An efficient resistance sensitivity extraction algorithm for conductors of arbitrary shapes

Abstract

Due to technology scaling, integrated circuit manufacturing techniques are producing structures with large variabilities in their dimensions. To guarantee high yield, the manufactured structures must have the proper electrical characteristics despite such geometrical variations. For a designer, this means extracting the electrical characteristics of a whole family of structure realizations in order to guarantee that they all satisfy the required electrical characteristics. Sensitivity extraction provides an efficient algorithm to extract all realizations concurrently. This paper presents a complete framework for efficient resistance sensitivity extraction. The framework is based on both the Finite Element Method (FEM) for resistance extraction and the adjoint method for sensitivity analysis. FEM enables the calculation of resistances of interconnects of arbitrary shapes, while the adjoint method enables sensitivity calculation in a computational complexity that is independent of the number of varying parameters. The accuracy and efficiency of the algorithm are demonstrated on a variety of complex examples. Categories and Subject Descriptors. J.6 [Computer Aided Engineering]: Computer-aided design (CAD)

Enhanced sensitivity computation for BEM based capacitance extraction using the Schur complement technique

“…As the modeling for resistances is relatively simple [1], [2], most work has concentrated on capacitances. The study started with the worst-case corner method, which was acknowledged to be over pessimistic.…”

“…The incidence matrix B relates the panels to conductors, i.e., B ij equals 1 if panel i lies on conductor j, and 0 otherwise. These partial short-circuit capacitancesC s can be obtained from the inversion of an influence matrixḠ ∈ R m×m (C s =Ḡ −1 ), and thus the short-circuit capacitances C s can be computed 1 as…”