Fast parameters extraction of multilayer and multiconductor interconnects using geometry independent measured equation of invariance

Abstract

Measured Equation of Invariance (MEI) is a new concept in computational electromagnetics. It has been demonstrated that the MEI is such an efficient boundary truncation technique that the meshes can be terminated very close to the object and still strictly preserves the sparsity of the FD equations. Therefore, the final 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 difficult, 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 VLSI multilayer and multiconductor interconnect. Numerical results are in good agreement with various published data. We also include a simple three-dimensional example and compared GIMEI with FASTCAP from MIT. The accuracy is maintained while GIMEI care generally an order of magnitude faster than FASTCAP with much less memory usage.