A combined BEM/FEM method for IC substrate modeling

Abstract

The research presented in this thesis was done in the context of the modeling of parasitic physical effects, like field couplings and crosstalk, that may adversely affect the functional performance of Integrated Circuits (ICs). The modeling of parasitic effects, through simulations with the resulting models, provides insight into the performance of the IC, before its actual fabrication. This thesis has particularly studied the modeling of the IC substrate as a medium for crosstalk between active devices. Modeling of the substrate can be done through modeling techniques like the Finite Element Method (FEM), or the Boundary Element Method (BEM), with each its own characteristics. The FEM is accurate and flexible, but typically slow, whereas the BEM is typically faster, but less flexible and only accurate in more restricted situations. When applied to modern substrate technologies, however, the speed limitations in the FEM and the accuracy limitations in the BEM are typically emphasized. In this context, this thesis proposes a combined BEM/FEM method, where the substrate modeling problem is consistently partitioned into a BEM and a FEM part, such that the structure of the modeling problem itself and the properties of the BEM and FEM modeling techniques are exploited. In particular, global parasitic couplings are captured with a coarse and sparse (i.e. fast) BEM, while local couplings are captured with a reduced-order FEM that contracts equipotential nodes. The result is a sparse, reduced-order BEM/FEM method that operates in a new trade-off between the speed of the BEM and the accuracy of the FEM.