An adaptive Copula function-based framework for fault detection in semiconductor wafer fabrication

Wafer fabrication is a complex manufacturing system. Timely identification of the key influencing factors associated with the cause of defects is critical to wafer yield enhancement. However, the massive wafer fabrication process dataset has various data types, uncertain data distribution, and complex correlation relationships. These issues make the statistical sense of correlation association measures, and fault detection (FD) methods face many challenges. Therefore, this study proposes an adaptive Copula function-based framework for FD in semiconductor wafer fabrication. Firstly, the marginal distribution of the wafer fabrication process data was determined. After that, a joint distribution model based on the Copula function was designed for the nonlinear relationship and the nonnormal distribution characteristics. Based on the model mentioned above, the traditional Copula function selection method has a high-dimensional spatial failure problem based on the Euclidean distance theory. Therefore, a high-dimensional spatial distance measurement method based on improved kernel distance measurement (IKDM) is designed to realize the adaptive selection of Copula functions. Afterward, the key influencing factors associated with wafer yield are identified through feature sensitivity analysis and validated with multiple prediction models for comparison. Finally, a case study using actual data from a semiconductor wafer fabrication system is used to validate the effectiveness of the proposed methodological framework.