Measured Equation of Invariance(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 and disagreeable Sommerfeld integrals make the traditional MEI very dicult, 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 three-dimension VLSI interconnect.Numerical results are i n g o o d agreement with published data and those obtained by using FASTCAP [1], while GIMEI is generally an order of magnitude faster than FASTCAP and uses signi cant less memory than FAST-CAP.

In this paper, we present a new capacitance extraction method named Dimension Reduction Technique (DRT) for 3D VLSI interconnects. The DRT converts a complex 3D problem into a series of cascading simple 2D problems. Each 3D problem is solved separately, so we can choose the most efficient method according to the arrangement of conductors. More importantly, it is very easy to obtain the analytical solutions of 2D problem in many layers such as the pure dielectric layers and the layers with parallel signal lines. Therefore, the domain that has to be analyzed numerically is minimized. This leads to the drastic reduction of the computing time and memory needs. We have used the DRT to extract the capacitances of multilayered and multiconductor cross-overs, bends, via with signal lines and open-end. The results are in good agreement with those of Ansoft's SPICELINK and MIT's FastCap, but the computing time and memory size used by the DRT are several even tens times less than those used by SPICELINK and FastCap.