A Physical Model for On-Chip Spiral Inductors With Accurate Substrate Modeling

A physical-based analytical model for on-chip inductors is developed. A ladder structure is used to model the skin and proximity effects in metal lines. The substrate electric and substrate magnetic losses are accurately modeled by RC and RL ladder structures, respectively. The effective inductance reduction due to the eddy current in the lossy silicon substrate at high frequency is modeled by a negative mutual inductance between the inductor and the substrate. All the model parameters can be calculated from the layout and process parameters. On-chip inductors with different geometries and substrate resistivities were fabricated for the verifications. The measured results are in very good agreement with the proposed model. This generic model can be applied to various substrate resistivities; thus, it is suitable for different technologies. This model can facilitate the design and optimization of on-chip inductors for RF IC applications