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Combining model-based measurement results of critical dimensions from multiple tools



Nien F. Zhang, Bryan M. Barnes, Hui Zhou, Mark Alexander Henn, Richard M. Silver


Model-based measurement techniques use experimental data and simulations of the underlying physics to extract quantitative estimates of the measurands of a specimen based upon a parametric model of that specimen. The uncertainties of these estimates are based upon not only the uncertainties in the experimental data, but also the sensitivity of that data to the model parameters, and parametric correlations among those parameters. Through and proofs experimental examples, the combination of two or more model-based techniques is shown to be optimal for obtaining the lowest possible uncertainties, even compared to the Bayesian methods. As an example, using this form of hybrid metrology, state-of-the-art sub-14 nm-wide lines from semiconductor manufacturing are measured using a combined regression from critical-dimension small-angle x-ray scattering and scanning electron microscopy that leads to lower uncertainties.
Measurement Science and Technology


Bayesian statistical analysis, bias, experimental-to-theory agreement, hybrid metrology, nonlinear regression, prior information, simulated values, uncertainty.


Zhang, N. , Barnes, B. , Zhou, H. , , M. and Silver, R. (2017), Combining model-based measurement results of critical dimensions from multiple tools, Measurement Science and Technology, [online], (Accessed June 19, 2024)


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Created April 7, 2017, Updated January 27, 2020