Extreme mask corrections: Technology and benefits

We establish criteria to recognize extreme OPC corrections and discuss their difference from the traditional corrections. Then we present new proximity correction methods for rigorous bi- and tri- tone mask optimization that cast problem as a constraint minimization over the space of piecewise constant or continuous functions. The primary optimization objective is stated as a contour integral over the target. The constraints on image amplitude form convex functionals for dark areas and non-convex functionals for bright areas. A Lagrangian of this constrained problem is minimized. This delivers extreme, aggressive mask corrections, which are not confined by the fragmentation schema or the orientation of its sites. We analyze performance of these corrections under challenging process conditions and evaluate fidelity benefits.