Efficient SAT-based ATPG techniques for all multiple stuck-at faults

Abstract

Due to the continuous shrinking of semiconductor technology, there are more and more subtle errors or faults widely distributed in manufactured chips, and traditional “single” stuck-at fault model may become inappropriate. It is definitely better if all combinations of multiple faults can be completely tested. In this paper, we present ATPG (Automatic Test Pattern Generation) techniques targeting all multiple stuck-at faults, i.e. all combinations of stuck-at faults. That is, given “n” possibly faulty locations in a circuit, the target set of faults consists of 3 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> - 1 fault combinations, as each possibly faulty location is under stuck-at 1, stuck-at 0, or normal/non-faulty. Traditional ATPG flows use fault simulators to eliminate all detectable faults by the current set of test vectors. The problem, however, fault simulators represent fault lists explicitly in the sense that all possible faults are enumerated in the fault lists. This prevents us from dealing with ultra large fault lists, such as 3 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> - 1 faults. We need “implicit” representation of faults in order to deal with such huge numbers of faults or fault combinations. We present SAT based formulations for ATPG of circuits having very large numbers of faults by implicitly eliminating detected faults. We solve a set of SAT problems whose constraints increase pure incrementally (here “pure” means never deleting constraints), and so the entire solving process can be very efficient, as all learnings obtained so far are valid in the following SAT problems. Experiments are performed on combinational parts of ISCAS89 circuits in their AIG (AND-Inverter Graph) representations. We have successfully generated the complete set of test vectors assuming that faults happen only at outputs of gates. Our ATPG techniques can also start with a given set of test vectors. If we start the ATPG processes with a set of test vectors for single stuck-at faults, we can obtain the set of additional test vectors required for multiple stuck-at faults. Results are a little bit surprising in the sense that we need very few additional test vectors for multiple faults, although the numbers of fault combinations are exponentially larger. As far as we know, for the first time, complete test vectors for all stuck-at faults for ISCAS89 circuits where faults happen only at outputs of gates in AIG representations of the circuits have been obtained.