Abstract More than 95% of 300 mm diameter single-crystal silicon ingots, the raw material for semiconductors, are produced by the Czochralski process. The demand for improving yield, throughput, and control performance has been increasing. The present study developed a gray-box model that can predict controlled variables from manipulated variables with higher accuracy than the conventional first-principle model (Zheng et al., 2018), aiming at realizing model predictive control of the Czochralski process. The proposed gray-box model used a statistical model to predict the temperature gradient of the crystal at the solid-liquid interface G cry , which was constant in the first-principle model. The crystal length and the melt temperature are used as the input variables to predict G cry . The prediction accuracy of the proposed gray-box model was compared with that of the first-principle model using real process data obtained during the production of four silicon ingots. The results demonstrated that the proposed model reduced the root mean square errors of the crystal radius, the crystal growth rate, and the heater temperature by 94.1%, 62.7%, and 70.6% on average, respectively.

中文翻译：

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300 毫米直径直拉单晶硅生产过程的灰盒建模

摘要 作为半导体的原材料，直径为 300 mm 的单晶硅锭 95% 以上是通过直拉法生产的。提高产量、产量和控制性能的需求一直在增加。本研究开发了一种灰盒模型，可以比传统的第一性原理模型（Zheng et al., 2018）更准确地从操纵变量中预测控制变量，旨在实现对直拉过程的模型预测控制。所提出的灰盒模型使用统计模型来预测固液界面处晶体的温度梯度 G cry ，其在第一原理模型中是恒定的。晶体长度和熔体温度用作输入变量来预测 Gcry。使用四个硅锭生产过程中获得的实际过程数据，将所提出的灰盒模型的预测精度与第一原理模型的预测精度进行了比较。结果表明，所提出的模型使晶体半径、晶体生长速率和加热器温度的均方根误差分别平均降低了 94.1%、62.7% 和 70.6%。