Data-driven clustering learning modeling for semiconductor silicon single crystal growth process based on fuzzy C-means and DBN

Abstract

The optimal operation of the semiconductor silicon single crystal (SSC) growth in an industrial single crystal furnace is contingent upon the precise measurement of both the crystal diameter and melt temperature. The Czochralski (CZ) silicon single crystal growth process (CZ-SSCGP) is a phase transition process from solid to liquid that takes place in a high-temperature, enclosed furnace designed for single crystal growth. The direct measurement of crystal diameter and melt temperature using sensors can pose a challenge due to the physical limitations of the furnace. This study introduces a novel approach for modeling clustering based on data that integrate fuzzy C-means (FCM) and deep belief network (DBN) techniques. The proposed method aims to estimate the online crystal diameter and melt temperature. The objective of this approach is to efficiently and precisely derive the CZ-SSCGP model. In order to address the negative impact of nonequilibrium properties of data on the model, it is advisable to employ FCM to produce numerous subsets of data that exhibit comparable operating conditions. This is especially important because data change over time and are different in different working situations. In order to enhance the precision of the fitting process for crystal diameter and melt temperature, we amalgamate the output outcomes of DBN that have been constructed for each individual subset. It is imperative to address the nonlinear and time-varying features manifested by the engineering data. Industrial data are utilized for conducting diverse data experiments and comparative analyses. The process takes into account the data’s susceptibility to contamination by outliers. The findings suggest that the method put forth exhibits superior precision and enhanced resilience in predicting crystal diameter and melt temperature compared to alternative modeling approaches.