Compact modeling of high frequency phenomena for on-chip spiral inductors

This paper presents a physics-based compact model for predicting high frequency performance of spiral inductors. The model accurately accounts for skin effect and proximity effect in the metal conductors as well as eddy current loss in the silicon substrate at high frequencies. Skin effect is modeled accurately up to 20 GHz using a reduced partial element equivalent circuit formulation (PEEC). Proximity effect in multi-turn inductors is modeled using an "effective width" approach. Substrate eddy current is modeled with an effective substrate image current profile, which accounts for dependence on substrate resistivity, oxide thickness, and inductor trace width. The model shows excellent agreements with measured data across a variety of inductor geometries and substrate resistivities up to 20 GHz. This model can also be applied to modeling on-chip coplanar lines at high frequencies.