Prediction Model of Diameter of Czochralski Silicon Single Crystal Based on NARX Dynamic Neural Network

Abstract

Abstract: In the process of preparing silicon single crystal, the Czochralski method has problems such as multiple mechanism assumptions, unclear boundary conditions under multiple field couplings, interlaced and mutual influence of physical and chemical changes, which makes it impossible to establish an accurate mechanism model for silicon single crystal growth process control. To solve this problem, based on a large amount of crystal growth data in the single crystal furnace pulling workshop, this paper analyzes the characteristic parameters related to crystal diameter based on the maximum information coefficient (MIC) algorithm proposed by the mutual information theory. Then, based on the nonlinear autoregressive with exogeneous inputs (NARX) dynamic neural network, a multi-input, and single-output equal-diameter phase crystal diameter prediction model was established, the diameter prediction was also performed for the three single crystal furnace pulling data, and the average mean square error value of the prediction is 0.000 774. Finally, the prediction model of crystal diameter in the equal diameter stage established based on the NARX dynamic neural network is compared with the prediction model of crystal diameter in the equal diameter stage established based on the back propagation (BP) neural network. The results of the comparative analysis verified the superiority of the NARX dynamic neural network model for predicting the crystal diameter in the isodiametric stage. The results show the NARX dynamic neural network provides a more accurate identification model for the control of crystal diameter.

Key words: silicon single crystal, diameter identification, nonlinear autoregression, BP neural network, Czochralski method, data-driven

CLC Number:

XU Shengzhe, GAO Dedong, WANG Shan, WU Haohao, ZHANG Xiya, HAN Yonglong, LI Lirong. Prediction Model of Diameter of Czochralski Silicon Single Crystal Based on NARX Dynamic Neural Network[J]. Journal of Synthetic Crystals, 2022, 51(12): 2031-2039.

References

[1] 李素青.GB/T 25076《太阳能电池用硅单晶》及GB/T 26071《太阳能电池用硅单晶片》标准解读[J].世界有色金属,2018(18):165-167.
LI S Q. Interpretation of GB/T 25076“Monocrystalline silicon for solar cell” and GB/T 26071 “Monocrystalline silicon wafers for solar cells”[J]. World Nonferrous Metals, 2018(18): 165-167(in Chinese).
[2] 刘涵,刘丁.基于支持向量机的参数自整定PID非线性系统控制[J].控制理论与应用,2008,25(3):468-474.
LIU H, LIU D. Self-tuning PID controller for a nonlinear system based on support vector machines[J]. Control Theory ＆ Applications, 2008, 25(3): 468-474(in Chinese).
[3] 俞金寿,顾幸生.过程控制工程[M].4版.北京:高等教育出版社,2012.
YU J S, GU X S. Process control engineering[M]. 4th ed. Beijing: Higher Education Press, 2012(in Chinese).
[4] 王展.恒拉速工艺下硅单晶直径控制方法研究[D].西安:西安理工大学,2020.
WANG Z. Research on diameter control method of silicon single crystal under constant pulling velocity process[D]. Xi’an: Xi’an University of Technology, 2020(in Chinese).
[5] WINKLER J, NEUBERT M, RUDOLPH J. Nonlinear model-based control of the Czochralski process I: motivation, modeling and feedback controller design[J]. Journal of Crystal Growth, 2010, 312(7): 1005-1018.
[6] RAHMANPOUR P, HOVD M, BONES J A. Nonlinear state estimation in the Czochralski process[J]. IFAC Proceedings Volumes, 2014, 47(3): 4891-4896.
[7] DERBY J J, BROWN R A. On the dynamics of Czochralski crystal growth[J]. Journal of Crystal Growth, 1987, 83(1): 137-151.
[8] 张妮,刘丁,冯雪亮.直拉硅单晶生长过程中工艺参数对相变界面形态的影响[J].物理学报,2018,67(21):415-426.
ZHANG N, LIU D, FENG X L. Effects of process parameters on melt-crystal interface in Czochralski silicon crystal growth[J]. Acta Physica Sinica, 2018, 67(21): 415-426(in Chinese).
[9] CHEN J C, CHIANG P Y, CHANG C H, et al. Three-dimensional numerical simulation of flow, thermal and oxygen distributions for a Czochralski silicon growth with in a transverse magnetic field[J]. Journal of Crystal Growth, 2014, 401: 813-819.
[10] 张晶,刘丁,杜燕军.直拉硅单晶非均匀相变温度场最优控制[J].控制理论与应用,2021,38(1):44-52.
ZHANG J, LIU D, DU Y J. Optimal control for heterogeneous phase transition temperature field of Czochralski monocrystalline silicon[J]. Control Theory ＆ Applications, 2021, 38(1): 44-52(in Chinese).
[11] 王春阳.直拉硅单晶等径阶段直径数据建模与模型预测控制[D].西安:西安科技大学,2019.
WANG C Y. Data modeling and model prediction control of equal diameter phase diameter of Cz single crystal[D]. Xi′an: Xi′an University of Science and Technology, 2019(in Chinese).
[12] 王可.直拉单晶炉热场模型参数辨识及模型预测控制[D].兰州:兰州大学,2014.
WANG K. Czochralski crystal furnace thermal field model parameter identification and the model predictive control[D]. Lanzhou: Lanzhou University, 2014(in Chinese).
[13] 李欣鸽.CZ硅单晶等径生长阶段关键参数优化研究[D].郑州:郑州大学,2020.
LI X G. Study on the optimization of key parameters of CZ single crystal in equal diameter growth stage[D]. Zhengzhou: Zhengzhou University, 2020(in Chinese).
[14] 刘聪聪.基于软测量建模的硅单晶品质预测控制[D].西安:西安理工大学,2021.
LIU C C. Predictive control of silicon single crystal quality based on soft sensor modeling[D]. Xi′an: Xi′an University of Technology, 2021(in Chinese).
[15] 张西亚,高德东,王珊,等.基于数据驱动的晶体直径模型辨识方法研究[J].人工晶体学报,2021,50(8):1552-1561+1574.
ZHANG X Y, GAO D D, WANG S, et al. Research on identification method of crystal diameter model based on data driven[J]. Journal of Synthetic Crystals, 2021, 50(8): 1552-1561+1574(in Chinese).
[16] 刘丁.直拉硅单晶生长过程建模与控制[M].北京:科学出版社,2015.
LIU D. Modeling and control of growth process of Czochralski silicon[M]. Beijing: Science Press, 2015(in Chinese).
[17] 赵翔,茹东恒,王鹏,等.基于NARX神经网络方法的汽轮机转子关键部位应力预测[J].应用数学和力学,2021,42(8):771-784.
ZHAO X, RU D H, WANG P, et al. On the stress prediction of key components in steam turbine rotors based on the NARX neural network[J]. Applied Mathematics and Mechanics, 2021, 42(8): 771-784(in Chinese).
[18] 常泽明,李璐祎.基于NARX和Kriging的时变可靠性分析的双层代理模型方法[J/OL].北京航空航天大学学报:1-16[2022-05-05].DOI:10.13700/j.bh.1001-5965.2021.0541.
CHANG Z M, LI L Y. Two-level surrogate model method for time-varying reliability analysis based on NARX and Kriging[J/OL]. Journal of Peking University of Aeronautics and Astronautics: 1-16 [2022-05]. DOI: 10.13700/j.bh.1001-5965.2021.0541(in Chinese).
[19] 李未,朱梦圆,王裕成,等.基于NARX神经网络的千岛湖藻类短期预测模型构建[J].环境科学研究,2022,35(4):918-925.
LI W, ZHU M Y, WANG Y C, et al. Short-term forecasting model for algae based on NARX neural network in Qiandaohu Reservoir[J]. Research of Environmental Sciences, 2022, 35(4): 918-925(in Chinese).
[20] 姜宇航,王伟,邹丽芳,等.基于PSO-VMD、NARX与GRU的滑坡位移动态预测模型研究[J/OL].岩土力学:1-12[2022-05-05].DOI:10.16285/j.rsm.2021.0247.
JIANG Y H, WANG W, ZOU L F, et al. Dynamic prediction model of landslide displacement based on PSO-VMD, NARX and GRU[J/OL].Geotechnical mechanics:1-12 [2022-05-05]. DOI: 10.16285/j.rsm.2021.0247(in Chinese).
[21] 王月.最大信息系数的算法分析及改进[D].西安:西安电子科技大学,2019.
WANG Y. Algorithm analysis and improvement of the maximal information coefficient[D]. Xi’an: Xidian University, 2019(in Chinese).
[22] 刘汉明.基于最大信息系数的复杂疾病全基因组关联算法研究[D].成都:电子科技大学,2015.
LIU H M. Reseach on algorithms of genome-wide association study for complex diseases based on maximal information coefficient[D]. Chengdu: University of Electronic Science and Technology of China, 2015(in Chinese).
[23] 魏孟,王桥,叶敏,等.基于NARX动态神经网络的锂离子电池剩余寿命间接预测[J].工程科学学报,2022,44(3):380-388.
WEI M, WANG Q, YE M, et al. An indirect remaining useful life prediction of lithium-ion batteries based on a NARX dynamic neural network[J]. Chinese Journal of Engineering, 2022, 44(3): 380-388(in Chinese).
[24] 陈文进,朱峰,张童彦,等.基于AFSA-BP神经网络的光伏功率预测方法[J].浙江电力,2022,41(4):7-13.
CHEN W J, ZHU F, ZHANG T Y, et al. A photovoltaic power prediction method based on AFSA-BP neural network[J]. Zhejiang Electric Power, 2022, 41(4): 7-13(in Chinese).