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Parametric uncertainty in nanoscale optical dimensional measurements



James E. Potzick, Egon Marx


Image modeling establishes the relation between an object and its image when an optical microscope is used to measure the dimensions of an object of size comparable to the illumination wavelength. It accounts for the influence of all of the parameters which can affect the image, and relates the apparent feature width in the image to the true feature width on the object. The values of these parameters, however, have uncertainties and these uncertainties propagate through the model and lead to parametric uncertainty in the feature width measurement, a key component of the combined measurement uncertainty. The combined uncertainty is required in order to decide if the result is adequate for its intended purpose and to ascertain if it is consistent with other results. The parametric uncertainty for optical photomask measurements derived using an edge intensity threshold approach has been described previously; this paper describes an image library approach to this issue and shows results for optical photomask metrology over a feature width range of 10 nm to 8 µm using light of wavelength 365 nm. The principles will be described, the 1-dimensional image library used and the method of comparing images, along with a simple interpolation method, will be explained, and results presented. This method is easily extended to any kind of imaging microscope and to more dimensions in parameter space. It is more general than the edge threshold method and leads to markedly different uncertainties for features smaller than the wavelength.
Applied Optics


dimensional metrology, photomask, photomask linewidth, measurement uncertainty, image modeling, image library, parametric uncertainty


Potzick, J. and Marx, E. (2012), Parametric uncertainty in nanoscale optical dimensional measurements, Applied Optics, [online], (Accessed May 20, 2024)


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Created June 9, 2012, Updated October 12, 2021