University of Rostock, Germany Department of Computer Science and Electrical Engineering

1. Probability Density Gate Delay Gaussian Distribution Best Case Worst Case -3σ +3σ 99,8% of all cases Wasted by conservative approach! Deterministic STA: (Worst Case Analysis) 2 4 6 0 Statistical Static Timing Analysis (SSTA) 2 4 6 0 New Approach for SSTA on Multi-Input Gates: As function of output signal results from multiplication of all input CDFs CDF is approximated as straight line => new CDF results from multiplication of all approximated straight lines of input signals Probability Density Function (PDF) Probability that gate delay has value x Cumulative probability Distribution Function (CDF) Probability that gate delay is lower than x accurate function for output signal new approach Probability Density Gate Delay ? A Y B function for output signal at established approach Error! accurate function for output signal Evaluated delay if only less parameters are described with Gaussian distribution (usually used, because high effort to describe more parameters) • Approach: • Gaussian description of gate delay • Extracted from Monte-Carlo Spice Simulation Monte-Carlo Simulations (#10k, Variation of NDEP, Leff, Weff, Temp, Vth) NAND2 in predictive 65nm BPTM technology Total Leakage Reduction by Observance of Parameter Variations Frank Sill, Dirk Timmermann THE NORDIC EVENT INASIC DESIGN Statistical STA Basics time New Approaches for Delay Modeling and SSTA at MIS Gates Library with Gaussian distribution of gate delays Gate-Netlist Statistical Static Timing Analysis (SSTA) New Approach for SSTA on gates with multiple inputs Dual Vt/To CMOS and Results University of Rostock, Germany Department of Computer Science and Electrical Engineering