Detecting Spatial Effects From Factorial Experiments: An Application From Integrated-Circuit Manufacturing

Abstract

In addition to the number of functional chips on a silicon wafer, spatial patterns of the nonfunctional chips can provide important information for improving integrated-circuit fabrication processes. In this article, we consider a binary (functional/nonfunctional) response for each chip and propose a method to detect spatial effects in such processes through factorial experimentation. By using a measure of spatial dependence, process factors (parameters) that influence the spatial clustering of functional or nonfunctional chips can be identified. The proposed method, which assumes that a wafer contains a moderately large number of chips and that at least one wafer is produced for each experimental setting, is demonstrated with data from an actual experiment.

KEY WORDS:

• Design of experiments
• Join-count statistics
• Log odds ratio
• Nearest neighbor
• Spatial clustering
• Yield models