Data-Driven and Mechanism-Based Hybrid Model for Semiconductor Silicon Monocrystalline Quality Prediction in the Czochralski Process

Abstract

The Czochralski (CZ) process is the core technology for producing semiconductor silicon monocrystalline (SMC), and it is a complex batch process. However, the crystal growth rate and crystal diameter, which are key quality indicators, are difficult to detect directly online, and the offline calculation process lags seriously, which easily causes blind crystal quality control. Therefore, this paper proposes a data-driven and mechanism-based hybrid model for semiconductor SMC quality variables prediction in the CZ process. Firstly, a data-driven model JITL-SAE-ELM based on just-in-time learning (JITL) fine-tuning strategy is proposed. This model is used to solve the nonlinear and time-varying relationship of the energy transfer process in the CZ process that cannot be accurately described by traditional mechanism models. Here, the SAE-ELM model integrates a stacked autoencoder (SAE) and an extreme learning machine (ELM), which are used to deeply capture the nonlinear and time-varying features of process data. Secondly, according to the hydrodynamics and geometric behavior, a crystal pulling dynamic mechanism model based on the crystal growth mechanism is constructed, which avoids the complicated heat transfer link. Further, considering the unmodeled dynamics caused by model parameter uncertainty during the combination of the energy transfer model and crystal pulling dynamic mechanism model, a crystal diameter compensation model SAE-ELM was developed to improve the prediction accuracy of the CZ process hybrid model. Finally, an industrial data experiment based on a CZ monocrystal furnace illustrates the proposed method.