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

A survey of scan-capture power reduction techniques

With the advent of sub-nanometer geometries, integrated circuits (ICs) are required to be checked for newer defects. While scan-based architectures help detect these defects using newer fault models, test data inflation happens, increasing test time and test cost. An automatic test pattern generator (ATPG) exercise’s multiple fault sites simultaneously to reduce test data which causes elevated switching activity during the capture cycle. The switching activity results in an IR drop exceeding the devices under test (DUT) specification. An increase in IR-drop leads to failure of the patterns and may cause good DUTs to fail the test. The problem is severe during at-speed scan testing, which uses a functional rated clock with a high frequency for the capture operation. Researchers have proposed several techniques to reduce capture power. They used various methods, including the reduction of switching activity. This paper reviews the recently proposed techniques. The principle, algorithm, and architecture used in them are discussed, along with key advantages and limitations. In addition, it provides a classification of the techniques based on the method used and its application. The goal is to present a survey of the techniques and prepare a platform for future development in capture power reduction during scan testing

A Comprehensive Test Pattern Generation Approach Exploiting SAT Attack for Logic Locking

The need for reducing manufacturing defect escape in today's safety-critical applications requires increased fault coverage. However, generating a test set using commercial automatic test pattern generation (ATPG) tools that lead to zero-defect escape is still an open problem. It is challenging to detect all stuck-at faults to reach 100% fault coverage. In parallel, the hardware security community has been actively involved in developing solutions for logic locking to prevent IP piracy. Locks (e.g., XOR gates) are inserted in different locations of the netlist so that an adversary cannot determine the secret key. Unfortunately, the Boolean satisfiability (SAT) based attack, introduced in [1], can break different logic locking schemes in minutes. In this paper, we propose a novel test pattern generation approach using the powerful SAT attack on logic locking. A stuck-at fault is modeled as a locked gate with a secret key. Our modeling of stuck-at faults preserves the property of fault activation and propagation. We show that the input pattern that determines the key is a test for the stuck-at fault. We propose two different approaches for test pattern generation. First, a single stuck-at fault is targeted, and a corresponding locked circuit with one key bit is created. This approach generates one test pattern per fault. Second, we consider a group of faults and convert the circuit to its locked version with multiple key bits. The inputs obtained from the SAT tool are the test set for detecting this group of faults. Our approach is able to find test patterns for hard-to-detect faults that were previously failed in commercial ATPG tools. The proposed test pattern generation approach can efficiently detect redundant faults present in a circuit. We demonstrate the effectiveness of the approach on ITC'99 benchmarks. The results show that we can achieve a perfect fault coverage reaching 100%.Comment: 12 pages, 7 figures, 5 table

Speeding up SAT-Based ATPG Using Dynamic Clause Activation

Abstract—SAT-based ATPG turned out to be a robust alter-native to classical structural ATPG algorithms such as FAN. The number of unclassified faults can be significantly reduced using a SAT-based ATPG approach. In contrast to structural ATPG, SAT solvers work on a Boolean formula in Conjunctive Normal Form (CNF). This results in some disadvantages for SAT solvers when applied to ATPG, e.g. CNF transformation time and loss of structural knowledge. As a result, SAT-based ATPG algorithms are very robust for hard-to-test faults, but suffer from the overhead for easy-to-test faults. We propose the SAT technique Dynamic Clause Activation (DCA) in order to reduce the run time gap between structural and SAT-based ATPG algorithms and, at the same time, retain the high level of robustness. Using DCA, the SAT solver works on a partial formula of a logic circuit which is dynamically extended during the search process using structural knowledge. Furthermore, efficient dynamic learning techniques can be easily integrated within the proposed technique. The approach is evaluated on large industrial circuits. Keywords-SAT; ATPG; Formal methods; CNF; I

High Quality Test Generation Targeting Power Supply Noise

Delay test is an essential structural manufacturing test used to determine the maximal frequency at which a chip can run without incurring any functional failures. The central unsolved challenge is achieving high delay correlation with the functional test, which is dominated by power supply noise (PSN). Differences in PSN between functional and structural tests can lead to differences in chip operating frequencies of 30% or more. Pseudo functional test (PFT), based on a multiple-cycle clocking scheme, has better PSN correlation with functional test compared with traditional two-cycle at-speed test. However, PFT is vulnerable to under-testing when applied to delay test. This work aims to generate high quality PFT patterns, achieving high PSN correlation with functional test. First, a simulation-based don’t-care filling algorithm, Bit-Flip, is proposed to improve the PSN for PFT. It relies on randomly flipping a group of bits in the test pattern to explore the search space and find patterns that stress the circuits with the worst-case, but close to functional PSN. Experimental results on un-compacted patterns show Bit-Flip is able to improve PSN as much as 38.7% compared with the best random fill. Second, techniques are developed to improve the efficiency of Bit-Flip. A set of partial patterns, which sensitize transitions on critical cells, are pre-computed and later used to guide the selection of bits to flip. Combining random and deterministic flipping, we achieve similar PSN control as Bit-Flip but with much less simulation time. Third, we address the problem of automatic test pattern generation for extracting circuit timing sensitivity to power supply noise during post-silicon validation. A layout-aware path selection algorithm selects long paths to fully span the power delivery network. The selected patterns are intelligently filled to bring the PSN to a desired level. These patterns can be used to understand timing sensitivity in post-silicon validation by repeatedly applying the path delay test while sweeping the PSN experienced by the path from low to high. Finally, the impacts of compression on power supply noise control are studied. Illinois Scan and embedded deterministic test (EDT) patterns are generated. Then Bit-Flip is extended to incorporate the compression constraints and applied to compressible patterns. The experimental results show that EDT lowers the maximal PSN by 24.15% and Illinois Scan lowers it by 2.77% on un-compacted patterns

Maximizing Crosstalk-Induced Slowdown During Path Delay Test

Capacitive crosstalk between adjacent signal wires in integrated circuits may lead to noise or a speedup or slowdown in signal transitions. These in turn may lead to circuit failure or reduced operating speed. This thesis focuses on generating test patterns to induce crosstalk-induced signal delays, in order to determine whether the circuit can still meet its timing specification. A timing-driven test generator is developed to sensitize multiple aligned aggressors coupled to a delay-sensitive victim path to detect the combination of a delay spot defect and crosstalk-induced slowdown. The framework uses parasitic capacitance information, timing windows and crosstalk-induced delay estimates to screen out unaligned or ineffective aggressors coupled to a victim path, speeding up crosstalk pattern generation. In order to induce maximum crosstalk slowdown along a path, aggressors are prioritized based on their potential delay increase and timing alignment. The test generation engine introduces the concept of alignment-driven path sensitization to generate paths from inputs to coupled aggressor nets that meet timing alignment and direction requirements. By using path delay information obtained from circuit preprocessing, preferred paths can be chosen during aggressor path propagation processes. As the test generator sensitizes aggressors in the presence of victim path necessary assignments, the search space is effectively reduced for aggressor path generation. This helps in reducing the test generation time for aligned aggressors. In addition, two new crosstalk-driven dynamic test compaction algorithms are developed to control the increase in test pattern count. The proposed test generation algorithm is applied to ISCAS85 and ISCAS89 benchmark circuits. SPICE simulation results demonstrate the ability of the alignment-driven test generator to increase crosstalk-induced delays along victim paths

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

Multi-Cycle at Speed Test

In this research, we focus on the development of an algorithm that is used to generate a minimal number of patterns for path delay test of integrated circuits using the multi-cycle at-speed test. We test the circuits in functional mode, where multiple functional cycles follow after the test pattern scan-in operation. This approach increases the delay correlation between the scan and functional test, due to more functionally realistic power supply noise. We use multiple at-speed cycles to compact K-longest paths per gate tests, which reduces the number of scan patterns. After a path is generated, we try to place each path in the first pattern in the pattern pool. If the path does not fit due to conflicts, we attempt to place it in later functional cycles. This compaction approach retains the greedy nature of the original dynamic compaction algorithm where it will stop if the path fits into a pattern. If the path is not able to compact in any of the functional cycles of patterns in the pool, we generate a new pattern. In this method, each path delay test is compared to at-speed patterns in the pool. The challenge is that the at-speed delay test in a given at-speed cycle must have its necessary value assignments set up in previous (preamble) cycles, and have the captured results propagated to a scan cell in the later (coda) cycles. For instance, if we consider three at-speed (capture) cycles after the scan-in operation, and if we need to place a fault in the first capture cycle, then we must generate it with two propagation cycles. In this case, we consider these propagation cycles as coda cycles, so the algorithm attempts to select the most observable path through them. Likewise, if we are placing the path test in the second capture cycle, then we need one preamble cycle and one coda cycle, and if we are placing the path test in the third capture cycle, we require two preamble cycles with no coda cycles