One-dimensional simulation of Ar dielectric barrier discharge driven by combined rf/dc sources at atmospheric pressure

Qi Bing; Tian Xiao; Wang Jing; Wang Yi-Shan; Si Jin-Hai; Tang Jie

doi:10.7498/aps.71.20221361

Abstract

We present the dielectric barrier discharge (DBD) mechanism of argon (Ar) plasma driven by a combination of radio frequency (rf) voltage source and direct current (dc) voltage source at atmospheric pressure, based on one-dimensional self-consistent coupled fluid model. Using the finite element method (FEM) to numerically calculate the model, the average value of period average electron density varying with the average value of period average gas voltage in one rf period, and the variation of the minimum rf sustaining voltage are obtained under different dc voltages. In addition, the spatiotemporal distribution of the electron density and electron generation rate, the spatial distribution of electron temperature, and the time-domain variation of electron conduction current flowing to the dielectric are studied. The results show that the introduction of the dc voltage source has a significant effect on the rf discharge process of atmospheric pressure Ar gas, and the parameters of the plasma state are changed correspondingly. The discharge process is mainly controlled by the air gap voltage, and the dc voltage affects the gap voltage by changing the charge density on the dielectric surface. The minimum rf sustaining voltage V_rf,minfirst increases and then decreases with the increase of dc voltage. The amplitude of rf minimum sustaining discharge voltage is changed by the dc voltage. And when the amplitude is reached or exceeded, the discharge is controlled by the rf power supply.On the one hand, in the α mode, when the dc voltage is low, electrons are generated near the ground electrode. The electric field intensity in the ionization area is too small to maintain ionization. When the dc voltage is high, the sheath is formed, and electrons are generated near the rf sheaths on both sides and the boundary of the plasma region. In the γ mode, when the rf voltage amplitude is equal to or greater than the rf minimum sustain discharge voltage amplitude, i.e. V_rf≥ V_rf,min, the generation and distribution of electrons are almost unaffected by the dc voltage.On the other hand, in the α mode, the ionization cannot be sustained for the low dc voltage, resulting in the failure to form the main plasma area. Therefore, the electron temperature is generally high. Owing to the high electron density near the ground electrode, the electron temperature is higher. The electron density near the dielectric is less than that near the electrode, so the temperature is lower. When the dc voltage is getting larger, the sheath and the main plasma region are formed. The dc voltage significantly affects the electron temperature by controlling the sheath voltage and the length of the main plasma region.Finally, in the α mode, the electron density near the medium is very low and the air gap voltage is negative for the low dc voltage. As a result, few electrons can reach the surface of the dielectric, and the conduction current of electrons flowing to the medium is very small. With the increase of the dc voltage, the electric field across air gap increases, and electrons, under the action of the electric field, flow from the dielectric surface. The sheath having formed, some speedy non-localization electrons that have reached the dielectric surface are reflected back to the sheath, resulting in a significant reduction in the number of electrons that can reach the dielectric surface.

Keywords:

Authors and contacts

1.
State Key Laboratory of Transient Optics and Photonics, Xi’an Institute of Optics and Precision Mechanics of Chinese Academy of Sciences, Xi’an 710119, China
2.
University of Chinese Academy of Sciences, Beijing 100049, China
3.
Shaanxi Key Lab of Information Photonic Technique, School of Electronic Science and Engineering, Xi’an Jiaotong University, Xi’an 710049, China
4.
School of Science, Xi’an University of Science and Technology, Xi’an 710054, China
5.
School of Science, Xi’an Aeronautical University, Xi’an 710077, China

Corresponding author: Tang Jie, tangjie@opt.ac.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 51877210, 52177166), the Natural Science Foundation of Shaanxi Province, China (Grant No. 2020JM-309), the Open Research Fund of Key Laboratory of Spectral Imaging Technology, Chinese Academy of Sciences (Grant No. LSIT201807G), the Natural Science Basic Research Program of Shaanxi Province, China (Grant No. 2019JCW-03), the Key Deployment Research Program of XIOPM, China (Grant No. S19-020-III), and the Major Science and Technology Infrastructure Pre-research Program of Chinese Academy of Sciences, China (Grant No. J20-021-III).

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References

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[2]	Wang J, Lei B Y, Xu Y G, Wang Y S, Tang J, Zhao W, Duan Y X 2020 Phys. Plasmas 27 043501 Google Scholar
[3]	Tang J, Duan Y X, Zhao W 2010 Appl. Phys. Lett. 96 191503 Google Scholar
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[9]	万海容, 郝艳捧, 房强, 苏恒炜, 阳林, 李立浧 2020 69 145203 Google Scholar Wan H R, Hao Y P, Fang Q, Su H W, Yang L, Li L C 2020 Acta Phys. Sin. 69 145203 Google Scholar
[10]	Kohler K, Coburn J W, Horne D E, Kay E, Keller J H 1985 J. Appl. Phys. 57 59 Google Scholar
[11]	Tian X B, Li J, Tian L, Gong C Z, Yang S Q, Chu K 2011 Surf. Coat. Technol. 206 1016 Google Scholar
[12]	Oyanagi Y, Hibino Y, Sawamoto N, Wakabayashi H, Ogura A 2020 Jpn. J. Appl. Phys. 59 065502 Google Scholar
[13]	Li H X, Xu T, Chen J M, Zhou H D, Liu H W 2004 Appl. Surf. Sci. 227 364 Google Scholar
[14]	解艳凤, 施芸城, 黄晓江, 石建军, 郭颖 2013 真空科学与技术学报 33 893 Xie Y F, Shi Y C, Huang X J, Shi J J, Guo Y 2013 Chin. J. Vac. Sci. Technol. 33 893
[15]	张权治 2014 博士学位论文 (大连: 大连理工大学) Zhang Q Z 2014 Ph. D. Dissertation (Dalian: Dalian University of Technology) (in Chinese)
[16]	Diomede P, Longo S, Economou D J, Capitelli M 2012 J. Phys. D: Appl. Phys. 45 175204 Google Scholar
[17]	Radmilović-Radjenović M, Radjenović B 2006 Plasma Sources Sci. Technol. 15 1 Google Scholar
[18]	Kawamura E, Lieberman M A, Lichtenberg A J 2007 J. Vac. Sci. Technol. , A 25 1456 Google Scholar
[19]	Wang S, Xu X, Wang Y N 2012 Plasma Sci. Technol. 14 32 Google Scholar
[20]	Kawajiri K, Ramachandran K, Nishiyama H 2005 Int. J. Heat. Mass Transfer 48 183 Google Scholar
[21]	罗海云, 冉俊霞, 王新新 2012 高电压技术 38 1070 Luo H Y, Ran J X, Wang X X 2012 High Voltage Eng. 38 1070
[22]	张增辉, 邵先军, 张冠军, 李娅西, 彭兆裕 2012 61 045205 Google Scholar Zhang Z H, Shao X J, Zhang G J, Li Y X, Peng Z Y 2012 Acta Phys. Sin. 61 045205 Google Scholar
[23]	胡艳婷, 张钰如, 宋远红, 王友年 2018 67 225203 Google Scholar Hu Y T, Zhang Y R, Song Y H, Wang Y N 2018 Acta Phys. Sin. 67 225203 Google Scholar
[24]	Balcon N, Hagelaar G J M, Boeuf J P 2008 IEEE Trans. Plasma Sci. 36 2782 Google Scholar
[25]	Ballah Z, Khelfaoui F 2020 J. King. Saud. Univ. Sci. 32 620 Google Scholar
[26]	Dyatko N A, Ionikh Y Z, Kochetov I V, Marinov D L, Meshchanov A V, Napartovich A P, Petrov F B, Starostin S A 2008 J. Phys. D: Appl. Phys. 41 055204 Google Scholar
[27]	Hagelaar G J M, Pitchford L C 2005 Plasma Sources Sci. Technol. 14 722 Google Scholar
[28]	Min B, Lee S H, Park H G 2000 J. Vac. Sci. Technol. A 18 349 Google Scholar
[29]	Makabe T, Petrovic Z 2014 Plasma Electronics: Applications in Microelectronic Device Fabrication Second Edition (New York and London: Taylor & Francis Group) pp268–269
[30]	Lisovsikiy V A, Kharchenko N D, Yegorenkov V D 2008 J. Phys. D: Appl. Phys. 41 125207 Google Scholar
[31]	E E Kunhardt 2000 IEEE Trans. Plasma Sci. 28 189 Google Scholar
[32]	Tarnev K, Pavlova R 2019 J. Plasma Phys. 85 905850201 Google Scholar
[33]	Brenning N, Gudmundsson J T, Lundin D, Minea T, Raadu M A, Helmersson U 2016 Plasma Sources Sci. Technol. 25 065024 Google Scholar
[34]	Lieberman M A, Lichtenberg A J 2005 Principles of Plasma Discharges and Materials Processing (New York: Wiley-Interscience Press) pp360–362
[35]	Balcon N, Aanesland A, Boswell R W 2007 Plasma Sources Sci. Technol. 16 217 Google Scholar
[36]	Wei J, Xiang X, Zhong L D, Wang Y N 2008 Phys. Plasmas 15 033502 Google Scholar

Cited By

图 1 (a) 放电模型结构; (b) 径向网格剖分图

Figure 1. (a) Structure diagram of discharge model; (b) radial meshing diagram.

DownLoad: Full-Size Img PowerPoint

图 2 (a)—(k) DBD放电参数时域波形; (l) 射频最小维持放电电压振幅随直流电压的变化曲线

Figure 2. (a)–(k) Time domain waveform of DBD discharge parameters; (l) variation of rf minimum sustaining discharge voltage amplitude with dc voltage.

DownLoad: Full-Size Img PowerPoint

图 3 不同直流电压下, 周期平均电子密度平均值随周期平均气体电压平均值的变化　(a) 0 V; (b) –100 V; (c) –200 V; (d) –300 V; (e) –400 V; (f) –500 V; (g) 0— –500 V

Figure 3. Average value of period average electron density varying with the average value of period average gas voltage with different voltage: (a) 0 V; (b) –100 V; (c) –200 V; (d) –300 V; (e) –400 V; (f) –500 V; (g) 0− –500 V.

DownLoad: Full-Size Img PowerPoint

图 4 V_rf = 55 V条件下, 直流电压为(a) 0, (b) –100, (c) –200, (d) –300, (e) –400和(f) –500 V时, 电子产生率时空分布; (g) 周期平均电子密度径向分布

Figure 4. Under the condition of V_rf = 55 V, spatial-temporal distribution of electron generation rate at different dc voltage of (a) 0, (b) –100, (c) –200, (d) –300, (e) –400 and (f) –500 V; (g) radial distribution of period average electron density.

DownLoad: Full-Size Img PowerPoint

图 5 V_rf = 500 V条件下, 直流电压分别为(a) 0, (b) –100, (c) –200, (d) –300, (e) –400和(f) –500 V时, 电子产生率时空分布;(g) 周期平均电子密度径向分布

Figure 5. Under the condition of V_rf = 500 V, spatial-temporal distribution of electron generation rate with dc voltage of (a) 0, (b) –100, (c) –200, (d) –300, (e) –400 and (f) –500 V; (g) radial distribution of period average electron density.

DownLoad: Full-Size Img PowerPoint

图 6 不同直流电压下, 周期平均电子温度径向分布(V_rf = 55 V)

Figure 6. Radial distribution of the period average electron temperature with different dc voltages (V_rf = 55 V).

DownLoad: Full-Size Img PowerPoint

图 7 V_rf = 55 V时, 不同直流电压下, (a)流向介质表面的电子传导电流密度; (b) 周期平均气体电压径向分布

Figure 7. Under different dc voltage and V_rf = 55 V, (a) electron conduction current density on dielectric surface; (b) radial distribution of period average gas voltage.

DownLoad: Full-Size Img PowerPoint

表 1 本文放电模型中所涉及的化学反应

Table 1. Chemical reaction formulas used in the discharge model.

反应方程	反应系数
${\text{e + Ar} } \to {\text{2e + A} }{ {\text{r} }^{\text{ + } } }$	BOLSIG+
$ {\text{e + Ar}} \to {\text{e + A}}{{\text{r}}^{\text{*}}} $	BOLSIG+
${\rm{e}} + {\rm{A}}{{\rm{r}}^*} \to 2 {\rm{e}} + {\rm{A}}{{\rm{r}}^ + }$	BOLSIG+
$2 {\rm{A}}{{\rm{r}}^*} \to {\rm{e}} + {\rm{A}}{{\rm{r}}^ + } + {\rm{Ar}}$	1.2×10^–9×N_A cm³·s^–1
${\rm{A}}{{\rm{r}}^ + } + 2 {\rm{Ar}} \to {\rm{Ar}}_2^ + + {\rm{Ar}}$	2.5×10^–31×$ N_{\rm A}^2 $ cm⁶·s^–1
${\rm{e}} + {\rm{Ar}}_2^ + \to {\rm{A}}{{\rm{r}}^*} + {\rm{Ar}}$	7×10^–7×(300/T_e×11600)^1/2×N_A cm³·s^–1
${\rm{A} }{ {\rm{r} }^*} \to {\rm{Ar} } + {{h} }\nu$	5×10⁵ s^–1
${\rm{e}} + {\rm{Ar}} \to {\rm{e}} + {\rm{Ar}}$	BOLSIG+

DownLoad: CSV

map

[1]	高书涵, 王绪成, 张远涛 2020 69 115204 Google Scholar Gao S H, Wang X C, Zhang Y T 2020 Acta Phys. Sin. 69 115204 Google Scholar
[2]	Wang J, Lei B Y, Xu Y G, Wang Y S, Tang J, Zhao W, Duan Y X 2020 Phys. Plasmas 27 043501 Google Scholar
[3]	Tang J, Duan Y X, Zhao W 2010 Appl. Phys. Lett. 96 191503 Google Scholar
[4]	孔德霖, 杨冰彦, 何锋, 韩若愚, 缪劲松, 宋廷鲁, 欧阳吉庭 2021 70 095205 Google Scholar Kong D L, Yang B Y, He F, Han R Y, Miao J S, Song Y L, Ouyang J T 2021 Acta Phys. Sin. 70 095205 Google Scholar
[5]	Zhang S, Gao Y, Sun H, Bai H, Wang R X, Shao T 2018 J. Phys. D: Appl. Phys. 51 274005 Google Scholar
[6]	Shao T, Liu F, Hai B, Ma Y F, Wang R X, Ren C Y 2017 IEEE Trans. Dielectr. Electr. Insul. 24 1557 Google Scholar
[7]	Inglezakis V J, Amzebek A, Kuspangaliyeva B, Sarbassov Y, Balbayeva G, Yerkinova A, Poulopoulos S G 2018 Desalin. Water Treat. 112 218 Google Scholar
[8]	Xiong Z, Lu X, Cao Y, Ning Q, Ostrikov, Lu Y, Zhou X, Liu J 2011 Appl. Phys. Lett. 99 253703 Google Scholar
[9]	万海容, 郝艳捧, 房强, 苏恒炜, 阳林, 李立浧 2020 69 145203 Google Scholar Wan H R, Hao Y P, Fang Q, Su H W, Yang L, Li L C 2020 Acta Phys. Sin. 69 145203 Google Scholar
[10]	Kohler K, Coburn J W, Horne D E, Kay E, Keller J H 1985 J. Appl. Phys. 57 59 Google Scholar
[11]	Tian X B, Li J, Tian L, Gong C Z, Yang S Q, Chu K 2011 Surf. Coat. Technol. 206 1016 Google Scholar
[12]	Oyanagi Y, Hibino Y, Sawamoto N, Wakabayashi H, Ogura A 2020 Jpn. J. Appl. Phys. 59 065502 Google Scholar
[13]	Li H X, Xu T, Chen J M, Zhou H D, Liu H W 2004 Appl. Surf. Sci. 227 364 Google Scholar
[14]	解艳凤, 施芸城, 黄晓江, 石建军, 郭颖 2013 真空科学与技术学报 33 893 Xie Y F, Shi Y C, Huang X J, Shi J J, Guo Y 2013 Chin. J. Vac. Sci. Technol. 33 893
[15]	张权治 2014 博士学位论文 (大连: 大连理工大学) Zhang Q Z 2014 Ph. D. Dissertation (Dalian: Dalian University of Technology) (in Chinese)
[16]	Diomede P, Longo S, Economou D J, Capitelli M 2012 J. Phys. D: Appl. Phys. 45 175204 Google Scholar
[17]	Radmilović-Radjenović M, Radjenović B 2006 Plasma Sources Sci. Technol. 15 1 Google Scholar
[18]	Kawamura E, Lieberman M A, Lichtenberg A J 2007 J. Vac. Sci. Technol. , A 25 1456 Google Scholar
[19]	Wang S, Xu X, Wang Y N 2012 Plasma Sci. Technol. 14 32 Google Scholar
[20]	Kawajiri K, Ramachandran K, Nishiyama H 2005 Int. J. Heat. Mass Transfer 48 183 Google Scholar
[21]	罗海云, 冉俊霞, 王新新 2012 高电压技术 38 1070 Luo H Y, Ran J X, Wang X X 2012 High Voltage Eng. 38 1070
[22]	张增辉, 邵先军, 张冠军, 李娅西, 彭兆裕 2012 61 045205 Google Scholar Zhang Z H, Shao X J, Zhang G J, Li Y X, Peng Z Y 2012 Acta Phys. Sin. 61 045205 Google Scholar
[23]	胡艳婷, 张钰如, 宋远红, 王友年 2018 67 225203 Google Scholar Hu Y T, Zhang Y R, Song Y H, Wang Y N 2018 Acta Phys. Sin. 67 225203 Google Scholar
[24]	Balcon N, Hagelaar G J M, Boeuf J P 2008 IEEE Trans. Plasma Sci. 36 2782 Google Scholar
[25]	Ballah Z, Khelfaoui F 2020 J. King. Saud. Univ. Sci. 32 620 Google Scholar
[26]	Dyatko N A, Ionikh Y Z, Kochetov I V, Marinov D L, Meshchanov A V, Napartovich A P, Petrov F B, Starostin S A 2008 J. Phys. D: Appl. Phys. 41 055204 Google Scholar
[27]	Hagelaar G J M, Pitchford L C 2005 Plasma Sources Sci. Technol. 14 722 Google Scholar
[28]	Min B, Lee S H, Park H G 2000 J. Vac. Sci. Technol. A 18 349 Google Scholar
[29]	Makabe T, Petrovic Z 2014 Plasma Electronics: Applications in Microelectronic Device Fabrication Second Edition (New York and London: Taylor & Francis Group) pp268–269
[30]	Lisovsikiy V A, Kharchenko N D, Yegorenkov V D 2008 J. Phys. D: Appl. Phys. 41 125207 Google Scholar
[31]	E E Kunhardt 2000 IEEE Trans. Plasma Sci. 28 189 Google Scholar
[32]	Tarnev K, Pavlova R 2019 J. Plasma Phys. 85 905850201 Google Scholar
[33]	Brenning N, Gudmundsson J T, Lundin D, Minea T, Raadu M A, Helmersson U 2016 Plasma Sources Sci. Technol. 25 065024 Google Scholar
[34]	Lieberman M A, Lichtenberg A J 2005 Principles of Plasma Discharges and Materials Processing (New York: Wiley-Interscience Press) pp360–362
[35]	Balcon N, Aanesland A, Boswell R W 2007 Plasma Sources Sci. Technol. 16 217 Google Scholar
[36]	Wei J, Xiang X, Zhong L D, Wang Y N 2008 Phys. Plasmas 15 033502 Google Scholar

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