Timing-driven via placement heuristics for three-dimensional ICs

The dependence of the interconnect delay on the interplane via location in three-dimensional (3-D) ICs is investigated in this paper. The delay of these interconnects can be significantly decreased by optimally placing the interplane vias. The via locations that minimize the propagation delay of two-terminal interconnects consisting of multiple interplane vias under the distributed Elmore delay model are determined. For interconnect trees, the interplane via locations that minimize the summation of the weighted delay of the sinks of the tree are also determined. For these interconnect structures, the interplane via locations are obtained both through geometric programming and near-optimal heuristics. Placement constraints are imposed such that the path is negligibly affected. The proposed heuristics are used to implement efficient algorithms that exhibit lower computational times as compared to general optimization solvers with negligible loss of optimality. Various interplane via placement scenarios are considered. Simulation results indicate delay improvements for relatively short point-to-point interconnects of up to 32% with optimally placed interplane vias. For interconnect trees, the maximum improvement in delay for optimally placed interplane vias is 19%. The proposed algorithms can be integrated into a design flow for 3-D circuits to enhance placement and routing where timing is a primary design criterion.