Diagnostic Test Pattern Generation and Fault Simulation for

Diagnostic Test Pattern Generation and Fault Simulation for Stuck-at and Transition Faults Committee: Vishwani D. Agrawal Adit Singh University Reader: Sanjeev Baskiyar, CSSE Victor P. Nelson Bogdan M. Wilamowski Student: Yu Zhang Auburn University, Auburn, Alabama 36849 USA Mar. 21, 2012 Zhang: Ph. D Defense 1

Purpose • Identification of fault is useful in the characterization phase of design. • Present ATPG tools emphasize only fault detection. • There is an accepted measure for fault detection coverage but none for diagnostic coverage. • Diagnosis must deal with non-classical faults, not just single stuck-at faults. Mar. 21, 2012 Zhang: Ph. D Defense 2

Outline • Purpose (motivation) • Introduction & Background • Diagnostic ATPG System – Diagnostic Fault Simulation – Exclusive Test Generation – Equivalence Identification • Exclusive test for transition fault • Experimental results • Conclusion Mar. 21, 2012 Zhang: Ph. D Defense 3

Diagnostic ATPG Problem • Given a circuit and a fault model, find: – Test vectors to distinguish between all, or most, fault-pairs. – Measure diagnostic coverage of vectors. • Present contributions: – A new diagnostic coverage metric. – A diagnostic ATPG system using new algorithms and conventional stuck-at fault detection tools. – A diagnostic ATPG system for transition faults using new algorithms and available fault-detection tools Mar. 21, 2012 Zhang: Ph. D Defense 4

Introduction Basic testing flow. Mar. 21, 2012 Zhang: Ph. D Defense 5

Fault Detection and Diagnosis 1 Fault D 0 CUT Fault D 1 • Fault detection: Need at least one vector that detects a target fault. • Fault diagnosis: Need at least one vector that produced different responses for every pair of faults. Mar. 21, 2012 Zhang: Ph. D Defense 6

Introduction* Fault detection test generation: Find an input vector such that faulty response differs from fault-free response. C 0 C 1 = 1 * Yu Zhang, V. D. Agrawal, “A Diagnostic Test Generation System, ” in Proc. International Test Conf. , Nov 2010. Mar. 21, 2012 Zhang: Ph. D Defense 7

Introduction Exclusive test: A test that detects only one Simplified: fault from a fault-pair. (C 0 C 1 ) (C 0 C 2 ) = 1 ⇒ C 1 C 2 = 1 sa 0 Mar. 21, 2012 Zhang: Ph. D Defense 8

Diagnostic Test Generation System Conventional ATPG 1. Structurally collapsed fault set 2. ATPG system for detection fault coverage Functionally equivalent fault-pair No Undiagnosed fault-pair Adequate diagnostic coverage? Yes Mar. 21, 2012 4. Exclusive test generator Detection vectors Exclusive vectors Test vectors 3. Diagnostic fault simulator Stop Diagnostic ATPG Zhang: Ph. D Defense 9

Diagnostic Fault Simulator* • Given a set of vectors and a set of faults, find: – Diagnostic coverage – Identify undiagnosed fault groups with two or more faults – Eliminate the need to target all n(n – 1)/2 fault pairs * Y. Zhang and V. D. Agrawal, “An Algorithm for Diagnostic Fault Simulation, ” Proc. 11 th IEEE Latin-American Workshop, March 2010. Mar. 21, 2012 Zhang: Ph. D Defense 10

Diagnostic Fault Simulation 1. For an input test vector find detected faults. 2. Group faults with same syndrome (detection pattern at primary outputs). 3. Calculate/update diagnostic coverage (DC). 4. Continue steps 1 through 3 with next test vector until no vectors left. Mar. 21, 2012 Zhang: Ph. D Defense 11

Diagnostic Fault Simulation Original fault set Simulate t 1 G 0 Simulate t 2 G 0 fa G 4 G 3 G 2 G 5 fb G 7 Simulate t 3 Simulate tn Mar. 21, 2012 fc fd fe Zhang: Ph. D Defense G 5 12

Diagnostic Fault Coverage (DC)* • Diagnostic coverage (new) • Fault coverage (conventional), Where g 0 is the set of undetected faults. * Yu Zhang, V. D. Agrawal, “A Diagnostic Test Generation System and a Coverage Metric, ” 15 th IEEE European Test Symp. , May 2010. Mar. 21, 2012 Zhang: Ph. D Defense 13

Coverage as fraction Diagnostic Coverage 1. 1 1 0. 9 0. 8 0. 7 0. 6 0. 5 0. 4 0. 3 0. 2 0. 1 0 1000 900 800 700 600 500 400 300 DC 200 Distin. FP/Total FP 100 No. of Un. FP 1 11 21 31 41 0 51 61 Number of Undistinguished Fault Pairs DC vs. Fault-Pair Coverage – C 432 Number of ATPG Vectors Mar. 21, 2012 Zhang: Ph. D Defense 14

Diagnostic Fault Simulation Take ISCAS 85 benchmark circuit c 17 as an example: 1 10 3 20 2 6 7 Mar. 21, 2012 5 11 14 15 Zhang: Ph. D Defense 22 16 21 19 23 15

Diagnostic Fault Simulation • 22 collapsed fault in c 17 (f 1~f 22): f 1: 22 sa 1 f 2: 10 sa 1 f 3: 22 sa 0 f 4: 16 ->22 sa 1 f 5: 3 ->10 sa 1 f 6: 1 sa 1 f 7: 3 sa 0 f 8: 3 sa 1 f 9: 16 sa 1 f 10: 16 sa 0 f 11: 11 ->16 sa 1 Mar. 21, 2012 f 12: f 13: f 14: f 15: f 16: f 17: f 18: f 19: f 20: f 21: f 22: Zhang: Ph. D Defense 2 sa 1 11 sa 0 3 ->11 sa 1 6 sa 1 23 sa 1 19 sa 1 23 sa 0 16 ->23 sa 1 11 ->19 sa 1 7 sa 1 16

Diagnostic Fault Simulation Test vector set for c 17 (generated by our diagnostic ATPG system): t 1: t 2: t 3: t 4: t 5: t 6: t 7: t 8: 00000 10110 11101 01110 100111 11000 01010 Mar. 21, 2012 00 10 11 00 01 00 11 11 1 10 3 2 6 22 20 14 5 11 7 Zhang: Ph. D Defense 15 16 21 19 23 17

Diagnostic Fault Simulation Fault simulation without fault dropping: test 1: 00000 00 f 1: * 10 f 2: 00 Fault free f 3: 00 response f 4: 00 for test 1 f 5: 00 f 6: 00 * indicates detected f 7: 00 faults f 8: 00 f 9: 00 f 10: * 11 f 11: 00 Mar. 21, 2012 Zhang: Ph. D Defense f 12: f 13: f 14: f 15: f 16: f 17: f 18: f 19: f 20: f 21: f 22: * 11 00 00 * 01 18

Diagnostic Fault Simulation Faults can be grouped according to syndromes (syndromes of t 1): Groups Faults Syndrome t 1 G 1 f 1 10 G 2 f 10, f 12 11 G 3 f 17, f 22 01 G 0 All other faults 00 In syndrome, ‘ 1’ represents a mismatch with fault free response. ‘ 0’ means match. f 1 will be dropped from further simulation. Mar. 21, 2012 Zhang: Ph. D Defense 19

Diagnostic Fault Simulation Mar. 21, 2012 Groups Faults Syndrome t 1 G 1 f 1 10 G 2 f 10, f 12 11 G 3 f 17, f 22 01 G 0 All other faults 00 Zhang: Ph. D Defense 20

Diagnostic Fault Simulation Fault simulation with t 2: test 2: 10110 G 2: f 10: * 11 f 12: 10 G 3: f 17: * 11 f 22: 10 Mar. 21, 2012 G 0: f 2: * 00 f 3: * 00 f 4: 10 f 5: 10 10 f 6: 10 f 7: * 00 Fault free f 8: 10 response f 9: 10 f 11: 10 f 13: 10 G 0 contains undetected faults. f 14: 10 f 15: 10 After test 2 f 2, f 3, f 16: 10 and f 7 will leave f 18: 10 G 0. f 19: 10 f 20: 10 f 21: 10 Zhang: Ph. D Defense 21

Diagnostic Fault Simulation After applying t 2: Groups G 2 G 4 G 3 G 5 G 0 G 6 Faults Syndrome t 2 f 10 01 f 12 00 f 17 01 f 22 00 All other faults 00 f 2, f 3, f 7 10 f 10, f 12, f 17, f 22 are dropped from further simulation Mar. 21, 2012 Zhang: Ph. D Defense 22

Diagnostic Fault Simulation Groups G 2 G 4 G 3 G 5 G 0 G 6 Mar. 21, 2012 Faults Syndrome t 2 f 10 01 f 12 00 f 17 01 f 22 00 All other faults 00 f 2, f 3, f 7 10 Zhang: Ph. D Defense 23

Dictionary Construction This is a fault dictionary constructed after applying t 2. It can be used for cause-effect diagnosis ‘X’ means don’t care or unknown Faults Syndrome t 1 Syndrome t 3 ~ t 8 f 1 10 X … f 10 11 01 … f 12 11 00 … f 17 01 01 … f 22 01 00 … f 2, f 3, f 7 00 10 … All other faults 00 00 … Mar. 21, 2012 Zhang: Ph. D Defense 24

Diagnostic Fault Simulation Continue to apply test vectors to all groups, and divide faults into sub groups. After t 1: f 1 is dropped G 1: f 1 (10) G 2: f 10, f 12 (11) G 0: f 1, f 2, f 3, …f 22 (no test applied) G 0: G 3: All other f 17, f 22 (01) faults (00) Mar. 21, 2012 Zhang: Ph. D Defense 25

Diagnostic Fault Simulation After t 2: G 2: f 10, f 12 G 2: f 10 (01) G 5: f 12 (00) Single fault groups are dropped. Mar. 21, 2012 Zhang: Ph. D Defense 26

Diagnostic Fault Simulation Similarly for G 3: f 17, f 22 G 3: f 17 (01) G 6: f 22 (00) Single fault groups are dropped. Mar. 21, 2012 Zhang: Ph. D Defense 27

Diagnostic Fault Simulation For G 0: f 2~f 9, f 11, f 13~f 16, f 18~f 21 G 7: f 2, f 3, f 7 (10) Mar. 21, 2012 No faults are dropped here. G 0: all other undetected faults (00) Zhang: Ph. D Defense 28

Diagnostic Fault Simulation • For c 17 after applying all 8 test vectors, we get 22 fault groups with only one fault in each group. Mar. 21, 2012 Zhang: Ph. D Defense 29

Fault Dropping • Each group contains faults that are not distinguished from others within that group, but are distinguished from those in other groups. • During simulation once a fault is placed alone in a single-fault group, it is dropped from further simulation. Mar. 21, 2012 Zhang: Ph. D Defense 30

Diagnostic Fault Simulation Summarize: Original fault set Simulate t 1 G 0 Simulate t 2 G 0 fa G 4 G 3 G 2 G 5 fb G 7 Simulate t 3 Simulate tn Mar. 21, 2012 fc fd fe Zhang: Ph. D Defense G 5 31

Summary for Fault Simulation • Diagnostic coverage metric defined. • Diagnostic fault simulation has similar complexity as conventional simulation with fault dropping. Mar. 21, 2012 Zhang: Ph. D Defense 32

Exclusive Test* Generation • An exclusive test for fault-pair (f 1, f 2) distinguishes between the two faults. • If no exclusive test exists, then the two faults cannot be distinguished from each other and form an equivalent fault-pair. * V. D. Agrawal, D. H. Baik, Y. C. Kim, and K. K. Saluja, “Exclusive Test and its Applications to Fault Diagnosis, ” Proc. 16 th International Conf. VLSI Design, Jan. 2003, pp. 143– 148. Mar. 21, 2012 Zhang: Ph. D Defense 33

Exclusive Test Generation Need two copies of circuit New model: Previous C 1 C 2 = 1 X G(X, y) Sa 0 or Sa 1 Mar. 21, 2012 Zhang: Ph. D Defense 34

Exclusive Test Generation Single circuit copy ATPG: find a test vector to distinguish fault f 1 (line x 1 s-a-a) from fault f 2 (line x 2 s-a-b) PO PI line x 1 line x 2 Mar. 21, 2012 s-a-a s-a-b Zhang: Ph. D Defense 35

New Diagnostic ATPG Model • Two-copy ATPG model with C 1 and C 2: • Substitue: • Single-copy ATPG model with C: Mar. 21, 2012 Zhang: Ph. D Defense 36

Single Copy Exclusive Test Generation Consider exclusive test for x 1 s-a-a and x 2 s-a-b y PO x 1 PI x 1’ a x 2 CUT C Mar. 21, 2012 G x 2’ b Zhang: Ph. D Defense 37

A Simplified Model Suppose a is 0 and b is 1, the model can be simplified: y x 1’ PO PI x 2’ CUT C Mar. 21, 2012 Zhang: Ph. D Defense 38

Exclusive Test Generation Example ISCAS 85 c 17 benchmark circuit: 1 10 3 sa 0 20 2 6 5 15 7 sa 1 t 1: 00000 00 t 2: 10110 10 Mar. 21, 2012 11 14 22 16 21 19 23 Seven test vectors generated by ATPG; 100% fault coverage but some fault-pairs not distinguished Zhang: Ph. D Defense 39

Exclusive Test Generation y 1 0 0 1 1 6 0 10 3 20 2 11 22 16 14 21 15 19 23 7 Sa 0 or Sa 1 Mar. 21, 2012 1/0 t 8: 10010 00 Zhang: Ph. D Defense 40 0/1

Advantages of Exclusive Test Algorithm • Reduced complexity: Single-copy ATPG model is no more complex than a single fault ATPG. • No need for especially designed diagnostic ATPG tools that try to propagate different logic values of two faults to POs. • Can take advantage of various existing fault detection ATPG algorithms. Mar. 21, 2012 Zhang: Ph. D Defense 41

Experimental Results Detection test Generation Circuit No. of faults c 17 Diagnostic test Generation Det. Vect. FC % CPU s* DC % Excl. Abort Equv. Vect. pairs DC % CPU s* 22 7 100. 03 95. 5 1 0 0 100. 03 c 432 524 51 99. 2 0. 03 92. 0 18 13 13 100. 03 c 499 758 53 100. 03 97. 4 0 12 12 100. 03 c 880 942 60 100. 05 92. 6 10 55 55 100. 05 c 1355 1574 85 100. 05 58. 9 2 740 100. 0 0. 13 c 1908 1879 114 99. 9 0. 05 84. 7 20 300 277 98. 8 0. 07 c 2670 2747 107 98. 8 0. 11 79. 1 43 494 466 98. 9 0. 34 c 3540 3428 145 100. 0 0. 13 85. 2 29 541 486 97. 2 0. 42 c 6288 7744 29 99. 6 0. 22 85. 3 108 842 977 99. 5 7. 60 c 7552 7550 209 98. 3 0. 39 86. 0 87 904 1091 99. 4 2. 18 * Core 2 Duo 2. 66 GHz 3 GB RAM Mar. 21, 2012 Zhang: Ph. D Defense 42

Need for Equivalence Identification • Some fault-pairs are functionally equivalent; not found in structural collapsing. • Exclusive test ATPG may leave many undiagnosed fault pairs as aborted faults. • Many techniques have been proposed for fault equivalence identification: – Structural analysis – Exhaustive enumeration – Learning & implication – Branch & bound – Circuit transformation & symmetry identification Mar. 21, 2012 Zhang: Ph. D Defense 43

Equivalence Identification* sa 1 Extract a small logic block Faults are functionally equivalent if, exclusive test impossible, or faulty circuits identical. Dominator gate for both faults sa 0 * M. E. Amyeen, W. K. Fuchs, I. Pomeranz, and V. Boppana, “Fault Equivalence Identification in Combinational Circuits Using Implication and Evaluation Techniques, ” IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 22, no. 7, Jul. 2003. Mar. 21, 2012 Zhang: Ph. D Defense 44

Summary of Test Generation • New diagnostic test generation algorithm uses conventional tools: – Diagnostic fault simulation drops diagnosed faults; similar complexity to conventional fault simulators. – Exclusive test generation requires only single fault detection. – Fault equivalence checking is important for DC; requires effective algorithm. Mar. 21, 2012 Zhang: Ph. D Defense 45

Exclusive Test Gen. For Tran. Faults • Introduction and background • Representing a transition fault as a single stuck-at fault • Exclusive test patterns for transition faults – One and two time frame models • Experimental Results • Summary Mar. 21, 2012 Zhang: Ph. D Defense 46

Purpose • Many modern design failures behave as non-classical faults. • Most failures are timing related. • Transition fault model is widely used due to its simplicity. • There exist a need for diagnosis using the transition fault model. Mar. 21, 2012 Zhang: Ph. D Defense 47

Problem Statement and Contribution • Modeling and test generation for transition faults: – Detection of single transition faults – Exclusive tests for fault-pairs • Contribution: – A diagnostic ATPG system for transition faults using conventional fault-detection tools. Mar. 21, 2012 Zhang: Ph. D Defense 48

Examples of Transition Fault * Mar. 21, 2012 Zhang: Ph. D Defense 49

Transition Fault Test with Scan Combinational Logic Scan out SFF Scan enable SFF Scan in Mar. 21, 2012 Zhang: Ph. D Defense 50

Two Time-Frame Model • There are 2 possible ways to model a transition fault with a single stuck-at fault: – First, since most digital designs are sequential, we can use a 2 -time-frame circuit. PI PO line x 1 1 st time frame Mar. 21, 2012 2 nd time frame Zhang: Ph. D Defense 51

Detection Test Generation Detection test for xx’ slow-to-rise Useful for equivalence identification Two-time-frame Model (Simplified): PI PO x x x’ x’ y Mar. 21, 2012 s-a-1 Zhang: Ph. D Defense 52

Representation of a Transition Fault 1 0 Clock Slow to rise x x’ MFF Model: x x’ MFF init. 1 Mar. 21, 2012 Zhang: Ph. D Defense x x’ 00 00 01 00 10 10 11 11 53

Detection Test Generation Using MFF Model: PI x 0 1 MFF init. 1 x’ PO s-a-1 y Test for y sa 1 is also a test for xx’ slow to rise Mar. 21, 2012 Zhang: Ph. D Defense 54

Detection Test Generation PI x x’ PO MFF init. 1 s-a-1 y Test for y sa 1 is also a test for xx’ slow to rise Mar. 21, 2012 Zhang: Ph. D Defense 55

Single Copy Exclusive Test Generation Exclusive test for x 1 x 1’ slow-to-fall and x 2 x 2’ slow-to-rise: PI x 1 y s-a-0/1 Mar. 21, 2012 x 2 0 1 MFF init. 0 MFF init. 1 Zhang: Ph. D Defense 0 1 PO x 1’ x 2’ 56

Single Copy Exclusive Test Generation Simplified version: PO PI x 1 MFF init. 0 s-a-0/1 x 2 Mar. 21, 2012 MFF init. 1 Zhang: Ph. D Defense x 1’ x 2’ 57

DC vs. Fault-Pair Coverage – s 27 Coverage as fraction 1. 2 50 45 1 40 35 0. 8 30 0. 6 25 20 0. 4 DC 15 0. 2 Distin. FP/Total FP 10 No. of Un. FP 5 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Number of Undistinguished Fault Pairs Diagnostic Coverage Number of ATPG Vectors Mar. 21, 2012 Zhang: Ph. D Defense 58

Experimental Results Detection test Generation Circuit No. of faults s 27 Diagnostic test Generation Det. Vect. FC % Un. Flt Grp DC % Excl. Vect. 46 11 100. 0 12 52. 2 18 1 2 97. 8 s 298 482 44 79. 9 62 62. 4 34 39 4 70. 1 s 382 616 51 80. 8 82 64. 1 24 58 4 68. 5 s 1423 2364 102 92. 9 280 79. 3 106 182 5 84. 1 s 5378 6589 205 91. 2 400 82. 0 472 85 7 90. 0 s 9234 10416 377 92. 8 1219 75. 8 597 754 8 82. 1 s 13207 14600 480 89. 1 1707 70. 0 543 1392 11 74. 1 s 15850 17517 306 87. 6 1961 71. 2 486 1565 7 74. 3 s 35932 52988 75 99. 0 3737 88. 3 725 2867 4 90. 2 s 38417 47888 244 98. 4 4090 87. 5 1336 2883 8 91. 0 s 38584 56226 395 95. 7 4042 86. 7 1793 2440 7 90. 3 Mar. 21, 2012 Zhang: Ph. D Defense Un. Flt Large Grp st Grp DC % 59

Experimental Results • Results compared to a recent work* Detection test Generation s 38584 No. of faults Previous Diagnostic test Generation Det. Vect. FC % Un. Flt DC % Excl. Un. Flt Vect. DC % 1000 2120 -- 14197 97. 16* 583 12881 97. 42* 174649 This work 56226 395 95. 7 4042 86. 7 1793 2440 14841 90. 3 CPUs * Y. Higami, Y. Kurose, S. Ohno, H. Yamaoka, H. Takahashi, Y. Takamatsu, Y. Shimizu, and T. Aikyo, “Diagnostic Test Generation for Transition Faults Using a Stuck-at ATPG Tool, ” in Proc. International Test Conf. , 2009. Paper 16. 3. Mar. 21, 2012 Zhang: Ph. D Defense 60

Future Work • Implement 2 -time frame model to get higher DC. • Targeting mixed/multiple fault models. • Test set compaction using DATPG and diagnostic fault simulation: – E. g. reverse/random order simulation of generated vector set, if no new faults are detected AND no new fault groups are formed, the vector in simulation can be dropped. – Combined with ILP for further compaction. Mar. 21, 2012 Zhang: Ph. D Defense 61

Future Work • Example of exclusive test generation for a stuck-at fault and a bridging fault: a b d e c a 0 1 1 c 1 1 y Mar. 21, 2012 s-a-0 a’ d b e 1 0 e’ c’ Zhang: Ph. D Defense 62

Future Work Fault dictionary for previous example: Test Syndrome Faults 010 011 100 111 a sa 0 0 1 0 a sa 1 1 0 0 b sa 1 0 0 c sa 0 0 1 0 0 0 c sa 1 1 0 0 e sa 0 AND bridge (a, c) 0 1 1 0 1 0 Mar. 21, 2012 Zhang: Ph. D Defense 63

Summary • A diagnostic coverage metric is proposed. • A new diagnostic ATPG system for stuck-at fault is constructed. • Experimental results show their effectiveness. • Extend the DATPG system for transition fault. • Experimental results show improved DC. • Only conventional tools are used. Mar. 21, 2012 Zhang: Ph. D Defense 64

References for Some Figures Used • Acknowledgement: * http: //courses. ece. uiuc. edu/ece 543/docs/ Delay. Fault_6_per_page. pdf (Slide 49) * http: //www. sciencephoto. com/media/347881/ enlarge (Slide 47) * http: //www. ami. ac. uk/courses/topics/0268_wb/ index. html (Slide 47) * http: //materials. usask. ca/images/photos/SEM 6 Level. Cu. Chip. P 98. GIF (Slide 2) Mar. 21, 2012 Zhang: Ph. D Defense 65

Publications • Y. Zhang and V. D. Agrawal, “Reduced complexity test generation algorithms for transition fault diagnosis, ” in International Conference on Computer Design (ICCD), Oct. 2011, pp. 96 -101. • Y. Zhang and V. D. Agrawal, “A Diagnostic Test Generation System, ” in Proc. International Test Conf. , 2010. Paper 12. 3. • Y. Zhang and V. D. Agrawal, “Diagnostic Test Generation and Fault Simulation Algorithms for Transition Faults” in Proc. 20 th North Atlantic Test Workshop, May, 2011 • Y. Zhang and V. D. Agrawal, “An Algorithm for Diagnostic Fault Simulation, ” in Proc. 11 th IEEE Latin-American Workshop, 2010. • Y. Zhang and V. D. Agrawal, “A Diagnostic Test Generation System, ” in Proc. 19 th North Atlantic Test Workshop, May, 2010. • Y. Zhang and V. D. Agrawal, “A Diagnostic Test Generation System and a Coverage Metric, ” in 15 th IEEE European Test Symp. , May 2010. • Y. Zhang and V. D. Agrawal, “On Diagnostic Test Generation for Stuck-at Faults, ” in preparation. • Y. Zhang and V. D. Agrawal, “A Diagnostic ATPG System Targeting Multiple/Mixed Fault Models, ” in preparation. Mar. 21, 2012 Zhang: Ph. D Defense 66

Thank you Questions? Mar. 21, 2012 Zhang: Ph. D Defense 67