3D stacked power distribution considering substrate coupling

Reliable design of power distribution network for stacked integrated circuits introduces new challenges i.e., substrate coupling among through silicon vias (TSVs) and tiers grid in addition to reliability issues such as electromigration and thermo-mechanical stress, compared to conventional System on Chip (SoC). In this paper a comprehensive modeling of the TSV and stacked power grid with frequency dependent parasitic is proposed. The analytical model considers the impact of the substrate coupling between the TSVs and layers grid. A frequency domain based analysis flow is introduced to incorporate frequency dependent parasitics. The design of a reliable power distribution network is formulated as an optimization problem to minimize power noise under reliability and electro-migration constraints. Experimental results demonstrate the efficacy of the problem formulation and solution technique.