Simple Waveform Model of Inductive Interconnects by Delayed Quadratic Transfer Function with Application to Scaling Trend of Inductive Effects in VLSI's

Danardono Dwi ANTONO  Kenichi INAGAKI  Hiroshi KAWAGUCHI  Takayasu SAKURAI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E89-A   No.12   pp.3569-3578
Publication Date: 2006/12/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e89-a.12.3569
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on VLSI Design and CAD Algorithms)
Category: Interconnect
on-chip interconnects,  inductive effect,  inductive index,  overshoot,  propagation delay,  

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A simple analytical model based on Delayed Quadratic (DQ) Transfer Function approximation is proposed for estimating waveforms of inductive single-line interconnects in VLSI's. An expression for overshoot voltage is derived by the model within 17% error for the line width less than 10 times the minimum line width and typical input signal. A delay expression is also proposed within 15% for the same condition. The strength of the inductive effect is shown to be expressed by a closed-form expression, A=2(L(CT+0.5C))1/2/(RT(CT+CJ)+RTC+RCT+0.4RC). By using the criteria, a scaling trend of inductive effects in VLSI's is discussed. It is shown that the inductive effect of single-line, minimum-width VLSI interconnect peaks off at 90 nm based on the ITRS predicted parameters.