基于前馈神经网络的等离子体光谱诊断方法

王彦飞; 朱悉铭; 张明志; 孟圣峰; 贾军伟; 柴昊; 王旸; 宁中喜

doi:10.7498/aps.70.20202248

摘要

光谱诊断在等离子体刻蚀、材料处理、等离子体设备和工艺开发, 以及航天等离子体推进等领域得到了广泛的应用. 光谱诊断依赖的碰撞辐射模型会受到碰撞截面等基础物理数据所含偏差的影响, 导致诊断结果出现误差. 针对这一问题, 本文开发了一种基于前馈神经网络的等离子体光谱解算方法. 通过对比新方法与以往常用的最小二乘诊断方法的误差特性, 发现神经网络诊断方法能够通过辨识光谱向量的主要特征, 减小基础数据偏差向诊断结果的传递. 对实验光谱数据的分析进一步印证了这一点. 本文还对神经网络算法对抗基础数据偏差的机理进行了分析. 这种方法在等离子体参数在线监测、成像监测海量数据处理等领域具有良好的应用前景.

关键词:

Abstract

Optical emission spectroscopy (OES) has been widely applied to plasma etching, material processing, development of plasma equipment and technology, as well as plasma propulsion. The collisional-radiative model used in OES is affected by the deviation of fundamental data such as collision cross sections, thus leading to the error in diagnostic results. In this work, a novel method is developed based on feedforward neural network for OES. By comparing the error characteristics of the new method with those of the traditional least-square diagnostic method, it is found that the neural network diagnosis method can reduce the transmission of basic data deviation to the diagnosis results by identifying the characteristics of the spectral vector. This is confirmed by the experimental results. Finally, the mechanism of the neural network algorithm against fundamental data deviation is analyzed. This method also has a good application prospect in plasma parameter online monitoring, imaging monitoring and mass data processing.

Keywords:

作者及机构信息

1.
哈尔滨工业大学, 哈尔滨　150001

2.
工信部“航天等离子体推进”重点实验室, 哈尔滨　150001

3.
北京东方计量测试研究所, 北京　100086

通信作者: 朱悉铭, zhuximing@hit.edu.cn ; 宁中喜, ningzx@hit.edu.cn

基金项目: 国家自然科学基金(批准号: 11775063)、国防基础科研计划(批准号: JCKY2018203B029)和国防计量基础课题(批准号: JSJL2016203B017)资助的课题

Authors and contacts

1.
Harbin Institute of Technology, Harbin 150001, China

2.
Key Laboratory of Aerospace Plasma Propulsion, Ministry of Industry and Information Technology, Harbin 150001, China

3.
Beijing Orient Institute of Measurement and Test, Beijing 100086, China

Corresponding author: Zhu Xi-Ming, zhuximing@hit.edu.cn ; Ning Zhong-Xi, ningzx@hit.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11775063), the Defense Industrial Technology Development Program, China (Grant No. JCKY2018203B029), and the Defense Industrial Metering Program, China (Grant No. JSJL2016203B017)

文章全文 : translate this paragraph

参考文献

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[2]	曲鹏程, 唐代飞, 向鹏飞, 袁安波 2017 电子科技 30 153 Google Scholar Qu P C, Tang D F, Xiang P F, Yuan A B 2017 Electr. Sci. Technol. 30 153 Google Scholar
[3]	Edy R, Huang G S, Zhao Y T, Guo Y, Zhang J, Mei Y F, Shi J J 2017 Surf. Coat. Technol. 329 149 Google Scholar
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[7]	Gao J, Zhou L, Liang J, Wang Z, Wu Y, Muhammad J, Dong X, Li S, Yu H, Quan X 2018 Nano Res. 11 1470 Google Scholar
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[9]	Yang J, Yokota S, Kaneko R, Komurasaki K 2010 Phys. Plasmas 17 103504 Google Scholar
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[17]	Zhu X M, Pu Y K 2009 J. Phys. D: Appl. Phys. 43 015204
[18]	Zhu X M, Pu Y K 2010 J Phys. D: Appl. Phys. 43 403001 Google Scholar
[19]	Zhu X M, Chen W C, Li J, Cheng Z W, Pu Y K 2012 Plasma Sources Sci. Technol. 21 045009 Google Scholar
[20]	Boffard J B, Lin C C, DeJoseph C A 2004 J. Phys. D: Appl. Phys. 37 R 37 R143 Google Scholar
[21]	Sadeghi N, Setser D W 2001 J. Chem. Phys. 115 3144
[22]	Weber T, Boffard J B, Lin C C 2003 Phys. Rev. A 68 032719 Google Scholar
[23]	Sharma L, Srivastava R, Stauffer A D 2011 Eur. Phys. J. D 62 399 Google Scholar
[24]	Zatsarinny O, Bartschat K 2013 J. Phys. B: At. Mol. Opt. 46 112001 Google Scholar
[25]	Bray I, Fursa D, Kadyrov A, Stelbovicsa A T, Kheifets A S, Mukhamedzhanov A M 2012 Phys. Rep. 520 135 Google Scholar
[26]	Chen Z B, Dong C Z, Xie L Y, Jiang J 2014 Chin. Phys. Lett. 31 033401 Google Scholar
[27]	Boffard J B, Jung R O, Lin C C, Wendt A E 2009 Plasma Sources Sci. Technol. 18 035017 Google Scholar
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[34]	彭向凯, 吉经纬, 李琳, 任伟, 项静峰, 刘亢亢, 程鹤楠, 张镇, 屈求智, 李唐, 刘亮, 吕德胜 2019 物理学报 68 130701 Google Scholar Peng X K, Ji J W, Li L, Ren W, Xiang J F, Liu K K, Cheng H N, Zhang Z, Qu Q Z, Li T, Liu L, Lv D S 2019 Acta Phys. Sin. 68 130701 Google Scholar
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[36]	彭相洲, 陈雨 2020 计算机应用研究 37 47 Peng X Z, Chen Y 2020 Appl. Res. Com. 37 47 (in Chinese)
[37]	孟圣峰 2019 硕士学位论文 (哈尔滨: 哈尔滨工业大学) Meng S F 2019 M. S. Thesis (Harbin: Harbin Institute of Technology)(in Chinese)
[38]	Zhu X M, Pu Y K 2008 Plasma Sources Sci. Technol. 17 024002 Google Scholar
[39]	Abdollah S, Nikiforov A Y, Leys C 2010 Phys. Plasmas 17 063504 Google Scholar
[40]	Zhu X M, Chen W C, Li J, Pu Y K 2008 J. Phys. D: Appl. Phys. 42 025203

施引文献

图 1 考夫曼电离室结构及测量实验方案

Fig. 1. Structure of the Kaufmann discharge chamber and the scheme of measurement.

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图 2 基于最小二乘的光谱诊断方法流程

Fig. 2. Diagram of optical emission spectroscopy based on least square method.

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图 3 基于前馈神经网络的光谱诊断方法流程

Fig. 3. Diagram of optical emission spectroscopy based on feedforward neural network.

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图 4 误差半径及偏心距定义(真实值)

Fig. 4. Definition of error radius and eccentricity.

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图 5 使用不同网络结构和数据正规化方法获得的均方误差随迭代次数的变化

Fig. 5. Variation of mean square error with the number of iterations using different network structures and data normalization methods.

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图 6 网络预测结果与训练目标的对应关系　(a)电子温度的对应关系; (b)电子密度的对应关系; (c)电子温度的预测误差; (d)电子密度的预测误差

Fig. 6. Corresponding relationship between the network prediction result and the training target: (a) Corresponding relationship of the electron temperature; (b) corresponding relationship of the electron density; (c) prediction error of the electron temperature; (d) prediction error of the electron density.

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图 7 使用最小二乘方法获得的拟合结果(为保证图的可读性, 对离子谱线强度进行了放大处理, 并将拟合所得光谱的波长进行了偏置)

Fig. 7. Fitting results obtained by the least square method (in order to improve the readability of the image, the intensity of the ion spectral line is amplified, and a bias is introduced into the wavelength of the fitting spectrum).

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图 8 (a)最小二乘方法诊断结果的平均误差半径; (b) 神经网络方法诊断结果的平均误差半径

Fig. 8. (a) Average error radius of the diagnosis result of the least square method; (b) average error radius of the diagnosis result of the neural network method.

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图 9 (a)最小二乘方法诊断结果的最大误差半径; (b) 神经网络方法诊断结果的最大误差半径

Fig. 9. (a) The maximum error radius of the diagnosis result of the least square method; (b) the maximum error radius of the diagnosis result of the neural network method.

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图 10 (a)最小二乘方法结果的偏心距; (b) 神经网络方法结果的偏心距

Fig. 10. (a) Eccentricity of the diagnosis result of the least square method; (b) the eccentricity of the diagnosis result of the neural network method.

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图 11 (a)考夫曼离子源中电子密度的诊断结果; (b)考夫曼离子源中电子温度的诊断结果; (c)最小二乘方法和神经网络方法获得的电子密度结果的相对误差; (d)最小二乘方法和神经网络方法获得的电子温度结果的相对误差. “探针”、“最小二乘”和“神经网络”分别表示由朗缪尔探针、最小二乘方法和神经网络方法获得的诊断结果

Fig. 11. (a) Diagnostic results of n_e in Kaufman ion source; (b) diagnostic results of T_e in Kaufman ion source; (c) relative error of n_e by least-square method and neural network method; (d) relative error of T_e by least-square method and neural network method. “探针”, “最小二乘”, “神经网络” denotes the diagnostic results obtained by Langmuir probe, least-square diagnostic method and neural network diagnostic method, respectively.

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表 1 本文研究中选用的氙谱线表

Table 1. Xenon spectral lines used in this work.

序号	波长/nm	上能级	序号	波长/nm	上能级
1	460.303	5p⁴(³P₂)6p $ {}^{2}{\left[1\right]}_{3/2}^\circ $	9	834.745	5p⁵($ {}^{2}{\mathrm{P}}_{1/2}^\circ $)6p ²[3/2]₂
2	484.433	5p⁴(³P₂)6p $ {}^{2}{\left[3\right]}_{7/2}^\circ $	10	840.919	5p⁵($ {}^{2}{\mathrm{P}}_{3/2}^\circ $)6p ²[3/2]₁
3	492.148	5p⁴(³P₁)6p $ {}^{2}{\left[2\right]}_{5/2}^\circ $	11	881.941	5p⁵($ {}^{2}{\mathrm{P}}_{3/2}^\circ $)6p ²[5/2]₃
4	529.222	5p⁴(³P²)6p $ {}^{2}{\left[2\right]}_{5/2}^\circ $	12	895.225	5p⁵($ {}^{2}{\mathrm{P}}_{3/2}^\circ $)6p ²[3/2]₂
5	541.915	5p⁴(³P₂)6p $ {}^{2}{\left[3\right]}_{5/2}^\circ $	13	904.545	5p⁵($ {}^{2}{\mathrm{P}}_{3/2}^\circ $)6p ²[5/2]₂
6	788.739	5p⁵(²P°_1/2)6p ²[1/2]₀	14	916.265	5p⁵($ {}^{2}{\mathrm{P}}_{3/2}^\circ $)6p ²[3/2]₁
7	823.163	5p⁵(²P°_3/2)6p ²[3/2]₂	15	979.970	5p⁵($ {}^{2}{\mathrm{P}}_{3/2}^\circ $)6p ²[1/2]₁
8	828.012	5p⁵(²P°_3/2)6p ²[1/2]₀	16	992.320	5p⁵($ {}^{2}{\mathrm{P}}_{3/2}^\circ $)6p ²[5/2]₂

下载: 导出CSV

[1]	Donnelly, Vincent M, Avinoam K 2013 J. Vac. Sci. Technol., A 31 050825 Google Scholar
[2]	曲鹏程, 唐代飞, 向鹏飞, 袁安波 2017 电子科技 30 153 Google Scholar Qu P C, Tang D F, Xiang P F, Yuan A B 2017 Electr. Sci. Technol. 30 153 Google Scholar
[3]	Edy R, Huang G S, Zhao Y T, Guo Y, Zhang J, Mei Y F, Shi J J 2017 Surf. Coat. Technol. 329 149 Google Scholar
[4]	王巍, 叶甜春, 李兵, 陈大鹏, 刘明 2005 半导体技术 30 13 Google Scholar Wang W, Ye T C, Li B, Chen D P, Liu M 2005 Semiconductor Technol. 30 13 Google Scholar
[5]	王巍, 王玉青, 孙江宏, 兰中文, 龚云贵 2008 红外与激光工程 4 748 Google Scholar Wang W, Wang Y Q, Sun J H, Lan Z W, Gong Y G 2008 Infrared Laser Eng. 4 748 Google Scholar
[6]	Sridhar S, Donnelly V M, Liu L, Economou D J 2016 J. Vac. Sci. Technol., A 34 061303 Google Scholar
[7]	Gao J, Zhou L, Liang J, Wang Z, Wu Y, Muhammad J, Dong X, Li S, Yu H, Quan X 2018 Nano Res. 11 1470 Google Scholar
[8]	Kyung K, Winderbaum S, Hameiri Z 2017 Surf. Coat. Technol. 328 204 Google Scholar
[9]	Yang J, Yokota S, Kaneko R, Komurasaki K 2010 Phys. Plasmas 17 103504 Google Scholar
[10]	Zhu X M, Wang Y F, Wang Y, Yu D R, Zatsarinny O, Bartschat K, Tsankov T V, Czarnetzki U 2019 Plasma Sources Sci. Technol. 28 105005 Google Scholar
[11]	Donnelly V M 2004 J. Phys. D: Appl. Phys. 3 7
[12]	Stafford L, Khare R, Donnelly V M, Margot J, Moisan M 2009 Appl. Phys. Lett. 94 021503 Google Scholar
[13]	Wang Q, Koleva I, Donnelly V M, Economou D J 2005 J. Phys. D: Appl. Phys. 38 1690 Google Scholar
[14]	Huang X J, Zhang J, Guo Y, Zhang J, Shi J J 2014 IEEE Trans. Plasma Sci. 42 3569 Google Scholar
[15]	孙殿平 2008 博士学位论文 (上海: 华东师范大学) Sun D P 2008 Ph. D. Dissertation (Shanghai: East China Normal University) (in Chinese)
[16]	刘冲, 何湘, 朱卫华 2016 光谱学与光谱分析 S1 469 Liu C, He X, Zhu W H 2016 Spectrosc. Spect. Anal. S1 469
[17]	Zhu X M, Pu Y K 2009 J. Phys. D: Appl. Phys. 43 015204
[18]	Zhu X M, Pu Y K 2010 J Phys. D: Appl. Phys. 43 403001 Google Scholar
[19]	Zhu X M, Chen W C, Li J, Cheng Z W, Pu Y K 2012 Plasma Sources Sci. Technol. 21 045009 Google Scholar
[20]	Boffard J B, Lin C C, DeJoseph C A 2004 J. Phys. D: Appl. Phys. 37 R 37 R143 Google Scholar
[21]	Sadeghi N, Setser D W 2001 J. Chem. Phys. 115 3144
[22]	Weber T, Boffard J B, Lin C C 2003 Phys. Rev. A 68 032719 Google Scholar
[23]	Sharma L, Srivastava R, Stauffer A D 2011 Eur. Phys. J. D 62 399 Google Scholar
[24]	Zatsarinny O, Bartschat K 2013 J. Phys. B: At. Mol. Opt. 46 112001 Google Scholar
[25]	Bray I, Fursa D, Kadyrov A, Stelbovicsa A T, Kheifets A S, Mukhamedzhanov A M 2012 Phys. Rep. 520 135 Google Scholar
[26]	Chen Z B, Dong C Z, Xie L Y, Jiang J 2014 Chin. Phys. Lett. 31 033401 Google Scholar
[27]	Boffard J B, Jung R O, Lin C C, Wendt A E 2009 Plasma Sources Sci. Technol. 18 035017 Google Scholar
[28]	Boffard J B, Jung R O, Lin C C, Wendt A E 2010 Plasma Sources Sci. Technol. 19 065001 Google Scholar
[29]	Terzi M, Masiero C, Beghi A, Maggipinto M, Susto G A 2017 IEEE 3rd International Forum on Research and Technologies for Society and Industry Modena, Italy, September 11−13, 2017 p17244916
[30]	Wang C Y, Hsu C C 2019 Plasma Sources Sci. Technol. 28 105013 Google Scholar
[31]	康志伟, 刘拓, 刘劲, 马辛, 陈晓 2020 物理学报 69 069701 Google Scholar Kang Z W, Liu T, Liu J, Ma X, Chen X 2020 Acta Phys. Sin. 69 069701 Google Scholar
[32]	丁刚, 钟诗胜 2007 物理学报 2 1224 Google Scholar Ding G, Zhong S S 2007 Acta Phys. Sin. 2 1224 Google Scholar
[33]	徐启伟, 王佩佩, 曾镇佳, 黄泽斌, 周新星, 刘俊敏, 李瑛, 陈书青, 范滇元 2020 物理学报 69 014209 Google Scholar Xu Q W, Wang P P, Zeng Z J, Huang Z B, Zhou X X, Liu J M, Li Y, Chen S Q, Fan D Y 2020 Acta Phys. Sin. 69 014209 Google Scholar
[34]	彭向凯, 吉经纬, 李琳, 任伟, 项静峰, 刘亢亢, 程鹤楠, 张镇, 屈求智, 李唐, 刘亮, 吕德胜 2019 物理学报 68 130701 Google Scholar Peng X K, Ji J W, Li L, Ren W, Xiang J F, Liu K K, Cheng H N, Zhang Z, Qu Q Z, Li T, Liu L, Lv D S 2019 Acta Phys. Sin. 68 130701 Google Scholar
[35]	王鹏举, 范俊宇, 苏艳, 赵纪军 2020 物理学报 69 238702 Wang P J, Fan J Y, Su Y, Zhao J J 2020 Acta Phys. Sin. 69 238702
[36]	彭相洲, 陈雨 2020 计算机应用研究 37 47 Peng X Z, Chen Y 2020 Appl. Res. Com. 37 47 (in Chinese)
[37]	孟圣峰 2019 硕士学位论文 (哈尔滨: 哈尔滨工业大学) Meng S F 2019 M. S. Thesis (Harbin: Harbin Institute of Technology)(in Chinese)
[38]	Zhu X M, Pu Y K 2008 Plasma Sources Sci. Technol. 17 024002 Google Scholar
[39]	Abdollah S, Nikiforov A Y, Leys C 2010 Phys. Plasmas 17 063504 Google Scholar
[40]	Zhu X M, Chen W C, Li J, Pu Y K 2008 J. Phys. D: Appl. Phys. 42 025203

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