PEEC Modeling in 3D IC/Packaging Applications Based on Layered Green's Functions

A circuit modeling application for three-dimensional (3D) integrated circuits (IC)/packages is proposed in this article. The method is based on the partial element equivalent circuit (PEEC) method and layered Green's functions (LGF). The LGFs are calculated from the discrete complex image method with three terms, direct coupling, complex images, and surface wave extracted to analyze the wave behaviors. The dominant terms for the LGFs are analyzed for four canonical stack-ups in 3D IC/packaging systems. Analytical formulas that include the contribution of the complex images calculated from the LGFs are used for the partial capacitance calculation. A fast-modeling approach is proposed by applying the LGF in PEEC using three acceleration treatments to handle the 3D IC/packaging geometry without sacrificing accuracy. An on-chip power distribution network geometry is used to illustrate and validate the method.