High-Frequency Scalable Electrical Model and Analysis of a Through Silicon Via (TSV)

We propose a high-frequency scalable electrical model of a through silicon via (TSV). The proposed model includes not only the TSV, but also the bump and the redistribution layer (RDL), which are additional components when using TSVs for 3-D integrated circuit (IC) design. The proposed model is developed with analytic <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RLGC</i> equations derived from the physical configuration. Each analytic equation is proposed as a function of design parameters of the TSV, bump, and RDL, and is therefore, scalable. The scalability of the proposed model is verified by simulation from the 3-D field solver with parameter variations, such as TSV diameter, pitch between TSVs, and TSV height. The proposed model is experimentally validated through measurements up to 20 GHz with fabricated test vehicles of a TSV channel, which includes TSVs, bumps, and RDLs. Based on the proposed scalable model, we analyze the electrical behaviors of a TSV channel with design parameter variations in the frequency domain. According to the frequency-domain analysis, the capacitive effect of a TSV is dominant under 2 GHz. On the other hand, as frequency increases over 2 GHz, the inductive effect from the RDLs becomes significant. The frequency dependent loss of a TSV channel, which is capacitive and resistive, is also analyzed in the time domain by eye-diagram measurements. Due to the frequency dependent loss, the voltage and timing margins decrease as the data rate increases.