Automatic design rule correction in presence of multiple grids and track patterns

Traditionally, automatic design rule correction (DRC) problem is modeled as a Linear Program (LP) with design rules as difference constraints under minimum perturbation objective. This yields Totally Uni-Modular (TUM) constraint matrices thereby guaranteeing integral grid-compliant solutions with LP solvers. However, advanced technology nodes introduce per-layer grids or discrete tracks that result into non-TUM constraint matrices for the DRC problem. Consequently, LP solvers do not guarantee integral solutions. In this work, we propose a novel formulation using an 'unrolling' technique. Our formulation guarantees TUM constraint matrices and hence integral multiple grid/track compliant solutions. We demonstrate its efficacy on layouts at advanced nodes.