On bounding the delay of a critical path

Process variations cause different behavior of timing-dependent effects across different chips. In this work, we analyze one example of timing-dependent effects, cross-coupling capacitance, and the complex problem space created by considering coupling and process variations together. The delay of a critical path under these conditions is difficult to bound for design and test. We develop a methodology that analyzes this complex space by decomposing the problem space along three dimensions: the aggressor space, test space, and sample space. For design, we utilize an OBDD-based approach to prune the aggressor space based on logical constraints, which can be combined with a worst-case timing window simulator to prune based on both logical and timing constraints. After pruning, the reduced aggressor space can be used to derive a more accurate timing bound. Solving the problems in the test and sample spaces is postponed to the post-silicon stage, where we propose a test selection methodology for bounding the delay of every sample. This methodology is based on probability density estimation and has a tradeoff between the number of tests to apply and the tightness of the delay bound obtained. Experimental results based on benchmark examples are presented to show the effectiveness of the proposed methodology.