Abstract:
A method for generating stimuli and test responses for testing faults in a scan-based integrated circuit in a selected scan-test mode or a selected self-test mode, the scan-based integrated circuit containing a plurality of scan chains, N clock domains, and C cross-clock domain blocks, each scan chain comprising multiple scan cells coupled in series, each clock domain having one capture clock, each cross-clock domain block comprising a combinational logic network. The method comprises compiling the scan-based integrated circuit into a sequential circuit model; specifying input constraints on the scan-based integrated circuit during a shift and capture operation; specifying a clock grouping to map the N clock domains into G clock domain groups, where N&gt;G&gt;1; transforming the sequential circuit model into an equivalent combinational circuit model according to the input constraints and the clock grouping; and generating the stimuli and test responses on the equivalent combinational circuit model according to the input constraints.

Description:
RELATED APPLICATION DATA  
       [0001]     This application claims the benefit of U.S. Provisional Application No. 60/442,901 filed May 23, 2003, titled “Smart ATPG (Automatic Test Pattern Generation) for Scan-Based Integrated Circuits”, which is hereby incorporated by reference. 
     
    
     FIELD OF THE INVENTION  
       [0002]     The present invention generally relates to the field of scan-based design and test using design-for-test (DFT) techniques. Specifically, the present invention relates to the field of Scan/ATPG (automatic test pattern generation), Logic BIST (built-in self-test), and Compressed Scan/ATPG.  
       BACKGROUND OF THE INVENTION  
       [0003]     In this specification, the term “integrated circuit” is used to describe a chip or MCM (multi-chip module) embedded with DFT (design-for-test) techniques.  
         [0004]     An integrated circuit or circuit assembly generally contains multiple clocks, which are either generated internally or supplied externally. Each clock is distributed to a set of storage elements via a skew-minimized network, which supplies clock pulses to all storage elements essentially at the same time. Such a clock, its related storage elements, and all combinational logic blocks bounded by these storage elements, form a clock domain. While the clock skew within a single clock domain is designed to be negligible, the clock skew between different clock domains is unbounded and can vary greatly for different storage elements.  
         [0005]     Scan-based design is the most widely used design-for-test (DFT) approach for producing high-quality integrated circuits. Scan-based design requires that all storage elements in an integrated circuit, such as D flip-flops, be replaced with their scan-equivalent storage elements, such as Scan D flip-flops, otherwise known as scan cells. These scan cells are connected to form one or more scan chains, with each scan chain being controlled by one or more scan enable (SE) signals and capture clocks (CK) each belonging to a separate clock or frequency domain.  
         [0006]     Testing a scan-based integrated circuit proceeds in a sequence of shift-in/shift-out operation and capture operation, repeated for a predetermined number of test patterns. During the shift operation, scan enable (SE) signals, local to all scan cells in a clock domain, are used to configure all scan cells in an integrated circuit into scan chains by selecting the scan data inputs as the input source of all scan cells in the scan chains, and a predetermined stimuli during scan-test or a pseudorandom stimuli during self-test is shifted serially through the scan chains into all scan cells in the circuit. During the capture operation, the scan enable (SE) signal is used to select the data inputs as the input source of all scan cells to test the functional path of the circuit using the stimulus loaded during the shift operation.  
         [0007]     Automatic test pattern generation (ATPG) and fault simulation are used to generate the scan test patterns, and to measure their fault coverage respectively. In order to simplify the ATPG and fault simulation process, an event-based logic simulator, as opposed to a timing logic simulator, is embedded within the ATPG and fault simulation engine, used to perform the logic simulation of the capture operation of the scan based test. This makes it impossible to apply the capture clocks of different clock domains simultaneously during the capture operation and simulate the results, since the clock skew between different clock domains would result in incorrect values being captured into some scan cells in the event-based simulation. Different approaches for applying the capture clocks during the capture operation have been developed in order to get around this problem.  
         [0008]     Prior-art solution #1, see  FIG. 2 , is commonly referred to as the one-hot method. In this method all capture clocks are used during the shift operation to set up the stimulus, but only one capture clock is applied during each capture operation. Multiple patterns are used to test the logic paths connected to scan cells belonging to different clock domains. The main advantage of this method is the simplicity in implementing the ATPG and fault simulation engine. The main disadvantage of this method is that a large number of test patterns are required to test the circuit, since only one clock domain can be tested in any given pattern. This further results in longer test time and larger test data volume, which increases the total test cost.  
         [0009]     Prior-art solution #2, see  FIG. 3 , is described in U.S. Pat. No. 6,195,776 by Ruiz et al. (2001). In this approach, a clock order is used to apply selected capture clocks sequentially during the capture operation. However, during ATPG and fault simulation, these capture clocks are simulated in parallel while selectively setting unknown values (‘X’) on different logic paths, depending on the clock order. This guarantees that the results of the parallel cycle-based simulation will match the results of the sequential application of the clocks during the actual capture operation of the test pattern. The main advantage of this approach is that it achieves the same fault coverage as prior-art #1 using a smaller set of test vectors and reduced CPU time. The main disadvantage of this approach is that the test size is still large, since the ATPG and fault simulator are pessimistic in calculating the fault coverage of different scan test patterns due to the unknown values.  
         [0010]     Prior-art solution #3, see  FIG. 4 , is described by Lin et al. In this approach, a clock order is used to apply selected capture clocks sequentially during the capture operation. Multi-timeframe ATPG and fault simulation is used during the capture operation to calculate the exact fault coverage of the test patterns applied. The main advantage of this approach is that the test size is smaller than the previous two approaches, and can approach the optimal set of test vectors, provided that all clocks are applied during the capture operation of the ATPG and fault simulation. In practice, this is difficult to perform, since it results in a dramatic increase in CPU time requirements. In practice, the number of clocks that can be applied is limited, resulting in a sub-optimal set of test patterns using longer CPU time.  
         [0011]     Prior-art solution #4, see  FIG. 5 , is described in U.S. patent application No. 20020184560 by Wang et al. In this approach, a clock order is used to apply selected capture clocks sequentially during the capture operation. A circuit expansion process is used to transform the circuit into an equivalent combinational circuit model, where logic paths are expanded to simulate the results of a multi-timeframe simulation with a single time-frame simulation of the expanded circuit. The main advantage of this approach is that its test size is small, and approaches the optimum set of test vectors for any given circuit. Furthermore, this is accomplished with a realistic increase in memory size, as opposed to an unrealistic increase in CPU time as in prior-art #3. The main disadvantage of this approach is that the increase in memory size might prevent the circuit from being able to fit within a given system memory, and might become un-reasonable as design size continues to grow.  
         [0012]     Therefore, there is a need for an improved ATPG and fault simulation, comprising a method and a computer-aided design (CAD) system, that is capable of achieving high fault coverage using an optimum set of test vectors within reasonable memory size and CPU time.  
       SUMMARY OF THE INVENTION  
       [0013]     Accordingly, the present invention is intended to achieve three objectives: (1) providing an improved ATPG (automatic test pattern generation) and fault simulation method capable of using a cycle-based logic simulator to simulate multiple-clock events and generate an optimal set of test patterns with low memory usage and short CPU time, (2) providing a method for conducting clock grouping and clock ordering automatically and efficiently, and (3) providing a method to improve the efficiency of the method of prior-art #2 summarized in BACKGROUND and detailed in U.S. Pat. No. 6,195,776 by Ruiz et al. (2001). The present invention further comprises a CAD (computer-aided design) system that implements the methods. The present invention is summarized as follow:  
         [0000]     (a) Circuit Expansion Based Improvement on ATPG and Fault Simulation  
         [0014]     The present invention comprises any method that uses a hybrid ATPG and fault simulation approach capable of selectively using the circuit expansion or multi-timeframe simulation method in conjunction with any number of other prior-art methods. This hybrid method allows the testing of all cross-clock domain blocks in a circuit while meeting input constraints regarding required memory usage, required CPU time and required test-pattern count. This is done by selectively grouping the clock domains into clock domain groups, and performing circuit expansion or a multi-timeframe simulation on selected clock domain groups and cross-clock domain blocks, while selecting other prior-art methods to test the remaining clock domain groups and cross-clock domain blocks to meet the required criteria.  
         [0000]     (b) Clock Domain Grouping  
         [0015]     The purpose of clock grouping in the present invention is to conduct circuit expansion on the combinational logic blocks related to the grouped clocks. The present invention comprises any method that identifies those clocks which, when grouped together and for which circuit expansion is conducted, will best improve the performance of ATPG and fault simulation.  
         [0000]     (c) Clock Domain Merging  
         [0016]     The present invention comprises any method that merges a set of clock domains together. For example, suppose that one clock domain CD 1  interacts to another clock domain CD 2  through a cross-clock domain logic block CCD 12 . Also suppose that CD 1  is captured before CD 2 . Merging CD 1  and CD 2  together means that two-time frames will be used for circuit transformation related to the two clock domains and their corresponding cross-clock domain logic blocks. The benefits are as follows: Even the clock domain CD 2  is captured after the clock domain CD 1  is captured, the controllability of the cross-clock domain logic block CCD 12  is still high since the clock domain CD 1  is also transformed to obtain the values in the clock domain CD 1  after it is captured. As a result, all faults in the cross-clock domain logic block CCD 12  can be detected or located. The benefit of clock domain grouping is that it can reduce the number of necessary ordered sequences of capture clocks.  
         [0000]     (d) Domain-Interconnect Graph Based Capture Order Selection  
         [0017]     In order to conduct circuit expansion on a clock group, it is necessary to select a capture order for all the grouped clocks. It is based on such an order that a sequential circuit can be transformed into its equivalent combinational circuit model. The present invention comprises any method that automatically selects an optimal or near-optimal set of capture orders for each clock group based on a domain-interconnect graph. A domain-interconnect graph is a directed graph, which is used to represent the relationship among all clock domains. A node represents a clock domain while a directed edge between any two nodes represents the corresponding cross-clock domain logic block. Such a domain-interconnect graph can be built based on the result of analyzing clock domains. Based on such a domain-interconnect graph, an optimal or near-optimal set of capture orders can be selected automatically.  
         [0000]     (e) Improvement on Unknown-Value Based Multiple Timeframe Handling  
         [0018]     As a summarized in BACKGROUND and detailed in U.S. Pat. No. 6,195,776 by Ruiz et al. (2001), prior-art #2 simulates all capture clocks in parallel by selectively setting unknown (X) values on different logic paths, depending on the clock order. The present invention comprises any method that generalizes this unknown-value based method into a constrained-value method. This is achieved by allowing the constraining of a cross-clock domain logic block with logic values, 1 and 0, as well as unknown-values, X&#39;s, to force an ATPG program to generate patterns where the cross-clock domain logic block does not change its state during a capture operation. As a result, a fault simulator can perform an accurate fault simulation of patterns where the cross-clock domain logic remains in a constant state during a capture operation. This further improves the accuracy of the fault simulation and ATPG of the unknown-value method. Therefore, a smaller test pattern set and greater measured fault coverage can be achieved.  
         [0019]     To summarize, the present invention uses a hybrid approach for ATPG and fault simulation based on circuit expansion, which is supported by automatic clock grouping and capture order selection. In addition, the present invention uses a new technique to improve the efficiency of an existing multiple timeframe handling solution for ATPG and fault simulation. In conclusion, the present invention provides an efficient solution to ATPG and fault simulation for testing complicated and large-scale scan-based integrated circuits or circuit assemblies by achieving high fault coverage for stuck-at faults, bridging faults, IDDQ faults, transition faults launched from capture, transition faults launched from shift, path-delay faults launched from capture, and path-delay faults launched from shift, with lower memory usage and a smaller number of test patterns.  
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0020]     The above and other objects, advantages and features of the invention will become more apparent when considered with the following specification and accompanying drawings wherein:  
         [0021]      FIG. 1  shows a block diagram of a scan-based integrated circuit with three clock domains, inter-related with each other through six cross-clock domain blocks;  
         [0022]      FIG. 2A  shows the domain-interconnect graph used to represent the relationship among the clock domains shown in  FIG. 1 , with regard to prior-art solution #1;  
         [0023]      FIG. 2B  shows the scan clock waveforms in ATPG (automatic test pattern generation) and fault simulation in order to detect or locate stuck-at faults, bridging faults, or IDDQ faults, with regard to prior-art solution #1;  
         [0024]      FIG. 2C  shows the scan clock waveforms in actual test application in order to detect or locate stuck-at faults, bridging faults, or IDDQ faults, with regard to prior-art solution #1;  
         [0025]      FIG. 3A  shows the domain-interconnect graph used to represent the relationship among the clock domains shown in  FIG. 1 , with regard to prior-art solution #2;  
         [0026]      FIG. 3B  shows the scan clock waveforms in ATPG (automatic test pattern generation) and fault simulation in order to detect or locate stuck-at faults, bridging faults, or IDDQ faults, with regard to prior-art solution #2;  
         [0027]      FIG. 3C  shows the scan clock waveforms in actual test application in order to detect or locate stuck-at faults, bridging faults, or IDDQ faults, with regard to prior-art solution #2;  
         [0028]      FIG. 4A  shows the domain-interconnect graph used to represent the relationship among the clock domains shown in  FIG. 1 , with regard to prior-art solution #3;  
         [0029]      FIG. 4B  shows the scan clock waveforms in ATPG (automatic test pattern generation) and fault simulation in order to detect or locate stuck-at faults, bridging faults, or IDDQ faults, with regard to prior-art solution #3;  
         [0030]      FIG. 4C  shows the scan clock waveforms in actual test application in order to detect or locate stuck-at faults, bridging faults, or IDDQ faults, with regard to prior-art solution #3;  
         [0031]      FIG. 5A  shows the domain-interconnect graph used to represent the relationship among the clock domains shown in  FIG. 1 , with regard to prior-art solution #4;  
         [0032]      FIG. 5B  shows the scan clock waveforms in ATPG (automatic test pattern generation) and fault simulation in order to detect or locate stuck-at faults, bridging faults, or IDDQ faults, with regard to prior-art solution #4;  
         [0033]      FIG. 5C  shows the scan clock waveforms in actual test application in order to detect or locate stuck-at faults, bridging faults, or IDDQ faults, with regard to prior-art solution #4;  
         [0034]      FIG. 6A  shows a flow diagram of the method for ATPG (automatic test pattern generation) and fault simulation with clock grouping and circuit expansion in scan-test mode, in accordance with the present invention;  
         [0035]      FIG. 6B  shows a flow diagram of the method for fault simulation with clock grouping and circuit expansion in self-test mode, in accordance with the present invention;  
         [0036]      FIG. 7A  shows the domain-interconnect graph used to represent the relationship among the clock domains shown in  FIG. 1 , with clock grouping in a first embodiment of the present invention;  
         [0037]      FIG. 7B  shows the scan clock waveforms in ATPG (automatic test pattern generation) and fault simulation in order to detect or locate stuck-at faults, bridging faults, or IDDQ faults, with regard to clock grouping in a first embodiment of the present invention;  
         [0038]      FIG. 7C  shows the scan clock waveforms in actual test application in order to detect or locate stuck-at faults, bridging faults, or IDDQ faults, with regard to clock grouping in a first embodiment of the present invention;  
         [0039]      FIG. 8A  shows the domain-interconnect graph used to represent the relationship among the clock domains shown in  FIG. 1 , with clock grouping in a second embodiment of the present invention;  
         [0040]      FIG. 8B  shows the scan clock waveforms in ATPG (automatic test pattern generation) and fault simulation in order to detect or locate stuck-at faults, bridging faults, or IDDQ faults, with regard to clock grouping in a second embodiment of the present invention;  
         [0041]      FIG. 8C  shows the scan clock waveforms in actual test application in order to detect or locate stuck-at faults, bridging faults, or IDDQ faults, with regard to clock grouping in a second embodiment of the present invention;  
         [0042]      FIG. 9A  shows the domain-interconnect graph used to represent the relationship among the clock domains shown in  FIG. 1 , with clock grouping in a third embodiment of the present invention;  
         [0043]      FIG. 9B  shows the scan clock waveforms in ATPG (automatic test pattern generation) and fault simulation in order to detect or locate stuck-at faults, bridging faults, or IDDQ faults, with regard to clock grouping in a third embodiment of the present invention;  
         [0044]      FIG. 9C  shows the scan clock waveforms in actual test application in order to detect or locate stuck-at faults, bridging faults, or IDDQ faults, with regard to clock grouping in a third embodiment of the present invention;  
         [0045]      FIG. 10A  shows the domain-interconnect graph used to represent the relationship among the clock domains shown in  FIG. 1 , with clock grouping in a fourth embodiment of the present invention;  
         [0046]      FIG. 10B  shows the scan clock waveforms in ATPG (automatic test pattern generation) and fault simulation in order to detect or locate transition faults or path-delay faults launched from capture, with regard to clock grouping in a fourth embodiment of the present invention;  
         [0047]      FIG. 10C  shows the scan clock waveforms in actual test application in order to detect or locate transition faults or path-delay faults launched from capture, with regard to clock grouping in a fourth embodiment of the present invention;  
         [0048]      FIG. 11A  shows the domain-interconnect graph used to represent the relationship among the clock domains shown in  FIG. 1 , with clock grouping in a fifth embodiment of the present invention;  
         [0049]      FIG. 11B  shows the scan clock waveforms in ATPG (automatic test pattern generation) and fault simulation in order to detect or locate transition faults or path-delay faults launched from capture, with regard to clock grouping in a fifth embodiment of the present invention;  
         [0050]      FIG. 11C  shows the scan clock waveforms in actual test application in order to detect or locate transition faults or path-delay faults launched from capture, with regard to clock grouping in a fifth embodiment of the present invention;  
         [0051]      FIG. 12A  shows the domain-interconnect graph used to represent the relationship among the clock domains shown in  FIG. 1 , with clock grouping in a sixth embodiment of the present invention;  
         [0052]      FIG. 12B  shows the scan clock waveforms in ATPG (automatic test pattern generation) and fault simulation in order to detect or locate transition faults or path-delay faults launched from capture, with regard to clock grouping in a sixth embodiment of the present invention;  
         [0053]      FIG. 12C  shows the scan clock waveforms in actual test application in order to detect or locate transition faults or path-delay faults launched from capture, with regard to clock grouping in a sixth embodiment of the present invention;  
         [0054]      FIG. 13A  shows the domain-interconnect graph used to represent the relationship among the clock domains shown in  FIG. 1 , with clock grouping in a seventh embodiment of the present invention;  
         [0055]      FIG. 13B  shows the scan clock waveforms in ATPG (automatic test pattern generation) and fault simulation in order to detect or locate transition faults or path-delay faults launched from shift, with regard to clock grouping in a seventh embodiment of the present invention;  
         [0056]      FIG. 13C  shows the scan clock waveforms in actual test application in order to detect or locate transition faults or path-delay faults launched from shift, with regard to clock grouping in a seventh embodiment of the present invention;  
         [0057]      FIG. 14A  shows the domain-interconnect graph used to represent the relationship among the clock domains shown in  FIG. 1 , with clock grouping in an eighth embodiment of the present invention;  
         [0058]      FIG. 14B  shows the scan clock waveforms in ATPG (automatic test pattern generation) and fault simulation in order to detect or locate transition faults or path-delay faults launched from shift, with regard to clock grouping in an eighth embodiment of the present invention;  
         [0059]      FIG. 14C  shows the scan clock waveforms in actual test application in order to detect or locate transition faults or path-delay faults launched from shift, with regard to clock grouping in an eighth embodiment of the present invention;  
         [0060]      FIG. 15A  shows the domain-interconnect graph used to represent the relationship among the clock domains shown in  FIG. 1 , with clock grouping in a ninth embodiment of the present invention;  
         [0061]      FIG. 15B  shows the scan clock waveforms in ATPG (automatic test pattern generation) and fault simulation in order to detect or locate transition faults or path-delay faults launched from shift, with regard to clock grouping in a ninth embodiment of the present invention;  
         [0062]      FIG. 15C  shows the scan clock waveforms in actual test application in order to detect or locate transition faults or path-delay faults launched from shift, with regard to clock grouping in a ninth embodiment of the present invention;  
         [0063]      FIG. 16A  shows the domain-interconnect graph used to represent the relationship among the clock domains shown in  FIG. 1 , with clock grouping in a tenth embodiment of the present invention;  
         [0064]      FIG. 16B  shows the scan clock waveforms in ATPG (automatic test pattern generation) and fault simulation in order to detect or locate stuck-at faults, bridging faults, or IDDQ faults, with regard to clock grouping in a tenth embodiment of the present invention;  
         [0065]      FIG. 16C  shows the scan clock waveforms in actual test application in order to detect or locate stuck-at faults, bridging faults, or IDDQ faults, with regard to clock grouping in a tenth embodiment of the present invention;  
         [0066]      FIG. 17A  shows the domain-interconnect graph used to represent the relationship among the clock domains shown in  FIG. 1 , with clock grouping in an eleventh embodiment of the present invention;  
         [0067]      FIG. 17B  shows the scan clock waveforms in ATPG (automatic test pattern generation) and fault simulation in order to detect or locate stuck-at faults, bridging faults, or IDDQ faults, with regard to clock grouping in an eleventh embodiment of the present invention;  
         [0068]      FIG. 17C  shows the scan clock waveforms in actual test application in order to detect or locate stuck-at faults, bridging faults, or IDDQ faults, with regard to clock grouping in an eleventh embodiment of the present invention;  
         [0069]      FIG. 18A  shows the domain-interconnect graph used to represent the relationship among the clock domains shown in  FIG. 1 , with clock grouping in a twelfth embodiment of the present invention;  
         [0070]      FIG. 18B  shows the scan clock waveforms in ATPG (automatic test pattern generation) and fault simulation in order to detect or locate transition faults or path-delay faults launched from capture, with regard to clock grouping in a twelfth embodiment of the present invention;  
         [0071]      FIG. 18C  shows the scan clock waveforms in actual test application in order to detect or locate transition faults or path-delay faults launched from capture, with regard to clock grouping in a twelfth embodiment of the present invention;  
         [0072]      FIG. 19A  shows the domain-interconnect graph used to represent the relationship among the clock domains shown in  FIG. 1 , with clock grouping in a thirteenth embodiment of the present invention;  
         [0073]      FIG. 19B  shows the scan clock waveforms in ATPG (automatic test pattern generation) and fault simulation in order to detect or locate transition faults or path-delay faults launched from capture, with regard to clock grouping in a thirteenth embodiment of the present invention;  
         [0074]      FIG. 19C  shows the scan clock waveforms in actual test application in order to detect or locate transition faults or path-delay faults launched from capture, with regard to clock grouping in a thirteenth embodiment of the present invention;  
         [0075]      FIG. 20A  shows the domain-interconnect graph used to represent the relationship among the clock domains shown in  FIG. 1 , with clock grouping in a fourteenth embodiment of the present invention;  
         [0076]      FIG. 20B  shows the scan clock waveforms in ATPG (automatic test pattern generation) and fault simulation in order to detect or locate transition faults or path-delay faults launched from shift, with regard to clock grouping in a fourteenth embodiment of the present invention;  
         [0077]      FIG. 20C  shows the scan clock waveforms in actual test application in order to detect or locate transition faults or path-delay faults launched from shift, with regard to clock grouping in a fourteenth embodiment of the present invention;  
         [0078]      FIG. 21A  shows the domain-interconnect graph used to represent the relationship among the clock domains shown in  FIG. 1 , with clock grouping in a fifteenth embodiment of the present invention;  
         [0079]      FIG. 21B  shows the scan clock waveforms in ATPG (automatic test pattern generation) and fault simulation in order to detect or locate transition faults or path-delay faults launched from shift, with regard to clock grouping in a fifteenth embodiment of the present invention;  
         [0080]      FIG. 21C  shows the scan clock waveforms in actual test application in order to detect or locate transition faults or path-delay faults launched from shift, with regard to clock grouping in a fifteenth embodiment of the present invention;  
         [0081]      FIG. 22A  shows a domain-interconnect graph for  8  inter-related clock domains;  
         [0082]      FIG. 22B  shows the fault detection or location range for one ordered sequence of capture clocks for the clock domains shown in  FIG. 22A , in accordance with the present invention, where clock domain grouping is conducted;  
         [0083]      FIG. 23A  shows a domain-interconnect graph for  5  inter-related clock domains;  
         [0084]      FIG. 23B  shows the fault detection or location range for one ordered sequence of capture clocks for the clock domains shown in  FIG. 23A , in accordance with the present invention;  
         [0085]      FIG. 23C  shows the fault detection or location range for one more ordered sequence of capture clocks for the clock domains shown in  FIG. 23A , in accordance with the present invention;  
         [0086]      FIG. 23D  shows the fault detection or location range for one ordered sequence of capture clocks for the clock domains shown in  FIG. 23A , in accordance with the present invention, where clock domain merging is conducted;  
         [0087]      FIG. 24A  shows a prior art solution for handling uncontrollability when using a single time-frame for the multiple-capture scheme;  
         [0088]      FIG. 24B  shows an embodiment of the method for handling uncontrollability when using a single time-frame for the multiple-capture scheme, in accordance with the present invention; and  
         [0089]      FIG. 25  shows an electronic design automation system, where a computer-readable program, in accordance with the present invention, performs clock grouping and circuit expansion based ATPG (automatic test pattern generation) and fault simulation for a scan-based integrated circuit.  
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0090]     The following description is presently contemplated as the best mode of carrying out the present invention. This description is not to be taken in a limiting sense but is made merely for the purpose of describing the principles of the invention. The scope of the invention should be determined by referring to the appended claims.  
         [0091]      FIG. 1  shows a block diagram of a scan-based integrated circuit  101  with three inter-related clock domains, CD 1   102  to CD 3   104 , and three scan clocks, CK 1   120  to CK 3   122 . Each clock controls one clock domain. In addition, CD 1   102  interacts to CD 2   103  through the cross-clock domain block CCD 12   105 , CD 2   103  interacts to CD 1   102  through the cross-clock domain block CCD 21   106 , CD 2   103  interacts to CD 3   104  through the cross-clock domain block CCD 23   107 , CD 3   104  interacts to CD 2   103  through the cross-clock domain block CCD 32   108 , CD 1   102  interacts to CD 3   104  through the cross-clock domain block CCD 13   109 , and CD 3   104  interacts to CD 1   102  through the cross-clock domain block CCD 3   1110 .  
         [0092]     The CUT (circuit-under-test)  101  is a scan-based integrated circuit, in which all of its storage cells are replaced with scan cells SC and all scan cells SC are connected into one or more scan chains SCN. Note that a scan cell is usually a clocked storage cell with two input ports, one called a data input port and the other called a scan input port, selectable with a scan enable (SE) signal. The data input port is connected to functional logic, which is used to capture test responses. The scan input port is connected to the output port of another scan cell or to an external scan input signal; this way, a scan chain, i.e. shift register, can be formed to bring in test stimuli or bring out captured test responses.  
         [0093]     The CUT  101  can be tested in either scan-test mode or self-test mode. The two modes differ in how test stimuli,  114  to  116 , are generated and provided, how test responses,  117  to  119 , are collected and analyzed, and how scan enable signals, SE 1   111  to SE 3   113 , and scan clocks, CK 1   120  to CK 3   122 , are controlled. In scan-test mode, test stimuli,  114  to  116 , are generated by an ATPG (automatic test pattern generation) program and applied by an ATE (automatic test equipment). The ATE also collects and analyzes test responses,  117  to  119 , and controls all scan enable signals SE 1   111  to SE 3   113 , and scan clocks, CK 1   120  to CK 3   122 . In self-test mode, test stimuli,  114  to  116 , are generated and provided by an on-chip PRPG (pseudo-random pattern generator). The test responses,  117  to  119 , are collected and analyzed by an on-chip MISR (multi-input signature register). Scan enable signals, SE 1   111  to SE 3   113 , and scan clocks, CK 1   120  to CK 3   122 , are also controlled by on-chip circuitry in self-test mode.  
         [0094]     In both scan-test and self-test mode, test is conducted by repeating two operations: namely shift and capture. During a shift operation, all scan cells SC are configured into one or more scan chains SCN, i.e. shift registers, by properly controlled scan enable signals, SE 1   111  to SE 3   113 . Test stimuli,  114  to  116 , are then shifted into these scan chains SCN. During a capture operation, all scan cells SC are configured by properly controlled scan enable signals, SE 1   111  to SE 3   113 , to catch data from their data input ports. During this capture operation, test responses,  117  to  119 , corresponding to the test stimuli,  114  to  116 , shifted into scan cells during the shift operation are captured into scan cells SC by activating scan clocks CK 1   120  to CK 3   122  in one way or another. During the next shift operation, captured test responses are shifted out of the CUT to either ATE in scan-test mode or to MISR in self-test mode. Note that, at the same time as this shift operation, new test stimuli are also shifted in.  
         [0095]     Obviously, both scan-test and self-test consist of an ATPG and fault simulation process. Test stimuli are either generated by an ATPG or by a PRPG and fault simulation is often needed to check if a fault is detected by a test stimulus or test pattern. In ATPG and fault simulation, it is necessary to assume what logic values are captured as test responses during a capture operation.  
         [0096]     If a CUT has only one scan clock, assumed test responses are generally the same as actual test responses. If a CUT has multiple scan clocks, assumed test responses may be different from actual test responses. The reason is that there are usually unpredictable clock skews between any two clock domains, although clock skews in each clock domain can be minimized through clock tree synthesis. Such cross-clock domain and unpredictable clock skews, if not handled properly in ATPG and fault simulation, will cause a difference in assumed test responses and actual test responses. As a result, ATPG results and fault coverage will become inaccurate. Therefore, it is critical to take the impact of such unpredictable clock skews into consideration in ATPG and fault simulation in order to guarantee correct ATPG and fault simulation results.  
         [0097]      FIG. 2A  shows the domain-interconnect graph used to represent the relationship among the clock domains shown in  FIG. 1 , with regard to prior-art solution #1. 3 nodes are used to represent the 3 clock domains, CD 1   102  to CD 3   104 . The corresponding scan clocks, CK 1   120  to CK 3   122 , are also shown in the nodes for easy comprehension. The directed edge between two nodes represents a cross-clock domain block. For example, the edge  201  represents the cross-clock domain block CCD 12   105  as shown in  FIG. 1 .  
         [0098]      FIG. 2B  shows the scan clock waveforms in ATPG (automatic test pattern generation) and fault simulation and  FIG. 2C  shows the scan clock waveforms in actual test application, both for detecting or locating stuck-at faults, bridging faults, or IDDQ faults (referred to as faults) and with regard to prior-art solution #1.  
         [0099]     In order to avoid the impact of unpredictable clock skews among different clock domains, this solution, also called the one-hot technique, requires that only one scan clock be activated during each capture operation as shown in  FIG. 2C . Generally, if scan clocks are activated in this manner, the circuit behavior during a capture operation can be fully represented by only one copy of the corresponding combinational logic portion in the circuit, for the purpose of ATPG and fault simulation. As a result, the impact of unpredictable clock skews can be easily avoided in ATPG and fault simulation.  
         [0100]     As shown in  FIG. 2B , whenever the scan clock CK 1   120  is activated, all faults in the clock domain CD 1   102  and cross-clock domain blocks, CCD 21   106  and CCD 31   110 , can be targeted in ATPG and fault simulation; whenever the scan clock CK 2   121  is activated, all faults in the clock domain CD 2   103  and cross-clock domain blocks, CCD 12   105  and CCD 32   108 , can be targeted in ATPG and fault simulation; and whenever the scan clock CK 3   122  is activated, all faults in the clock domain CD 3   104  and cross-clock domain blocks, CCD 13   109  and CCD 23   107 , can be targeted in ATPG and fault simulation. As a result, all faults in the CUT  101  can be targeted in ATPG and fault simulation.  
         [0101]     The fault coverage of this solution is usually high since all faults can be targeted in ATPG and fault simulation. In addition, a combinational ATPG program is enough when test patterns are to be generated deterministically. Furthermore, its memory usage is low since, in order to conduct ATPG and fault simulation for one capture operation with regard to one scan clock, it is only necessary to keep the circuit model data for the corresponding clock domain and the cross-clock domain blocks that interact to the clock domain. However, the number of test patterns generated by this solution is large and CPU time is long. The reasons are that each run of ATPG and fault simulation can only target faults in one clock domain and a few corresponding cross-clock domain blocks and that after a capture operation is conducted for a scan clock, a shift operation must be conducted in order to shift out the test responses and shift in new test stimuli.  
         [0102]      FIG. 3A  shows the domain-interconnect graph used to represent the relationship among the clock domains shown in  FIG. 1 , with regard to prior-art solution #2. The meanings of nodes and edges are the same as explained for  FIG. 2A .  
         [0103]      FIG. 3B  shows the scan clock waveforms in ATPG (automatic test pattern generation) and fault simulation and  FIG. 3C  shows the scan clock waveforms in actual test application, both for detecting or locating stuck-at faults, bridging faults, or IDDQ faults (referred to as faults) and with regard to prior-art solution #2.  
         [0104]     As shown in  FIG. 3C , this solution requires that scan clocks, CK 1   120  to CK 3   122 , be activated one by one in a selected order during each capture operation, and that the capture pulse delays between CK 1   120  and CK 2   121  and between CK 2   121  and CK 3   122  are larger than the possible corresponding clock skews. This will guarantee that the test responses captured during a capture operation are not affected by unpredictable clock skews.  
         [0105]     Generally, if scan clocks are activated in this manner, the circuit behavior during a capture operation can only be fully represented by several copies of the corresponding combinational logic portion in the circuit, each with a different set of constraints on its inputs and outputs and each corresponding to a different timeframe, for the purpose of ATPG and fault simulation. This solution, however, only selects one copy of the combinational logic portion corresponding to the so-called PCE (primary capture event) and uses it for ATPG and fault simulation. Obviously, some constraints on the inputs and outputs of the selected copy have to be set to unknown (X) values since other related copies are discarded.  
         [0106]     This solution only needs a combinational ATPG program when test patterns are to be generated deterministically. Its memory usage is also low since, in order to handle each capture operation, it is only necessary to keep one copy of the circuit model data. However, the fault coverage of this solution may be low since unknown values assigned as constraints may result in more undetected faults. Some techniques can be used to contain the impact of unknown values in fault coverage, but may result in a larger number of test patterns or longer CPU time.  
         [0107]      FIG. 4A  shows the domain-interconnect graph used to represent the relationship among the clock domains shown in  FIG. 1 , with regard to prior-art solution #3. The meanings of nodes and edges are the same as explained for  FIG. 2A .  
         [0108]      FIG. 4B  shows the scan clock waveforms in ATPG (automatic test pattern generation) and fault simulation and  FIG. 4C  shows the scan clock waveforms in actual test application, both for detecting or locating stuck-at faults, bridging faults, or IDDQ faults (referred to as faults) and with regard to prior-art solution #3.  
         [0109]     As shown in  FIG. 4C , this solution requires that scan clocks, CK 1   120  to CK 3   122 , be activated one by one in a selected order during each capture operation, and that the capture pulse delays between CK 1   120  and CK 2   121  and between CK 2   121  and CK 3   122  are larger than the possible corresponding clock skews. This will guarantee that the test responses captured during a capture operation are not affected by unpredictable clock skews.  
         [0110]     Generally, if scan clocks are activated in this manner, the circuit behavior during a capture operation can only be fully represented by several copies of the corresponding combinational logic portion in the circuit, each with a different set of constraints on its inputs and outputs and each corresponding to a different timeframe, for the purpose of ATPG and fault simulation. This solution processes the multiple circuit model copies for different timeframes in a serial manner one by one.  
         [0111]     When the scan clock CK 1   120  is activated, all faults in the clock domain CD 1   102  and the cross-clock domain blocks CCD 21   106  and CCD 31   110  can be targeted in ATPG and fault simulation, corresponding to test stimuli shifted-in through scan chains in three clock domains, CD 1   102  to CD 3   104 . When the scan clock CK 2   121  is activated, all faults in the clock domain CD 2   103  and the cross-clock domain blocks CCD 12   105  and CCD 32   108  can be targeted in ATPG and fault simulation, corresponding to test stimuli shifted-in through scan chains in two clock domains, CD 2   103  and CD 3   104 , as well as test responses captured by CK 1   120 . When the scan clock CK 3   122  is activated, all faults in the clock domain CD 3   104  and the cross-clock domain blocks CCD 13   109  and CCD 23   107  can be targeted in ATPG and fault simulation, corresponding to test stimuli shifted-in through scan chains in one clock domain, CD 3   104 , as well as test responses captured by CK 1   120  and CK 2   121 .  
         [0112]     This solution can target all faults in a whole circuit without the need of assigning any unknown values. As a result, it is possible to achieve high fault coverage. The number of test pattern is also smaller than that of prior-art solution #1 and prior-art solution #2 since a fault in any clock domain or any cross-clock domain block can be targeted in ATPG and fault simulation corresponding to any capture operation. However, a sequential ATPG program needs to be used with the capability of handling multiple timeframes. This will significantly increase CPU time and memory usage so that in practice, the number of timeframes may have to be limited to a rather smaller number than the number of scan clocks. Obviously, this limitation will compromise the usefulness of this solution.  
         [0113]      FIG. 5A  shows the domain-interconnect graph used to represent the relationship among the clock domains shown in  FIG. 1 , with regard to prior-art solution #4. The meanings of nodes and edges are the same as explained for  FIG. 2A .  
         [0114]      FIG. 5B  shows the scan clock waveforms in ATPG (automatic test pattern generation) and fault simulation and  FIG. 5C  shows the scan clock waveforms in actual test application, both for detecting or locating stuck-at faults, bridging faults, or IDDQ faults (referred to as faults) and with regard to prior-art solution #4.  
         [0115]     As shown in  FIG. 5C , this solution requires that scan clocks, CK 1   120  to CK 3   122 , be activated one by one in a selected order during each capture operation, and that the capture pulse delays between CK 1   120  and CK 2   121  and between CK 2   121  and CK 3   122  are larger than the possible corresponding clock skews. This will guarantee that the test responses captured during a capture operation are not affected by unpredictable clock skews.  
         [0116]     Generally, if scan clocks are activated in this manner, the circuit behavior during a capture operation can only be fully represented by several copies of the corresponding combinational logic portion in the circuit, each with a different set of constraints on its inputs and outputs and each corresponding to a different timeframe, for the purpose of ATPG and fault simulation. This solution processes the multiple circuit model copies for different timeframes all at the same time by conducting circuit expansion to generate a complete set of data containing all the circuit model copies. That is, circuit expansion is a circuit modeling technique that uses multiple copies of a block to represent the different state of the block at different times. Note that circuit expansion needs to be conducted under a given order of capture clock pulses. In the example shown in  FIG. 5B  and  FIG. 5C , the capture order is CK 1   120 →CK 2   121 →CK 3   122 . Different capture orders will result in different results of circuit expansion. Obviously, after circuit expansion, it is not necessary to handle scan clocks explicitly and ATPG and fault simulation can be complete conducted on a combinational circuit model.  
         [0117]     This solution can use a combinational ATPG program when test patterns are to be generated deterministically. Fault coverage is high since all faults in a whole circuit can be targeted in ATPG and fault simulation. The CPU time is also less than that of prior-art solution #3 since the latter needs to use a sequential ATPG program. The number of test pattern is smaller than that of prior-art solution #1 and prior-art solution #2 since a fault in any clock domain or any cross-clock domain block can be targeted in ATPG and fault simulation corresponding to any capture operation. However, the memory usage may be high in some cases since multiple copies of the same block may be needed at the same time.  
         [0118]      FIG. 6A  shows a flow diagram of the method for ATPG (automatic test pattern generation) and fault simulation with clock grouping and circuit expansion in scan-test mode, in accordance with the present invention. The method accepts the user-supplied RTL (register-transfer level) or gate-level HDL (hardware design language) code  601  representing a scan-based integrated circuit design. In addition, input constraints  602  and an optional foundry library  603  are also provided. The input constraints  602  contain input constraint information on all clocks and scan enable (SE) signals. This method consists of compilation  604 , model transformation  607 , predetermined pattern fault simulation  609 , ATPG  610 , and post-processing  611 . The compilation step  604  compiles the HDL code  601  into a sequential circuit model  605 . The model transformation step  607  converts the sequential circuit model  605  into an equivalent combinational circuit model  608 . Circuit expansion based on the clock grouping information  606  is also conducted at this step. The predetermined pattern fault simulation step  609  identifies the faults that are detected by a set of predetermined patterns. The ATPG step  610  generates test patterns for detecting faults. Finally, the post-processing step  611  generates HDL test benches and ATE (automatic test equipment) test programs  612 . All reports and errors are stored in the report files  613 .  
         [0119]      FIG. 6B  shows a flow diagram of the method for fault simulation with clock grouping and circuit expansion in self-test mode, in accordance with the present invention. The method accepts the user-supplied RTL (register-transfer level) or gate-level HDL (hardware design language) code  651  representing a scan-based integrated circuit design. In addition, input constraints  652  and an optional foundry library  653  are also provided. The input constraints  652  contain input constraint information on all clocks and scan enable (SE) signals. This method consists of compilation  654 , model transformation  657 , pseudo-random pattern fault simulation  659 , and post-processing  660 . The compilation step  654  compiles the HDL code  651  into a sequential circuit model  655 . The model transformation step  657  converts the sequential circuit model  655  into an equivalent combinational circuit model  658 . Circuit expansion based on the clock grouping information  656  is also conducted at this step. The pseudo-random pattern fault simulation step  659  identifies the faults that are detected by a set of pseudo-random patterns. Finally, the post-processing step  660  generates HDL test benches and ATE (automatic test equipment) test programs  661 . All reports and errors are stored in the report files  662 .  
         [0120]      FIG. 7A  shows the domain-interconnect graph used to represent the relationship among the clock domains shown in  FIG. 1 , with clock grouping in a first embodiment of the present invention.  3  nodes are used to represent the  3  clock domains, CD 1   102  to CD 3   104 . The corresponding scan clocks, CK 1   120  to CK 3   122 , are also shown in the nodes for easy comprehension. The directed edge between two nodes represents a cross-clock domain block. For example, the edge  701  represents the cross-clock domain block CCD 12   105  as shown in  FIG. 1 . In addition, there are two clock groups. One consists of two scan clocks, CK 1   120  and CK 2   121 , as well as the corresponding clock domains, CD 1   102  and CD 2   103 . The other consists of one scan clock CK 3   122  and its corresponding clock domain, CD 3   104 .  
         [0121]      FIG. 7B  shows the scan clock waveforms in ATPG (automatic test pattern generation) and fault simulation and  FIG. 7C  shows the scan clock waveforms in actual test application, both for detecting or locating stuck-at faults, bridging faults, or IDDQ faults, (referred to as faults) with regard to clock grouping in a first embodiment of the present invention.  
         [0122]     This embodiment requires that all scan clocks be grouped into a set of clock groups and that the scan clocks in only one clock group be activated during each capture operation. In addition, if a clock group contains multiple scan clocks, this embodiment requires that the scan clocks be activated one by one in a selected order and that the capture pulse delay between any scan clocks is larger than the possible corresponding clock skew. For example,  FIG. 7A  shows two scan clock groups, CG 1   707 ={CK 1   120 , CK 121 } and CG 2   708 ={CK 3   122 }, which capture in different capture operations. When clock group CG 1   707  captures, a capture order of CK 1   120 →CK 2   121  is used. That is, scan clocks CK 1   120  and CK 2   121  are allowed to capture one by one during a capture operation but the capture pulse delay between CK 1   120  and CK 2   121  should be larger than the possible corresponding clock skew.  
         [0123]     Generally, if a clock group contains only one scan clock, the circuit behavior when the scan clock captures can be fully represented by only one copy of the corresponding combinational logic portion in the circuit. If a clock group contains multiple scan clocks, this embodiment conducts circuit expansion in order to represent the circuit behavior with only one set of circuit data. The reason why this is possible is that circuit expansion uses multiple copies of a logic block to represent the different state of the block at different times. In  FIG. 7B , for example, circuit expansion is conducted for clock domains CD 1   102  and CD 2   103 . Optionally, circuit expansion can also be conducted for cross-clock domain blocks between CD 1   102  and CD 2   103 . During a capture operation where scan clocks CK 1   120  and CK 2   121  capture, all faults in clock domains CD 1   102  and CD 2   103  as well as cross-clock domain blocks between CD 1   102  and CD 2   103  can be targeted. During a capture operation where scan clock CK 3   122  captures, all faults in clock domains CD 3   104  as well as cross-clock domain blocks CCD 13   109  and CCD 23   107  can be targeted.  
         [0124]     This embodiment of the present invention only needs a combinational ATPG program when test patterns are to be generated deterministically. In addition, this embodiment can alleviate the disadvantages of both prior-art solution #1 and prior-art solution #4. The number of test patterns will be smaller than that of prior-art solution #1 since any fault in clock domains CD 1   102  and CD 2   103  can be targeted during the same capture operation. The memory usage will be less than that of prior-art solution #4 since circuit expansion is only conducted for part of a circuit.  
         [0125]      FIG. 8A  shows the domain-interconnect graph used to represent the relationship among the clock domains shown in  FIG. 1 , with clock grouping in a second embodiment of the present invention. The meanings of nodes, edges, and clock groups are the same as explained in  FIG. 7A .  
         [0126]      FIG. 8B  shows the scan clock waveforms in ATPG (automatic test pattern generation) and fault simulation and  FIG. 8C  shows the scan clock waveforms in actual test application, both for detecting or locating stuck-at faults, bridging faults, or IDDQ faults, (referred to as faults) with regard to clock grouping in a second embodiment of the present invention.  
         [0127]     This embodiment requires that all scan clocks be grouped into a set of clock groups and that the clock groups be activated one by one in a selected order during each capture operation. In addition, the capture pulse delays between each clock group should be larger than the possible corresponding clock skew. Furthermore, if a clock group contains multiple scan clocks, this embodiment requires that the scan clocks are activated one by one in a selected order and that the capture pulse delay between any scan clocks is larger than the possible corresponding clock skew. For example,  FIG. 8A  shows two scan clock groups, CG 1   807 ={CK 1   120 , CK 121 } and CG 2   808 ={CK 3   122 }, which capture one by one during any capture operation. When clock group CG 1   808  captures, a capture order of CK 1   120 →CK 2   121  is used. That is, scan clocks CK 1   120  and CK 2   121  are allowed to capture one by one during a capture operation but the capture pulse delay between CK 1   120  and CK 2   121  should be larger than the possible corresponding clock skew.  
         [0128]     Generally, if scan clocks are activated in this manner, the circuit behavior during a capture operation can only be fully represented by several copies of the corresponding combinational logic portion in the circuit, each with a different set of constraints on its inputs and outputs and each corresponding to a different timeframe, for the purpose of ATPG and fault simulation. This embodiment only selects one copy of the combinational logic portion. Obviously, some constraints on the inputs and outputs of the selected copy have to be set to unknown (X) values since other related copies are discarded. In addition, for those scan clocks in one clock group, this embodiment conducts circuit expansion in order to represent the corresponding circuit behavior with only one set of circuit data. The reason why this is possible is that circuit expansion uses multiple copies of a logic block to represent the different state of the block at different times. In  FIG. 8B , for example, circuit expansion is conducted for clock domains CD 1   102  and CD 2   103 . Optionally, circuit expansion can also be conducted for cross-clock domain blocks between CD 1   102  and CD 2   103 . For example, in ATPG and fault simulation for the clock domains CD 1   102  and CD 2   103 , it is necessary to assign unknown values to the signal lines coming from CCD 311   110  and CCD 32   108 . However, only one expanded copy of the clock domains CD 1   102  and CD 2   103  is used. This way, the ATPG results are guaranteed to be accurate even clock skews may exist between different clock domains.  
         [0129]     This embodiment of the present invention only needs a combinational ATPG program when test patterns are to be generated deterministically. In addition, this embodiment can alleviate the disadvantages of both prior-art solution #2 and prior-art solution #4. The fault coverage of this embodiment will be higher than that of prior-art solution #2 since a smaller number of unknown values are assigned. The memory usage will be less than that of prior-art solution # 4  since circuit expansion is only conducted for part of a circuit.  
         [0130]      FIG. 9A  shows the domain-interconnect graph used to represent the relationship among the clock domains shown in  FIG. 1 , with clock grouping in a third embodiment of the present invention. The meanings of nodes, edges, and clock groups are the same as explained in  FIG. 7A .  
         [0131]      FIG. 9B  shows the scan clock waveforms in ATPG (automatic test pattern generation) and fault simulation and  FIG. 9C  shows the scan clock waveforms in actual test application, both for detecting or locating stuck-at faults, bridging faults, or IDDQ faults, (referred to as faults) with regard to clock grouping in a third embodiment of the present invention.  
         [0132]     This embodiment requires that all scan clocks be grouped into a set of clock groups and that the clock groups be activated one by one in a selected order during each capture operation. In addition, the capture pulse delays between each clock group should be larger than the possible corresponding clock skew. Furthermore, if a clock group contains multiple scan clocks, this embodiment requires that the scan clocks are activated one by one in a selected order and that the capture pulse delay between any scan clocks is larger than the possible corresponding clock skew. For example,  FIG. 9A  shows two scan clock groups, CG 1   907 ={CK 1   120 , CK 121 } and CG 2   908 ={CK 3   122 }, which capture one by one during any capture operation. When clock group CG 1   908  captures, a capture order of CK 1   120 →CK 2   121  is assumed. That is, scan clocks CK 1   120  and CK 2   121  are allowed to capture one by one during a capture operation but the capture pulse delay between CK 1   120  and CK 2   121  should be larger than the possible corresponding clock skew.  
         [0133]     Generally, if scan clocks are activated in this manner, the circuit behavior during a capture operation can only be fully represented by several copies of the corresponding combinational logic portion in the circuit, each with a different set of constraints on its inputs and outputs and each corresponding to a different timeframe, for the purpose of ATPG and fault simulation. This embodiment processes the multiple circuit model copies for different timeframes in a series manner one by one. In addition, for those scan clocks in one clock group, this embodiment conducts circuit expansion in order to represent the corresponding circuit behavior with only one set of circuit data. The reason why this is possible is that circuit expansion uses multiple copies of a logic block to represent the different state of the block at different times. In  FIG. 9B , for example, circuit expansion is conducted for clock domains CD 1   102  and CD 2   103 . Optionally, circuit expansion can also be conducted for cross-clock domain blocks between CD 1   102  and CD 2   103 .  
         [0134]     When scan clocks CK 1   120  and CK 2   121  are activated one by one, all stuck-at faults in the clock domains CD 1   102  and CD 2   103 , as well as the cross-clock domain blocks CCD 12   105  and CCD 21   106 , can be targeted in the same run of ATPG and fault simulation, corresponding to test stimuli shifted-in through scan chains in three clock domains, CD 1   102  to CD 3   104 . When the scan clock CK 3   122  is activated, all stuck-at fault in the clock domain CD 3   104  and the cross-clock domain blocks CCD 13   109  and CCD 23   107  can be targeted in ATPG and fault simulation, corresponding to test stimuli shifted-in through scan chains in two clock domains, CD 2   103  and CD 3   104 , as well as test responses captured by CK 1   120  and CK 2   121 .  
         [0135]     This embodiment of the present invention can alleviate the disadvantages of both prior-art solution #3 and prior-art solution #4. A sequential ATPG program needs to be used but with fewer timeframes. This will result in less CPU time and memory usage than prior-art solution #3. The memory usage will be less than that of prior-art solution #4 since circuit expansion is only conducted for part of a circuit.  
         [0136]      FIG. 10A  shows the domain-interconnect graph used to represent the relationship among the clock domains shown in  FIG. 1 , with clock grouping in a fourth embodiment of the present invention. The meanings of nodes, edges, and clock groups are the same as explained in  FIG. 7A .  
         [0137]      FIG. 10B  shows the scan clock waveforms in ATPG (automatic test pattern generation) and fault simulation and  FIG. 10C  shows the scan clock waveforms in actual test application, both for detecting or locating transition faults or path-delay faults launched from capture, with regard to clock grouping in a fourth embodiment of the present invention. This embodiment is basically the same as the embodiment shown in  FIG. 7 . The only difference is that this embodiment uses two at-speed pulses for each capture. This allows this embodiment to detect or locate transition faults or path-delay faults launched from capture. Refer to the descriptions of  FIG. 7  for more details.  
         [0138]      FIG. 11A  shows the domain-interconnect graph used to represent the relationship among the clock domains shown in  FIG. 1 , with clock grouping in a fifth embodiment of the present invention. The meanings of nodes, edges, and clock groups are the same as explained in  FIG. 7A .  
         [0139]      FIG. 11B  shows the scan clock waveforms in ATPG (automatic test pattern generation) and fault simulation and  FIG. 11C  shows the scan clock waveforms in actual test application, both for detecting or locating transition faults or path-delay faults launched from capture, with regard to clock grouping in a fifth embodiment of the present invention. This embodiment is basically the same as the embodiment shown in  FIG. 8 . The only difference is that this embodiment uses two at-speed pulses for each capture. This allows this embodiment to detect or locate transition faults or path-delay faults launched from capture. Refer to the descriptions of  FIG. 8  for more details.  
         [0140]      FIG. 12A  shows the domain-interconnect graph used to represent the relationship among the clock domains shown in  FIG. 1 , with clock grouping in a sixth embodiment of the present invention. The meanings of nodes, edges, and clock groups are the same as explained in  FIG. 7A .  
         [0141]      FIG. 12B  shows the scan clock waveforms in ATPG (automatic test pattern generation) and fault simulation and  FIG. 12C  shows the scan clock waveforms in actual test application, both for detecting or locating transition faults or path-delay faults launched from capture, with regard to clock grouping in a sixth embodiment of the present invention. This embodiment is basically the same as the embodiment shown in  FIG. 9 . The only difference is that this embodiment uses two at-speed pulses for each capture. This allows this embodiment to detect or locate transition faults or path-delay faults launched from capture. Refer to the descriptions of  FIG. 9  for more details.  
         [0142]      FIG. 13A  shows the domain-interconnect graph used to represent the relationship among the clock domains shown in  FIG. 1 , with clock grouping in a seventh embodiment of the present invention. The meanings of nodes, edges, and clock groups are the same as explained in  FIG. 7A .  
         [0143]      FIG. 13B  shows the scan clock waveforms in ATPG (automatic test pattern generation) and fault simulation and  FIG. 13C  shows the scan clock waveforms in actual test application, both for detecting or locating transition faults or path-delay faults launched from shift with regard to clock grouping in a seventh embodiment of the present invention. This embodiment is basically the same as the embodiment shown in  FIG. 7 . The only difference is that this embodiment uses one at-speed pulse for each capture. This allows this embodiment to detect or locate transition faults or path-delay faults launched from shift. Refer to the descriptions of  FIG. 7  for more details.  
         [0144]      FIG. 14A  shows the domain-interconnect graph used to represent the relationship among the clock domains shown in  FIG. 1 , with clock grouping in an eighth embodiment of the present invention. The meanings of nodes, edges, and clock groups are the same as explained in  FIG. 7A .  
         [0145]      FIG. 14B  shows the scan clock waveforms in ATPG (automatic test pattern generation) and fault simulation and  FIG. 14C  shows the scan clock waveforms in actual test application, both for detecting or locating transition faults or path-delay faults launched from shift, with regard to clock grouping in an eighth embodiment of the present invention. This embodiment is basically the same as the embodiment shown in  FIG. 8 . The only difference is that this embodiment uses one at-speed pulse for each capture. This allows this A embodiment to detect or locate transition faults or path-delay faults launched from shift. Refer to the descriptions of  FIG. 8  for more details.  
         [0146]      FIG. 15A  shows the domain-interconnect graph used to represent the relationship among the clock domains shown in  FIG. 1 , with clock grouping in a ninth embodiment of the present invention. The meanings of nodes, edges, and clock groups are the same as explained in  FIG. 7A .  
         [0147]      FIG. 15B  shows the scan clock waveforms in ATPG (automatic test pattern generation) and fault simulation and  FIG. 15C  shows the scan clock waveforms in actual test application, both for detecting or locating transition faults or path-delay faults launched from shift, with regard to clock grouping in a ninth embodiment of the present invention. This embodiment is basically the same as the embodiment shown in  FIG. 9 . The only difference is that this embodiment uses one at-speed pulse for each capture. This allows this embodiment to detect or locate transition faults or path-delay faults launched from shift. Refer to the descriptions of  FIG. 9  for more details.  
         [0148]      FIG. 16A  shows the domain-interconnect graph used to represent the relationship among the clock domains shown in  FIG. 1 , with clock grouping in a tenth embodiment of the present invention. The meanings of nodes, edges, and clock groups are the same as explained in  FIG. 7A .  
         [0149]      FIG. 16B  shows the scan clock waveforms in ATPG (automatic test pattern generation) and fault simulation and  FIG. 16C  shows the scan clock waveforms in actual test application, both for detecting or locating stuck-at faults, bridging faults, or IDDQ faults, with regard to clock grouping in a tenth embodiment of the present invention.  
         [0150]     This embodiment requires that all scan clocks be grouped into a set of clock groups and that the scan clocks in only one clock group be activated during each capture operation. In addition, if a clock group contains multiple scan clocks, this embodiment requires that the scan clocks be activated one by one in a selected order and that the capture pulse delay between any scan clocks is larger than the possible corresponding clock skew.  
         [0151]     Generally, if a clock group contains only one scan clock, the circuit behavior when the scan clock captures can be fully represented by only one copy of the corresponding combinational logic portion in the circuit. If a clock group contains multiple scan clocks that are activated one by one in a selected order, the circuit behavior during a capture operation can only be fully represented by several copies of the corresponding combinational logic portion in the circuit, each with a different set of constraints on its inputs and outputs and each corresponding to a different timeframe, for the purpose of ATPG and fault simulation. This embodiment processes the multiple circuit model copies for different timeframes in a serial manner one by one.  
         [0152]     This embodiment of the present invention only needs a sequential ATPG program when test patterns are to be generated deterministically. In addition, this embodiment can alleviate the disadvantage of prior-art solution #3 by reducing CPU time and memory usage.  
         [0153]      FIG. 17A  shows the domain-interconnect graph used to represent the relationship among the clock domains shown in  FIG. 1 , with clock grouping in an eleventh embodiment of the present invention. The meanings of nodes, edges, and clock groups are the same as explained in  FIG. 7A .  
         [0154]      FIG. 17B  shows the scan clock waveforms in ATPG (automatic test pattern generation) and fault simulation and  FIG. 17C  shows the scan clock waveforms in actual test application, both for detecting or locating stuck-at faults, bridging faults, or IDDQ faults, with regard to clock grouping in an eleventh embodiment of the present invention.  
         [0155]     This embodiment requires that all scan clocks be grouped into a set of clock groups and that the scan clocks in all clock groups be activated during each capture operation. In addition, this embodiment requires that the scan clocks be activated one by one in a selected order and that the capture pulse delay between any scan clocks is larger than the possible corresponding clock skew.  
         [0156]     Generally, if scan clocks are activated in this manner, the circuit behavior during a capture operation can only be fully represented by several copies of the corresponding combinational logic portion in the circuit, each with a different set of constraints on its inputs and outputs and each corresponding to a different timeframe, for the purpose of ATPG and fault simulation. This embodiment processes the multiple circuit model copies for different timeframes in a series manner one by one for scan clocks in the clock group CG 1   1707 . However, for the scan clock in the clock group CG 2   1708 , some constraints on the inputs and outputs of the corresponding circuit copy are set to unknown (X) values.  
         [0157]     This embodiment of the present invention only needs a sequential ATPG program when test patterns are to be generated deterministically. In addition, this embodiment can alleviate the disadvantages of prior-art solution #2 and prior-art solution #3 by achieving higher fault coverage with lower memory usage.  
         [0158]      FIG. 18A  shows the domain-interconnect graph used to represent the relationship among the clock domains shown in  FIG. 1 , with clock grouping in a twelfth embodiment of the present invention. The meanings of nodes, edges, and clock groups are the same as explained in  FIG. 7A .  
         [0159]      FIG. 18B  shows the scan clock waveforms in ATPG (automatic test pattern generation) and fault simulation and  FIG. 18C  shows the scan clock waveforms in actual test application, both for detecting or locating transition faults or path-delay faults launched from capture, with regard to clock grouping in a twelfth embodiment of the present invention. This embodiment is basically the same as the embodiment shown in  FIG. 16 . The only difference is that this embodiment uses two at-speed pulses for each capture. This allows this embodiment to detect or locate transition faults or path-delay faults launched from capture. Refer to the descriptions of  FIG. 16  for more details.  
         [0160]      FIG. 19A  shows the domain-interconnect graph used to represent the relationship among the clock domains shown in  FIG. 1 , with clock grouping in a thirteenth embodiment of the present invention. The meanings of nodes, edges, and clock groups are the same as explained in  FIG. 7A .  
         [0161]      FIG. 19B  shows the scan clock waveforms in ATPG (automatic test pattern generation) and fault simulation and  FIG. 19C  shows the scan clock waveforms in actual test application, both for detecting or locating transition faults or path-delay faults launched from capture, with regard to clock grouping in a thirteenth embodiment of the present invention. This embodiment is basically the same as the embodiment shown in  FIG. 17 . The only difference is that this embodiment uses two at-speed pulses for each capture. This allows this embodiment to detect or locate transition faults or path-delay faults launched from capture. Refer to the descriptions of  FIG. 17  for more details.  
         [0162]      FIG. 20A  shows the domain-interconnect graph used to represent the relationship among the clock domains shown in  FIG. 1 , with clock grouping in a thirteenth embodiment of the present invention. The meanings of nodes, edges, and clock groups are the same as explained in  FIG. 7A .  
         [0163]      FIG. 20B  shows the scan clock waveforms in ATPG (automatic test pattern generation) and fault simulation and  FIG. 20C  shows the scan clock waveforms in actual test application, both for detecting or locating transition faults or path-delay faults launched from shift, with regard to clock grouping in a thirteenth embodiment of the present invention. This embodiment is basically the same as the embodiment shown in  FIG. 16 . The only difference is that this embodiment uses one at-speed pulse for each capture. This allows this embodiment to detect or locate transition faults or path-delay faults launched from shift. Refer to the descriptions of  FIG. 16  for more details.  
         [0164]      FIG. 21A  shows the domain-interconnect graph used to represent the relationship among the clock domains shown in  FIG. 1 , with clock grouping in a fifteenth embodiment of the present invention. The meanings of nodes, edges, and clock groups are the same as explained in  FIG. 7A .  
         [0165]      FIG. 21B  shows the scan clock waveforms in ATPG (automatic test pattern generation) and fault simulation and  FIG. 21C  shows the scan clock waveforms in actual test application, both for detecting or locating transition faults or path-delay faults launched from shift, with regard to clock grouping in a fifteenth embodiment of the present invention. This embodiment is basically the same as the embodiment shown in  FIG. 17 . The only difference is that this embodiment uses one at-speed pulse for each capture. This allows this embodiment to detect or locate transition faults or path-delay faults launched from shift. Refer to the descriptions of  FIG. 17  for more details.  
         [0166]      FIG. 22A  shows a domain-interconnect graph used to represent the relationship among 8 inter-related clock domains, CD 1   2201  to CD 8   2208 . Here, 8 vertexes are used to represent the 8 clock domains, CD 1   2201  to CD 8   2208 . The corresponding clocks, CK 1   2221  to CK 8   2228 , for the clock domains are also shown in the vertexes for the purpose of easy comprehension. The directed arc between any two vertexes represents a cross-clock domain logic block. For example, the arc  2232  represents the cross-clock domain logic block from the clock domain CD 2   2202  to the clock domain CD 1   2201 .  
         [0167]      FIG. 22B  shows the fault detection or location range for one ordered sequence of capture clocks for the clock domains shown in  FIG. 22A , in accordance with the present invention, where clock domain grouping is conducted.  
         [0168]     Since clock domains CD 7   2207  and CD 8   2208  do not interact with each other, they can be captured at the same time. In addition, since clock domains CD 3   2203  and CD 5   2205  do not interact with each other, they can be captured at the same time. Similarly, since clock domains CD 3   2203  and CD 6   2206  do not interact with each other, they can be captured at the same time. However, since clock domains CD 5   2205  and CD 6   2206  interact with each other, they cannot be captured at the same time. Based on this analysis, it can be seen the ordered sequence of capture clocks can be picked up as follows: {CK 7   2227 , CK 8   2228 }→CK 1   2221 →CK 2   2222 →{CK 3   2223 , CK 5   2225 }→CK 6   2226 →CK 4   2224 . Alternatively, the ordered sequence of capture clocks can be picked up as follows: {CD 7   2227 , CD 8   2228 }→CD 1   2221 →CK 2   2222 →{CK 3   2223 , CK 6   2224 }→CK 5   2225 →CK 4   2224 . That is, some clock domains can be grouped together and captured simultaneously. This will reduce test time.  
         [0169]      FIG. 23A  shows a domain-interconnect graph used to represent the relationship among 5 inter-related clock domains, CD 1   2301  to CD 4   2305 . Here, 5 vertexes are used to represent the 5 clock domains, CD 1   2301  to CD 4   2305 . The corresponding clocks, CK 1   2321  to CK 5   2325 , for the clock domains are also shown in the vertexes for the purpose of easy comprehension. The directed arc between any two vertexes represents a cross-clock domain logic block. For example, the arc  2351  represents the cross-clock domain logic block from the clock domain CD 2   2302  to the clock domain CD 1   2301 .  
         [0170]      FIG. 23B  shows the fault detection or location range for one ordered sequence of capture clocks, {CK 1   2321 , CK 5   2325 }→CK 2   2322 →CK 3   2323 →CK 4   2324 , for the clock domains, CD 1   2321  to CD 4   2324 , shown in  FIG. 23A , in accordance with the present invention. The ordered sequence of capture clocks is determined automatically based on the domain-interconnect graph shown in  FIG. 23A . It can also be specified directly.  
         [0171]     Note that test stimuli are shifted into the scan chains in all clock domains simultaneously. Then the capture operation is conducted in the following manner: First, the clocks CK 1   2321  and CK 5   2325 , which do not interact with each other, capture. As a result, faults in the clock domain CD 1   2301  as well as in the cross-clock domain logic blocks  2351  and  2357  can be detected or located. In addition, faults in the clock domain CD 5   2305  as well as in the cross-clock domain logic blocks  2356  and  2359  can be detected or located. Second, the clock CK 2   2322  captures. As a result, faults in the clock domain CD 2   2302  as well as in the cross-clock domain logic block  2352  can be detected or located. Third, the clock CK 3   2323  captures. As a result, faults in the clock domain CD 3   2303  as well as in the cross-clock domain logic block  2354  can be detected or located. Fourth, the clock CK 4   2324  captures. As a result, faults in the clock domain CD 4   2304  can be detected or located.  
         [0172]     Obviously, after ATPG is conducted for the ordered sequence of capture clocks, {CK 1   2321 , CK 5   2325 }→CK 2   2322 →CK 3   2323 →CK 4   2324 , all faults except those in the cross-clock domain logic blocks represented by the arcs  2353  and  2355  can be detected or located. The reason is that, when the clocks CK 2   2322  and CK 3   2323  capture, test responses will be captured into all scan cells in the clock domains CD 2   2302  and CD 3   2303 , replacing any previous values shifted into these scan cells when the clocks CK 3   2323  and CK 4   2324  capture, respectively.  
         [0173]      FIG. 23C  shows the fault detection or location range for one more ordered sequence of capture clocks, CK 4   2324 →CK 3   2323 , for the clock domains, CD 4   2304  to CD 3   2303 , shown in  FIG. 23A , in accordance with the present invention. The ordered sequence of capture clocks is determined automatically based on the domain-interconnect graph shown in  FIG. 23A . It can also be specified directly.  
         [0174]     Note that test stimuli are shifted into the scan chains in all clock domains simultaneously. Then the capture operation is conducted in the following manner: First, the clock CK 4   2324  captures. As a result, faults in the clock domain CD 4   2304  as well as in the cross-clock domain logic block  2355  can be detected or located. Second, the clock CK 3   2323  captures. As a result, faults in the clock domain CD 3   2303  as well as in the cross-clock domain logic block  2353  can be detected or located.  
         [0175]     Combined with results shown in  FIG. 23B , it can be seen that all faults in the scan-based integrated circuit can be detected or located, after using these two ordered sequence of capture clocks.  
         [0176]      FIG. 23D  shows the fault detection or location range for one ordered sequence of capture clocks, {CK 1   2321 , CK 5   2325 }→CK 2   2322 →CK 3   2323 →CK 4   2324 , for the clock domains, CD 1   2301  to CD 4   2304 , shown in  FIG. 23A , in accordance with the present invention, where clock domain merging is conducted.  
         [0177]     In this case, three clock domains, CD 2   2302 , CD 3   2303 , and CD 4   2304 , are merged together. It means that two-time frames will be used for circuit transformation related to these three clock domains and their corresponding cross-clock domain logic blocks. The benefits are as follows: Even the clock CK 3   2323  captures after the clock CK 2   2322  does, the controllability of the cross-clock domain logic block  2353  is still high since the clock domain CD 2   2302  is also transformed to obtain the values in the clock domain CD 2   2302  after the clock CK 2   2322  captures. As a result, all faults in the cross-clock domain logic block  2353  can be detected or located. In addition, even the clock CK 4   2324  captures after the clocks CK 2   2322  and CK 3   2323  do, the controllability of the cross-clock domain logic block  2355  is still high since the clock domains CD 2   2302  and CD 3   2303  as well as the cross-clock domain logic block  2353  are also transformed to obtain the values in the clock domains CD 2   2302  and CD 3   2303  as well as the cross-clock domain logic block  2353  after the clocks CK 2   2322  and CK 3   2323  capture. As a result, all faults in the cross-clock domain logic block  2355  can be detected or located. That is, by merging the  3  clock domains, CD 2   2302 , CD 3   2303 , and CD 4   2304 , only one ordered sequence of capture clocks is enough to detect or locate all faults in the scan-based integrated circuit.  
         [0178]      FIG. 24A  shows a prior art solution for handling uncontrollability when using a single time-frame in the multiple-capture scheme. The clock domain CD 1   2401  interacts to the clock domain CD 2   2402  through the cross-clock domain logic block CCD 12   2403 . The Q output  2409  of the scan cell SC 1   2404 , driven by the clock CK 1   2406 , is connected to the cross-clock domain logic block CCD 12   2403 . The D input  2410  of the D input of the scan cell SC 2   2405 , driven by the clock CK 2   2407 , is connected to the cross-clock domain logic block CCD 12   2403 .  
         [0179]     Suppose that the clock CK 1   2406  is activated before the clock CK 2   2407  is activated in the multiple-capture scheme. When the clock CK 1   2406  captures, the clock domain CD 1   2401  needs to be transformed during ATPG (automatic test pattern generation) for detecting or locating all faults in the clock domain CD 1   2401 . Note that, after the clock CK 1   2406  is activated, test responses will be captured into all scan cells in the clock domain CD 1   2401 , replacing any previous values shifted into these scan cells. Now, when the clock CK 2   2407  captures, the clock domain CD 1   2401 , the cross-clock domain CCD 12   2403 , and the clock domain CD 2   2402  need to be transformed during ATPG for detecting or locating all faults in the cross-clock domain logic block CCD 12   303  and the clock domain CD 2   2402 . Here, two time-frames are involved: the first one for CK 1   2406  and the second one for CK 2   2407 . The purpose of transforming the clock domain CD 1   2401  is to get the values for the first time-frame for CK 1   2406 .  
         [0180]     Due to the ATPG memory consumption issue, it is sometimes desirable to use a single time-frame even in the multiple-capture scheme for multiple capture clocks. In this example, this means to transform only the cross-clock domain CCD 12   2403  and the clock domain CD 2   2402  during ATPG when the clock CK 2   2407  captures. The advantage of this approach is that it reduces memory usage during ATPG. However, it is necessary to provide a solution to handle the values provided from the clock domain CD 1   2401  to the cross-clock domain logic block CCD 21   2403 .  
         [0181]     A prior art solution for handling this uncontrollability issue is to use unknown values, represented by X. As shown in  FIG. 24A , X is assigned to the Q output  2409  of the scan cell SC 1   2404 . The disadvantage of this solution is that it reduces the controllability significantly, which will results in a larger set of test patterns with lower fault coverage.  
         [0182]      FIG. 24B  shows an embodiment of the method for handling uncontrollability when using a single time-frame in the multiple-capture scheme, in accordance with the present invention.  
         [0183]     Same as the case shown in  FIG. 24A , if the clock CK 1   2406  captures before the clock CK 2   2407  captures, test responses will be captured into all scan cells in the clock domain CD 1   2401 , replacing any previous values shifted into these scan cells. Suppose that a single time-frame needs to be used in the multiple-capture scheme for multiple capture clocks in order to reduce memory usage. In this example, this means to transform only the cross-clock domain CCD 12   2403  and the clock domain CD 2   2402  during ATPG when the clock CK 2   2407  captures. Obviously, it is necessary to provide a solution to handle the values provided from the clock domain CD 1   2401  to the cross-clock domain logic block CCD 21   2403 .  
         [0184]     In order to handle this uncontrollability issue, the present invention makes sure that the value of the Q output  2409  of the scan cell SC 1   2404  remains the same before and after the clock CK 1   2406  captures. This can be achieved by setting a proper value either to the D input  2408  or the R (reset) input  2411  of the scan cell SC 1   2404 . Since a logic value, 0 or 1, is used instead of an unknown value X, the controllability for the cross-clock domain CCD 12   2403  and the clock domain CD 2   2402  can be improved significantly. This will result in a smaller set of test patterns with higher fault coverage.  
         [0185]      FIG. 25  shows an electronic design automation system which includes a processor  2502 , a bus  2505  coupled to the processor, a computer-readable memory  2501  coupled to the bus, an input device  2503 , and an output device  2504 . The computer-readable memory  2501  contains a computer-readable program, in accordance with the present invention and described in  FIG. 6A  and  FIG. 6B , to cause the electronic design automation system to perform a method of ATPG (automatic test pattern generation) and fault simulation based on clock grouping and circuit expansion for testing a scan-based integrated in scan-test mode or self-test mode.  
         [0186]     The processor  2502  may represent a central processing unit of a personal computer, workstation, mainframe computer or other suitable digital processing device. The memory  2501  can be an electronic memory or a magnetic or optical disk-based memory, or various combinations thereof. A designer interacts with the clock grouping and circuit expansion based ATPG and fault simulation software run by the processor  2502  to provide appropriate inputs via an input device  2503 , which may be a keyboard, disk drive or other suitable source of design information. The processor  2502  provides outputs to the designer via an output device  2504 , which may be a display, a printer, a disk drive or various combinations of these and other elements.  
         [0187]     Having thus described presently preferred embodiments of the present invention, it can now be appreciated that the objectives of the invention have been fully achieved. And it will be understood by those skilled in the art that many changes in construction and circuitry, and widely differing embodiments and applications of the invention will suggest themselves without departing from the spirit and scope of the present invention. The disclosures and the description herein are intended to be illustrative and are not in any sense limitation of the invention, more preferably defined in scope by the following claims.