Computation of Waveform Sensitivity using Geometric Transforms for SSTA

Ratnakar Goyal,  Harindranath Parameswaran,  Sachin Shrivastava
Cadence Design Systems


Statistical Static Timing Analysis (SSTA) is being used a method for estimating the yield of a circuit. The accuracy of SSTA depends on the accuracy of timing sensitivities as computed using a Statistical Delay calculation Engine which in turn depends on the accuracy and availability of required information in the timing library. For SSTA, libraries need to contain information of the effect that process variations have on timing data. Waveform sensitivities are required for accurate computation of gate and interconnect delay sensitivities. However, modeling waveform sensitivities in the library increases the library size significantly (~40% per process parameter). Also in certain scenarios their characterization may not be possible. In this paper, we propose a technique for computing waveform sensitivities when such information is not part of the standard cell library. We use geometric transforms and the nominal waveform information, along with available sensitivities of the timing activities in non-linear delay models to derive waveform sensitivities. We show that using our approach the size of a statistical library with 700 cells is reduced by ~65%. We also show that the methodology provides an accuracy improvement of 15-20% in the computation of standard deviation.