Simplified Model of a Layer of Interconnects under a Spiral Inductor

Abstract

An empirical effective medium approximation that provides a homogeneous equivalent for a layer of interconnects un-derneath a spiral inductor is presented. When used as part of a numerical 3D model of the inductor, this approach yields a faster simulation that uses less memory, yet still predicts the quality factor and inductance to within 1%. We expect this technique to find use in the electromagnetic modeling of System-on-Chip

Empirical Mixing Model for the Electromagnetic Compatibility Analysis of On-Chip Interconnects

“…In earlier work a limited example of such an approach for a fixed value of  applicable to a single structure was presented [6][7][8]. Further, the approach was expanded by developing a compact equation to calculate the appropriate value of  for a broad range of parameters [4,5].…”

“…From a package-level point of view, the on-chip interconnects can be seen as a mixture of metal inclusions located in a host dielectric [4][5][6][7][8]. Most of the current studies based on numerical analysis of 2-D or 3-D structures with two constituents show that the effective properties of the mixture strongly depend on the volume fraction, its geometrical profile and spatial orientation in periodic or random arrangements [9,10].…”

“…Metal-dielectric mixtures have been less thoroughly explored, with work limited to treating spherical or ellipsoidal metal inclusions [12,13]. The approach was extended [4][5][6][7][8] to cope with rectangular cuboid metal inclusions representative of on-chip interconnect structures. The use of a single fitting parameter was retained, and is calculated for a wide range of aspect ratios (0.6 -3), dielectric host materials (1 -11.7), metal fill factors (0.2 -0.6) and signal frequencies (1 -10 GHz) that are likely to be of interest to System-in-Package designers.…”

Quasi-Dynamic Green’s Functions for Efficient Full-Wave Integral Formulations for Microstrip Interconnects

“…In these structures the conductors fill a limited region of space, and thus integral approaches to Maxwell equations are widely used, e.g., [1][2][3][4][5][6]. A popular approach for numerical solution of integral equations is the Method of Moments [3].…”

“…A simplified approach consists in deriving an effective dielectric constant, and keep on using the Green's functions (GFs) for homogeneous media. An example of definition of effective permittivity is given in [6]. The second approach is the use of the GFs for inhomogeneous media, starting from their expression in the spectral domain.…”