Hybrid integrated modeling of thermal field temperature in Cz silicon single crystal growth process based on VMD-CNN-LSTM-ELM

Czochralski (Cz) silicon single crystal growth is a dynamic time-varying process with complex physical changes, multi-phase coupling of multiple fields, model uncertainty and large hysteresis and nonlinearity, while mechanistic models based on a large number of assumptions are difficult to be applied practically. In order to establish a stable and reliable model of crystal growth process, this paper proposes a variational modal decomposition- -convolutional neural network-long and short-term memory network-extreme learning machine (VMD-CNN-LSTM-ELM) nonlinear hybrid integrated modeling method based on the idea of data-driven modeling to construct a model between heater power and thermal field temperature. The model consists of feature extraction, deep learning network, and optimization algorithm. First, VMD is used to decompose the original data into multiple Intrinsic Mode Function (IMF) from low to high frequencies, preserving the variation characteristics of the signal at different frequencies. Second, for each eigenmode function sequence, CNN feature extraction and LSTM prediction are performed in turn. Then, ELM is used to nonlinearly integrate the prediction results of multiple sequences to obtain the final prediction output. Finally, the simulation experimental results based on industrial data show that the proposed VMD-LSTM-ELM based thermal field temperature has excellent prediction performance and generalization ability.