A general framework for accurate statistical timing analysis considering correlations

The impact of parameter variations on timing due to process and environmental variations has become significant in recent years. With each new technology node this variability is becoming more prominent. In this work, we present a general statistical timing analysis (STA) framework that captures spatial correlations between gate delays. The technique presented does not make any assumption about the distributions of the parameter variations, gate delay and arrival times. The authors proposed a Taylor-series expansion based polynomial representation of gate delays and arrival times which is able to effectively capture the non-linear dependencies that arise due to increasing parameter variations. In order to reduce the computational complexity introduced due to polynomial modeling during STA, an efficient linear-modeling driven polynomial STA scheme was proposed. On an average the degree-2 polynomial scheme had a 7.3 × speedup as compared to Monte Carlo with 0.049 units of rms error with respect to Monte Carlo. The technique is generic and could be applied to arbitrary variations in the underlying parameters.