Rigorous conductor modeling of signal integrity in integrated circuits

We present a multi-region, multi-solver domain decomposition method (MS-DDM) to accurately analyzing the signal integrity problems in integrated circuits with complex geometries. Specifically, we discuss in detail a 3-D full-wave method to model the conductor loss due to finite conductivities in metals. The proposed MS-DDM follows a hierarchical domain partitioning strategy and the original problem is decomposed into non-overlapping subregions. A finite element domain decomposition method (FE-DDM) is adopted for the dielectric subregion with complex geometries and non-uniform material properties. A surface integral equation domain decomposition method (SIE-DDM) is applied for the conductor subregions. To further improve the convergence in the DDM iterations, optimized transmission conditions are introduced to enforce the field continuities across sub-domain interfaces. Moreover, a hierarchical multi-level fast multiple method is adopted to address the low frequency issues that are prominent in IC applications. Rigorous numerical experiments validate the potential benefits offered by the proposed method.