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 Padi-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 Pade-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. (C) 1998 Published by Elsevier Science Ltd. All rights reserved.