Lithographic tolerances based on vector diffraction theory

The classic rules for scaling lithographic resolution derive from scalar models of image formation in air, and must be reexamined as numerical apertures (NAs) increase beyond 0.5. This article describes a vector image code (VIC) based on plane wave decomposition of the radiation that propagates from the exit pupil, and a modified thin film treatment of propagation into the photoresist. Tolerances on resolution, depth-of-focus (DOF), and source polarization can be derived from VIC simulations. The strongest vector diffraction effects arise from polarization in the illumination, producing nonscalar effects in exposure-to-clear curves (‘‘swing curves’’), as well as orientation-dependent asymmetries in printed patterns. Modeling shows that the small asymmetries previously reported [D. Flagello, A. E. Rosenbluth, C. Progler, and J. Armitage, Microcircuit Engineering 1991 (Elsevier, New York, 1991)] at 0.55 NA increase rapidly for NAs beyond 0.7. Resolution increases more slowly than NA−1 at high NA, even with unpolarized illumination and perfect focus control. The contrast loss can largely be ascribed to the in-plane or parallel component of the E field within any image slice; the out-of-plane or perpendicular component actually shows a slight contrast increase. Snell’s law reduces the angular range of E orientations in the resist, so the contrast loss in resist is much less than in air. At high NA, the aerial image loses its relevance as a predictor of lithographic performance. Snell’s law also implies spherical aberration in the refracted field, reducing DOF in thick resist layers. Further, focal tolerances calculated with the traditional ±λ/2 NA2 criterion are shown to be optimistic, since this criterion is derived from the paraxial form for defocus.