Chebyshev affine-arithmetic-based parametric yield prediction under limited descriptions of uncertainty

Due to the hard-to-measure distributions of real process data, it is difficult to provide accurate parametric yield prediction for modern circuit design. Most existing approaches are not able to handle the uncertain distribution properties coming from the process data. Other approaches are inadequate in considering correlations among the distributions of variations. This paper suggests a new approach that not only takes care of correlations among distributions but also provides a low-cost and efficient computation scheme. The proposed method approximates the parameter variations with Chebyshev affine arithmetic (CAA) to capture both the uncertainty and nonlinearity in a cumulative distribution function. The CAA-based probabilistic range presentation describes, both fully and partially, specified process and environmental parameters. Thus, we are able to predict the probability bounds for leakage consumption with unknown dependences among variations. The end result is the chip-level parametric yield estimation based on leakage prediction. Experimental results demonstrate that the new approach provides a reliable bound estimation, which leads to a 20% yield improvement compared with only using the intervals of partially specified uncertainties.