An Analytical Capacitance Model for Through-Silicon Vias in Floating Silicon Substrate

Through-silicon via (TSV) is an integral part of 2.5-D IC technology leveraged for multichip heterogeneous integration to achieve shorter interconnects, faster speed, and lower power consumption in the state-of-the-art circuit systems. These 2.5-D ICs use a silicon substrate, where there are no ground contacts unlike traditional 2-D ICs or 3-D ICs. TSVs in such electrically floating substrates call for new electrical models as well as improved parasitic extraction (PEX) methodology. Therefore, in this paper, an analytical capacitance model for TSVs in a 2.5-D IC is derived and validated. A TSV-to-TSV crosstalk expression is also validated and further extended to create an accurate 2.5-D IC PEX framework in addition to design robust grounding schemes, such that the TSV-to-TSV crosstalk coupling in an entire 2.5-D IC would be minimal even with floating silicon substrate. It is shown that a large number of regularly distributed power and ground TSVs provide an effective shield for the TSV-to-TSV crosstalk coupling and are highly recommended in the 2.5-D ICs.