Robust linear regression for modeling systematic spatial wafer variation

James McNames; Byungsool Moon; Bruce Whitefield; David Abercrombie

doi:10.1117/12.600198

17 May 2005 Robust linear regression for modeling systematic spatial wafer variation

James McNames, Byungsool Moon, Bruce Whitefield, David Abercrombie

Author Affiliations +

Proceedings Volume 5755, Data Analysis and Modeling for Process Control II; (2005) https://doi.org/10.1117/12.600198
Event: Microlithography 2005, 2005, San Jose, California, United States

Abstract

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.

Citation Download Citation

James McNames, Byungsool Moon, Bruce Whitefield, and David Abercrombie "Robust linear regression for modeling systematic spatial wafer variation", Proc. SPIE 5755, Data Analysis and Modeling for Process Control II, (17 May 2005); https://doi.org/10.1117/12.600198

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