Time-Domain Orthogonal Finite-Element Reduction-Recovery Method for Electromagnetics-Based Analysis of Large-Scale Integrated Circuit and Package Problems

A time-domain orthogonal finite-element reduction-recovery method is developed to overcome the large problem sizes encountered in the simulation of large-scale integrated-circuit and package problems. In this method, a set of orthogonal prism vector basis functions is developed. Based on this set of bases, an arbitrary 3-D multilayered system such as a combined package and die is reduced to a single-layer system with negligible computational cost. More importantly, the reduced single-layer system is diagonal and, hence, can be solved readily. From the solution of the reduced system, the solution of the other unknowns is recovered in linear complexity. The method entails no theoretical approximation. It applies to any arbitrarily shaped multilayer structure involving inhomogeneous materials or any structure that can be geometrically modeled by triangular prism elements. In addition, it permits nonlinear device modeling and broadband simulation within one run. Numerical and experimental results have demonstrated its accuracy and high capacity in simulating on-chip, package, and die-package interface problems.