Compact Modeling of High-Speed Interconnects

Abstract

High-speed interconnects are essentially planar transmission lines. The fundamental mode of propagation in transmission line interconnects is the transverse electromagnetic (TEM) wave. In ideal case, when the conductivity of the line is infinity the basic mode of propagation would be the TEM mode. This is assuming that the medium in which the line is embedded is considered to be homogeneous, lossless and isotropic. However for most practical cases, the lines have finite conductivity that results in a deviation from the TEM mode. The properties of the dielectric material are also far from ideal with dielectric losses dominating conductor losses as frequency scales up. Therefore, interconnect lines embedded in inhomogeneous substrates cannot support pure TEM mode. The modified mode of propagation has small axial components of the electric and magnetic fields. The field distribution in such a non-ideal transmission line interconnect closely represents the ideal TEM mode with negligible electric/magnetic field components and is called the quasi-TEM mode. Transmission line theory has two aspects: In one case, the propagation of electromagnetic waves is studied when the characteristic parameters of the line are given. In the other case, the conductor geometry is known and the line parameters such as the characteristic impedance, attenuation constant, propagation constant and the shunt capacitance are to be obtained. This aspect is particularly suited for interconnect design and analysis. With the quasi-TEM approximation, the calculation of these line parameters requires the solution of the two-dimensional Laplace’s equation. This solution is based on the computation of the boundary conditions governed by the geometry of the line.