Comparative characteristics studies on on-chip single- and double-level square inductors

Detailed experimental investigations are carried out in this paper to show the inductance, Q-factor as well as resonant frequency of on-chip square single- and double-level inductors on silicon substrates. Based on the equivalent circuit model developed and the S-parameters measured using a de-embedding technique, inductances, Q-factors and resonant frequencies of these inductors are determined and compared with one another. Parametric studies are carried out to show the effects of both strip length and inner empty area on the coupling capacitance and resonant frequency of these inductors, and some scalable formulas are derived for extrapolating inductance and resonant frequency of other inductors. It is demonstrated that in the double-level cases very strong self-inductor resonance can take place with lower resonant frequency, and Q-factor is degraded rapidly.