In this paper, we investigate the challenges of applying statistical static timing analysis in hierarchical design flow, where modules supplied by IP vendors are used to hide design details for IP protection and to reduce the complexity of design and verification. For the three basic circuit types, combinational, flip-flop-based, and latch-controlled, we propose methods for extracting timing models that contain interfacing and compressed internal constraints. Using these compact timing models, the runtime of full-chip timing analysis can be reduced, while circuit details from IP vendors are not exposed. We also propose a method for reconstructing correlation between modules during full-chip timing analysis. This correlation cannot be incorporated into timing models because it depends on the layout of the corresponding modules in the chip. In addition, we investigate how to apply the extracted timing models with the reconstructed correlation to evaluate the performance of the complete design. Experiments demonstrate that using the extracted timing models and reconstructed correlation full-chip timing analysis can be several times faster than applying the flattened circuit directly, while the accuracy of statistical timing analysis is still well maintained.

Level-sensitive latches are widely used in high-performance designs. For such circuits, efficient statistical timing analysis algorithms are needed to take increasing process variations into account. The existing methods for solving this problem are still computationally expensive and can only provide the yield at a given clock period. In this paper, we propose a method combining reduced iterations and graph transformations. The reduced iterations extract setup time constraints and identify a subgraph for the following graph transformations handling the constraints from nonpositive loops. The combined algorithms are very efficient, more than ten times faster than other existing methods, and result in a parametric minimum clock period, which, together with the hold-time constraints, can be used to compute the yield at any given clock period very easily.

Post-Silicon Tunable (PST) clock buffers are widely used in high performance designs to counter process variations. By allowing delay compensation between consecutive register stages, PST buffers can effectively improve the yield of digital circuits. To date, the evaluation of manufacturing yield in the presence of PST buffers is only possible using Monte Carlo simulation. In this paper, we propose an alternative method based on graph transformations, which is much faster, more than 1000 times, and computes a parametric minimum clock period. It also identifies the gates which are most critical to the circuit performance, therefore enabling a fast analysis-optimization flow.

Latch-controlled circuits have a remarkable advantage in timing performance as process variations become more relevant for circuit design. Existing methods of statistical timing analysis for such circuits, however, still need improvement in runtime and their results should be extended to provide yield information for any given clock period. In this paper, we propose a method combining a simplified iteration and a graph transformation algorithm. The result of this method is in a parametric form so that the yield for any given clock period can easily be evaluated. The graph transformation algorithm handles the constraints from nonpositive loops effectively, completely avoiding the heuristics used in other existing methods. Therefore the accuracy of the timing analysis is well maintained. Additionally, the proposed method is much faster than other existing methods. Especially for large circuits it offers about 100 times performance improvement in timing verification.

Statistical static timing analysis deals with the increasing variations in manufacturing processes to reduce the pessimism in the worst case timing analysis. Because of the correlation between delays of circuit components, timing model generation and hierarchical timing analysis face more challenges than in static timing analysis. In this paper, a novel method to generate timing models for combinational circuits considering variations is proposed. The resulting timing models have accurate input-output delays and are about 80% smaller than the original circuits. Additionally, an accurate hierarchical timing analysis method at design level using pre-characterized timing models is proposed. This method incorporates the correlation between modules by replacing independent random variables to improve timing accuracy. Experimental results show that the correlation between modules strongly affects the delay distribution of the hierarchical design and the proposed method has good accuracy compared with Monte Carlo simulation, but is faster by three orders of magnitude.

As semiconductor devices continue to scale down, process variations become more relevant for circuit design. Facing such variations, statistical static timing analysis is introduced to model variations more accurately so that the pessimism in traditional worst case timing analysis is reduced. Because all delays are modeled using correlated random variables, most statistical timing methods are much slower than corner based timing analysis. To speed up statistical timing analysis, we propose a method to extract timing models for flip-flop and latch based sequential circuits respectively. When such a circuit is used as a module in a hierarchical design, the timing model instead of the original circuit is used for timing analysis. The extracted timing models are much smaller than the original circuits. Experiments show that using extracted timing models accelerates timing verification by orders of magnitude compared to previous approaches using flat netlists directly. Accuracy is maintained, however, with the mean and standard deviation of the clock period both showing usually less than 1% error compared to Monte Carlo simulation on a number of benchmark circuits.