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A Bayesian Statistical Model for Hybrid Metrology to Improve Measurement Accuracy



Richard M. Silver, Nien F. Zhang, Bryan M. Barnes, Jing Qin, Hui Zhou, Ronald G. Dixson


We present a method to combine measurements from different techniques that reduces uncertainties and can improve measurement throughput. The approach directly integrates the measurement analysis of multiple techniques that can include different configurations or platforms. This approach has immediate application when performing model-based optical critical dimension (OCD) measurements. When modeling optical measurements, a library of curves is assembled through the simulation of a multi-dimensional parameter space. Parametric correlation and measurement noise lead to measurement uncertainty in the fitting process with fundamental limitations resulting from the parametric correlations. A strategy to decouple parametric correlation and reduce measurement uncertainties is described. We develop the rigorous underlying Bayesian statistical model and apply this methodology to OCD metrology. We then introduce an approach to damp the regression process to achieve more stable and rapid regression fitting. These methods that use a priori information are shown to reduce measurement uncertainty and improve throughput while also providing an improved foundation for comprehensive reference metrology.
Proceedings Title
Modeling Aspects in Optical Metrology
Conference Dates
May 23-26, 2011
Conference Location
Conference Title
SPIE Optical Metrology


Silver, R. , Zhang, N. , Barnes, B. , Qin, J. , Zhou, H. and Dixson, R. (2011), A Bayesian Statistical Model for Hybrid Metrology to Improve Measurement Accuracy, Modeling Aspects in Optical Metrology, Munich, -1, [online], (Accessed April 18, 2024)
Created July 31, 2011, Updated February 19, 2017