Broadband and scalable on-silicon-chip inductor model for varying substrate resistivities

Abstract

A broadband and scalable model is developed to accurately simulate on-chip inductors of various dimensions and substrate resistivities. The broadband accuracy is proven over frequencies up to 20 GHz, even beyond resonance. A new scheme of RLC networks is deployed for spiral coils and substrate to account for 3D eddy current, substrate return path, and spiral coil to substrate coupling effects, etc. The 3D eddy current is identified as the key element essential to accurately simulate broadband characteristics. A key element (R(P)) introduced in our model can successfully accounts for the conductor loss due to eddy current arising from magnetic field coupling through substrate return path. This broadband and scalable model is useful for RF circuit simulation. Besides, it can facilitate on-chip inductor design and optimization through physics-based model parameters relevant to lossy substrate.