Surface Impedance Formulation for Electric Field Integral Equation in Magneto-Quasistatic and Full-Wave Boundary Element Models of Interconnects

Today's high-speed propagation channels formed by the chip, package, and board level interconnects can be rigorously modeled with the boundary element method based on the surface discretization of the electric field integral equation (EFIE). The accuracy of such models critically depends on the surface impedance model, which has to accurately map the behavior of the electromagnetic field inside the wire volumes to their surfaces. In this thesis I propose a surface impedance model, which is obtained as a result of direct reduction of the volumetric EFIE to the surface EFIE under condition of negligible displacement current inside the interconnect wires. In order to cast the accurate but computationally intensive volumetric EFIE formulation to the boundary element framework, the volumetric current density is approximated as a product of the known exponential factor corresponding to the skin-effect behavior of the field inside the wires and the unknown surface current density on the conductor's boundary. The reduction of the volumetric EFIE to its surface counterpart results in a physically consistent surface impedance model which allows to achieve the volumetric EFIE accuracy within the boundary element formulation. The method is initially introduced for lossy 2D interconnects and later generalized to 3D interconnects under the magneto-quasistatic approximation. Finally, this work is extended to the Rao-Wilton-Glisson (RWG) method-of-moments (MoM) solution of the full-wave EFIE. The developed surface impedance model is validated via comparisons against numerical results obtained using alternative surface impedance models demonstrated in the literature and utilized in integral equation based CAD software for electronic design automation. These alternative models exhibit various limitations. For example, in the double-plane model the planar interconnect structure is replaced by two infinitely thin metal sheets at its top and bottom surfaces. This model succeeds for several practical scenarios where the conductor width is sufficiently larger than its thickness, or when the operating frequency is sufficiently low for the current distribution across the conductor cross section to be assumed uniform. The alternative "multi-sheet model" represents an interconnect by a number of infinitely thin metal sheets, which uniformly span its cross section such that the spacing between each two consecutive sheets is small compared to skin-depth. The model succeeds in accurately extracting conductor loss, however, it may require a large number of sheets, which makes the number of unknowns in MoM discretizations of the same order as the number of unknowns in volumetric models. As the MoM based models result in dense matrix discrete models their large size often leads to prolonged execution times and prohibitively large memory usage.