FABRICATION, MODELING AND PERFORMANCE ANALYSIS OF SILICON­EMBEDDED 3­D TOROIDAL INDUCTORS

This paper presents the fabrication, modeling, characterization and analysis of silicon-embedded, air- core, three-dimensional toroidal inductors for power converter applications. The inductors are fabricated within deep silicon recesses by means of a 3-D silicon shadow mask coupled with electroplating techniques. The losses in the inductor and the surrounding silicon are analytically modeled using simplified circuit models as well as energy methods, and the effects of using silicon wafers with both standard and high resistivities as embedding substrates are discussed and experimentally characterized. Inductors with inductances of 45 nH and peak quality factors of 22 at 100 MHz were achieved for devices embedded in high-resistivity wafers. Devices embedded within standard-resistivity wafers achieved similar inductances but lower peak quality factors of 16 at 40 MHz. Inductors embedded in standard-resistivity wafers also showed lower self-resonant frequencies than their high- resistivity-wafer counterparts. For standard-resistivity wafers, substrate-induced losses are negligible compared to the winding loss at frequencies below 50 MHz, and become dominant above 70-80 MHz. For high-resistivity wafers, substrate and winding losses are comparable at 100 MHz.