Efficient integral equation based algorithms for parasitic extraction of interconnects with smooth or rough surface

Abstract

This thesis describes a few efficient parasitic extraction algorithms based on integral equation methods. It has two parts. Part one describes 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 Pre-corrected 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. Part two describes an efficient Stochastic Integral Equation (SIE) Method for computing the mean value and variance of the capacitance of interconnects with random surface roughness in O(Nlog2̂(N)) time. An ensemble average Green's function is used to account for the surface roughness. A second-order correction scheme is used to improve the accuracy. A sparsification technique based on the Hierarchical Matrix method is proposed to significantly reduce the computational cost. The SIE method avoids the time-consuming Monte Carlo simulations and the discretization of rough surfaces. Numerical experiments show that the results of the new method agree very well with those of Monte Carlo simulations.