Surrogate modeling and variability analysis of on-chip spiral inductors

This paper presents an approach to the analysis of on-chip integrated spiral inductors in terms of parametric variabilities. An enhanced single-π model is proposed to compensate for high frequency deviations. In addition to the single-π model parameters, the skin effect and the proximity effect are included in the surrogate model to reflect high frequency behavior much more accurately while retaining a simple structure. Y-parameters of the equivalent circuit are derived to extract the frequency-dependent inductance and quality factor representations using the shunt and differential configurations. This study introduces a novel algorithm able to yield model parameter values through iterations converging on the predetermined inductance curve within an error margin of 5%. High-Q and low-Q characteristics of inductors arising from process variations were also captured with the proposed algorithm, along with the failure points of the inductance, the quality factor, and the self-resonance frequency. Variability analysis results demonstrate that the differential configuration is more robust to inductance and quality factor failures, but also that it is more vulnerable to self-resonance frequency failures.