Statistical Leakage Analysis Framework Using Artificial Neural Networks Considering Process And Environmental Variations
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Leakage current and process variations are two primary hurdles in modern VLSI design. It depends exponentially on process and environmental parameters and hence small variations in these result in a large spread in leakage current of manufactured dies. Traditionally, Exponential Quadratic(EQ) models have been used to model leakage current as a function of process parameters which can model limited non-linearity and hence become inaccurate for large process variations. Artificial Neural Networks (ANN) have shown great promise in modeling circuit parameters for CAD applications. We model leakage with ANN models which perform better than the EQ models for increased process variations. However, the complex nature of the ANN model, with the standard sigmoidal activation functions, does not allow analytical expressions for its mean and variance for the case of Gaussian process variations. We propose the use of a new activation function that allows us to derive an analytical expression for the mean and a semi-analytical expression for the variance of the ANN based leakage model. To the best of our knowledge this is the first result in this direction. All existing SLA frameworks are closely tied to the EQ leakage model and hence fail to work with sophisticated ANN models. We therefore set up an SLA framework that can efficiently work with these ANN models. Results show that the CDF of leakage current of ISCAS'85 circuits can be predicted accurately with the error in mean and standard deviation, compared to Monte Carlo based simulations, being less than 1\% and 2\% respectively across a range of voltage and temperature values. The complexity of our framework is similar to existing SLA frameworks yet more accurate over a larger range of variations. Ignoring the thermal profile of the chip leads to a gross error of nearly 50\% in the prediction of leakage yield. Our neural network model also includes the voltage and temperature as input parameters, thereby enabling voltage and temperature aware statistical leakage analysis (SLA). Similarly leakage CDF can be predicted across a range of supply and body voltages since they are both part of the model. Our framework used analytical techniques to account for local variations and Monte Carlo techniques for global variations and hence it can also be used for Non-Gaussian global variations.
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