Abstract
Design of power delivery network (PDN) is a constrained optimization problem. An ideal PDN must limit voltage drop that results from switching circuits' transients, satisfy current density constraints that arise from electromigration limits, yet use only minimal metal resources so that design density targets can be met. It should also provide an efficient thermal conduit to address heat flux. Furthermore, an ideal PDN should be a regular structure to facilitate design productivity and manufacturability, yet be resilient to address varying power demands across its distribution area. In 3-D ICs, these problems are further constrained by the need to minimize through-silicon via (TSV) area and bridge power lines of different dimensions across tiers, while addressing varying power demands in lateral and vertical directions. In this paper, we propose an unconventional power grid optimization solution that allows us to resize each tier individually by applying tier-specific constraints and yet be optimal in a multitier network, where each tier is locally resized while globally constrained. Tier-specific constraints are derived from electrical and thermal targets of 3-D PDNs. Two resizing algorithms are presented that optimize 3-D PDNs standalone or 3-D PDNs together with TSVs. We demonstrate these solutions on a three-tier setup where significant area savings can be achieved.