Segmentation method for modeling and simulation of electromagnetic bandgap (EBG) structures in three-dimensional integrated circuit (3D-IC) and package

Abstract

Driven by the demand for increasing the operating frequency and data rates, a large number of researches on a three dimensional integrated circuit (3D-IC) are conducted, which is a promising technology that leads to a shortened interconnect length, a high clock frequency, and a low power consumption. Power and ground noise (P/G noise), however, becomes a more serious in 3D-ICs and packages because the high clock frequency and data rates result in the wideband spectra of P/G noise. Electromagnetic bandgap (EBG) structures can be a solution for suppression of wideband P/G noise in 3D-ICs and packages due to their wideband suppression characteristics, ease of fabrication, simplicity in design, low cost, and compatibility with power distribution networks. Estimating the performance of EBG structures embedded in the 3D-ICs and packages is a key of the 3D-IC free from the P/G noise, which results in the performance improvement. In this dissertation, we propose a hybrid analytical modeling method based on a segmentation method to predict the P/G noise coupling coefficient of EBG structures in 3D-ICs and packages. The proposed modeling method remarkably reduces the computation time of calculating the P/G noise coupling coefficient of the EBG structures with high accuracy compared to the finite-difference time-domain (FDTD) method and finite element method (FEM). The proposed modeling method consists of three steps of segmentation, segment modeling, and recombination of the segments. In the first step, the EBG structure is divided into multiple segments such as the unit cell of the EBG structure, rectangular power/ground planes, and power/ground planes having an aperture. In the next step, the segments are modeled analytically using a modal decomposition and a resonant cavity model. In the final step of the proposed modeling method, the impedance matrices of the segmented EBG structure are recombined. In the recombination step, generalized impedance matrices (GIM) for...