Concurrent Path Selection Algorithm in Statistical Timing Analysis

Abstract

Circuit timing is becoming more and more uncertain under greater process variation as technology scales. Given the fault probability of each timing path and their statistical correlation from a statistical timing framework, the path selection problem for delay faults has a nature similar to the problem of designing a portfolio of stocks or assets or determining the size of bets in gambling to minimize risk. This observation allows us to develop a very different path selection approach from the conventional ones. If selection of k paths is required in a set of paths, we partition the set into two path sets and determine how many paths should be selected in each path set out of the k paths based on the probabilities of each path set containing faulty paths. We recursively continue this process, which results in the paths to be targeted during tests. The partitioning is easily performed because the paths are already grouped into the depth-first search tree based on their suffix or prefix. Experimental results show that the proposed algorithm can effectively use the correlation to generate high-quality path sets. In addition, we study the issues that occur after automatic test pattern generation on the selected paths, and discuss possible solutions to them.