A broadband and scalable model is developed to accurately simulate on-chip inductors with various dimensions and substrate resistivities. The broadband accuracy is proven over frequencies of up to 20 GHz, even beyond resonance. A new scheme of resistance-inductance-capacitance networks is deployed for the spiral coils and substrate to account for 3-D eddy current, substrate return path, and spiral coil to substrate coupling effects. The 3-D eddy current is identified as the key element essential to accurately simulate the broadband characteristics. Electromagnetic simulation using the Advanced Design System momentum is conducted to predict the on-chip inductor performance corresponding to a wide range of substrate resistivities (ρSi = 0.05 -1 kΩ · cm). Three operation modes such as transverse electromagnetic mode, slow-wave mode, and eddy current mode are reproduced. The model parameters manifest themselves as physics-based through relevant correlation with ρSi over three operation modes. The onset of slow-wave mode can be consistently explained by a key element RP introduced in our model, which accounts for the conductor loss due to an eddy current arising from magnetic field coupling through a substrate return path. This broadband and scalable model is useful for radio frequency circuit simulation. In addition, it can facilitate an optimum design of on-chip inductors through the physics-based model parameters relevant to varying substrate resistivities.
- Eddy current
- Substrate resistivity