Aerial image model and application to aberration measurement

In this paper, we present a streamlined aerial image model that is linear with respect to projection optic's aberrations. The model includes the impact of the NA, partial coherence, as well as the aberrations on the full aerial image as measured on an x-z grid. The model allows for automatic identification of image's primary degrees of freedom, such as bananicity and Y-icity among others. The model is based on physical simulation and statistical analysis. Through several stages of multivariate analysis a reduced dimensionality description of image formation is obtained, using principal components on the image side and lumped factors on the parameter side. The modeling process is applied to the aerial images produced by the alignment sensor in a 0.75NA ArF scanner while the tool is integration mode and aberration levels are high. Approximately 20 principal components are found to have a high signal-to-noise ratio in the image set produced by varying illumination conditions and considering aberrations represented by 33 Zernike polynomials. The combined coefficients are extracted and the measurement repeatability is presented. The analysis portion of the model is then applied to the measured coefficients and a subset of projection lens' aberrations are solved for.