Parasitic Capacitance Extraction Using Finite Element Method on Polygonal Mesh through Piecewise Interpolation

Abstract

Parasitic capacitance extraction is a critical issue in the area of integrated circuit (IC), its performance heavily depends on the electromagnetic field solver involved. To improve the computation accuracy and efficiency, the interpolation finite element methods (FEM) have been investigated to deal with polygonal elements. Such methods are based on the thinking of generalized barycentric coordinates, such as mostly used mean value coordinates, Sibson coordinates, andetc. They have demonstrated good convergence and accuracy. However, they are time consuming during processing shape functions for Galerkin-schema FEM. A kind of piecewise interpolation method within convex polygonal element is presented. The polygon is divided into triangular sub-regions utilizing its barycenter, where the shape functions related to the whole polygon are conveniently and quickly acquired. The method has excellent performance in computation speed and shows good convergence and high accuracy. A comparison between different FEMs is performed with a typical electrostatic capacitance extraction example.