Predictive modeling of advanced illumination pupils used as imaging enhancement for low k1 applications

The specific properties of the illumination system are of increasing importance for the realization of low-k1 applications in modern lithography. In this paper, we present numerical investigations of optical imaging performance using real illuminator pupils in contrast to conventional simulations based on an idealized tophat pupil assumption. We study the impact of non-idealized radial and azimuthal intensity distributions as well as the consequence of local in-homogeneities in the pupil. Furthermore, we discuss the effect of scanning, and details of the numerical implementation. We quantify the imaging impact of the different illumination pupils by computing the through pitch, and through focus behavior of several low-k1 applications. We demonstrate that the tophat assumption often does not provide sufficiently accurate results. In particular, for annular and multi-pole settings, the real radial, and azimuthal intensity distribution have to be taken in to account. Accordingly, we introduce a simple heuristic model describing the real illumination pupil. Using this smooth pupil model, we demonstrate a significantly improved imaging performance prediction accuracy. Local pupil inhomogeneities have a minor impact. For coherent, and conventional settings, finally, we find that a modified tophat assumption gives already sufficiently accurate results, and can be applied for predictive simulations.