Delay Fault Testing Research Articles

Path delay fault diagnosis and coverage-a metric and an estimation technique

Published research on path delay fault (PDF) testing has largely focused on the PDF classification and test-vector generation problems. Little attention has been paid to the diagnosis of delay faults and in defining realistic metrics for delay-fault coverage, We present a statistical diagnosis framework to detect which parts of the circuit are likely to have caused a chip failure for a set of delay-fault tests. Under a model where distributed fabrication-process perturbations contribute to the occurrence of delay faults, we also find the associated likely fabrication-process parameter deviations from their nominal values as part of the diagnosis framework. We present results of experiments performed on some International Symposium on Circuits and Systems 1989 (ISCAS'89) benchmark circuits and also relate the slack of a path segment to its probability of contributing to the circuit failure. We also quantify the diagnosability of a PDF for a test and develop a methodology based on our statistical diagnosis framework to determine the diagnosability of each PDF detected by a given test set. We apply this approach to find the diagnosability of robust PDFs for the ISCAS'89 benchmark circuits. Furthermore, we propose a new and realistic definition of delay-fault coverage based on the percentage of fabricated faulty chips that can be detected as faulty by a given test set. This metric takes into account the probability distribution of delay-fault sizes caused by the chip manufacturing process as opposed to previously defined metrics that have been based primarily on the percentage of faults tested. We present a computationally viable scheme for using this metric to estimate the coverage of any given test set for a class of PDFs caused by distributed fabrication-process variations. We use the results for the ISCAS'89 benchmark circuits to demonstrate wide discrepancies between PDF coverage estimates for robust test sets obtained using our realistic definition and the ones obtained by using the traditional notion of coverage as the percentage of paths tested.

Delay Fault Testing: Choosing Between Random SIC and Random MIC Test Sequences

The combination of higher quality requirements and sensitivity of high performance circuits to delay defects has led to an increasing emphasis on delay testing of VLSI circuits. In this context, it has been proven that Single Input Change (SIC) test sequences are more effective than classical Multiple Input Change (MIC) test sequences when a high robust delay fault coverage is targeted. In this paper, we show that random SIC (RSIC) test sequences achieve a higher fault coverage than random MIC (RMIC) test sequences when both robust and non-robust tests are under consideration. Experimental results given in this paper are based on a software generation of RSIC test sequences that can be easily generated in this case. For a built-in self-test (BIST) purpose, hardware generated RSIC sequences have to be used. This kind of generation will be shortly discussed at the end of the paper.

Line coverage of path delay faults

We propose a new coverage metric for delay fault tests. The coverage is measured for each line with a rising and a falling transition, but the test criterion differs from that of the slow-to-rise and slow-to-fall transition faults. A line is tested by a line delay test, which is a robust path delay test for the longest sensitizable path producing a given transition on the target line. Thus, the test criterion resembles path delay test and not the gate or transition delay test. Yet, the maximum number of tests (or faults) is limited to twice the number of lines. In a two-pass test-generation procedure, we first attempt delay tests for a minimal set of longest paths for all lines. Fault simulation is used to determine the coverage metric. For uncovered lines, in the second pass, several paths of decreasing lengths are targeted. We give results for several benchmark circuits.

A probabilistic model for path delay fault testing

Testing path delay faults (PDFs) in VLSI circuits is becoming an important issue as we enter the deep submicron age. However, it is difficult in general since the number of faults is normally very large and most faults are either hard to sensitize or are untestable. In this paper, we propose a probabilistic PDF model. We investigate probability functions for the wire and path delay size to model the fault effect in the circuit under test. In our approach, the delay fault size is assumed to be randomly distributed. An analytical model is proposed to evaluate the PDF coverage. We show that the delay sizes of the untested paths are actually reduced if these paths are conjoined with other tested good paths. Therefore, using our approach, path selection and synthesis of PDF testable circuits can be done more accurately. Also, given a test set, more accurate fault coverage can be predicted by calculating the mean delay of the paths.

Testable Path Delay Fault Cover for Sequential Circuits

We present an algorithm for identifying a set of faults that do not have to be targeted by a sequential delay fault test generator. These faults either cannot independently affect the performance of the circuit, or no test can be generated for them. To find such faults, our methodology takes advantage of the sequential behavior of the circuit as well as of the information about uncontrollable signals in the sequential circuit. It can handle sequential circuits described as two- or multi-level netlists. The outcome of applying our methodology is a smaller fault set and possibly a smaller test set. We present experimental results on several ISCAS 89 benchmark circuits demonstrating that a large number of path delay faults in these circuits either cannot or do not have to be examined for delay defects.

Design-for-testability techniques for detecting delay faults in CMOS/BiCMOS logic families

The delay fault testing in logic circuits is studied. It is shown that by detecting delayed time response in a transistor circuit, two types of faults are detected: (1) faults which cause delayed transitions at the output node due to some open defects and (2) faults which cause an intermediate voltage level at the output node. A test circuit is presented which enables the concurrent detection of delay faults. The proposed delay fault testing circuit does not substantially degrade the speed of the circuit under test (CUT). Simulation results show that this technique fits any design style.

Oscillation Ring Delay Test for High Performance Microprocessors

This paper proposes a new test scheme, oscillation ring test, and its associated test circuit organization for delay fault testing for high performance microprocessors. For this test scheme, the outputs of the circuit under test are connected to its inputs to form oscillation rings and test vectors which sensitize circuit paths are sought to make the rings oscillate. High speed transition counters or oscillation detectors can then be used to detect whether the circuit is working normally or not. The sensitizable paths of oscillation rings cover all circuit lines, detecting all gate delay faults, a large part of hazard free robust path delay faults and all the stuck-at faults. It has the advantage of testing the circuit at the working speed of the circuit. Also, with some modification, the scheme can also be used to measure the maximum speed of the circuit. The scheme needs minimal simple added hardware, thus ideal for testing, embedded circuits and microprocessors.

Primitive delay faults: identification, testing, and design for testability

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.

Universal delay test sets for logic networks

It has been shown earlier that, if we are restricted to unate gate network (UGN) realizations, there exist universal test sets for Boolean functions. Such a test set only depends on the function f, and checks any UGN realization of f for all multiple stuck-at faults and all robustly testable stuck-open faults. In this paper, we prove that these universal test sets are much more powerful than implied by the above results. They also constitute complete delay fault test sets for arbitrary UGN implementations of a given function. This is even true for UGN networks which are not completely testable with respect to the gate or path delay fault model. Our ability to prove the temporal correctness of such circuit realizations comes from the fact that we do not argue the correctness of individual paths, but rather complete path systems.

Tree-Structured Linear Cellular Automata and Their Applications in BIST

A novel implementation structure of linear finite state machines, named tree-structured linear cellular automata (TLCA), is introduced. The structures and operations of TLCA are defined. The minimal cost maximum length machines and their implementation procedure are given. Our empirical study on the ISCAS‘85 benchmark circuits shows the effectiveness of TLCA for testing stuck-open and delay faults.

Quality Determination for Gate Delay Fault Tests Considering Three-State Elements

Most industrial digital circuits contain three-state elements besides pure logic gates. This paper presents a gate delay fault simulator for combinational circuits that can handle three-state elements like bus drivers, transmission gates and pulled busses. The well known delay faults—“slow-to-rise” and “slow-to-fall”—are considered as well as delayed transitions from isolating signal state “high impedance” to binary states ‘0’ and ‘1’ and vice versa. The presented parallel delay fault simulator distinguishes between non-robust, robust and hazard free tests and determines the quality of a test. Experimental results for ISCAS85/89 benchmark circuits are presented as well as results for industrial circuits containing three-state elements.

Maximum weighted independent sets on transitive graphs and applications

We present a polynomial-time algorithm that finds the maximum weighted independent set of a transitive graph. The studied problem finds applications in a variety of VLSI contexts, including path delay fault testing, scheduling in high-level synthesis, and channel routing in physical design automation. The algorithm has been implemented and incorporated in a CAD tool for path delay fault testing. We experimentally verify its impact in the latter context.

A Scan-BIST Structure to Test Delay Faults in Sequential Circuits

Delay testing that requires the application of consecutive two-pattern tests is not an easy task in a scan-based environment. This paper proposes a novel approach to the delay fault testing problem in scan-based sequential circuits. This solution is based on the combination of a BIST structure with a scan-based design to apply delay test pairs to the circuit under test.

Dynamic digital integrated circuit testing usingoscillation-test method

A new technique to deal with simultaneous testing of delay and stuck-at faults in digital integrated circuits is proposed. It consists of sensitising a path in the digital circuit under test and then incorporating it in a ring oscillator to test for delay and stuck-at faults in the path. This procedure should be exercised for all, or at least critical, paths in the circuit. This test technique can be used along with scan techniques or implemented as a complete built-in self-test solution.

Design-for-testability for path delay faults in large combinational circuits using test points

We present a method for test-point insertion in large combinational circuits, to increase their path delay fault testability. Using an appropriate test application scheme with multiple clock periods, a test point on a line g divides the set of paths through g for testing purposes into a subset of paths from the primary inputs up to g, and a subset of paths from g to the primary outputs. Each one of these subsets can be tested separately. The number of paths that need to be tested directly is thus reduced. In addition, by breaking an untestable path into two or more testable subpaths, it is possible to obtain a fully testable circuit. Test-point insertion is done to reduce the number of paths, using a time-efficient procedure. Indirectly, it also reduces the number of tests and renders untestable paths testable. When the number of paths is sufficiently small, and if the test generation procedure to be used for the circuit is known, a procedure is given to perform test-point insertion directly targeting the path delay faults that are still untestable. Experimental results are presented to demonstrate the effectiveness of the proposed methods in increasing the testability of large benchmark circuits, and to demonstrate the overheads involved.

Functional test generation for delay faults in combinational circuits

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.

Partial-scan delay fault testing of asynchronous circuits

Asynchronous circuits operate correctly only under timing assumptions. Hence testing those circuits for delay faults is crucial. Previous work has shown that full-scan delay-fault testing of asynchronous circuits is feasible. In this work, we tackle the problem of partial-scan testing, which requires test-pattern generation on a sequential circuit. We show how this problem can be effectively reduced to a classical problem of stuck-at test-pattern generation for a related combinational circuit. The reduction is done in three steps. The first step reduces testing of an asynchronous sequential circuit, by using a partial-scan approach, to testing an object called an asynchronous net, in which feedback is allowed only inside asynchronous memory elements. We then decompose the problem of testing asynchronous nets into that of initializing memory elements (the second step), followed by robust path delay fault testing (the third step). We provide effective procedures to solve both the initialization and the test-pattern generation problem. The technique is complete, automated, and requires only partial scan of some memory element outputs.

Deriving logic systems for path delay test generation

We present an algorithm to derive logic systems for various classes of path delay test problems. In these logic systems, the value of a signal represents the relevant conditions that occur during a set of consecutively applied vectors. Starting from a set of basic values for valid signals at primary inputs, a state transition graph is constructed to enumerate all possible signal states relevant to path activation that are reachable by Boolean operations. These states include all incompletely specified states, composed as combinations of basic values. A distinguishability analysis then finds all state-pairs that need to be distinguished during test generation. The final step minimizes the number of states. For forward and backward implications of test generation in combinational or sequential circuits, the procedure provides optimal logic systems. We define optimality as the smallest set of logic states that provides the least possible ambiguity in implications. Thus, an optimal set of logic states will minimize the number of backtracks in test generation. A 10-valued logic described in the literature is found to be optimal for generating tests for single path delay faults. Other problems addressed in this paper include compact test generation through activation of many single path delay faults, test generation for rated-clock test application, and test generation for multiple path delay faults. The limitations and capabilities of various logic systems are illustrated by examples.

Cluster-cover

This article introduces a mathematical framework called cluster-cover. We show that this framework captures the combinatorial structure of a class of VLSI design optimization problems, including two-level logic minimization, constrained encoding, multilayer topological planar routing, application timing assignment for delay-fault testing, and minimization of monitoring logic for BIST enchancement. These apparently unrelated problems can all be cast into two metaproblems in our framework: finding a maximum cluster and finding a minimum cover. We describe paradigms for developing algorithms for these problems. First, a simple heuristic called greedy peeling is presented and characterized. We derive sufficient conditions that guarantee optimum solutions by greedy peeling. We generalize the performance analysis of a multilayer topological planar routing heuristic to greedy peeling for the general cluster-cover problems. We propose a performance bound of greedy set covering that can be computed efficiently for a given problem instance; this bound is much tighter than the previously known bounds. Second, prime covering—orignally developed for logic minimization—is generalized to finding exact solutions for cluster-cover problems. Previously, only the connection between logic minimizaton and constrained encoding was known.

A statistical methodology for modeling and analysis of path delay faults in VLSI circuits

Due to the rapid development of semiconductor technology, the complexity of VLSI circuits has dramatically increased. Testing such circuits is becoming a severe problem. With the increased densities of integrated circuits, several different types of faults can occur. Faults in digital circuits which result 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 (Shelly, J. H. and Trayon, D. R., Statistical techniques of timing verification. In Proc. 20th Design Automation Conf., 1983, pp. 396–402; Tendokar, N. N., Analysis of timing failures due to random AC defects in VLSI circuits. In Proc. 22nd Design Automation Conf., 1985, pp. 709–714; Park, E. S., Mercer, M. R. and Williams, T. W., A statistical model for delay fault testing. IEEE Design and Test of Computers, 1989, February, 45–55). 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 (Hamad, M. and Landis, D., A statistical model for path delay faults in VLSI circuits. In Proc. IEEE South East Conf., April 1996, pp. 388–392) which takes into account multiple delay faults along any signal path. We define and compute the path delay fault probabilities for all paths in a circuit; the single fault assumption is only a special case of our path delay fault model. Furthermore, we demonstrate how our statistical model is used to predict such important information as the maximum number of path delay faults in a circuit. Finally, we show that when multiple faults are considered during circuit analysis, the path delay fault probability, pp, and not the delay defect probability, p, should be used in the evaluation of system parameters such as statistical delay fault coverage, yield, and AC quality level.