基于NARX动态神经网络直拉硅单晶直径预测模型

摘要/Abstract

摘要： 直拉法在制备硅单晶的过程中存在机理假设多、多场耦合下边界条件不明确和化学变化交错且相互影响等问题,导致无法建立准确的机理模型用于硅单晶生长过程控制。针对此问题,本文以单晶炉拉晶车间的大量晶体生长数据为基础,基于互信息理论提出的最大信息系数(MIC)算法,对与晶体直径相关的特征参数进行分析,然后基于带外源输入的非线性自回归(NARX)动态神经网络,建立多输入单输出的等径阶段晶体直径预测模型,并对三台单晶炉拉晶数据进行直径预测,预测的平均均方误差值为0.000 774。最后将NARX动态神经网络同反向传播(BP)神经网络进行对比分析,验证了该模型的优越性。结果表明,NARX动态神经网络为晶体直径的控制提供了一种更准确的辨识模型。

关键词: 硅单晶, 直径辨识, 非线性自回归, BP神经网络, 直拉法, 数据驱动

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

中图分类号:

徐圣哲, 高德东, 王珊, 吴昊昊, 张西亚, 韩永龙, 李丽荣. 基于NARX动态神经网络直拉硅单晶直径预测模型[J]. 人工晶体学报, 2022, 51(12): 2031-2039.

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.

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