Mixed-Cell-Height Placement with Complex Minimum-Implant-Area Constraints

Mixed-cell-height standard cells are prevailingly used in advanced technologies to achieve better design trade-offs among timing, power, and routability. As feature size decreases, placement of cells with multiple threshold voltages may violate the complex minimum-implant-area (MIA) layer rule arising from the limitations of patterning technologies. Existing works consider the mixed-cell-height placement problem only during legalization, or handle the MIA constraints during detailed placement. In this paper, we address the mixed-cell-height placement problem with MIA constraints into two major stages: post global placement and MIA-aware legalization. In the post global placement stage, we first present a continuous and differentiable cost function to address the Vdd/Vss alignment constraints, and add weighted pseudo nets to MIA violation cells dynamically. Then, we propose a proximal optimization method based on the given global placement result to simultaneously consider Vdd/Vss alignment constraints, MIA constraints, cell distribution, cell displacement, and total wirelength. In the MIA-aware legalization stage, we develop a graph-based method to cluster cells of specific threshold voltages, and apply a strip-packing-based binary linear programming to reshape cells. Then, we propose a matching-based technique to resolve intra-row MIA violations and reduce filler insertion. Furthermore, we formulate inter-row MIA-aware legalization as a quadratic programming problem, which is efficiently solved by a modulus-based matrix splitting iteration method. Finally, MIA-aware cell allocation and refinement are performed to further improve the result. Experimental results show that, without any extra area overhead, our algorithm still can achieve 8.5% shorter final total wirelength than the state-of-the-art work.