Modeling and analysis of silicon-embedded MEMS toroidal inductors

This paper presents the modeling and analysis of three-dimensional silicon-embedded toroidal inductors designed for power converter applications. Special attention is given to modeling phenomena associated with the presence of silicon, namely an increase in loss and parasitic capacitance. Silicon-embedded inductors can be fabricated with silicon inside the donut-shaped toroidal core and inside the donut hole, as well as with silicon above, below and outside the inductor. It is argued here that, with the exception of the losses in the core at high doping densities, the losses in the silicon can be tolerated in many power applications, making fully-integrated silicon-embedded air-core inductors viable for power applications. An equivalent circuit model is presented for such inductors which captures the stored magnetic energy, the parasitic electric energy stored between the windings and the silicon, the loss in the toroidal windings, and the electrically- and magnetically-driven losses inside the silicon. The model developed here is verified against experimental data, and the comparison shows a good match over the frequency range of interest to power electronics applications.