A broadband and scalable on-chip inductor model appropriate for operation modes of varying substrate resistivities

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. EM simulation using ADS momentum is conducted to predict the on-chip inductor performance corresponding to wide range of substrate resistivities (ρ_Si=0.05-1Kω-cm). Three operation modes such as TEM, slow-wave, and eddy current are reproduced. The model parameters manifest themselves physics-base through relevant correlation with ρ_Si over three operation modes. The onset of slow-wave mode can be consistently explained by a key element (R_P) introduced in our model, which 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 optimization design of on-chip inductors through physics-based model parameters relevant to varying substrate resistivities.