Method and apparatus for broadband modeling of current flow in three-dimensional wires of integrated circuits

Abstract

A new surface impedance model for extraction in lossy two-dimensional (2D) interconnects of rectangular cross-section is presented. The model is derived directly from the volumetric electric field integral equation (EFiE) under the approximation of the unknown volumetric current density as a product of the exponential factor describing the skin-effect and the unknown surface current density on the conductor's periphery. By proper accounting for the coupling between the boundary elements situated on the top and bottom surfaces of conductor with the elements located on the side-walls, the model maintains accuracy from DC to multi-GHz frequencies as well as for conductors with both large and small thickness/width ratios. A generalization of the full-periphery surface impedance model to the three-dimensional electric field integral equation is also described.