Automatic Test Generation for Combinational Threshold Logic Networks

We propose an automatic test pattern generation (ATPG) framework for combinational threshold networks. The motivation behind this work lies in the fact that many emerging nanotechnologies, such as resonant tunneling diodes (RTDs), single electron transistor (SET), and quantum cellular automata (QCA), implement threshold logic. Consequently, there is a need to develop an ATPG methodology for this type of logic. We have built the first automatic test pattern generator and fault simulator for threshold logic which has been integrated on top of an existing computer-aided design (CAD) tool. These exploit new fault collapsing techniques we have developed for threshold networks. We perform fault modeling, backed by HSPICE simulations, to show that many cuts and shorts in RTD-based threshold gates are equivalent to stuck-at faults at the inputs and output of the gate. Experimental results with the MCNC benchmarks indicate that test vectors were found for all testable stuck-at faults in their threshold network implementations.     

Multiple Stuck-at Fault Testability Analysis of ROBDD Based Combinational Circuit Design

Automatic test pattern generation (ATPG) is the next step after synthesis in the process of chip manufacturing. The ATPG may not be successful in generating tests for all multiple stuck-at faults since the number of fault combinations is large. Hence a need arises for highly testable designs which have 100% fault efficiency under the multiple stuck-at fault(MSAF) model. In this paper we investigate the testability of ROBDD based 2×1 mux implemented combinational circuit design. We show that the ROBDD based 2×1 mux implemented circuit is fully testable under multiple stuck-at fault model. Principles of pseudoexhaustive testing and multiple stuck-at fault testing of two level AND-OR gates are applied to one sub-circuit(2×1 mux). We show that the composite test vector set derived for all 2×1 muxes is capable of detecting multiple stuck-at faults of the circuit as a whole. Algorithms to derive test set for multiple stuck-at faults are demonstrated. The multiple stuck-at fault test set is larger than the single stuck-at fault test set. We show that the multiple stuck-at fault test set can be derived from the Disjoint Sum of Product expression which allows test pattern generation at design time, eliminating the need of an ATPG after the synthesis stage.     

An Exact approach for Complete Test Set Generation of Toffoli-Fredkin-Peres based Reversible Circuits

Reversible logic has gained interest of researchers worldwide for its ultra-low power and high speed computing abilities in the future quantum information processing. Testing of these circuits is important for ensuring high reliability of their operation. In this work, we propose an ATPG algorithm for reversible circuits using an exact approach to generate CTS (Complete Test Set) which can detect single stuck-at faults, multiple stuck-at faults, repeated gate fault, partial and complete missing gate faults which are very useful logical fault models for reversible logic to model any physical defect. Proposed algorithm can be used to test a reversible circuit designed with k-CNOT, Peres and Fredkin gates. Through extensive experiments, we have validated our proposed algorithm for several benchmark circuits and other circuits with family of reversible gates. This algorithm produces a minimal and complete test set while reducing test generation time as compared to existing state-of-the-art algorithms. A testing tool is developed satisfying the purpose of generating all possible CTS’s indicating the simulation time, number of levels and gates in the circuit. This paper also contributes to the detection and removal of redundant faults for optimal test set generation.     

False-Path Removal Using Delay Fault Simulation

Some false paths are caused by redundant stuck-at faults. Removal of those stuck-at faults automatically eliminates such false paths from the circuit. However, there are other false paths that are not associated with any redundant stuck-at fault. All segments of such a false path are shared with other testable paths. We focus on the elimination of this type of false paths. We use a non-enumerative path delay fault simulator based on the path status graph (PSG) data-structure, which duplicates selected gates to separate the detected and undetected path delay faults. The expanded circuit may contain new redundant stuck-at faults, corresponding to those undetected paths that are false. This happens because the expanded circuit has some new interconnects with only false paths passing through them. Such links become the sites for redundant stuck-at faults. Removal of these redundant faults eliminates false paths. The reported results show that the quality of the result may depend on the coverage of testable paths by the vectors that are simulated. When non-enumerative path delay simulation and implication-based redundancy removal techniques are used, the present procedure of false-path elimination can be applied to very large circuits.     

Efficient design of parity preserving logic in quantum-dot cellular automata targeting enhanced scalability in testing

Design of parity preserving logic based on emerging nanotechnology is very limited due to present technological limitation in tackling its high error rate. In this work, Quantum-dot cellular automata (QCA), a potential alternative to CMOS, is investigated for designing easily testable logic circuit. A novel self-testable logic structure referred to as the testable-QCA (t-QCA), using parity preserving logic, is proposed. Design flexibility of t-QCA then evaluated through synthesis of standard functions. The programmability feature of t-QCA is utilized to implement an ALU, realizing six important functions. Although the parity preservation property of t-QCA enables concurrent detection of permanent as well as the transient faults, an augmented test logic circuit (TC) using QCA primitives has been introduced to cover the cell defects in nanotechnology. Experimental results establish the efficiency of the proposed design that outperforms the existing technologies in terms of design cost and test overhead. The achievement of 100% stuck-at fault coverage and the 100% fault coverage for single missing/additional cell defects in QCA layout of the t-QCA gate, address the reliability issues of QCA nano-circuit design.     

Experimental Results for Self-Dual Multi-Output Combinational Circuits

In this short note, the possibilities and the limitations for the application of self-dual circuits with alternating inputs are experimentally investigated. The original circuit is assumed to be given as a netlist of gates. The necessary area overhead, the fault coverage for single stuck-at faults in test mode and the error detection probability in on-line mode due to internal stuck-at faults and stuck-at faults at the input lines are determined for MCNC benchmark circuits.     

A test set embedding approach based on twisted-ring counter with few seeds

Test data storage, test application time and test power dissipation increase dramatically for single stuck-at faults while tens of million gates are integrated in a System-on-a-Chip (SoC), which makes implementing fault testing for embedded cores based SoC become a challenging task. To further reduce test data storage, test application time and test power dissipation, this paper presents a new test set embedding approach based on twisted-ring counter (TRC) with few seeds. This approach includes two improvements. The first is that an efficient seed-selection algorithm is employed to exploit the high-density unspecified bits in the deterministic test set and so the test data storage for complete coverage of single stuck-at faults is minimized. The second is that a novel test-sequence-reduction scheme based on shifting seeds is proposed to reduce test application time that in turn reduces test power dissipation. Compared with the conventional approach, experiments on ISCAS’89 benchmark circuits show that the proposed approach requires 65% less test data storage, 68% shorter test application time and 67% less test power dissipation. Moreover, its hardware overhead is very small.     

Test Generation and Fault Simulation for Cell Fault Model using Stuck-at Fault Model based Test Tools

Cell Fault Model (CFM) is a well-adopted functional fault model used for cell-based circuits. Despite of the wide adoption of CFM, no test tool is available for the estimation of CFM testability. The vast majority of test tools are based on the single stuck-at fault model.In this paper we introduce a method to calculate the CFM testability of a cell-based circuit using any single stuck-at fault based test tool. Cells are substituted by equivalent cells and Test Generation and Fault Simulation for CFM are emulated by Test Generation and Fault Simulation for a set of single stuck-at faults of the equivalent cells. The equivalent cell is constructed from the original cell with a simple procedure, with no need of knowledge of gate-level implementation, or its function. With the proposed methodology, the maturity and effectiveness of stuck-at fault based tools is used in testing of digital circuits, with respect to Cell Fault Model, without developing new tools.     

Resynthesis of combinational logic circuits for improved path delayfault testability using comparison units

We propose a resynthesis method that modifies a given circuit to reduce the number of paths in the circuit and thus improve its path delay fault testability. The resynthesis procedure is based on replacing subcircuits of the given circuit by structures called comparison units. A subcircuit can be replaced by a comparison unit if it implements a function belonging to the class of comparison functions defined here. Comparison units are fully testable for stuck-at faults and for path delay faults. In addition, they have small numbers of paths and gates. These properties make them effective building blocks for resynthesis to improve the path delay fault testability of a circuit. Experimental results demonstrate considerable reductions in the number of paths and increased path delay fault testability. These are achieved without increasing the number of gates, or the number of gates along the longest path in the circuit. The random pattern testability for stuck-at faults remains unchanged     

Reversible Gates and Testability of One Dimensional Arrays of Molecular QCA

An extensive literature exists on the mathematical characterization of reversible logic. However, the possible technological basis of this computing paradigm still remains unsolved. In this paper, quantum-dot cellular automata (QCA) is investigated for testable implementations of reversible logic. Two new reversible gates (referred to as QCA1 and QCA2) are proposed. These gates are compared (in terms of delay, area and logic synthesis) with other reversible gates (such as Toffoli and Fredkin) for QCA implementation. Due to the expected high error rates in nano-scale manufacturing, testing of nano devices, including QCA, has received considerable attention. The focus of this paper is on the testability of a one-dimensional array made of QCA reversible gates, because the bijective nature of reversible gates significantly facilitates testing of arrays. The investigation of testability relies on a fault model for molecular QCA that is based on a single missing/additional cell assumption. It is shown that C-testability of a 1D reversible QCA gate array can be guaranteed for single fault. Theory and circuit examples show that error masking can occur when multiple faults are considered.     

Modular Design of testable reversible ALU by QCA multiplexer with increase in programmability

The quantum-dot cellular automata have emerged as one of the potential computational fabrics for the emerging nanocomputing systems due to their ultra-high speed and integration density. On the other hand, reversible computing promises low power consuming circuits by nullifying the energy dissipation during the computation. This work targets the design of a reversible arithmetic logic unit (RALU) in the quantum-dot cellular automata (QCA) framework. The design is based on the reversible multiplexer (RM) synthesized by compact 2:1 QCA multiplexers introduced in this paper. The proposed reversible multiplexer is able to achieve 100% fault tolerance in the presence of single missing or additional cell defects in QCA layout. Furthermore, the advantage of modular design of reversible multiplexer is shown by its application in synthesizing the RALU with separate reversible arithmetic unit (RAU) and reversible logic unit (RLU). The RALU circuit can be tested for classical unidirectional stuck-at faults using the constant variable used in this design. The experimentation establishes that the proposed RALU outperforms the conventional reversible ALU in terms of programming flexibility and testability.     

A synthesis-based test generation and compaction algorithm for multifaults

Because of its inherent complexity, the problem of automatic test pattern generation for multiple stuck-at faults (multifaults) has been largely ignored. Recently, the observation that multifault testability is retained by algebraic factorization demonstrated that single fault (and therefore multifault) vector sets for two-level circuits could give complete multifault coverage for multilevel circuits constructed by algebraic factorization. Unfortunately, in using this method the vector set size can be much larger than what is really required to achieve multifault coverage, and the approach has some limitations in its applicability.In this article we first present a multifault test generation and compaction strategy for algebraically factored multilevel circuits, synthesized from two-level representations. We give a basic sufficiency condition for multifault testability of such networks.We next focus on the relationship between hazard-free robust path-delay-fault testability and multifault testability. We show that the former implies the latter for arbitrary multilevel circuits. This allows the use of previously developed composition rules that maintain path-delay-fault testability for the synthesis of multifault testable circuits.We identify a class of multiplexor-based networks and prove an interesting property of such networks—if the networks are fully single stuck-at fault testable, or made fully single stuck-at fault testable, they are completely multifault testable. We give a multifault test generation and compaction algorithm for such networks.We provide experimental results which indicate that a compacted multifault test set derived using the above strategies can be significantly smaller than the test set derived using previously proposed procedures. These results also indicate the substantially wider applicability of our procedures, as compared to previous techniques.     

Robust tests for parity trees

Linear logic circuits are used extensively in digital computing and signal processing systems. They are constructed as regular arrays (for example as cascade or tree circuits), employing linear gates such as Exclusive OR (EOR) and Exclusive NOR (ENOR) gates. Earlier studies on fault diagnosis in linear logic circuits were based on the classical fault model of line stuck-at faults. Transistor stuck-open (SOP) and stuck-on (SON) faults in linear circuits were studied recently, but the effect of signal transients due to circuit delays and time skews in input changes were not considered in the derivation of test sequences. These latter factors are known to cause invalidation of two pattern tests for stuck-open faults. In this article we consider the problem of generating robust tests for linear logic circuits. These tests are not affected by circuit transients caused by delays. A major finding in this paper is that, if the test invalidation problem is redressed by introducing robust tests, the test length becomes a linear function of the depth of the circuit as opposed to the constant number of tests derived in previous studies, by neglecting circuit transients. A lower bound on minimum number of distinct test patterns needed for a tree of EOR gates of depthd is derived. This number depends on the specific implementation of the gate. Robust test-generation procedures are proposed for both single and multiple fault models and their optimalities are argued. Given that every gate in a parity tree is robustly testable, a test sequence that can test for all faults in the circuit, regardless of the nature of gate implementation, is calleduniversal robust test sequence for a parity tree. Finally we propose an optimal universal robust test sequence.     

Functional fault models for non-scan sequential circuits

The paper presents two functional fault models that are applied for functional delay test generation for non-scan synchronous sequential circuits: the pin pair state (PPS) fault model and the pin pair full state (PPFS) fault model. The PPS fault model deals with the pairs of stuck-at faults on the primary inputs and the primary outputs, as well as, with the pairs of stuck-at faults on the previous state bits and the primary outputs. The PPFS fault model encompasses the PPS model, and additionally deals with the pairs of stuck-at faults on the primary inputs and the next state bits, as well as, with the pairs of stuck-at faults on the previous state bits and the next state bits. The main factor in assessing the quality of obtained test sequences was the transition fault coverage at the gate level of the selected according to the appropriate fault model test sequences from the generated randomly ones. The experimental results demonstrate that the implementation using presented functional fault models allow selecting the test sequences from the initial test set without the loss of transition fault coverage in many cases, and the number of the selected test sequences is much lesser than that of the initial test set. This result demonstrates that the functional delay test can be generated using the presented functional delay fault models before structural synthesis of the circuit.     

Using nano-scale QCA technology for designing fault-tolerant 2:1 multiplexer

Recently, Quantum-dot Cellular Automata (QCA) has appeared as a noteworthy substitution to CMOS technology. It contains ultra-high-velocity, efficient energy, low area for design circuits, one potential computational fabric for Nano computing systems, and integration density. On the other hand, fault-tolerant circuits promise reliability circuits by computation redundancy cells. This work targets to form two designs of fault-tolerant 2:1 multiplexer in the QCA framework. This proposed QCA multiplexer designs use cell redundancy on the wire, NOT gates, and majority gates. The coplanar structures for the proposed 2:1 QCA fault-tolerant multiplexers are provided and operated based on cell interactions. Four types of faults, cell misalignment, cell missing, cell displacement, and extra cell, are essential in analyzing the fault attributes. The proposed fault-tolerant multiplexers can attain 100% fault-tolerance while extra cell deficiencies or single missing exist in the layout of the QCA. The simulation outcomes reached by the software, QCA Designer 2.0.3, approve that the suggested multiplexers work correctly and can be utilized in QCA technology as a high-performance schematization. The outcomes show that the proposed construct outperforms any prior schematization.

     

Improving the stuck-at fault coverage of functional test sequences by using limited-scan operations

Functional test sequences were shown to detect unique defects in VLSI circuits. This is thought to be due to the fact that they are applied at-speed. However, functional test sequences do not achieve complete stuck-at fault coverage. Therefore, scan-based stuck-at tests, as well as other types of tests, are typically also applied. This increases the amount of test resources required for test application. We describe a procedure for inserting (limited) scan operations into a functional sequence in order to improve its stuck-at fault coverage, thus reducing or eliminating the need for separate scan-based stuck-at tests. Between scan operations, the functional test sequence can still be applied at-speed; however, a higher stuck-at fault coverage is achieved.     

Test Challenges in Nanometer Technologies

Device scaling has led to the blurring of the boundary between design and test: marginalities introduced by design tool approximations can cause failures when aggressive designs are subjected to process variation. Larger die sizes are more vulnerable to intra-die variations, invalidating analyses based on a number of given process corners. These trends are eroding the predictability of test quality based on stuck-at fault coverage. Industry studies have shown that an at-speed functional test with poor stuck-at fault coverage can be a better DPM screen than a set of scan tests with very high stuck-at fault coverage. Contrary to conventional wisdom, we have observed that a high stuck-at fault test set is not necessarily good at detecting faults that model actual failure mechanisms. One approach to address the test quality crisis is to rethink the fault model that is at the core of these tests. Targeting realistic fault models is a challenge that spans the design, test and manufacturing domains: the extraction of realistic faults has to analyze the design at the physical and circuit levels of abstraction while taking into account the failure modes observed during manufacture. Practical fault models need to be defined that adequately model failing behavior while remaining amenable to automatic test generation. The addition of these fault models place increasing performance and capacity demands on already stressed test generation and fault simulation tools. A new generation of analysis and test generation tools is needed to address the challenge of defect-based test. We provide a detailed discussion of process technology trends that are responsible for next generation test problems, and present a test automation infrastructure being developed at Intel to meet the challenge.     

Bilateral Testing of Nano-scale Fault-Tolerant Circuits

As the technology enters the nano dimension, the inherent unreliability of nanoelectronics is making fault-tolerant architectures increasingly necessary in building nano systems. Because fault-tolerant hardwares help to mask the effects caused by increased levels of defects, testing the functionality of the chip together with the embedded fault-tolerance becomes a tremendous challenge. In this paper, a new bilateral testing framework for nano circuits is proposed, where multiple stuck-at faults across different modules in a triple module redundancy (TMR) architecture are considered. In addition, a new test generator is presented for the bilateral testing that takes into account the enormous number of bilateral stuck-at faults possible with new types of guidance in the search, and it can generate a set of vectors that can test the TMR-based nano circuit as a single entity. Experimental results reported for ISCAS’85 and ITC99 circuits demonstrate that the bilateral testing can help to capture many more defects which the single stuck-at fault misses.     

IEEE Standard 1500 Compatible Oscillation Ring Test Methodology for Interconnect Delay and Crosstalk Detection

A novel oscillation ring (OR) test scheme and architecture for testing interconnects in SOC is proposed and demonstrated. In addition to stuck-at and open faults, this scheme can also detect delay faults and crosstalk glitches, which are otherwise very difficult to be tested under the traditional test schemes. IEEE Std. 1500 wrapper cells are modified to accommodate the test scheme. An efficient algorithm is proposed to construct ORs for SOC based on a graph model. Experimental results on MCNC benchmark circuits have been included to show the effectiveness of the algorithm. In all experiments, the scheme achieves 100% fault coverage with a small number of tests.     

BiCMOS logic testing

With the anticipated growth of BiCMOS technology for high-performance ASIC design, the issue of testing takes on great significance. This paper addresses the testing of BiCMOS logic circuits. Since many different implementations of BiCMOS gates have been proposed, four representative ones are studied. The adequacy of stuck-at, quiescent current, and delay testing are examined based on circuit level faults. It is demonstrated that a large portion of the defects cannot be detected by common stuck-at or quiescent current tests since they manifest themselves as delay faults. By using the results presented, the test methodologies and the logic families can be ranked based on fault coverage. This ranking can then be used to help decide which BiCMOS solution is proper for a given application