A Physical Model of Solenoid Inductors on Silicon Substrates

In this paper, a physical model is presented to predict the frequency-dependent characteristics of solenoid-type inductors on standard silicon substrates. The model considers the skin-depth effect in the conductor, interwinding capacitance, parasitic capacitance between the conductor and substrate, substrate resistance, and substrate capacitance of a solenoid inductor on the silicon substrate, which are all computed based on the inductor's geometric dimensions and related material properties. Surface-micromachined inductors of various geometries have been tested to validate the physical model and found a satisfactory consistency between the measured results and the theoretical predictions in the multigigahertz frequency range. It is also suggested that the increase of the solenoid aspect ratio is beneficial in enhancing quality factors of solenoid inductors on the silicon substrate at a high frequency.