Sequential measurement strategy for wafer geometric profile estimation

The geometric profile, factors such as thickness, flatness, and local warp, are important quality features for a wafer. Fast and accurate measurements of those features are crucial in multistage wafer manufacturing processes to ensure product quality, process monitoring, and quality improvement. The current wafer profile measurement schemes are time-consuming and are essentially an offline technology and hence are unable to provide a quick assessment of wafer quality. This article proposes a sequential measurement strategy to reduce the number of samples measured in wafers while still providing an adequate accuracy for quality feature estimation. In the proposed approach, initial samples are measured and then a Gaussian process model is used to fit the measured data and generate a true profile of the measured wafer. The profile prediction and its uncertainty serve as guidelines to determine the measurement locations for the next sampling iteration. The measurement stops when the prediction error of the testing sample set satisfies a pre-designated accuracy requirement. A case study is provided to illustrate the procedures and effectiveness of the proposed methods based on the wafer thickness profile measurement in slicing processes.