Modeling and Analysis of Power Distribution Networks in 3-D ICs

This paper addresses the modeling and analysis problems for power distribution networks (PDNs) in 3-D ICs. An on-chip distributed model is proposed for 3-D power grids, in which the details of metal layers are considered. The distributed model is demonstrated to be essential to identifying the unique noise behavior of 3-D PDNs. A lumped model is proposed based on the distributed model. The lumped model features the connection impedance between tiers and is proven to be useful for designers to understand the global effects of 3-D PDNs. Based on the models, an analysis flow is designed for 3-D PDNs in both frequency domain and time domain. With the analysis flow, the electrical characteristics of 3-D PDNs are studied systematically for the first time. The frequency-domain analysis identifies the global and local resonance phenomena in 3-D PDNs that are distinct from those in 2-D PDNs. The physical mechanisms behind the resonance phenomena are investigated. The time-domain analysis predicts the worst-case supply noise based on distributed current constraints. The “Rogue Wave” concept is introduced to explain the spatial and temporal relations of the worst-case on-chip noise responses in 3-D PDNs.