High performance domain decomposition methods for signal integrity modeling in 3-D interconnects

Advances in interconnect technologies, such as the increase of the number of metal layers and 3-D stacking technique, have paved the way for higher functionality and superior performance while reducing size, power, and cost in modern integrated circuit and packages. However, whether or not the package preserves signal integrity has become a crucial concern for system designers. In this study, a scalable multi-scale full-wave electromagnetic solver is proposed for 3-D circuit/package simulations. The key ideas of the proposed work include: (1) adaptive geometry-aware domain decomposition methods to conquer the geometric complexity of physical domain, by which an arbitrarily complicated interconnect model can be decomposed into a collection of components, the so-called sub-domains; (2) a flexibly hybrid solution strategy, where volume-based differential equation solvers and surface-based integral solvers can be applied to individual sub-domain problems based on local characteristics; and (3) parallel and scalable computational algorithms to reduce the time complexity via high performance computing architectures. The strength and flexibility of the proposed method will be illustrated by means of several product-level package benchmark.