PDN impedance modeling and analysis of 3D TSV IC by using proposed P/G TSV array model based on separated P/G TSV and chip-PDN models

The impedance of a power-distribution network (PDN) in three-dimensionally stacked chips with multiple through-silicon-via (TSV) connections (a 3D TSV IC) was modeled and analyzed using a power/ground (P/G) TSV array model based on separated P/G TSV and chip-PDN models at frequencies up to 20 GHz. The proposed modeling and analysis methods for the P/G TSV and chip-PDN are fundamental for estimating the PDN impedances of 3D TSV ICs because they are composed of several chip-PDNs and several thousands of P/G TSV connections. Using the proposed P/G TSV array model, we obtained very efficient analyses and estimations of 3D TSV IC PDNs, including the effects of TSV inductance and multiple-TSV inductance, depending on P/G TSV arrangement and the number of stacked chip-PDNs of a 3D TSV IC PDN. Inductances related to TSVs, combined with chip-PDN inductance and capacitance, created high upper peaks of PDN impedance, near 1 GHz. Additionally, the P/G TSV array produced various TSV array inductance effects on stacked chip-PDN impedance, according to their arrangement, and induced high PDN impedance, over 10 GHz.