Hybrid simulation of radio frequency biased inductively coupled Ar/O<sub>2</sub>/Cl<sub>2</sub> plasmas

Tong Lei; Zhao Ming-Liang; Zhang Yu-Ru; Song Yuan-Hong; Wang You-Nian

doi:10.7498/aps.73.20231369

Abstract

In the etching process, a bias source is usually applied to the substrate of the inductively coupled plasma (ICP) to realize independent modulation of the ion energy and ion flux. In this work, a hybrid model, i.e. a global model combined bi-directionally with a fluid sheath model, is employed to investigate the plasma properties and ion energy distribution function (IEDF) in biased inductively coupled Ar/O₂/Cl₂ plasmas. The results indicate that at a bias frequency of 2.26 MHz, the Cl^– ion density and ClO⁺ ion density first increase with bias voltage rising, and then they decrease, and finally they rise again, which is different from the densities of other charged species, such as O and Cl atoms. At the bias frequency of 13.56 MHz and 27.12 MHz, except Cl^– and $ {\text{Cl}}_2^ + $ ions, the evolutions of other species densities with bias voltage are similar to the results at lower bias frequency. The evolution of the species densities with bias frequency depends on the bias voltage. For instance, in the low bias voltage range (< 200 V), the densities of charges species, O and Cl atoms increase with bias frequency increasing due to a significant increase in the heating of the plasma by the bias source. However, when the bias voltage is high, say, higher than 300 V, except $ {\text{Cl}}_2^ + $ and Cl^– ions, the densities of other charged species, O and Cl atoms first decrease with bias frequency increasing and then they increase due to a decrease and then an increase in the heating of the plasma by the bias source. In addition, as the bias frequency increases, the peak separation of IEDF becomes narrow, the high energy peak and low energy peak approach each other and they almost merge into one peak at high bias frequency. The results obtained in this work are of significant importance in improving the etching process.

Keywords:

Authors and contacts

Key Laboratory of Materials Modification by Laser, Ion, and Electron Beams, Ministry of Education, School of Physics, Dalian University of Technology, Dalian 116024 China

Corresponding author: Zhang Yu-Ru, yrzhang@dlut.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 12275041, 11935005, 12020101005).

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References

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Cited By

图 1 混合模型示意图

Figure 1. Schematic of configuration for the hybrid model.

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图 2 不同偏压频率下, 基态中性粒子密度随偏压幅值的变化

Figure 2. Evolutions of the densities of ground state neutral particles with bias voltage for different bias frequencies.

DownLoad: Full-Size Img PowerPoint

图 3 不同偏压频率下, 吸收功率和损失功率随偏压幅值的变化　(a) 2.26 MHz; (b) 6.78 MHz; (c) 13.56 MHz; (d) 27.12 MHz

Figure 3. Evolutions of the power deposition and power loss with bias voltage for different bias frequencies: (a) 2.26 MHz; (b) 6.78 MHz; (c) 13.56 MHz; (d) 27.12 MHz.

DownLoad: Full-Size Img PowerPoint

图 4 不同偏压频率下, ClO分子的产生速率和损失速率随偏压幅值的变化　(a) 2.26 MHz; (b) 6.78 MHz; (c) 13.56 MHz; (d) 27.12 MHz

Figure 4. Evolutions of the generation and loss rates of ClO molecules with bias voltage for different bias frequencies: (a) 2.26 MHz; (b) 6.78 MHz; (c) 13.56 MHz; (d) 27.12 MHz.

DownLoad: Full-Size Img PowerPoint

图 5 不同偏压频率下, 带电粒子密度随偏压幅值的变化　(a) Ar⁺; (b) $ {\text{O}}_2^ + $; (c) O⁺; (d) O^–; (e) $ {\text{Cl}}_2^ + $; (f) Cl⁺; (g) Cl^–; (h) ClO⁺; (i) 电子密度

Figure 5. Evolutions of the densities of charged species with bias voltage for different bias frequencies: (a) Ar⁺; (b) $ {\text{O}}_2^ + $; (c) O⁺; (d) O^–; (e) $ {\text{Cl}}_2^ + $; (f) Cl⁺; (g) Cl^–; (h) ClO⁺; (i) electron density.

DownLoad: Full-Size Img PowerPoint

图 6 不同偏压频率下, Cl^–离子的产生速率和损失速率随偏压幅值的变化　(a) 2.26 MHz; (b) 6.78 MHz; (c) 13.56 MHz; (d) 27.12 MHz

Figure 6. Evolutions of the generation and loss rates of Cl^– ions with bias voltage for different bias frequencies: (a) 2.26 MHz; (b) 6.78 MHz; (c) 13.56 MHz; (d) 27.12 MHz.

DownLoad: Full-Size Img PowerPoint

图 7 不同偏压频率下, ClO⁺离子的产生速率和损失速率随偏压幅值的变化　(a) 2.26 MHz; (b) 6.78 MHz; (c) 13.56 MHz; (d) 27.12 MHz

Figure 7. Evolutions of the generation and loss rates of ClO⁺ ions with bias voltage for different bias frequencies: (a) 2.26 MHz; (b) 6.78 MHz; (c) 13.56 MHz; (d) 27.12 MHz.

DownLoad: Full-Size Img PowerPoint

图 8 偏压频率为27.12 MHz时, $ {\text{Cl}}_2^ + $离子的产生速率和损失速率随偏压幅值的变化

Figure 8. Evolutions of the generation and loss rates of $ {\text{Cl}}_2^ + $ ions with bias voltage at bias frequency of 27.12 MHz.

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图 9 不同偏压频率下, 解离率随偏压幅值的变化　(a) Cl₂ (ν = 0); (b) O₂

Figure 9. Evolutions of the dissociation fraction with bias voltage for different bias frequencies: (a) Cl₂ (ν = 0); (b) O₂

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图 10 不同偏压频率下, 电负度随偏压幅值的变化

Figure 10. Evolution of the electronegativity with bias voltage for different bias frequencies.

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图 11 不同偏压频率和幅值下, Ar⁺离子的离子能量角度分布

Figure 11. IEADFs of Ar⁺ ions for different bias frequencies and bias voltages.

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图 12 偏压幅值为125 V, 不同偏压频率下各离子的能量分布　(a) $ {\text{O}}_2^ + $; (b) O⁺; (c) $ {\text{Cl}}_2^ + $; (d) Cl⁺

Figure 12. IEDFs of ions for different bias frequencies at bias voltage of 125 V: (a) $ {\text{O}}_2^ + $; (b) O⁺; (c) $ {\text{Cl}}_2^ + $; (d) Cl⁺.

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表 1 Ar/O₂/Cl₂混合气体放电中考虑的粒子

Table 1. Plasma species considered in Ar/O₂/Cl₂ discharges.

基态中性粒子	Ar, O₂, O₃, O, Cl₂ (ν = 0), Cl, ClO
激发态中性粒子	Ar^m, Ar^r, Ar(4p), O₂(a), O(D), Cl₂ (ν = 1), Cl₂ (ν = 2), Cl₂ (ν = 3)
正离子	Ar⁺, $ {\text{O}}_2^ + $, O⁺, $ {\text{Cl}}_2^ + $, Cl⁺, ClO⁺
负离子/电子	O^–, Cl^–, e

DownLoad: CSV

表 2 中性粒子与器壁的相互作用^[6,29-32,35]

Table 2. Reactions of neutral species on the wall^[6,29-32,35].

No.	Reaction	${\gamma _l}$
1	${\text{Cl + wall }} \to {\text{ }}\dfrac{{1}}{{2}}{\text{C}}{{\text{l}}_{2}}\left( {\nu = {0}} \right)$	方程(3)
2	${\text{Cl + wall }} \to {\text{ }}\dfrac{{1}}{{2}}{\text{ClO}}$	方程(4)
3	${\text{O + wall }} \to {\text{ }}\dfrac{{1}}{{2}}{{\text{O}}_{2}}$	0.09
4	${\text{O}}\left( {\text{D}} \right){\text{ + wall }} \to {\text{ }}\dfrac{{1}}{{2}}{{\text{O}}_{2}}$	0.09
5	${\text{C}}{{\text{l}}_{2}}\left( \nu \right){\text{ + wall }} \to {\text{ C}}{{\text{l}}_{2}}\left( {\nu - {1}} \right)$	1
6	${{\text{O}}_{2}}\left( {\text{a}} \right){\text{ + wall }} \to {\text{ }}{{\text{O}}_{2}}$	0.007
7	${\text{O}}\left( {\text{D}} \right){\text{ + wall }} \to {\text{ O}}$	0.1
8	${\text{A}}{{\text{r}}^ * }{\text{ + wall }} \to {\text{ Ar}}$	1

DownLoad: CSV

表 3 偏压频率为13.56 MHz时, 不同偏压幅值下的时间平均鞘层厚度和鞘层电压降

Table 3. Time-averaged sheath thickness and voltage drop across the sheath for different bias voltage amplitudes, at bias frequency of 13.56 MHz.

	25 V	50 V	75 V	100 V	125 V	150 V	175 V	200 V
${\bar d_{\text{s}}}{\text{ /mm}}$	4.67	4.75	4.79	4.80	4.81	4.85	4.93	5.03
${\bar V_{\text{s}}}{\text{ /V}}$	31.32	55.47	79.98	104.63	129.34	154.1	178.88	203.70

DownLoad: CSV

map

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[5]	Lee Y J, Han H R, Lee J, Yeom G Y 2000 Surf. Coat. Technol. 131 257 Google Scholar
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[7]	Wen D, Zhang Y, Lieberman M A, Wang Y 2017 Plasma Processes Polym. 14 1600100 Google Scholar
[8]	Zhang Y R, Gao F, Li X C, Bogaerts A, Wang Y N 2015 J. Vac. Sci. Technol., A 33 061303 Google Scholar
[9]	Lee H C, Lee M H, Chung C W 2010 Appl. Phys. Lett. 96 071501 Google Scholar
[10]	Lee H C, Chung C W 2012 Appl. Phys. Lett. 101 244104 Google Scholar
[11]	Lee H C, Bang J Y, Chung C W 2011 Thin Solid Films 519 7009 Google Scholar
[12]	Lee C, Lieberman M A 1995 J. Vac. Sci. Technol., A 13 368 Google Scholar
[13]	Gudmundsson J T 2004 J. Phys. D: Appl. Phys. 37 2073 Google Scholar
[14]	Jung J, Kim M S, Park J, Lim C M, Hwang T W, Seo B J, Chung C W 2023 Phys. Plasmas 30 023504 Google Scholar
[15]	Tong L, Zhang Y R, Huang J W, Zhao M L, Wen D Q, Song Y H, Wang Y N 2021 Phys. Plasmas 28 053512 Google Scholar
[16]	Tong L, Zhao M L, Zhang Y R, Song Y H, Wang Y N 2023 J. Phys. D: Appl. Phys. 56 365202
[17]	Khater M H, Overzet L J 2004 Plasma Sources Sci. Technol. 13 466 Google Scholar
[18]	Dai Z L, Zhang S Q, Wang Y N 2013 Vacuum 89 197 Google Scholar
[19]	Zhang S Q, Dai Z L, Song Y H, Wang Y N 2014 Vacuum 99 180 Google Scholar
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[22]	Malyshev M V, Donnelly V M, Colonell J I, Samukawa S 1999 J. Appl. Phys. 86 4813 Google Scholar
[23]	Malyshev M V, Donnelly V M 2000 Plasma Sources Sci. Technol. 9 353 Google Scholar
[24]	Donnelly V M, Malyshev M V 2000 Appl. Phys. Lett. 77 2467 Google Scholar
[25]	Malyshev M V, Donnelly V M 2001 J. Appl. Phys. 90 1130 Google Scholar
[26]	Malyshev M V, Fuller N C M, Bogart K H A, Donnelly V M, Herman I P 2000 J. Appl. Phys. 88 2246 Google Scholar
[27]	Malyshev M V, Donnelly V M 2000 J. Appl. Phys. 88 6207 Google Scholar
[28]	Malyshev M V, Donnelly V M 2000 J. Appl. Phys. 87 1642 Google Scholar
[29]	Thorsteinsson E G, Gudmundsson J T 2010 Plasma Sources Sci. Technol. 19 015001 Google Scholar
[30]	Thorsteinsson E G, Gudmundsson J T 2010 J. Phys. D: Appl. Phys. 43 115201 Google Scholar
[31]	Thorsteinsson E G, Gudmundsson J T 2010 J. Phys. D: Appl. Phys. 43 115202 Google Scholar
[32]	Thorsteinsson E G, Gudmundsson J T 2010 Plasma Sources Sci. Technol. 19 055008 Google Scholar
[33]	Gudmundsson J T, Hjartarson A T, Thorsteinsson E G 2012 Vacuum 86 808 Google Scholar
[34]	Zhang Y R, Zhao Z Z, Xue C, Gao F, Wang Y N 2019 J. Phys. D: Appl. Phys. 52 295204
[35]	Liu W, Wen D Q, Zhao S X, Gao F, Wang Y N 2015 Plasma Sources Sci. Technol. 24 025035 Google Scholar
[36]	范惠泽, 刘凯, 黄永清, 蔡世伟, 任晓敏, 段晓峰, 王琦, 刘昊, 吴瑶, 费嘉瑞 2017 真空科学与技术学报 37 286 Google Scholar Fan H Z, Liu K, Huang Y Q, Cai S W, Ren X M, Duan X F, Wang Q, Liu H, Wu Y, Fei J R 2017 Chin. J. Vac. Sci. Technol. 37 286 Google Scholar
[37]	Smith S A, Lampert W V, Rajagopal P, Banks A D, Thomson D, Davis R F 2000 J. Vac. Sci. Technol., A 18 879 Google Scholar
[38]	Lee J M, Chang K M, Lee I H, Park S J 2000 J. Vac. Sci. Technol., B 18 1409 Google Scholar
[39]	Taube A, Kamiński M, Ekielski M, et al. 2021 Mater. Sci. Semicond. Process. 122 105450 Google Scholar
[40]	Chung C W, Chung I 2000 J. Vac. Sci. Technol., A 18 835 Google Scholar
[41]	Park J S, Kim T H, Choi C S, Hahn Y B 2002 Korean J. Chem. Eng. 19 486 Google Scholar
[42]	Kwon K H, Efremov A, Yun S J, Chun I, Kim K 2014 Thin Solid Films 552 105 Google Scholar
[43]	Kang S, Efremov A, Yun S J, Son J, Kwon K H 2013 Plasma Chem. Plasma Process. 33 527 Google Scholar
[44]	Tinck S, Boullart W, Bogaerts A 2009 J. Phys. D: Appl. Phys. 42 095204 Google Scholar
[45]	Tinck S, Boullart W, Bogaerts A 2011 Plasma Sources Sci. Technol. 20 045012 Google Scholar
[46]	Tinck S, Bogaerts A, Shamiryan D 2011 Plasma Processes Polym. 8 490 Google Scholar
[47]	Hsu C C, Coburn J W, Graves D B 2006 J. Vac. Sci. Technol., A 24 1 Google Scholar
[48]	Efremov A, Amirov I, Izyumov M 2023 Vacuum 207 111664 Google Scholar
[49]	Hsu C C, Nierode M A, Coburn J W, Graves D B 2006 J. Phys. D: Appl. Phys. 39 3272 Google Scholar
[50]	Schulze J, Schüngel E, Czarnetzki U 2012 Appl. Phys. Lett. 100 024102 Google Scholar
[51]	Ahr P, Schüngel E, Schulze J, Tsankov T V, Czarnetzki U 2015 Plasma Sources Sci. Technol. 24 044006 Google Scholar
[52]	Lieberman M A, Lichtenberg A J 2005 Principles of Plasma Discharges and Materials Processing (Hoboken, NJ, USA: John Wiley & Sons, Inc.) p268
[53]	张钰如, 高飞, 王友年 2021 70 095206 Google Scholar Zhang Y R, Gao F, Wang Y N A 2021 Acta Phys. Sin. 70 095206 Google Scholar
[54]	Yang W, Zhao S X, Wen D Q, Liu W, Liu Y X, Li X C, Wang Y N 2016 J. Vac. Sci. Technol., A 34 031305 Google Scholar
[55]	Toneli D A, Pessoa R S, Roberto M, Gudmundsson J T 2015 J. Phys. D: Appl. Phys. 48 325202 Google Scholar
[56]	Proto A 2021 Ph. D. Dissertation (Iceland: University of Iceland
[57]	Stafford L, Khare R, Guha J, Donnelly V M, Poirier J S, Margot J 2009 J. Phys. D: Appl. Phys. 42 055206 Google Scholar
[58]	Guha J, Donnelly V M 2009 J. Appl. Phys. 105 113307 Google Scholar
[59]	Boyd R L F, Thomson J B 1959 Proc. R. Soc. London, Ser. A 252 102 Google Scholar
[60]	Kokkoris G, Goodyear A, Cooke M, Gogolides E 2008 J. Phys. D: Appl. Phys. 41 195211 Google Scholar
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[65]	Dai Z L, Wang Y N 2003 Surf. Coat. Technol. 165 224 Google Scholar
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Hybrid simulation of radio frequency biased inductively coupled Ar/O₂/Cl₂ plasmas

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Hybrid simulation of radio frequency biased inductively coupled Ar/O2/Cl2 plasmas

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Hybrid simulation of radio frequency biased inductively coupled Ar/O₂/Cl₂ plasmas