An Improved Inductance and Self-Resonance Frequency Modelling and Estimation of Single Turn On-chip Inductors for Millimeter-wave Applications

This article reports accurate, unique, yet simple closed-form expressions for estimating the inductance and self-resonant frequency of single-turn on-chip inductors of different geometries. The proposed expressions are solely dependent on the geometry and the sizing of the inductors without requiring detailed process information. Theoretically estimated results are extensively verified with measurements and electromagnetic (EM) simulations, for i) different geometries, ii) different dimensions of the inductors, and iii) different metal thicknesses. Various single-turn octagonal inductors are designed and implemented using the top metal of a 1-poly 6-metal 180nm CMOS process. The inductors are measured by manual wafer-probing with appropriate calibration and de-embedding techniques. The proposed expression estimates the inductance with an accuracy of 95 % or an error of less than 5% for all inductors ranging from 70 pH to over 250 pH. A new approach based on transmission line theory to model and estimate the self-resonance frequency (SRF) is proposed and a closed-form expression is developed to estimate the SRF of single-turn inductors of different geometries. This expression is easier to use and does not require the knowledge of obscure process-related data. The accuracy of the proposed expression is better than 95% when compared with the EM simulation results.