Efficient three-dimensional extraction based on static and full-wave layered Green´s functions

Integral equation approaches based on layered media Green´s functions are often used to extract models of integrated circuit structures. The primary advantage of these approaches over equivalent-source based schemes is the dramatic reduction in problem size. When combined with an SVD accelerated scheme for the solution of the associated dense linear system, this leads to a substantial speedup. In this paper we derive and solve for these multilayered 3D Green´s functions using a transmission line circuit analog. A generalized image method for an arbitrary number of layers is presented. This method is rapidly convergent for near-field interactions. For the far field, a Chebyshev interpolation approach is adopted, where a database is precomputed (using a fast Wankel transform) and stored. The combination of these two approaches leads to an extremely efficient scheme for the generation of Green´s functions. We combine the SVD-accelerated integral equation solver IES/sup 3/ with the multilayered Green´s function approach, apply it to the extraction of IC parasitics and passive components, and we demonstrate its speed, accuracy and versatility via a number of examples.