Simplified model for on-chip interconnects in electromagnetic modelling of System-in-Package

Abstract

We present effective medium approximation (EMA) that provides an homogeneous equivalent for the top layer of onchip interconnects in an integrated circuit. An empirical mixing model for straightforward and fast extraction of the effective dielectric constant of a slab of integrated circuit wiring and its analytical formulation based on Maxwell-Garnett rule is presented for a range of aspect ratios, dielectric materials, metal fills, and frequencies. We expect this approach to find use in the electromagnetic modeling of System-in-Package. Experimental validation of proposed approach is demonstrated by free space measurement of a grating structure illuminated by a pair of lens horn antennas.

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]. Here a new empirical model is presented where the considered values of aspect ratio are within 1.4 -3.…”

“…While metal layer height is fixed for any given layer in any given process, track width is less restricted. Aspect ratios (xAR) are continuing to increase as technology develops [16], hence structures with narrowed down [4,5] values within 1.4 ≤ xAR ≤ 3 are studied. Due to the growing use of low-k dielectrics a host materials with permittivity e in the range 1 ≤ e ≤ 11.7 are considered.…”

“…The model is at the same time straightforward and more accessible as well as more accurate. The accuracy improvement is related to the neglected range of low aspect ratios where the scaling factor  has more rapid increment [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.…”