The problem of optimal placement of Sub-Resolution Assist Features (SRAF)

In this paper, we present a formulation of the Sub-Resolution Assist Feature (SRAF) placement problem as a geometric optimization problem. We present three independent geometric methodologies that use the above formulation to optimize SRAF placements under mask and lithographic process constraints. Traditional rules-based methodology, are mainly one dimensional in nature. These methods, though apparently very simple, has proven to be inadequate for complex two-dimensional layouts. The methodologies presented in this paper, on the other hand, are inherently two-dimensional and attempt to maximize SRAF coverage on real and complex designs, and minimizes mask rule and lithographic violations.