Extension of an Efficient Moment-Methods-Based Full-Wave Layered Interconnect Simulator to Finite-Width Expansion Functions

A computationally efficient full-wave tool, which can correctly model the high frequency effects in advanced 3D packaging designs, e.g., crosstalk, signal distortion, etc., is highly desirable for the design iteration process. A prototype full-wave layered interconnect simulator, which employs a filamentary approximation, was previously developed to model stripline circuits. It demonstrated the promise of new analytical techniques used to accelerate the method-of-moments-based full-wave simulator. Recently, a series of extensions has been made to enhance the prototype simulator. One key extension that is discussed in this paper is the incorporation of rectangular-based finite-width expansion functions into the simulator, which allows the simulator to handle more practical cases. Furthermore, this extension provides the technical foundation required to model bends, steps, and other interconnect features in the future. Some critical issues, which were not properly addressed in the prototype simulator, are also addressed in this paper. They are the branch point contribution to the reaction element and the exact solution for an angular canonical function. A computationally efficient expression for the computation of the semi-infinite integral is also included. This enhanced simulator is validated by comparing it with results produced by agilent momentum, and great improvements in matrix fill times are demonstrated.