Primitive Path Delay Fault Identification

We investigate two strategies to guarantee temporal correctness of a combinational circuit. We first propose a new technique to identify and test primitive faults. A primitive fault is a path delay fault that has to be tested to guarantee the performance of the circuit. Primitive faults can consist of single- (SPDF's) or multiple path delay faults (MPDF's). Testing strategies for single primitive faults exist. In this paper, we focus on identifying and testing multiple primitive faults. Identification and testing of these faults is important for at least two reasons: (1) a large percentage of paths in production circuits remain untestable under the SPDF model, and (2) distributed manufacturing defects usually adversely affect more than one path and these defects can be detected only by analyzing multiple affected paths. The SPDF's contained in a multiple primitive fault have to merge at some gate(s). Our methodology can quickly (1) rule out a large number of gates as possible merging gates for primitive faults, and (2) prune the combinations of paths that can never belong to any primitive fault. Our identification procedure also finds a test for the fault. We present a complete algorithm for identifying and testing double path delay faults, Identifying and testing all primitive faults is impractical for large designs. This is because no efficient methods are known for testing primitive faults that include a large number of paths. However, to guarantee that the performance of a digital circuit is not affected by timing defects, it is necessary to test all primitive faults. Our second contribution is a new design for testability method. Our method guarantees that only primitive faults with at most two paths can exist in the circuit in the test mode. The main idea is to efficiently identify a small set of signals for inserting test points to eliminate primitive faults with more than two paths. Our test points only provide controllability. Addition of a single test point can lower the cardinality of several primitive faults. Our approach efficiently re-evaluates primitive delay fault testability of the circuit after insertion of a test point. After a few iterations only primitive faults with at most two paths can exist in the circuit in the test mode. Experimental results on several multilevel combinational benchmark circuits are included to demonstrate the usefulness of our techniques.

With the increased densities of integrated circuits, several different types of faults can occur. Faults in digital circuits resulting from random defects can introduce DC (stuck-at) faults as well as AC (delay) faults. Previous work in statistical modeling and analysis for delay fault testing generally assumes that at most a single delay fault can occur along any given path in the circuit under test. In this paper we investigate the statistical effect of multiple delay faults along any path in a circuit under test, and predict the path delay fault probabilities as well as the maximum number of path delay faults for both combinational and sequential benchmark circuits. We begin with the development of a statistical model for path delay faults in VLSI circuits [4], which takes into account multiple delay faults along any signal path.

The goal of fault diagnosis is to identify the causes of device failures. Different techniques have been proposed for stuck-at fault diagnosis in combinational as well as sequential circuits. On the other side, diagnosis of delay faults has received attention for the first category of circuits, but not for synchronous sequential circuits. So, this paper concerns delay fault diagnosis for non-scan circuits. A preliminary version of the proposed method is first given. New concepts for allowing path tracing in the proposed diagnosis process (identification of self-masking) are also presented. As the method is based on path tracing through the sequential circuit, gate delay faults as well as path delay faults are considered and may be located in a faulty machine. Results of experiments on ISCAS-89 benchmark circuits are finally discussed.

Article Free Access Share on Delay fault coverage and performance tradeoffs Authors: William K. Lam View Profile , Alexander Saldanha View Profile , Robert K. Brayton View Profile , Alberto L. Sangiovanni-Vincentelli View Profile Authors Info & Claims DAC '93: Proceedings of the 30th international Design Automation ConferenceJuly 1993Pages 446–452https://doi.org/10.1145/157485.164970Published:01 July 1993Publication History 89citation253DownloadsMetricsTotal Citations89Total Downloads253Last 12 Months17Last 6 weeks1 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

To guarantee the temporal correctness of a digital circuit a set of multiple path delay faults called primitive faults need to be tested. Primitive faults can contain one or more faulty paths. Existing techniques can identify and test primitive faults containing up to two or three paths. Identifying and testing primitive faults that consist of a larger number of paths is impractical for large designs. We propose a design for testability method that assures the temporal correctness of the circuit without the need to test all primitive faults in the circuit. In the test mode, only primitive faults that contain up to two paths can affect the circuit performance. Our methodology efficiently identifies a small set of potential locations for inserting control points to eliminate primitive faults with more than two paths. Addition of a single control point can lower the cardinality of several primitive faults. Our approach re-evaluates primitive delay fault testability of the circuit after insertion of every control point. After a few iterations only primitive faults with at most two paths can exist in the circuit in the test mode. Experimental results on several circuits are included to demonstrate our method.

We propose a functional fault model for delay faults in combinational circuits and describe a functional test generation procedure based on this model. The proposed method is most suitable when a gate-level description of the circuit-under-test, necessary for employing existing gate-level delay fault test generators, is not available or does not accurately describe the circuit. It is also suitable for generating tests in early design stages of a circuit, before a gate-level implementation is selected. In addition, it can potentially be employed to supplement conventional test generators for gate-level circuits to reduce the cost of handling large numbers of paths. A parameter called Δ is used to control the number of funtional faults targeted and thus the number of tests generated. If Δ is unlimited, the functional test set detects every robustly testable path delay fault in any gate-level implementation of the given ciruit. An appropriate subset of tests can be selected once the implentation is known. The test sets generated for various values of Δ are fault simulated on gate-level realizations to demonstrate their effectiveness. The experiments indicate that functional test sets may be able to identify functions whose realizations have low path delay fault coverage.

A test generation procedure for path delay faults is proposed, that targets all path delay faults in the circuit-under-test. The procedure overcomes the difficulties in handling the exorbitant numbers of path delay faults in practical circuits by using a non-enumerative method of considering faults, i.e., it never explicitly targets any specific path delay fault. Experimental results demonstrate the effectiveness of the method in deriving tests to detect very large numbers of path delay faults in short run times.

Specific physical defects of high performance circuits manifest themselves as path delay faults (PDFs). A pair (v1, v2) of test patterns is required to detect a PDF. A PDF is robust testable if there is a test pair on which the fault manifestation does not depend on delays of other circuit paths. A PDF is non robust testable if manifestation of the fault on any test pair is possible only when all other paths of the circuit are fault free. For high quality delay testing it is desirable to detect delay of any path regardless of delays of other paths. In this paper, synthesis of a circuit by covering each nonterminal node of the reduced ordered binary decision diagram (ROBDD) or free binary decision diagram (Free BDD) system with the original subcircuit from gates is suggested. Delay testability of such circuits is investigated. It is specified that the PDF of each path of the circuit is detected without injecting additional inputs into the circuit. It is well known that the BDD is a directed acyclic graph based on the Shannon decomposition in each nonterminal node v: 0 1 i i x x v i v i v f x f x f = = = ∨ . Here fv is the function corresponding to the node v, and the decomposition variable xi marks the node v. The dashed edge drops in the node corresponding to the function 0 i x v f = , and the bold edge drops in the node corresponding to the function 1 i x v f = . The BDD is called ordered (OBDD) if variables are encountered in the same order in all paths connecting the BDD root with the terminal node. The BDD is called reduced (RBDD) if it does not contain either isomorphic subgraphs or nonterminal nodes such that 0 1 i i x x v v f f = = = . An example of reduced and ordered BDD (ROBDD) is shown in Fig. 1. When deriving the Free BDD, a suitable decomposition variable is chosen for each nonterminal node v independently of other nonterminal nodes. That may cut the number of Free BDD of nonterminal nodes in comparison with the ROBDD (for the same function). Let 1 { ,..., } m F f f = be a system of Boolean functions describing combinational circuit behavior. Derive the ROBDD using the same order of variables for each Boolean function from F. Join isomorphic subgraphs in different ROBDDs. Combine different ROBDDs of 1-terminal nodes into one 1-terminal node and their 0-terminal nodes into one 0-terminal node. As a result, we obtain the graph with m roots and two terminal nodes. This graph represents a system of m Boolean functions. It is called the shared ROBDD. Without loss of generality, we will further consider systems with one function as an example. In Fig. 1, the ROBDD for one Boolean function is shown. The ROBDD represents the disjoint sum of products (DSoP) of the function f as follows:

Recently published results have shown that, for many circuits, only a small percentage of path delay faults is robust testable, Among the robust untestable faults, a significant percentage is not nonrobust testable either. In this paper, we take a closer look at the properties of these nonrobust untestable faults with the goal of determining whether and how these faults should be tested. We define a path delay fault to be functional redundant (f-redundant) if, regardless of the delays at all other signals, the circuit performance will not be determined by the path. These paths are false paths-regardless of the delays of all signals. Therefore, these paths cannot and need not be tested. We present a sufficient condition for functional redundancy. We will show that nonrobust untestable faults are not necessarily f-redundant. For those nonrobust untestable but functional irredundant (f-irredundant) faults, the corresponding path may become a true path, and thus may determine the circuit performance under the faulty condition. We present an efficient algorithm for identifying f-redundant path delay faults. Results show that a significant percentage of path delay faults are f-redundant for ISCAS'85 benchmark circuits. Identification of f-redundant faults has two important applications: 1) it provides a more realistic fault coverage measure (as the number of detected faults divided by the total number of f-irredundant faults), 2) For circuits with a large number of paths, testing only a subset of paths becomes a common practice. The path selection process can be guided to avoid selecting f-redundant paths. To illustrate this application, we present an algorithm for selecting a set of f-irredundant path delay faults that includes at least one of the longest f-irredundant paths for each signal in the circuits.

In this paper, we discuss the relationship between the test generation complexity for path delay faults (PDFs) and that for stuck-at faults (SAFs) in combinational and sequential circuits using the recently introduced τk-notation. On the other hand, we also introduce a class of cyclic sequential circuits that are easily testable, namely two-column distributive state-shiftable finite state machine realizations (2CD-SSFSM). Then, we discuss the relevant conjectures and unsolved problems related to the test generation for sequential circuits with PDFs under different clock schemes and test generation models.

In this paper, we propose a new testability metric for path delay faults. The metric is computed efficiently using a non-enumerative algorithm. It has been validated through extensive experiments and the results indicate a strong correlation between the proposed metric and the path delay fault testability of the circuit. We further apply this metric to derive a path delay fault test application scheme for scan-based BIST. The selection of the test scheme Is guided by the proposed metric. The experimental results illustrate that the derived test application scheme can achieve a higher path delay fault coverage in scan-based BIST. Because of the effectiveness and efficient computation of this metric, it can be used to derive other design-for-testability techniques for path delay faults.

The author addresses static hazards in multi-level combinational logic circuits. A novel approach is introduced based on a uniform hybrid method that is capable of identifying race conditions and detecting all types of hazards: static, logic, function, and dynamic, that have the potential to exist in combinational logic circuits under given conditions. This method is based on a binary switching algebra, and uses hardware simulation techniques together with more formal symbol manipulation mechanisms in order to identify potential hazards in logic design.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Test data compression is based on storage of compressed tests and use of on-chip decompression logic for test application. Further reductions in the input test data volume are achieved by methods that apply several different tests based on every compressed test. This article makes the new observation that by keeping the same number of compressed tests and applying several different tests based on every compressed test, it is possible to improve the quality of the test set applied to the circuit. This article studies such an approach for path delay faults (PDFs) using a linear-feedback shift register (LFSR) as the decompression logic. Because of the nature of PDFs, targeting an extended subset of PDFs increases the confidence that important PDFs are detected. However, the benefit of detecting additional faults may not justify an increase in the number of stored tests. The approach suggested in this article is used for detecting an extended subset of target PDFs using the same set of LFSR seeds. Extra clocking of the LFSR is used for obtaining scan-in states for several new two-cycle tests based on the same seed. Experimental results for benchmark circuits demonstrate the effectiveness of this approach.

Path delay fault model is the most suitable model for detecting distributed manufacturing defects which can cause delay faults. However, the number of paths in a modern design can be extremely large and the path delay testability of many practical designs is very low. In this paper we show how to resynthesize a combinational circuit in order to reduce the total number of paths in the circuit. Our results show that it is possible to obtain circuits with a significant reduction in the number of paths while not increasing area and/or delay of the longest sensitizable path in the circuit. Research on path delay testing shows that in many circuits a large portion of paths does not have a test that can guarantee detection of a delay fault. The path delay testability of a circuit would increase if the number of such paths is reduced. We show that addition of a small number of test points into the circuit can help reducing the number of such paths in the given design.

The problem of test generation for path delay faults in synchronous sequential circuits is addressed. In existing testing methods, a single fast clock cycle is used to activate path delay faults and a fault is said to be detected only if the fault free response is different from the faulty response at a single output and at a specified time unit in the test sequence. We refer to these methods as single fast clock cycle and single observation time testing methods. We show that testable faults may exist, which are untestable using a single fast clock cycle and a single observation time. Such faults are testable when multiple fast clock cycles and/or multiple observation times are used. A test generation procedure is given that uses multiple fast clock cycles and multiple observation times. Experimental results are presented on MCNC synthesis benchmarks to demonstrate the effectiveness of the proposed strategy in increasing the fault coverage and reducing the test length.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>