Proc. SPIE. 5755, Data Analysis and Modeling for Process Control II
KEYWORDS: Signal to noise ratio, Statistical analysis, Detection and tracking algorithms, Sensors, Manufacturing, Inspection, Monte Carlo methods, Semiconductor manufacturing, Algorithm development, Semiconducting wafers
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.
We describe a new method of estimating the systematic spatial variation across wafers. Current methods for this task share some common deficiencies. For example, few of these techniques are able to decompose the systematic variation into components that can be assigned to different types of tools. Most of these methods are also sensitive to outliers and require that the outliers be manually removed before the model can be estimated. Almost none of the previous
methods can account for high-frequency effects caused by reticle
non-uniformity. Our method is based on a linear regression model with various components to account for the systematic variation that occurs in practice. Polynomial components model the smooth variation caused by tools that cannot process the wafer uniformly. Reticle components model the variation that occurs due to non-uniformities in the microlithography and etch tools. To generate distinct patterns, we apply QR orthogonalization to the systematic patterns prior to regression. To limit the effects of outliers, we employ robust regression. We demonstrate the performance of our technique with an
example on data collected from production wafers.