An accurate impedance modeling of a multi-stacked on-chip power distributed network (PDN) based on through-silicon-vias (TSVs) is vitally important to estimate the electrical performance in three-dimensional integrated circuits (3D ICs). This paper proposes a method for calculating the impedance matrix of the multi-stacked on-chip PDN, which mainly consists of arbitrarily distributed TSVs and grid-type on-chip PDNs. First, a real stack-up structure of a multi-stacked on-chip PDN is separated into discrete components intentionally. Then, the equivalent lumped circuit models of all discrete components are assembled into a whole to build the transmission matrix of the multi-stacked on-chip PDN through the relationship between the nodal voltage and the nodal current. Finally, the impedance matrix can be derived through the transmission matrix. In this paper, the coupling of the arbitrarily distributed TSVs and the distributional effect of the on-chip PDN are considered in the impedance matrix through the transmission matrix method (TMM). The proposed method replaces the simulation of the complex equivalent circuit model with the matrix calculation. The verification results show that the deviation of resonant frequency is about 6 $$\%$$ and the conversation of the simulation time is about 99.9 $$\%$$ compared with the HFSS model. It can accurately and quickly calculate the impedance of the multi-stacked on-chip PDN. 

/pdf/impedance-modeling-and-analysis-of-multi-stacked-on-chip-1ka7a0cd.pdf

Impedance modeling and analysis of multi-stacked on-chip power distribution network in 3D ICs

The grid power distribution network (PDN) is an essential component in electronic packages to provide the dc power to circuits. In this paper, an integral equation hybrid method is proposed for the efficient calculation of the impedance of the complex grid PDN. First, the original 3-D grid PDN is reduced to a simple 2-D plane PDN. Both of them have the same input and mutual parasitic impedances. After that, this equivalent plane PDN is solved by using the 2-D integral equation method to consider its arbitrary shape. By comparing between the obtained impedances from the proposed method, full-wave method, and measurement, the accuracy and efficiency of the proposed method is verified. The proposed method provides a simple and useful electronics design automation tool for the power integrity analysis of complex circuits.

Yanbin Yang

Papers

An Integral Equation Hybrid Method for the Impedance Calculation of the Grid Power Distribution Network With an Arbitrary Shape