Impact of Random Dopant Fluctuations on the Timing Characteristics of Flip-Flops

In this work, we have analyzed the effects of variability, due to random dopant fluctuation (RDF), on the timing characteristics of flip-flops for the future technology generations of 25, 18, and 13 nm, based on extensive Monte Carlo simulations. The results show that RDF has a significant impact on all of the timing parameters and that these parameters do not follow a normal distribution; in particular, they are skewed and exhibit a large tail. Moreover, the dispersion and skewness of the timing parameters increase with technology scaling. The study of the exact shape of these distributions, especially in the tail section, is of fundamental importance in the design and modeling of high-performance, reliable, and economically feasible circuits. In this paper, the distribution tails are estimated based on simulation data, with the aid of statistical nonparametric probability density functions, and it has been found that timing distributions can better be represented by certain nonparametric distributions, in particular Pearson and Johnson systems. The use of these representations during the statistical static timing analysis will provide more accurate results as compared with the normal approximation of distributions and will eventually reduce the probability of yield loss.