A Hybrid Boundary Element and Analytical Method (BEAM) for Efficient Capacitance Extraction in Multilayer Dielectrics

Abstract

In this article, a hybrid approach combining the boundary element method (BEM) with analytical solution of stacked dielectrics is proposed for the capacitance extraction of multilayer dielectric structures. First, the flexible BEM employs an adaptive refined mesh to address the interconnect region, which contains complex conductors and conformal dielectrics. Second, for the upper and lower stacked dielectrics, the analytical solution based on separation of variables technique is derived to construct interface equations. After that, these equations are treated as the numerical boundary conditions and incorporated into the matrix equation formed by the BEM in the interconnect region. By this means, the proposed hybrid boundary element and analytical method efficiently compresses the regular stacked dielectrics into interface equations through analytical expressions, ensuring high accuracy without introducing additional errors. Furthermore, the numerical discretization is confined to the interconnect region, greatly reducing the number of unknowns and resulting in significant savings in computational resources. Numerical examples validate the accuracy and efficiency of the proposed method.