3-D IC Interconnect Capacitance Extraction Using Dual Discrete Geometric Methods With Prism Elements

The dual discrete geometry methods (DGMs) in terms of scalar potential using prism elements are employed in 3-D interconnect capacitance extraction of integral circuits. The energy complementarity property of the dual methods is explored to speed up the extraction. The dual DGMs work on the mutually orthogonal primal-dual mesh doublets, i.e., dual Delaunay-Voronoi mesh complex. As the orthogonal dual mesh is built based on the circumcenter of the primal mesh, the stability of the dual DGM heavily depends on the quality of the mesh. Elements with circumcenter dropping outside of the elements inevitably appear in the nonstructured prismatic meshes, due to the complicated structures in practical problems. The impact of these elements on the stability of the DGM is discussed. Comprehensive comparison between dual DGMs and dual finite-element methods (FEMs) and other golden references is performed. The dual DGM in terms of scalar potential has a reduced number of unknowns and simpler forms and works without extra links as required in the dual FEM in terms of vector potential. Capacitance extraction examples, such as a CMOS inverter and multilayer crossover parallel wires, are studied. The results demonstrate the energy bounds of dual DGMs and the improvement of accuracy with reduced cost.