Consideration of Transition-Time Variability in Statistical Timing Analysis

This paper discusses the treatment of the transition-time variability in statistical static timing analysis (SSTA). In SSTA, the signal arrival time is treated as a statistical variable. In reality, the signal transition time also fluctuates due to process variations, which effect should be taken into account. Also, in a multiple fan-in gate, there exist multiple transition-time variabilities associated with each input. Effective treatment of the multiple possibilities is required. This paper first discusses the effect of transition-time variability on the delay distribution. A method is proposed that derives the variability of transition time from the delay variability and considers the effect of transition-time variability using a linearized model. An experiment shows that the error of the method is less than 0.2% whereas the error grows to 4% if we neglect the effect of transition-time variability. For multiple fan-in gates, we convert multiple transition time variabilities into a single variability by taking a weighted average of the variabilities. The error of the conversion is around 1% in our experiments. The proposed treatments of the transition-time variability improve the accuracy of SSTA without changing the framework of existing SSTA methods.