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Optimizing Hybrid Metrology: Rigorous Implementation of Bayesian and Combined Regression



Mark Alexander Henn, Richard M. Silver, Nien F. Zhang, Hui Zhou, Bryan M. Barnes, Bin Ming, Andras Vladar, John S. Villarrubia


Hybrid metrology, e.g. the combination of several measurement techniques to determine critical dimensions, is an important approach to meet the needs of semiconductor industry. A proper use of hybrid metrology may not only yield more reliable estimates for the quantitative characterization of 3-D structures but also a more realistic estimation of the corresponding uncertainties. Recent developments at the National Institute of Standards and Technology (NIST) feature the combination of optical critical dimension (OCD) measurements and scanning electron microscope (SEM) results. The hybrid methodology offers the potential to make measurements of essential 3-D attributes that may not be otherwise feasible. However, combining techniques gives rise to essential challenges in the error analysis and combined model function spaces, especially the effect of systematic and highly correlated errors in the measurement on the chi square function that is minimized. Both hypothetical examples and measurement data are used to illustrate solutions to these challenges.
Conference Dates
February 22-26, 2015
Conference Location
San Jose, CA
Conference Title
Metrology, Inspection, and Process Control for Microlithography XXIX


hybrid metrology, electromagnetic simulation, sensitivity and uncertainty evaluation, Bayesian data analysis


, M. , Silver, R. , Zhang, N. , Zhou, H. , Barnes, B. , Ming, B. , Vladar, A. and Villarrubia, J. (2015), Optimizing Hybrid Metrology: Rigorous Implementation of Bayesian and Combined Regression, Metrology, Inspection, and Process Control for Microlithography XXIX, San Jose, CA, [online], (Accessed July 19, 2024)


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Created March 19, 2015, Updated November 10, 2018