Fast parameter extraction of general interconnects using geometry independent measured equation of invariance

Abstract

(MEI) is a new concept in computational electromagnetics. It has been demonstrated that the MEI technique can be used to terminate the meshes very close to the object boundary and still strictly preserves the sparsity of the FD equations. Therefore, the nal system matrix encountered by MEI is a sparse matrix with size similar to that of integral equation methods. However, complicated Green's function, disagreeable Sommerfeld integrals, and very di cult umbilical meshes for multiconductors make the traditional MEI very di cult, if not impossible, to be applied to analyze multilayer and multiconductor interconnects. In this paper, we propose the Geometry Independent MEI (GIMEI) which substantially improved the original MEI method. We use GIMEI for capacitance extraction of general two-dimension and threedimension VLSI interconnect. Numerical results are in good agreement with published data and those obtained by using FASTCAP from MIT and some other commercial tools, while GIMEI are generally an order of magnitude faster than FASTCAP with much less memory usage. Keywords|interconnects, fast 3D extraction, Measured Equation of Invariance (MEI), geometry independent, measuring loop, capacitance matrix

Fast capacitance extraction of actual 3-D VLSI interconnects using quasi-multiple medium accelerated BEM

“…Compared with the semianalytical approaches proposed by Hong et al [9] and Zhu et al [10], [11], the direct BEM can deal with more complicated 3-D structure of the interconnects. In fact, the geometry that the semianalytical approaches can deal with has some limitations [8]. However, the direct BEM generally leads to a nonsymmetric coefficient matrix and the matrix for a single dielectric region is dense.…”

“…They can be classified as the indirect boundary element method (BEM) [1]- [4], direct BEM [5], [6], the method of the measured equation of invariance (MEI) [7], [8], [18], and several kinds of semianalytical approaches Manuscript [9]- [11]. In both the indirect and direct BEM, only surfaces of three-dimensional (3-D) objects are discretized, and a smaller system of linear equations is obtained.…”

“…The MEI technique can terminate the meshes very close to the object boundary and still preserves the sparsity of the finite-difference (FD) equations. The geometry independent measured equation of invariance (GIMEI) is proposed for the capacitance extraction of the general two-dimensional (2-D) and 3-D interconnects by using free-space Green's function only [8]. The MEI method has now been developed to on-surface level, where a surface mesh is used to keep the number of unknowns in minimum [18].…”

Hierarchical Block Boundary-Element Method (HBBEM): A Fast Field Solver for 3-D Capacitance Extraction

“…The local approaches are well-known flat field solutions that solve the Laplace equation with a preset bias on conductors by using the finite-difference method (FDM) [5], finite-element method (FEM) [2] or boundary-element method (BEM) [6], [21], [24], [25], etc. [15], [17], [18], [23]. Many acceleration methods have been presented, such as the multipole acceleration [6], hierarchical acceleration [21], and quasi-multiple medium (QMM) [25].…”

BBE: hierarchical computation of 3-D interconnect capacitance with BEM block extraction

“…In this section, the BBE method is used to analyze one simple 3-D structures first whose results are compared with those in [9] and [10]. Then, 89 3-D cases cut from the real layout are used to depict the performance of BBE method, whose computational results are compared with the 3-D field solver software "RAPHAEL".…”