| The requirement to simulate larger and more complex interconnect circuits is being driven by the rapid developments that are taking place in the integrated circuit industry, where more complex circuits are continually being designed. Since full-wave analyses rigorously account for all the higher-order modes, in addition to the transmission line mode (i.e., the Transverse ElectroMagnetic (TEM) mode), they provide more accurate results than conventional 2-D analysis tools, which are based on the assumption that only a TEM mode exists. Furthermore, a full-wave analysis is required to accurately model the physics of complex 3-D interconnects.; In order to address this need a Full-Wave Layered Interconnect Simulator (UA-FWLIS) was previously developed. UA-FWLIS is a Method of Moments (MoM) based tool for the analysis of stripline interconnects. However, UA-FWLIS could only handle a maximum of 10000 unknowns for signal traces in a single layer. Our final goal is to simulate complex practical systems, which have hundreds of thousands of unknowns and consist of multiple layers with vias interconnecting the different layers. In this dissertation, we extend the prototype full-wave simulator so that it can handle reactions between signal traces and vias, as well as reactions between two multiple layers. This is accomplished by employing analytical techniques to the reactions elements, thereby avoiding the use of inefficient numerical integration algorithms. This leads to substantial reductions in the matrix fill time, e.g., two orders of magnitude reductions for moderate size problems.; In addition to improving the matrix fill time, we also dramatically reduce the matrix solution time by employing sparse matrix solution techniques. We demonstrate that sparse reaction matrices are produced when modeling stripline interconnects provided that a parallel-plate Green's function is employed in the analysis. We found that by applying sparse matrix storage techniques and a sparse matrix solver, it is possible to dramatically improve the matrix solution time when compared with a commercial MoM-based simulator. This also makes it possible to solve much larger problems. The contribution of this dissertation empowers the current full-wave simulator to handle more realistic problems and makes full-wave simulations of very large scale stripline interconnect structures feasible. |
