A Scalable, Broadband, and Physics-Based Model for On-Chip Rectangular Spiral Inductors

Abstract

A scalable, broadband, and physics-based compact model for on-chip spiral inductors with rectangular outline shape is demonstrated for the first time in this paper. A simple dc inductance model is developed based on the current sheet approximation. The reduction in inductance due to the flow of eddy current in a back metal plate is considered using the method of images. A three-ladder network is shown to be sufficient to accurately model skin effect caused due to the magnetic field setup at high frequencies. Geometry-dependent expression suitable for rectangular cross-sectional metal strips is presented to predict the proximity effect. Physics-based expression for the substrate capacitance is derived. The proposed model is also shown to have a good correlation in the presence of a patterned ground shield. The proposed model is verified across CMOS process parameters that affect the inductor performance, such as metal thickness, substrate resistivity, and substrate thickness. Furthermore, model accuracy is also validated across design parameters such as spiral width, spacing between turns, number of turns, and diameter. The model is shown to have a good agreement with both EM simulations and measurements.