High-Sigma Performance Analysis using Multi-Objective Evolutionary Algorithms

Semiconductor devices have rapidly improved in performance and function density over the past 25 years enabled by the continuous shrinking of technology feature sizes. Fabricating transistors that small, even with advanced processes, results in structural irregularities at the atomic scale, which affect device characteristics in a random manner. To simulate performance of circuits comprising a large number of devices using statistical models and ensuring low failure rates, performance outliers are required to be investigated. Standard Monte Carlo analysis will quickly become intractable because of the large number of circuit simulations required. Cases where the number of samples exceeds 10 are known as “high-sigma problems”. This work proposes a highsigma sampling methodology based on multi-objective optimisation using evolutionary algorithms. A D-type Flip Flop is presented as a case study and it is shown that higher sigma outliers can be reached using a similar number of SPICE evaluations as Monte Carlo analysis.