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A transmission line-type electrical model for tapered TSV considering MOS effect and frequency-dependent behavior

Song Liu, Guangbao Shan, Chengmin Xie and Xinrong Du

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 Corresponding author: Guangbao Shan, E-mail: 18092060235@189.cn

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Abstract: The analytical model of voltage-controlled MOS capacitance of tapered through silicon via (TSV) is derived. To capture the frequency-dependent behavior of tapered TSV, the conventional analytical equations of RLCG for two-wire transmission lines are revised. With the adoption of MOS capacitance model and the revised RLCG analytical equations, a transmission line-type electrical model for tapered TSV is proposed finally. All the proposed models are validated by simulation tools, and a good correlation is obtained between the proposed models and simulations up to 100 GHz. With the proposed model, both the semiconductor phenomenon and frequency-dependent behavior of tapered TSV can be fully captured at high frequency, and the performance of tapered TSV can be evaluated accurately and conveniently prior to 3D IC design.

Key words: 3D ICTSVTSV electrical modelMOS effecttransmission line



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Fig. 1.  (a) Top cross-sectional view of tapered TSV. (b) Two-tapered TSV system.

Fig. 2.  Transmission line-type electrical model for two-tapered TSV system.

Fig. 3.  Transmission line-type TSV electrical model for a three-tapered TSV system.

Fig. 4.  Verification of TSV voltage controlled MOS analytical model.

Fig. 5.  Verification of the proposed analytical mode of $R_{\rm tsv}L_{\rm tsv} C_{\rm tsv}^{\ast}G_{\rm tsv}^{\ast}$. (a) Resistance $R_{\rm tsv}$. (b) Inductance $L_{\rm tsv}$. (c) Capacitance $C_{\rm tsv}^{\ast}$. (d) Conductance $G_{\rm tsv}^{\ast}$.

Fig. 6.  Comparison of the $S_{21}$ magnitude obtained by the proposed model and HFSS simulation. (a) The comparison results for the two TSV system. (b) The comparison results for the three TSV system.

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    Received: 19 August 2014 Revised: Online: Published: 01 February 2015

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      Song Liu, Guangbao Shan, Chengmin Xie, Xinrong Du. A transmission line-type electrical model for tapered TSV considering MOS effect and frequency-dependent behavior[J]. Journal of Semiconductors, 2015, 36(2): 024009. doi: 10.1088/1674-4926/36/2/024009 S Liu, G B Shan, C M Xie, X R Du. A transmission line-type electrical model for tapered TSV considering MOS effect and frequency-dependent behavior[J]. J. Semicond., 2015, 36(2): 024009. doi: 10.1088/1674-4926/36/2/024009.Export: BibTex EndNote
      Citation:
      Song Liu, Guangbao Shan, Chengmin Xie, Xinrong Du. A transmission line-type electrical model for tapered TSV considering MOS effect and frequency-dependent behavior[J]. Journal of Semiconductors, 2015, 36(2): 024009. doi: 10.1088/1674-4926/36/2/024009

      S Liu, G B Shan, C M Xie, X R Du. A transmission line-type electrical model for tapered TSV considering MOS effect and frequency-dependent behavior[J]. J. Semicond., 2015, 36(2): 024009. doi: 10.1088/1674-4926/36/2/024009.
      Export: BibTex EndNote

      A transmission line-type electrical model for tapered TSV considering MOS effect and frequency-dependent behavior

      doi: 10.1088/1674-4926/36/2/024009
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      Project supported by the National Defense Basic Scientific Research Program of China (No. A0320132012).

      More Information
      • Corresponding author: E-mail: 18092060235@189.cn
      • Received Date: 2014-08-19
      • Accepted Date: 2014-09-15
      • Published Date: 2015-01-25

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