Behavior and Analysis of Deep Sub-micron Integrated Circuits Including Self and Mutual Inductances

Abstract

Here a set of Elmore-like closed form solutions to analyze the behavior of integrated circuits in the presence of self and mutual inductances is presented. These expressions have linear complexity with the number of elements in the interconnect network, and Elmore delay accuracy characteristics. Besides the use of these expressions in evaluating signal characteristics, the simplicity of the solutions allows an intuitive understanding of the behavior of integrated circuits in the presence of self and mutual inductances together with capacitive coupling. Three problems are analyzed based on these solutions. First, a simple figure of merit to determine the importance of inductance in a bus is introduced. Second, the problem of shielding inductive coupling is investigated analytically. It is shown that inserting ground lines is not very effective in reducing inductive coupling compared to the differential signaling technique. Finally, the delay uncertainty due to different line-switching patterns is investigated. It is shown that inductive coupling reduces the delay variation (switching window width). With these applications of the delay model the opposite impacts of capacitive and inductive coupling in different signal switching patterns are illustrated with reference to the work of Kahng, Muddu, and Sarto.