In this study, a new approach for designing the TSV test structures and extracting the equivalent circuit model parameters is proposed. Compared with the conventional two-port method, the proposed extract structures consumed only a small chip area, and the small serial parasitic elements in the model can be extracted precisely without optimization.
The proposed equivalent model, composed of R, L, C, and G elements, is based on the physical structure of the TSVs and is verified up to 50 GHz. R and L are extracted by the short test structure; C and G are extracted by the open test structure. The parameters calculated using the derived analytical equations confirmed that the proposed approach leads to a well-defined physical-based model. Based on the proposed RF modeling of TSVs, the magnitude differences of S21 and S11 among the equivalent circuit model, the analytical equations, and the EM simulation are smaller than 0.03 dB and 2 dB, respectively from 1 GHz to 50 GHz. The associated magnitude standard errors and average phase differences of S21 and S11 are 1.25% and 1.81° in average.
Moreover, scalable models of TSVs are also included in different conditions. By changing some elements from the original model, the model still agrees well with the physical structures. The maximum magnitude standard error and average phase difference do not exceed 6.60% and 7.80°.

此篇論文提出一種直通矽晶穿孔測試結構的設計，以及等效電路模型參數的萃取。與傳統兩埠方法相比，本篇提到的萃取結構只需佔用較小的面積，且在模型中的寄生效應也較小，因此可被準確地萃取且不需最佳化。
等效模型根據直通矽晶穿孔的物理結構，共包含電阻、電感、電容、電導，且可應用到50GHz。利用短路測試結構萃取出電阻與電感；電容與電導則使用開路測試結構。使用推導的解析方程式所計算的參數更可證實本篇是具有良好物理根據與定義的模型。根據此篇的直通矽晶穿孔射頻模型，在1GHz到50GHz與解析方程式和電磁模擬之S21與S11的強度差異分別小於0.03dB與2dB。其S21與S11的強度標準誤差以及平均相位差異平均分別為1.25%和1.81°。
除此之外，更包含不同的情況下時，直通矽晶穿孔模型的可變性。藉由改變原來模型的一些部分，其模型依舊能夠符合物理結構。其強度標準誤差以及平均相位差異的最大值皆不超過6.60%與7.80°。

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