Alexander Czutro

Small-delay-fault ATPG with waveform accuracy

The detection of small-delay faults is traditionally performed by sensitizing transitions on a path of sufficient length from an input to an output of the circuit going through the fault site. While this approach allows efficient test generation algorithms, it may result in false positives and false negatives as well, i.e. undetected faults are classified as detected or detectable faults are classified as undetectable. We present an automatic test pattern generation algorithm which considers waveforms and their propagation on each relevant line of the circuit. The model incorporates individual delays for each gate and filtering of small glitches. The algorithm is based on an optimized encoding of the test generation problem by a Boolean satisfiability (SAT) instance and is implemented in the tool WaveSAT. Experimental results for ISCAS-85, ITC-99 and industrial circuits show that no known definition of path sensitization can eliminate false positives and false negatives at the same time, thus resulting in inadequate small-delay fault detection. WaveSAT generates a test if the fault is testable and is also capable of automatically generating a formal redundancy proof for undetectable small-delay faults; to the best of our knowledge this is the first such algorithm that is both scalable and complete.

Efficient SAT-Based Search for Longest Sensitisable Paths

We present a versatile method that enumerates all or a user-specified number of longest sensitisable paths in the whole circuit or through specific components. The path information can be used for design and test of circuits affected by statistical process variations. The algorithm encodes all aspects of the path search as an instance of the Boolean Satisfiability Problem (SAT), which allows the method not only to benefit from recent advances in SAT-solving technology, but also to avoid some of the drawbacks of previous structural approaches. Experimental results for academic and industrial benchmark circuits demonstrate the methods accuracy and scalability.

Dynamic Compaction in SAT-Based ATPG

SAT-based automatic test pattern generation has several advantages compared to conventional structural procedures, yet often yields too large test sets. We present a dynamic compaction procedure for SAT-based ATPG which utilizes internal data structures of the SAT solver to extract essential fault detection conditions and to generate patterns which cover multiple faults. We complement this technique by a state-of-the-art forward-looking reverse-order simulation procedure. Experimental results obtained for an industrial benchmark circuit suite show that the new method outperforms earlier static approaches by approximately 23%.

Functional test of small-delay faults using SAT and Craig interpolation

We present SATSEQ, a timing-aware ATPG system for small-delay faults in non-scan circuits. The tool identifies the longest paths suitable for functional fault propagation and generates the shortest possible sub-sequences per fault. Based on advanced model-checking techniques, SATSEQ provides detection of small-delay faults through the longest functional paths. All test sequences start at the circuits initial state; therefore, overtesting is avoided. Moreover, potential invalidation of the fault detection is taken into account. Experimental results show high detection and better performance than scan testing in terms of test application time and overtesting-avoidance.

SAT-based analysis of sensitisable paths

Manufacturing defects in nanoscale technologies have highly complex timing behaviour that is also affected by process variations. While conventional wisdom suggests that it is optimal to detect a delay defect through the longest sensitisable path, non-trivial defect behaviour along with modelling inaccuracies necessitate consideration of paths of well-controlled length during test generation. We present a generic methodology that yields tests through all sensitisable paths of user-specified length. The resulting tests can be employed within the framework of adaptive testing. The methodology is based on encoding the problem as a Boolean-satisfiability (SAT) instance and thereby leverages recent advances in SAT-solving technology.

SAT-ATPG using preferences for improved detection of complex defect mechanisms

Failures caused by phenomena such as crosstalk or power-supply noise are gaining in importance in advanced nanoscale technologies. The detection of such complex defects benefits from the satisfaction of certain constraints, for instance justifying specific transitions on neighbouring lines of the defect location. We present a SAT-based ATPG-tool that supports the enhanced conditional multiple-stuck-at fault model (ECMS@). This model can specify multiple fault locations along with a set of hard conditions imposed on arbitrary lines; hard conditions must hold in order for the fault effect to become active. Additionally, optimisation constraints that may be required for best coverage can be specified via a set of soft conditions. The introduced tool justifies as many of these conditions as possible, using a mechanism known as SAT with preferences. Several applications are discussed and evaluated by extensive experimental data. Furthermore, a novel fault-clustering technique is introduced, thanks to which the time required to classify all stuck-at faults in a suite of industrial benchmarks was reduced by up to 65%.

Multi-conditional SAT-ATPG for power-droop testing

Power droop is a non-trivial signal-integrity-related effect triggered by specific power-supply conditions. High-frequency and low-frequency power droop may lead to failure of an IC during application time, but they usually remain undetected by state-of-the-art manufacturing test methods, as the fault excitation imposes particular conditions on global switching activity over several time frames. Hence, ATPG for power-droop test (PD-ATPG) is an extremely hard problem that has not yet been solved optimally. In this paper, we use a SAT-based ATPG engine that employs a mechanism known as SAT-solving with qualitative preferences to generate a solution guaranteed to be optimal for a given set of optimisation criteria, however at the expense of high SAT-solving times. Therefore, a well-balanced set of criteria has to be chosen for the SAT-formulation in order to get as good solutions as possible without rendering the SAT-instances impracticably hard. We explore several strategies and evaluate them experimentally.

On the optimality of K longest path generation algorithm under memory constraints

Adequate coverage of small-delay defects in circuits affected by statistical process variations requires identification and sensitization of multiple paths through potential defect sites. Existing K longest path generation (KLPG) algorithms use a data structure called path store to prune the search space by restricting the number of sub-paths considered at the same time. While this restriction speeds up the KLPG process, the algorithms lose their optimality and do not guarantee that the K longest sensitizable paths are indeed found. We investigate, for the first time, the effects of missing some of the longest paths on the defect coverage. We systematically quantify how setting different limits on the path-store size affects the numbers and relative lengths of identified paths, as well as the run-times of the algorithm. We also introduce a new optimal KLPG algorithm that works iteratively and pinpointedly addresses defect locations for which the path-store size limit has been exceeded in previous iterations. We compare this algorithm with a naïve KLPG approach that achieves optimality by setting the path-store size limit to a very large value. Extensive experiments are reported for 45nm-technology data.

Variation-Aware Fault Grading

An iterative flow to generate test sets providing high fault coverage under extreme parameter variations is presented. The generation is guided by the novel metric of circuit coverage, calculated by massively parallel statistical fault simulation on GPGPUs. Experiments show that the statistical fault coverage of the generated test sets exceeds by far that achieved by standard approaches.

Variation-aware deterministic ATPG

In technologies affected by variability, the detection status of a small-delay fault may vary among manufactured circuit instances. The same fault may be detected, missed or provably undetectable in different circuit instances. We introduce the first complete flow to accurately evaluate and systematically maximize the test quality under variability. As the number of possible circuit instances is infinite, we employ statistical analysis to obtain a test set that achieves a fault-efficiency target with an user-defined confidence level. The algorithm combines a classical path-oriented test-generation procedure with a novel waveform-accurate engine that can formally prove that a small-delay fault is not detectable and does not count towards fault efficiency. Extensive simulation results demonstrate the performance of the generated test sets for industrial circuits affected by uncorrelated and correlated variations.