Contact area as the intuitive definition of contact CD based on aerial image analysis

As feature sizes continue to diminish, optical lithography is driven into the extreme low-k1 regime, where the high MEEF increasingly complicates the relationship between the mask pattern and the aerial image. This is true in particular for twodimensional mask patterns, which are by nature much more complicated than patterns possessing one-dimensional symmetry. Thus, the intricacy of 2D image formation typically requires a much broader arsenal of resolution enhancement techniques over complex phase shift masks, including SRAFs and OPC, as well as exotic off-axis illumination geometries. This complexity on the mask side makes the printability effect of a random defect on a 2D pattern a field of rich and delicate phenomenology. This complexity is reflected in the dispute over the CD definition of 2D patterns: some sources use the X and Y values, while others use the contact area. Here, we argue that for compact features, for which the largest dimension is not wider than the PSF of the stepper optics, the area definition is the natural one. We study the response of the aerial image to small perturbations in mask pattern. We show that any perturbation creates an effect extending in all directions, thus affecting the area and not the size in a single direction. We also show that, irrespective of the source of perturbation, the aerial signal is proportional to the variation in the area of the printed feature. The consequence of this effect is that aerial inspection signal scales linearly with the variation of printed area of the tested feature.