New and Exact Filling Algorithms for Layout Density Control

To reduce manufacturing variation due to chemicalmechanical polishing and to improve yield, layout must be made uniform with respect to density criteria. This is achieved by layout postprocessing to add ll geometries, either at the foundry or, for better convergence of performance veri cation ows, during layout synthesis [10]. This paper proposes a new min-variation objective for the synthesis of ll geometries. Within the so-called xed-dissection regime (where density bounds are imposed on a predetermined set of windows in the layout), we exactly solve the min-variation objective using a linear programming formulation. We also state criteria for ll pattern synthesis, and discuss additional criteria that apply when ll must be grounded for predictability of circuit performance. We believe that density control for CMP will become an important research topic in the VLSI design-manufacturing interface over the next several years.