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

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.

I. Introduction

Modern interconnect structures are becoming ever more miniaturized and complex, operating up to very high frequencies for which the corresponding wavelengths are comparable to their longitudinal dimension. However, as the dimensions of their cross Section most often remain sufficiently small with respect to the smallest wavelength of the transported signals, it is still possible to describe these interconnects using frequency-dependent, per unit-of-length (p.u.l.), RLGC transmission line parameters [1] derived from a suitable quasi-transverse magnetic (quasi-TM) electromagnetic analysis, as thoroughly motivated and validated in [2] and [3]. The quasi-TM regime implies that the longitudinal component of the magnetic field remains negligible. Moreover, the broadband nature of the signals, with frequency components ranging from dc to several tens of GHz, necessitates an analysis that accounts for current crowding, conductor losses, and the skin effect in the cross Section as these phenomena change dramatically over the considered frequency range.