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Improving Optical Measurement Uncertainty with Combined Multitool Metrology Using a Bayesian Approach



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


Recently, there has been significant research investigating new optical technologies for dimensional metrology of features 22 nm in critical dimension and smaller. When modeling optical measurements, a library of curves is assembled through the simulation of a multidimensional parameter space. A nonlinear regression routine described in this paper is then used to identify an optimum set of parameters that yields the closest experiment-to-theory agreement. However, parametric correlation, measurement noise, and model inaccuracy all lead to measurement uncertainty in the fitting process for optical critical dimension measurements. To improve the optical measurements, other techniques such as atomic force microscopy and scanning electronic microscopy can also be used to provide supplemental a priori information. In this paper, a Bayesian statistical approach is proposed to allow the combination of different measurement techniques that are based on different physical measurements. The effect of this hybrid metrology approach will be shown to reduce the uncertainties of the parameter estimators.
Applied Optics


linear unbiased estimator, generalized least squares, nonlinear regression, optical critical dimension measurements, scatterfield microscopy.


Zhang, N. , Silver, R. , Zhou, H. and Barnes, B. (2012), Improving Optical Measurement Uncertainty with Combined Multitool Metrology Using a Bayesian Approach, Applied Optics, [online], (Accessed April 14, 2024)
Created August 30, 2012, Updated January 27, 2020