Compact and Physics-Based Modeling of 3-D Inductor Based on Through Silicon Via

This letter presents a compact and physics based model for through silicon via (TSV) based 3-D inductors. By utilizing frequency-independent lumped elements, this model accounts for skin and proximity effects in TSVs and redistribution layers (RDL), feedforward capacitance, parasitic capacitance introduced by the oxide liner of TSVs, and the parasitics of substrate. The accuracy of the model is confirmed by experimental and electromagnetic simulation results. By using the proposed model, the
${R}$
,
${L}$
and
${Q}$
characteristics of TSV-based inductors can be evaluated accurately and conveniently in a wideband frequency range.