Transistor sizing of custom high-performance digital circuits with parametric yield considerations

Transistor sizing is a classic Computer-Aided Design problem that has received much attention in the literature. Due to the increasing importance of process variations in deep sub-micron circuits, nominal circuit tuning is not sufficient, and the sizing problem warrants revisiting. This paper addresses the sizing problem statistically in which transistor sizes are automatically adjusted to maximize parametric yield at a given timing performance, or maximize performance at a required parametric yield. Specifically, we describe an implementation of a statistical tuner using interior point nonlinear optimization with an objective function that is directly dependent on statistical process variation. Our results show that for process variation sensitive circuits, consisting of thousands of independently tunable devices, a statistically aware tuner can give more robust, higher yield solutions when compared to deterministic circuit tuning and is thus an attractive alternative to the Monte Carlo methods that are typically used to size devices in such circuits. To the best of our knowledge, this is the first publication of a working system to optimize device sizes in custom circuits using a process variation aware tuner.