Fast Calculation of Interconnect Capacitances Using the Finite Difference Method Applied in Conjunction With the Perfectly Matched Layer (PML) Approach for Mesh Truncation

A finite difference (FD) method for rapid and accurate evaluation of capacitance matrices of interconnect configurations is described in this work. The method utilizes the newly developed Perfectly Matching Layer technique for mesh truncation, specially adapted to the static case in conjunction with a mixed boundary condition, referred to herein as the ?>-technique. Applications of the proposed approach to the modeling of complex structures, comprising multiple metal layers, crossovers, vias and bends embedded in a layered dielectric medium, are illustrated in this chapter. The technique has been combined with the domain decomposition approach to compute the capacitance matrices of complex interconnect configurations in an efficient manner. Both the overlapping and nonoverlapping domain types of approaches are employed to model the interconnects, and convergence and efficiency issues of the proposed algorithms are examined. A novel approach for efficient truncation of a class of large interconnects called the wraparound scheme, is introduced in this work. Several numerical examples that illustrate the efficiency and flexibility of the approaches, described above, are included.