title: Optimizing Hybrid Metrology: Rigorous Implementation of Bayesian and Combined Regression.
abstract: Hybrid metrology, e.g., the combination of several measurement techniques to determine critical dimensions, is an increasingly important approach to meet the needs of the semiconductor industry. A proper use of hybrid metrology may yield not only 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 error analysis and comparing results from different instrument models, especially the effect of systematic and highly correlated errors in the measurement on the χ2function that is minimized. Both hypothetical examples and measurement data are used to illustrate solutions to these challenges.
authors.affiliation: Engineering Physics Division, National Institute of Standards and Technology, 100 Bureau Drive MS 8212, Gaithersburg, MD, USA 20899-8212.
authors.forename: Mark-Alexander
authors.initials: MA
authors.lastname: Henn
authors.affiliation: Engineering Physics Division, National Institute of Standards and Technology, 100 Bureau Drive MS 8212, Gaithersburg, MD, USA 20899-8212.
authors.forename: Richard M
authors.initials: RM
authors.lastname: Silver
authors.affiliation: Engineering Physics Division, National Institute of Standards and Technology, 100 Bureau Drive MS 8212, Gaithersburg, MD, USA 20899-8212.
authors.forename: John S
authors.initials: JS
authors.lastname: Villarrubia
authors.affiliation: Statistical Engineering Division, National Institute of Standards and Technology, 100 Bureau Drive MS 8212, Gaithersburg, MD, USA 20899-8212.
authors.forename: Nien Fan
authors.initials: NF
authors.lastname: Zhang
authors.affiliation: Engineering Physics Division, National Institute of Standards and Technology, 100 Bureau Drive MS 8212, Gaithersburg, MD, USA 20899-8212.
authors.forename: Hui
authors.initials: H
authors.lastname: Zhou
authors.affiliation: Engineering Physics Division, National Institute of Standards and Technology, 100 Bureau Drive MS 8212, Gaithersburg, MD, USA 20899-8212.
authors.forename: Bryan M
authors.initials: BM
authors.lastname: Barnes
authors.affiliation: Engineering Physics Division, National Institute of Standards and Technology, 100 Bureau Drive MS 8212, Gaithersburg, MD, USA 20899-8212.
authors.forename: Bin
authors.initials: B
authors.lastname: Ming
authors.affiliation: Engineering Physics Division, National Institute of Standards and Technology, 100 Bureau Drive MS 8212, Gaithersburg, MD, USA 20899-8212.
authors.forename: András E
authors.initials: AE
authors.lastname: Vladár
keywords: Bayesian data analysis; electromagnetic simulation; hybrid metrology; sensitivity and uncertainty evaluation