Characterization and modeling of sub-nH integrated inductances

This paper presents the characterization and modeling of sub-nH radial patterned around shield circular inductors fabricated in a silicon bipolar technology for RF applications. The accuracy of experimental data in the range 0.3-0.8 nH is first validated by comparing the measured low-frequency inductance with 2D¹/₂ EM simulations. Based on the above results, the well-known current sheet expression for circular spirals is revised and modified to improve its accuracy at lower inductance values. Finally, the original and modified expressions are employed in a lumped scalable model for integrated inductors. Comparisons between simulations and measurements revealed that the modified expression allows error reductions as large as 20% with respect to the original one on both the inductance and quality factor.