Efficient Characterization of Interconnects With Arbitrary Polygonal Cross Sections Using Fokas-Derived Dirichlet-to-Neumann Operators

Abstract

A novel technique to accurately characterize interconnects with general, piecewise homogeneous material parameters and arbitrary polygonal cross sections is presented. To compute the per-unit-of-length (p.u.l.) complex inductance and capacitance matrices of the considered structures, we apply a boundary integral equation (BIE) framework, invoking a Dirichlet-to-Neumann (DtN) formalism to recast the problem at hand. The pertinent operators are constructed by means of the numerically fast Fokas method, leveraging fully analytical expressions for the pertinent matrix elements. Numerical examples of various multiconductor transmission lines demonstrate that our proposed scheme is flexible and precise. Since our method is not limited to rectangular cross sections, manufacturing effects such as etching can also be taken into account. Moreover, the examples are not restricted to resistance, inductance, conductance and capacitance (RLGC) data as we also consider signal attenuation, slow-wave factors, and crosstalk.