Statistical timing analysis based on simulation of lithographic process

Abstract

The length of poly-gate printed on silicon depends on exposure dose, depth of focus, photo-resist thickness and planarity of the surface. In sub-wavelength lithography, polygate length also varies with layout topology. Poly-gate length determines the effective channel length of a transistor, which determines its performance. Since the sources of error are hard to control, statistical analysis can be used to measure the impact on circuit timing characteristics. Typical lithography-aware methodologies consider only systematic variation such as across chip linewidth variation (ACLV). In this paper we propose a statistical technique for timing yield prediction, based on variational lithography modeling of physical circuit layout. By statistically varying lithographic process parameters we estimate the difference in timing yield estimation of a design. Our simulation results show that if manufacturing process parameters follow a Gaussian distribution, resulting transistors follow a skewed normal distribution, where a greater number of them will have shorter channel length. This led us to investigate whether Statistical Static Timing Analysis (SSTA) is overly pessimistic. The baseline delay model assumed for SSTA in out approach is a Gaussian delay model fitted to skew normal distribution data obtained from statistical litho simulation. Our experiments showed that even after re-centering Gaussian delay model to fit the channel length data with minimum error, it is still overly pessimistic and significantly underestimates circuit performance.