A Skew-Normal Canonical Model for Statistical Static Timing Analysis

The use of quadratic gate delay models and arrival times results in improved accuracies for a parameterized block-based statistical static timing analysis (SSTA). However, the computational complexity is significantly higher. As an alternative to this, we propose a canonical model based on skew-normal random variables (SN model). This model is derived from the quadratic canonical models and can consider the skewness in the gate delay distribution as well as the nonlinearity of the MAX operation. Based on conditional expectations, we derive the analytical expressions for the moments of the MAX operator and the tightness probability that can be used along with the SN canonical models. The computational complexity for both timing and criticality analysis is comparable with SSTA using linear models. There is a two to three orders of magnitude improvement in the run time as compared with the quadratic models. Results on ISCAS benchmarks show that the SN models have a lower variance error than the quadratic model, but the error in the third moment is comparable with that of the semiquadratic model.