Wafer Sampling by Regression for Systematic Wafer Variation Detection

摘要

In-line measurements are used to monitor semiconductor manufacturing processes for excessive variation using statistical process control (SPC) chart techniques. Systematic spatial wafer variation often occurs in a recognizable pattern across the wafer that is characteristic of a particular manufacturing step. Visualization tools are used to associate these patterns with specific manufacturing steps preceding the measurement. Acquiring the measurements is an expensive and slow process. The number of sites measured on a wafer must be minimized while still providing sufficient data to monitor the process. We address two key challenges to effective wafer-level monitoring. The first challenge is to select a small sample of inspection sites that maximize detection sensitivity to the patterns of interest, while minimizing the confounding effects of other types of wafer variation. The second challenge is to develop a detection algorithm that maximizes sensitivity to the patterns of interest without exceeding a user-specified false positive rate. We propose new sampling and detection methods. Both methods are based on a linear regression model with distinct and orthogonal components. The model is flexible enough to include many types of systematic spatial variation across the wafer. Because the components are orthogonal, the degree of each type of variation can be estimated and detected independently with very few samples. A formal hypothesis test can then be used to determine whether specific patterns are present. This approach enables one to determine the sensitivity of a sample plan to patterns of interest and the minimum number of measurements necessary to adequately monitor the process.