Frequency-Dependent Characteristics and Parametric Modeling of the Silicon Substrate in TSV-Based 3-D ICs

This paper presents an in- depth investigation of the silicon substrate characteristics based on frequency-dependent parameters in the through-silicon via (TSV)-based 3-D ICs. It is the first time to define the frequency bands accurately on the ground of a quantitative standard of calibration to represent different characteristics of the silicon substrate. Moreover, by converting the conventional model of a TSV pair into an RC parallel circuit, a simplified model is established which makes the analysis of the silicon substrate concise associated with the frequency variation. To further reveal the influence of silicon substrate on the signal transmission between adjacent TSVs, relevant impedance parameters of the silicon substrate are converted into the impedance ( $Z$ ) matrix for parametric modeling, which is validated by 3D full-wave simulations. This work contributes a systematic examination of the silicon substrate characteristics with the variation of frequency, and provides significant guidance for parametric analysis and modeling in TSV-based 3-D ICs.