Empirical Mixing Model for the Electro- Magnetic Modelling of On-chip Intercon- Nects

We present an empirical mixing model for rectangular cuboid metal inclusions in a host dielectric, suitable for replacing the detailed structure of a layer of on-chip interconnects with a homogeneous dielectric slab. Such an approximation is required to facilitate the accurate and efficient package-level electromagnetic modelling of complicated miniaturised systems, such as System-inPackage. Without such an approach, the direct inclusion of large areas of on-chip interconnect structures often results in intractable computation times. Our model allows us to predict the reflection (transmission) coefficient of impinging plane waves to within 3.5% (0.2%) error for incident angles up to 30◦ off-normal, aspect ratios 0.6–3, metal fill factors 0.3–0.6, and host dielectric constants 1–11.7, over the frequency range 1–10 GHz.