Efficient Path Delay Test Generation with Boolean Satisfiability

This dissertation focuses on improving the accuracy and efficiency of path delay test generation using a Boolean satisfiability (SAT) solver. As part of this research, one of the most commonly used SAT solvers, MiniSat, was integrated into the path delay test generator CodGen. A mixed structural-functional approach was implemented in CodGen where longest paths were detected using the K Longest Path Per Gate (KLPG) algorithm and path justification and dynamic compaction were handled with the SAT solver. Advanced techniques were implemented in CodGen to further speed up the performance of SAT based path delay test generation using the knowledge of the circuit structure. SAT solvers are inherently circuit structure unaware, and significant speedup can be availed if structure information of the circuit is provided to the SAT solver. The advanced techniques explored include: Dynamic SAT Solving (DSS), Circuit Observability Don’t Care (Cir-ODC), SAT based static learning, dynamic learnt clause management and Approximate Observability Don’t Care (ACODC). Both ISCAS 89 and ITC 99 benchmarks as well as industrial circuits were used to demonstrate that the performance of CodGen was significantly improved with MiniSat and the use of circuit structure

Optimization of Pseudo Functional Path Delay Test Through Embedded Memories

Traditional automatic test pattern generation achieves high coverage of logic faults in integrated circuits. Automatic test of embedded memory arrays uses built-in self-test. Testing the memories and logic separately does not fully test the critical timing paths that go into or out of memories. Prior research has developed algorithms and software to test the longest paths into and out of embedded memories. However, in this prior work, the test generation time increased superlinearly with memory size. This is contrary to the intuition that the time should rise approximately linearly with memory size. This behavior limits the algorithm to circuits with relatively small memories. The focus of this research is to analyze the time complexity of the algorithm and propose changes to reduce the time required to test circuits with large memories. We use our prior work on pseudo functional K longest path per gate test generation, and the benchmark circuits with embedded memories developed in the prior work. Since the cells within a memory array are not scan cells, a value that is captured in a memory cell must be moved to a scan cell using low-speed coda cycles. This approach will also support the test of any non-scan flip-flop or latch, in addition to embedded memory arrays. In addition to testing the critical timing paths, testing through memories eliminates the logic “shadows” around the memory where faults cannot be tested. In this research our complexity analysis has identified the reason for the superlinear increase in test generation time with larger memories and verified this analysis with experimental results. We have also developed and implemented several heuristics to increase performance, with experimental results. This research also identifies the major algorithm changes required to further increase performance

High Quality Compact Delay Test Generation

Delay testing is used to detect timing defects and ensure that a circuit meets its timing specifications. The growing need for delay testing is a result of the advances in deep submicron (DSM) semiconductor technology and the increase in clock frequency. Small delay defects that previously were benign now produce delay faults, due to reduced timing margins. This research focuses on the development of new test methods for small delay defects, within the limits of affordable test generation cost and pattern count. First, a new dynamic compaction algorithm has been proposed to generate compacted test sets for K longest paths per gate (KLPG) in combinational circuits or scan-based sequential circuits. This algorithm uses a greedy approach to compact paths with non-conflicting necessary assignments together during test generation. Second, to make this dynamic compaction approach practical for industrial use, a recursive learning algorithm has been implemented to identify more necessary assignments for each path, so that the path-to-test-pattern matching using necessary assignments is more accurate. Third, a realistic low cost fault coverage metric targeting both global and local delay faults has been developed. The metric suggests the test strategy of generating a different number of longest paths for each line in the circuit while maintaining high fault coverage. The number of paths and type of test depends on the timing slack of the paths under this metric. Experimental results for ISCAS89 benchmark circuits and three industry circuits show that the pattern count of KLPG can be significantly reduced using the proposed methods. The pattern count is comparable to that of transition fault test, while achieving higher test quality. Finally, the proposed ATPG methodology has been applied to an industrial quad-core microprocessor. FMAX testing has been done on many devices and silicon data has shown the benefit of KLPG test