Analytical approach to high-NA images

Since 193 nm ArF lithography is the practical wavelength, the high and hyper numerical aperture technologies prolong and start its lithography ending for further improvement of the resolution. Application of polarization illumination leads to the 25 % increase of depth of focus and exposure latitude. Hence, polarization simulation becomes a key technology for its control and application. In this paper, polarization of numerical aperture is modeled into aerial image by using a vector model as an improved scalar model. In terms of small half pitch nodes, polarized effects are described into aerial and resist images. For high and hyper numerical aperture, the TM polarized degradation of aerial and resist images are severe, so that the reduction of TM polarization is required for below 45 nm half pitch pattern formation. In the comparison with the un-polarized small half pitch formation, the optical proximity effects of TE polarization are similar for dense patterns, but those effects are different for sparse patterns. Hence, the sparse pattern formation of TE polarization is preferred to the optical proximity correction.