Statistical Compact Model Extraction for Skew Normal Distributions

A technique to extract statistical model parameters for skewed Gaussian process variations is proposed. Statistical compact model extraction traditionally assumes that underlying process variations are Gaussian in nature. ON currents in certain high voltage technologies, which are linear in process deviations, show skew in their distribution and hence is indicative of skew in the underlying process variations. The use of skew-normal random variables is proposed to model such variations. Artificial neural networks (ANNs) are used to empirically model the functional relation of performance on process deviations and a framework to propagate skew-normal random variables through ANNs is proposed. A non-linear optimisation problem is formulated to extract the parameters that characterise the skew-normal process variations, with constraints imposed on the objective function to penalise any deviation from Gaussian variations. Results show that the extracted parameters, when simulated, match the performance parameter targets to within 3% for both Gaussian and skewed process variations.