{\Sigma}}_{\mathbf{g}})$ | O${(}^{3}$P) |
---|---|---|---|---|

10 mTorr | $0.9684$ | $0.0265$ | $0.0018$ | $0.0015$ |

25 mTorr | $0.9607$ | $0.0350$ | $0.0019$ | $0.0007$ |

50 mTorr | $0.9739$ | $0.0215$ | $0.0022$ | $0.0004$ |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Proto, A.; Gudmundsson, J.T.
The Influence of Secondary Electron Emission and Electron Reflection on a Capacitively Coupled Oxygen Discharge. *Atoms* **2018**, *6*, 65.
https://doi.org/10.3390/atoms6040065

**AMA Style**

Proto A, Gudmundsson JT.
The Influence of Secondary Electron Emission and Electron Reflection on a Capacitively Coupled Oxygen Discharge. *Atoms*. 2018; 6(4):65.
https://doi.org/10.3390/atoms6040065

**Chicago/Turabian Style**

Proto, Andrea, and Jon Tomas Gudmundsson.
2018. "The Influence of Secondary Electron Emission and Electron Reflection on a Capacitively Coupled Oxygen Discharge" *Atoms* 6, no. 4: 65.
https://doi.org/10.3390/atoms6040065