For different CD metrologies like average CD from CD SEM and optical CD (OCD) from scatterometry, CD point-to-point R2 has been well adopted as the CD correlation index. For different overlay metrologies like image-based box-in-box overlay and scatterometry-based overlay, we propose the cosine similarity as the correlation index of overlay. The cosine similarity is a measure of similarity between two vectors of n dimensions by finding the cosine of the angle
between them, often used to compare documents in text mining. It has been widely used in web and document search engines and can be used as the similarity index of overlay tool-to-tool matching and scanner tool-to-tool or day-to-day fingerprint.
In this paper, we demonstrate that the cosine similarity has a very high sensitivity to the overly tool performance. We compared the similarities of three generations (A1, A2, A3) of the overlay tools of venders A and B and found that after target re-training and TIS correction on each tool A1 similarity to A3 can be improved from 0.9837 to 0.9951. Overlay point-to-point matching with A3 vs. A1 can be reduced from 4.8 to 2.1 nm. The tool precision similarities, i.e. tool self best similarity, for A1, A2, A3 and B are 0.9986, 0.9990, 0.9995, and 0.9994 respectively. From this table, we demonstrate that we can use old-generation overlay tool with suitable hardware maintenance, to match to the latest-generation overlay tool.