Accurate Electromagnetic Modeling Methods for Integrated Circuits

Abstract

The present development of modern integrated circuits (IC’s) is characterized by a number of critical factors that make their design and verification considerably more difficult than before. This dissertation addresses the important questions of modeling all electromagnetic behavior of features on the chip, efficient methods to solve large systems of equations and Model Order Reduction techniques in layout-to-circuit extraction. More specifically, it covers the following issues: • The Surface Integrated Field Equations Method which solves, in an unified framework and even for difficult high contrast situations, the static and stationary electric and magnetic field problems and the electromagnetic field problems in both time and frequency domain. • The Hierarchically Semi-separable theory that is based on exploiting structural properties of sub-matrices of the original. • The Mult-Level Hierarchical Schur Algorithm which succeeds in reducing the computational complexity while computing an accurate estimation to the values of the neglected capacitances in 3D layout-to-circuit extraction.