Image simulation in immersion lithography using Debye integral and scattering matrix method

Abstract

Three dimensional image theory developed by Flagello <i>et al </i>is applied to the modeling of immersion lithography, which is characterized by the combination of vector image theory, Debye integral theorem, and the response of layered structure. Using this formulation, the behavior of contrast and DOF against numerical aperture(NA) are investigated, which are related with polarization and multilayer interference. It is shown that the contrast for TM wave decreases significantly with NA up to half of the contrast for TE wave when NA is 1.3. Noticeably, in this result, an inflection point is observed, which does not exist in the contrast curve of aqua image. We try to explain this phenomenon using the difference in the coupling property of TE and TM wave. In addition, DOF of immersion and dry lithography are compared to show that immersion lithography has larger DOF than dry lithography, and the ratio of DOF in immersion lithography to DOF in dry lithography is plotted to show that it increases considerably with NA, contrary to the result of Rayleigh’s equation, in which the ratio must be a constant.