Placement optimization of power supply pads based on locality

This paper presents an efficient algorithm for the placement of power supply pads in flip-chip packaging for high-performance VLSI circuits. The placement problem is formulated as a mixed-integer linear program (MILP), subject to the constraints on mean-time-to-failure (MTTF) for the pads and the voltage drop in the power grid. To improve the performance of the optimizer, the pad placement problem is solved based on the divide-and-conquer principle, and the locality properties of the power grid are exploited by modeling the distant nodes and sources coarsely, following the coarsening stage in multigrid-like approach. An accurate electromigration (EM) model that captures current crowding and Joule heating effects is developed and integrated with our C4 placement approach. The effectiveness of the proposed approach is demonstrated on several designs adapted from publicly released benchmarks.