An efficient transient modeling for 3-D multilevel interconnections in a stratified dielectric medium

Abstract

An efficient method is presented to model the transient characteristics of distributed resistor–capacitor of ULSI multilevel interconnections on complex topography, in which the reformulation of the boundary-element method (BEM) associated with the Padè-via-Lanczos (PVL) algorithm can avoid the redundant works on both volume mesh and transient analysis associated with the finite-difference method. An adaptive multilayer closed-form spatial Green's function for BEM is developed to examine the voltage and current responses of the multilevel conductor system by using the boundary-element method of integral formulation, in which arbitrary triangular elements on the surface of conductors are used to efficiently calculate the free-charge distributions of complex structure based on actual topography/processes. Applying the Galerkin principle over boundary elements, all of the surface integrals of charge distribution have been discretized and evaluated analytically for constant element. To improve the timing-analysis efficiency of the finite-difference method, the dominant poles are obtained by introducing the Padè-via-Lanczos (PVL) algorithm for model-order reduction. Hence, it is easy to calculate the transient characteristics of both parallel conductors and complicated configurations such as crossing lines, corners, contacts, multilayers and their combinations. Therefore, a simple and more general method is proposed for solving the combinations of complex structures based on actual topography/processes and arbitrary geometric configurations of multilevel interconnection lines in order to link with the present CAD tools.