Capacitance extraction for electrostatic multiconductor problems by on-surface MEI

In this paper, on-surface measured equation of invariance (OSMEI) method is implemented for capacitance extraction of electrostatic multiconductor interconnect problems. OSMEI uses the same mesh as that in method of moments (MoM), but generates highly sparse matrices rather than a full matrix. In comparison with "standard" MEI which contains a few finite difference (FD) or finite element (FE) mesh layers, the number of unknowns and the computation memory can be saved. For each OSMEI equation in the multiconductor interconnects, a given node on a given conductor is forced into coupling with the few adjacent nodes on conductor itself and the few sampled nodes on other conductors. Thus, the system sparse matrices can be generated. The convergent behavior of the capacitance with the number of the nodes in the OSMEI equations has been widely investigated, Numerical examples of the capacitance extraction for two-dimensional (2-D) and three-dimensional (3-D) multiconductor interconnects show that the computing errors are within 24%. The OSMEI method may become a powerful technique for the more complex interconnect problems.