Modeling the “Effective capacitance” for the RC interconnect of CMOS gates

With finer line widths and faster switching speeds, the resistance of on-chip metal interconnect is having a dominant impact on the timing behavior of logic gates. Specifically, the gates are switching faster and the interconnect delays are getting longer due to scaling. This results in a trend in which the RC interconnect delay is beginning to comprise a larger portion of the overall logic stage delay. This shift in relative delay dominance from the gate to the RC interconnect is increased by resistance shielding. That is, as the gate “resistance” gets smaller and the metal resistance gets larger, the gate no longer “sees” the total net capacitance and the gate delay may be significantly less than expected. This trend complicates the timing analysis of digital circuits, which relies upon simple, empirical gate delay equations for efficiency. In this paper, we develop an analytical expression for the “effective load capacitance” of a pc interconnect. In addition, when there is significant shielding, the response waveforms at the gate output may have a large exponential tail. We show that this waveform tail can strongly influence the delay of the RC interconnect. Therefore, we propose an extension of the effective capacitance equation that captures the complete waveform response accurately, with a two-piece gate-output-waveform approximation