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Use of Bayesian statistics to improve optical measurement uncertainty by combined multi-tool metrology


Develop a new approach to combine measurements by various reference metrology results in the uncertainty analysis and library-fitting process to reduce parametric uncertainties.


There has been significant recent research investigating new optical technologies for critical dimension and overlay metrology for the 32 nm node semiconductor devices and beyond.  Much of this work has focused on scatterometry and alternative techniques such as scatterfield microscopy. These optical methods are of particular interest due to their non-destructive, high-throughput characteristics combined with their potential for excellent sensitivity and accuracy.  However, the measurement uncertainties for these optical methods are fundamentally limited by the underlying cross-correlations within the parameter space.To reduce parametric correlation and improve measurement performance and uncertainties, we have been developing a Bayesian statistical approach that integrates a priori information gleaned from other measurements.  This allows us to embed information obtained from reference metrology, complimentary ellipsometry measurements of the optical constants, or to constrain the floating parametric range based on physical limits or known manufacturing variability. 

Major Accomplishments:

This new approach has generated significant interest by the semiconductor industry and has been featured in several plenary and invited presentations as well as invited articles by SPIE and SEMATECH.  Nien Fan Zhang has played a central role in the development of this new approach with his statistical expertise.  We have modeled experimental results from a new optical platform with advanced electromagnetic simulations using the new statistical methods.  The results are lower uncertainties and improved metrology throughput.

Lead Organizational Unit:



Nien Fan Zhang (SED),
Rick Silver (MEL),
Bryne Barnes (MEL),
Hui Zhou (MEL)

Related Programs and Projects:

Scatterfield competence project on statistical modeling of optical critical dimension study


Nien-fan Zhang

100 Bureau Drive, M/S 8980
Gaithersburg, MD 20899-8980