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Use of Bayesian Statistics to Improve Optical Measurement Uncertainty by Combined Multi-Tool Metrology



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 32 nm in critical dimension and smaller. When modeling optical measurements a library of curves is assembled through the simulation of a multi-dimensional parameter space. A nonlinear regression routine described in this paper is then used to identify the 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 (OCD) measurements. To improve the optical measurements, other techniques such as atomic force microscopy (AFM) and scanning electronic microscopy (SEM) 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 measurement. The effect of this approach will be shown to reduce the uncertainties of the parameter estimators.
Advances in Mathematical and Computational Tools in Metrology and Testing X (vol. 10)
Publisher Info
World Scientific, Singapore, -1


Zhang, N. , Silver, R. , Zhou, H. and Barnes, B. (2015), Use of Bayesian Statistics to Improve Optical Measurement Uncertainty by Combined Multi-Tool Metrology, World Scientific, Singapore, -1, [online], (Accessed May 20, 2024)


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Created June 25, 2015, Updated January 27, 2020