"Unobserved Corner" Prediction: Reducing Timing Analysis Effort for Faster Design Convergence in Advanced-Node Design

With diminishing margins for leading-edge products in advanced technology nodes, design closure and accuracy of timing analysis have emerged as serious concerns. A significant portion of design turnaround time is spent on timing analysis at combinations of process, voltage and temperature (PVT) corners. At the same time, accurate, signoff-quality timing analysis is desired during place-and-route and optimization steps, to avoid loops in the flow as well as overdesign that wastes area and power. We observe that timing results for a given path at different corners will have strong correlations, if only as a consequence of physics of devices and interconnects. We investigate a data-driven approach, based on multivariate linear regression, to predict the timing analysis at unobserved corners from analysis results at observed corners. We use a simple backward stepwise selection strategy to choose which corners to observe and which to predict. In order to accelerate convergence of the design process, the model must yield predicted values (from analysis at a limited number of observed corners) that are sufficiently accurate to substitute for unobserved ones. Our empirical results indicate that this is likely the case. With a 1M-instance example in foundry 16nm enablement, we obtain a model based on 10 observed corners that predicts timing results at the remaining 48 unobserved corners with less than 0.5% relative root mean squared error, and 99% of the model's relative prediction errors are less than 0.6%.