Nonlinear Generalized Predictive Control of the Crystal Diameter in CZ-Si Crystal Growth Process Based on Stacked Sparse Autoencoder

Abstract

A new control structure with constant pulling speed for growing high-quality crystal in the Czochralski (CZ) method is presented in this brief. In this control structure, the pulling speed is not involved in the controlling of crystal diameter and only the temperature is used as the control quantity. Due to the time delay and the nonlinearity relationship are commonly involved between the temperature and crystal diameter, which make the diameter control difficult and complicated, a generalized predictive controller (GPC) based on the stacked sparse autoencoder (SSAE) is proposed under the new control structure. The time delay is obtained by using the correlation identification algorithm, the input order and output order are determined by the Lipchitz quotients algorithm, and the prediction model is trained by SSAE. Combining the SSAE with the nonlinear GPC algorithm, the control law of the temperature is calculated for diameter control. The simulation result verifies the correctness of the proposed control algorithm. The experimental result indicates that the new control structure with constant pulling speed is more conducive to growing high-quality crystal, avoiding the fluctuation of pulling speed. The proposed SSAE-based GPC algorithm can accurately track the reference diameter. The studies in this brief provide a feasible strategy for growing large size and high-quality crystal in the CZ method.