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Unformatted text preview: MIT OpenCourseWare ____________ http://ocw.mit.edu 2.830J / 6.780J / ESD.63J Control of Manufacturing Processes (SMA 6303) Spring 2008 For information about citing these materials or our Terms of Use, visit: ________________ http://ocw.mit.edu/terms . 1 M anufacturing Control of Manufacturing Processes Subject 2.830/6.780/ESD.63 Spring 2008 Lecture #21 Case Study: Spatial Modeling May 6, 2008 2 M anufacturing Case Study Reading J. C. Davis, R. S. Gyurcsik, J.-C. Lu, and J. M. Hughes-Oliver, A Robust Metric for Measuring Within-Wafer Uniformity, IEEE Trans. on Components, Packaging, and Manuf. Tech. - Part C, vol.19, no. 4, pp. 283-289, Oct. 1996. P. K. Mozumder and L. M. Loewenstein, Method for Semiconductor Process Optimization Using Functional Representations of Spatial Variations and Selectivity, IEEE Trans. on Components, Hybrids, and Manuf. Tech., vol. 15, no. 3, pp. 311-316, June 1992. R.-S. Guo and E. Sachs, Modeling, Optimization and Control of Spatial Uniformity in Manufacturing Processes, IEEE Trans. on Semiconductor Manuf. , vol. 6, no. 1, pp. 41-57, Feb. 1993. 3 M anufacturing Agenda Spatial Sampling Example: impact of sampling plan on response regression Spatial Non-Uniformity Models DOE/RSM with both process and spatial dependencies Multiple Response Surface (MRS) vs. Single Response Surface (SRS) approaches 4 M anufacturing Spatial Trends In many manufacturing processes, a spatial trend in some response is observed Wafer fabrication: wafer scale trends in film thicknesses, electrical properties, etc. resulting from inherent equipment/process asymmetries Key questions: How model? How summarize (e.g. nonuniformity metric)? Image removed due to copyright restrictions. Please see Fig. 2 in Davis, Joseph C., et al. A Robust Metric for Measuring Within-Wafer Uniformity. IEEE Transactions on Components, Packaging, and Manufacturing Technology C 19 (October 1996): 283-289. 5 M anufacturing-100 100 y 45.000 46.000 47.000 48.000 49.000-100 100 x Synthetic data We construct a spatial response for some parameter (resistivity) so we know the true spatial dependency: Generate data sets Common circular wafer map Rectangular grid C a l c u l a t e : Response surface model Non-uniformity metric, e.g. / Example 6 M anufacturing-100-50 50 100 y-100-50 50 100 x 1. Radial Sampling Plan 8 points at a radius of 75 mm 8 points at a radius of 50 mm 8 points at 25 mm radius 1 point at the center of the wafer X Y rho 25 49.9601097 17.68 17.68 49.1136113 25 49.7359187-17.68 17.68 49.8140025-25 48.2246087-17.68-17.68 50.1927006-25 49.2427469 17.68-17.68 49.6791275 50 49.8336576 35.36 35.36 49.2292189 50 48.9286926-35.36 35.36 48.2485797-50 47.8966527-35.36-35.36 49.2351389-50 49.426475 35.36-35.36 48.6728475 75 48.8338909 53.03 53.03 49.0658809 75 49.4461394-53.03 53.03 47.4035767-75 46.4175911-53.03-53.03-53....
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