Modeling and Analysis of a Power Distribution Network in TSV-Based 3-D Memory IC Including P/G TSVs, On-Chip Decoupling Capacitors, and Silicon Substrate Effects

In this paper, we propose a model for 3-D stacked on-chip power distribution networks (PDNs) in through silicon via (TSV)-based 3-D memory ICs that includes the effects of power/ground TSVs (P/G TSVs), on-chip decoupling capacitors (on-chip decaps), and the silicon substrate. In the modeling procedure of 3-D stacked on-chip PDNs, the distributed RLGC-lumped model of an on-chip PDN, including the effects of the on-chip decaps and silicon substrate, is proposed. Additionally, the RLGC-lumped model of a P/G TSV pair is introduced. The proposed model of the 3-D stacked on-chip PDN combines the proposed models of on-chip PDNs with the models of P/G TSV pairs in a hierarchical order with a segmentation method. The proposed models of the on-chip PDN and 3-D stacked on-chip PDN are successfully validated by simulations and measurements up to 20 GHz. Additionally, with these models, the impedances of the 3-D stacked on-chip PDNs are analyzed with respect to the variations in the number of P/G TSV pairs, the capacitance of on-chip decaps, and the height of an interlayer dielectric layer between the on-chip PDN and silicon substrate. These variations critically affect the impedance of the 3-D stacked on-chip PDN by changing the capacitance and inductance of the PDN.