Mechanism and Data-based Hybrid Model for Czochralski Silicon Single Crystal Growth Process

Abstract

The Czochralski (CZ) silicon single crystal growth process is a dynamic time-varying process with the multi-field, multi-phase strong coupling, nonlinear and large delay. The traditional mechanism modeling method is difficult to accomplish. To solve this problem, a hybrid modeling method combining mechanism-driven and data-driven is proposed. Firstly, according to the fluid dynamics and geometric relationship at the meniscus during crystal growth, a mechanism-driven model (MDM) of crystal diameter was constructed. Secondly, a deep learning SAE-ELM data-driven model (DDM) based on industrial process data is established by combining the stack autoencoder (SAE) and extreme learning machine (ELM) to compensate the unmodeled dynamics of the crystal diameter MDM, to improve the accuracy of the crystal diameter MDM. Here, ELM is used in the regression layer of SAE, and its purpose is to perform regression prediction on the data feature information extracted by SAE. Considering that the SAE-ELM network involves multiple model parameters, this paper uses the gray wolf optimization algorithm (GWO) to optimize the model parameters to obtain the best prediction performance. Then, the crystal diameter MDM and SAE-ELM DDM are connected in parallel to establish a hybrid model(MDM-SAE-ELM) of CZ silicon single crystal diameter, which takes into account both interpretations and accuracy. Finally, several experiments based on industrial process data verify the effectiveness of the proposed method.