A Soft Measurement Method for the Tail Diameter in the Growing Process of Czochralski Silicon Single Crystals

In the Czochralski silicon single crystal growth process, the tail diameter is a key parameter that cannot be directly measured. In this paper, we propose a real-time soft measurement method that combines a deep belief network (DBN) and a support vector regression (SVR) network based on system identification to accurately predict the crystal diameter. The main steps of the proposed method are as follows: First, we address the delay problem of the effects of the temperature and crystal pulling speed on the tail diameter growth by using a back propagation (BP) neural network based on the mean impact value (MIV) method to determine the optimal delay time. Second, we construct a prediction model of the tail diameter by using the DBN network with the temperature and crystal pulling speed as input variables in the crystal growth process. Third, we improve the DBN network by using the SVR network to enhance its linear regression capability. We also employ the ant colony optimization (ACO) algorithm to obtain the optimal parameters of the SVR network. Finally, we compare the performance of the DBN-ACO-SVR network based on system identification with the DBN and SVR networks, and the results show that our method can effectively deal with the delay problem and achieve the accurate prediction of the tail diameter in the Czochralski silicon single crystal growth process.