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

  • Authors:

  • Danardono Dwi Antono;Kenichi Inagaki;Hiroshi Kawaguchi;Takayasu Sakurai

  • Affiliations:

  • The authors are with the University of Tokyo, Tokyo, 153-8505 Japan. E-mail: danardono@ieee.org,;The authors are with the University of Tokyo, Tokyo, 153-8505 Japan. E-mail: danardono@ieee.org,;The authors are with the University of Tokyo, Tokyo, 153-8505 Japan. E-mail: danardono@ieee.org,;The authors are with the University of Tokyo, Tokyo, 153-8505 Japan. E-mail: danardono@ieee.org,

  • Venue:
  • IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
  • Year:
  • 2006

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Abstract

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 para-meters.