Shot-Noise-Induced Failure in Nanoscale Flip-Flops—Part I: Numerical Framework

As CMOS technology continues the path of miniaturization, noise-induced fluctuations raise heightened reliability concerns. In previous work, an analytical framework based on Markov queueing theory and Poisson shot noise was presented to model the probabilistic behavior of a CMOS flip-flop operated in the subthreshold regime. In this paper, this model is extended to also account for the above-threshold shot noise, where the noise distribution is no longer Poissonian. The formulas for the time-dependent charging and discharging of node capacitors of a four-transistor flip-flop are derived for different regimes of operation characterized by distinct Fano factors. The statistics of electron arrival and departure at node capacitors is incorporated in an algebraic representation based on Markov queueing theory to map the effects of charge fluctuations on the logic stability of a flip-flop. This framework is used in Part II of this work to investigate failure in time for end-of-roadmap CMOS at the 10-nm gate-length scale.