Fully Symmetric 3-D Transformers With Through-Silicon via IPD Technology for RF Applications

This article presents the design, characterization, and modeling for the novel 3-D transformer structures based on the in-house developed 3-D integrated circuit (3-D IC) via-last backside-through-silicon via (TSV) interposer process. Differing from the conventional 2-D planar structure, the 3-D TSV design allows achieving a fully symmetric transformer with a compact size. The equivalent circuit model parameters are extracted based on the S-parameters to investigate the design tradeoff. With an inner diameter of $40~\mu \text{m}$ in the 3-D 1:1 transformer, the measured inductances of the primary and second coils are 439 and 482 pH with the $Q$ factors of 4.59 and 5.11, respectively, and the coupling coefficient is 0.136.