CMP238: Projeto e Teste de Sistemas VLSI

1. CMP238: Projeto e Teste de Sistemas VLSI Marcelo Lubaszewski Aula 1 - Teste PPGC - UFRGS 2005/I

2. Lecture 2 - Fault Modeling • Defects, Errors, and Faults • Why model faults? • Some real defects in VLSI and PCB • Common fault models • Stuck-at faults • Single stuck-at faults • Fault equivalence • Fault dominance and checkpoint theorem • Classes of stuck-at faults and multiple faults • Other Common Faults • Faults in FPGAs

3. Defects, Faults, and Errors • Defect: unintendent difference between the implemented HW and its intendent design • May or may not cause a system failure • Fault: representation of a defect at the abstracted function level Defect X Fault Imperfections in the HW Imperfections in the function

4. Defects, Faults, and Errors • Error: Manifestation of a fault that results in incorrect circuit (system) outputs or states • Caused by faults • Failure: Deviation of a circuit or system from its specified behavior • Fails to do what it should do • Caused by an error • Defect --> Fault ---> Error ---> Failure

5. Some Real Defects in Chips • Processing defects • Missing contact windows • Parasitic transistors • Oxide breakdown • . . . • Material defects • Bulk defects (cracks, crystal imperfections) • Surface impurities (ion migration) • . . . • Time-dependent defects • Dielectric breakdown • Electromigration • . . . • Packaging defects • Contact degradation • Seal leaks. . . Ref.: M. J. Howes and D. V. Morgan, Reliability and Degradation - Semiconductor Devices and Circuits, Wiley, 1981.

6. a 0 1 1 z 0 1 b Example • Defect: a short to ground • Fault: signal b stuck at logic 0 • Error: z has the wrong value if a = b = 1

7. a 1 1 0 z 0 1 b Example • Defect: a short to ground • Fault: signal b stuck at logic 0 • Error: z has the wrong value if a = b = 1 • But, if a = 0, fault exists, but no error!

8. Why Model Faults? • Real defects (often mechanical) too numerous and often not analyzable • A fault model identifies targets for testing • Model faults most likely to occur • Fault model limits the scope of test generation • Create tests only for the modeled faults • A fault model makes analysis possible • Associate specific defects with specific test patterns • Effectiveness measurable by experiments • Fault coverage can be computed for specific test patterns to reflect its effectiveness

9. Common Fault Models • Single stuck-at faults • Transistor open and short faults • Memory faults • PLA faults (stuck-at, cross-point, bridging) • Functional faults (processors) • Delay faults (transition, path) • Analog faults

10. Single Stuck-at Fault • Three properties define a single stuck-at fault • Only one line is faulty • The faulty line is permanently set to 0 or 1 • The fault can be at an input or output of a gate

11. Single Stuck-at Fault • Three properties define a single stuck-at fault • Only one line is faulty • The faulty line is permanently set to 0 or 1 • The fault can be at an input or output of a gate • Example: NAND gate has 3 fault sites ( ) and 6 single stuck-at faults s-a-0 fault, s-a-1 fault a 1 z 1 b

12. Single Stuck-at Fault • Three properties define a single stuck-at fault • Only one line is faulty • The faulty line is permanently set to 0 or 1 • The fault can be at an input or output of a gate • Example: NAND gate has 3 fault sites ( ) and 6 single stuck-at faults Good circuit value Faulty circuit value s-a-0 a 1 (0) 1 z 1 b 1

13. Single Stuck-at Fault • Three properties define a single stuck-at fault • Only one line is faulty • The faulty line is permanently set to 0 or 1 • The fault can be at an input or output of a gate • Example: NAND gate has 3 fault sites ( ) and 6 single stuck-at faults Good circuit value Faulty circuit value s-a-0 a 1 (0) 1 z 1 b 1 Test vector for a s-a-0 fault

14. Single Stuck-at Fault Example: XOR circuit has 12 fault sites and 24 single stuck-at faults Good circuit value j c 0 d a 1 g h 1 z i 0 1 e b 1 k f

15. Single Stuck-at Fault Example: XOR circuit has 12 fault sites and 24 single stuck-at faults Faulty circuit value Good circuit value j c 0(1) s-a-0 d a 1(0) g h 1 z i 0 1 e b 1 k f Test vector for h s-a-0 fault

16. Fault Equivalence • Fault equivalence: Two faults f1 and f2 are equivalent if all tests that detect f1 also detect f2. • If faults f1 and f2 are equivalent then the corresponding faulty functions are identical. • Fault collapsing: All single faults of a logic circuit can be divided into disjoint equivalence subsets, where all faults in a subset are mutually equivalent. A collapsed fault set contains one fault from each equivalence subset.

17. Equivalence Rules sa0 sa1 sa0 sa1 sa0 sa1 WIRE sa0 sa1 sa0 sa1 AND OR sa0 sa1 sa0 sa1 sa0 sa1 NOT sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 NAND NOR sa0 sa0 sa1 sa0 sa1 sa1 FANOUT

18. sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 Equivalence Rules sa0 sa0 sa1 sa1 WIRE AND OR sa0 sa1 NOT sa0 sa1 sa0 sa1 sa0 sa1 sa0 NAND NOR sa1 sa0 sa0 sa1 sa1 sa0 sa1 FANOUT

19. Equivalence Example sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1

20. Equivalence Example sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 16 Collapse ratio = ----- = 0.533 30

21. Equivalence Example sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1

22. Equivalence Example sa0 sa1 Faults in red removed by equivalence collapsing sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 20 Collapse ratio = ----- = 0.625 32

23. Fault Dominance • If all tests of some fault F1 detect another fault F2, then F2 is said to dominate F1. • Dominance fault collapsing: If fault F2 dominates F1, then F2 is removed from the fault list. • When dominance fault collapsing is used, it is sufficient to consider only the input faults of Boolean gates. See the next example.

24. F2 s-a-1 Dominance Example F1 s-a-1

25. F2 s-a-1 Dominance Example All tests of F2 F1 s-a-1 001 110 010 000 101 100 011 Only test of F1

26. F2 s-a-1 Dominance Example All tests of F2 F1 s-a-1 001 110 010 000 101 100 011 Only test of F1 s-a-1 s-a-1 s-a-0 s-a-1 A dominance collapsed fault set

27. Dominance Example sa1 sa0 sa1 sa1 sa1 sa0 sa0 sa1 sa1 sa1 sa0 sa1 sa1 sa1 sa0 sa1

28. Dominance Example sa1 sa0 sa1 sa1 sa1 sa0 sa0 sa1 sa1 sa1 sa0 sa1 sa1 sa1 sa0 sa1

29. Dominance Example sa1 sa0 sa1 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa1 sa0 sa0 sa1 sa1 sa1 sa0 sa1

30. Dominance Example sa1 Faults in red removed by equivalence collapsing sa0 sa1 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa0 sa1 sa1 sa0 sa0 sa1 sa1 sa1 sa0 sa1

31. Checkpoints • Primary inputs and fanout branches of a combinational circuit are called checkpoints. Total fault sites = 16

32. Checkpoints • Primary inputs and fanout branches of a combinational circuit are called checkpoints. Total fault sites = 16 Checkpoints ( ) = 10

33. Checkpoints • Primary inputs and fanout branches of a combinational circuit are called checkpoints. Total fault sites = 16 Checkpoints ( ) = 10 Checkpoint theorem: A test set that detects all single (multiple) stuck-at faults on all checkpoints of a combinational circuit, also detects all single (multiple) stuck-at faults in that circuit.

34. Why Fault Collapsing? • Memory & CPU- Time saving • To ease the burden for test generation and fault simulation in testing

35. Multiple Stuck-at Faults • A multiple stuck-at fault means that any set of lines is stuck-at some combination of (0,1) values. • The total number of single and multiple stuck-at faults in a circuit with k single fault sites is 3k-1. • A single fault test can fail to detect the target fault if another fault is also present, however, such masking of one fault by another is rare. • Statistically, single fault tests cover a very large number of multiple faults.

36. Why Single Stuck- At Fault Model? • Complexity is greatly reduced. • Many different physical defects may be modeled by the same logical single stuck- at fault. • Single stuck- at fault is technology independent • Can be applied to TTL, ECL, CMOS, etc. • Single stuck- at fault is design style independent • Gate Arrays, Standard Cell, Custom VLSI • Even when single stuck- at fault does not accurately model some physical defects, the tests derived for logic faults are still valid for most defects. • Single stuck- at tests cover a large percentage of multiple stuck- at faults.

37. Bridging Faults • Two or more normally distinct points (lines) are shorted together • Logic effect depends on technology • Wired- AND for TTL • Wired- OR for ECL • CMOS?

38. Transistor (Switch) Faults • MOS transistor is considered an ideal switch and two types of faults are modeled: • Stuck-open -- a single transistor is permanently stuck in the open state. • Stuck-short -- a single transistor is permanently shorted irrespective of its gate voltage. • Detection of a stuck-open fault requires two vectors. • Detection of a stuck-short fault requires the measurement of quiescent current (IDDQ).

39. CMOS Transistor Stuck- Short • Transistor stuck- on may cause ambiguous logic level • depends on the relative impedances of the pull- up & pull- down networks • When input is low, both P and N transistors are conducting causing increased quiescent current, called IDDQ fault.

40. CMOS Transistor Stuck- OPEN • Transistor stuck- open may cause output floating.

41. Functional Faults • Fault effects modeled at a higher level than logic for function modules, such as • Decoders • Multiplexers • Adders • Counters • RAMs • ROMs

42. Functional Faults of Decoder • f( L i /L j ): Instead of line L i , Line L j is selected • f( L i /L i +L j ): In addition to L i , L j is selected • f( L i /0): None of the lines are selected

43. Memory Faults • Parametric Faults – Output Levels • Power Consumption • Noise Margin • Data Retention Time • Functional Faults • Stuck Faults in Address Register, Data Register, and Address Decoder • Cell Stuck Faults • Adjacent Cell Coupling Faults • Pattern- Sensitive Faults

44. Memory Faults • Pattern- sensitive faults: the presence of a faulty signal depends on the signal values of the nearby points • Most common in DRAMs • Adjacent cell coupling faults • Pattern sensitivity between a pair of cells

45. PLA Faults • Stuck Faults • Crosspoint Faults • Extra/ Missing Transistors • Bridging Faults • Break Faults

46. Missing Crosspoint Faults in PLA • Missing crosspoint in AND- array • Growth fault • Missing crosspoint in OR- array • Disappearance fault

47. Extra Crosspoint Faults in PLA • Extra crosspoint in AND- array • Shrinkage or disappearance fault • Extra crosspoint in OR- array • Appearance fault

48. Gate- Delay- Fault • Slow to rise, slow to fall • x is slow to rise when channel resistance R1 is abnormally high

49. Gate- Delay- Fault • Disadvantage: • Delay faults resulting from the sum of several small incremental delay defects may not be detected.

50. Path- Delay- Fault • Propagation delay of the path exceeds the clock interval. • The number of paths grows exponentially with the number of gates.