Signal Propagation Delay Model in Vertically Stacked Chips

Nanako NIIOKA
Masayuki WATANABE
Masa-aki FUKASE
Masashi IMAI
Atsushi KUROKAWA

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E98-A    No.12    pp.2614-2624
Publication Date: 2015/12/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E98.A.2614
Type of Manuscript: Special Section PAPER (Special Section on VLSI Design and CAD Algorithms)
Category: Device and Circuit Modeling and Analysis
Keyword: 
3-D IC,  delay,  through silicon via,  sensitivity analysis,  

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Summary: 
To design high quality three-dimensional integrated circuits (3-D ICs), the effect of process and design parameters on delay must be adequately understood. This paper presents an electrical circuit model of an entire structure in through silicon via (TSV) based 3-D ICs with a new equation for on-chip interconnect capacitance and then proposes an effective model for evaluating signal propagation delay in vertically stacked chips. All electrical parameter values can be calculated by the closed-form equations without a field solver. The delay model is constructed with the first- or second-order function of each parameter to the delay obtained from a typical structure. The results obtained by on-chip interconnect capacitance equations and delay model are in excellent agreement with those by a field solver and circuit simulator, respectively. We also show that the model is very useful for evaluating effects of the process and design parameters on vertical signal propagation delay such as the sensitivity and variability analysis.