Spatial Correlated Data Monitoring in Semiconductor Manufacturing Using Gaussian Process Model

In semiconductor manufacturing, various wafer tests are conducted in each stage. The analysis and monitoring of collected wafer testing data plays an important role in identifying potential problems and improving process yield. There exists three variation sources: 1) lot-to-lot variation; 2) wafer-to-wafer variation; and 3) site-to-site variation, which means the measurements cannot be considered independently. However, most existing control charts for monitoring wafer quality are based on the assumption that data are independently and identically distributed. To deal with the variations, we propose a mixed-effects model incorporating a Gaussian process to account for the variations. Based on the model, two control charts are implemented to detect anomalies of the measurements which can monitor the changes of the variations and the quality of products, respectively. Simulation studies and results from real applications show that this model and control scheme is effective in estimating and monitoring the variation sources in the manufacturing process.