Modeling of signal and power integrity in system on package applications

We present a method for fast analysis of signal and power integrity in system-on-package applications based on a recently developed multilayered finite difference method (M-FDM). First we present a rapid solver that can be used to extract materials properties of dielectrics. The extracted frequency-dependent dielectric constant and loss tangent can then be used in any field simulator for improved accuracy. Then we present M-FDM for simulation of system-on-package applications. In order to accurately model multilayered planar structures, which are three dimensional, M-FDM combines two-dimensional models for power/ground planes using a multilayered unit cell approach. In this way, noise coupling can be considered not only in the transversal direction between two planes, but also vertically from one plane pair to another through the apertures and via holes. For a co-simulation of signal and power integrity, transmission line models also need to be included. The interaction between the signal transmission and power distribution modes is taken into account using a modal decomposition technique. An equivalent circuit model becomes available based on this finite difference approximation as well. Based on this network representation, second order effects such as fringe and gap fields can be included in M-FDM using equivalent circuit models for these fields. This results in a very accurate method that can be used for fast analysis of signal and power integrity in arbitrary package and board designs having any stack-up configuration and number of layers.