In this paper, we describe the algorithms used in FastImp, a program for accurate analysis of wide-band electromagnetic effects in very complicated geometries of conductors. The program is based on a recently developed surface integral formulation and a precorrected fast Fourier transform (FFT) accelerated iterative method, but includes a new piecewise quadrature panel integration scheme, a new scaling and preconditioning technique as well as a generalized grid interpolation and projection strategy. Computational results are given on a variety of integrated circuit interconnect structures to demonstrate that FastImp is robust and can accurately analyze very complicated geometries of conductors.

In this paper we describe the algorithms used in FastImp, a program for accurate analysis of wide-band electromagnetic effects in very complicated geometries of conductors. The program is based on a recently developed surface integral formulation and a precorrected-FFT accelerated iterative method, but includes a new scaling and preconditioning technique as well as a generalized grid interpolation and projection strategy. Computational results are given on a variety of integrated circuit interconnect structures to demonstrate that FastImp is robust and can accurately analyze very complicated geometries of conductors.

Detailed electromagnetic analysis of three-dimensional structures in multi-layered dielectric media is critical for automatic generation of equivalent circuit models for the interconnects and packages in RF or mixed signal integrated circuits. In this paper we present a new wideband surface integral formulation that can be readily combined with the well-established layered Green's function techniques. In discretizing the formulation, we have used the well-known RWG linear basis function to reduce the number of unknowns. Using a so-called loop-star basis transformation and the frequency normalization, the accuracy at low frequencies has been improved substantially. Several numerical examples are used to validate the accuracy and robustness of this new formulation.

There exist the complicated waveguide modes as well as the surface waves in the electromagnetic field induced by a horizontal electric dipole in layered lossless dielectrics between two ground planes. In spectral domain, all these modes can be characterized by the rational parts with the real poles of the vector and scalar potentials. The accurate extraction of these modes plays an important role in the evaluation of the Green’s function in spatial domain. In this paper, a new algorithm based on rational approximation is presented, which can accurately extract all the real poles and the residues of each pole simultaneously. Thus, we can get all the surface wave modes and waveguide modes, which is of great help to the calculation of the spatial domain Green’s function. The numerical results demonstrated the accuracy and efficiency of the proposed method.

In order for parasitic extraction of high-speed integrated circuit interconnect to be sufficiently efficient, and fit with model-order reduction techniques, a robust wideband surface integral formulation is essential. One recently developed surface integral formulation has shown promise, but was plagued with numerical difficulties of poorly understood origin. We show that one of that formulation's difficulties was related to the inaccuracy in the approach to evaluate integrals over discretization panels, and we present an accurate approach based on an adapted piecewise quadrature scheme. We also show that the condition number of the original system of integral equations can be reduced by differentiating one of the integral equations. Computational results on a ring and a spiral inductor are used to show that the new quadrature scheme and the differentiated integral formulation improve accuracy and accelerate the convergence of iterative solution methods.

In this paper, we present a new capacitance extraction method named Dimension Reduction Technique (DRT) for 3D VLSI interconnects. The DRT converts a complex 3D problem into a series of cascading simple 2D problems. Each 3D problem is solved separately, so we can choose the most efficient method according to the arrangement of conductors. More importantly, it is very easy to obtain the analytical solutions of 2D problem in many layers such as the pure dielectric layers and the layers with parallel signal lines. Therefore, the domain that has to be analyzed numerically is minimized. This leads to the drastic reduction of the computing time and memory needs. We have used the DRT to extract the capacitances of multilayered and multiconductor cross-overs, bends, via with signal lines and open-end. The results are in good agreement with those of Ansoft's SPICELINK and MIT's FastCap, but the computing time and memory size used by the DRT are several even tens times less than those used by SPICELINK and FastCap.