Fault Coverage Analysis of RAM Test Algorithms

1. Fault Coverage Analysis of RAM Test Algorithms Marc Riedel McGill University, Montreal, Canada Janusz Rajski Mentor Graphics, Wilsonville, Oregon

2. Outline • Motivation • Fault Models • Methodology and Complexity • Fault Simulation Results • Conclusions

3. Motivation Coverage Measures Needed • Functional Memory Testing • A multitude of fault models and test schemes proposed. • Quality of fault coverage difficult to assess. • To evaluate and rank existing test algorithms: • Deterministic/regular tests. • Pseudo-random/irregular tests. • To validate new test schemes for: • Embedded memories and BIST designs. • Specialized memory architectures (e.g., multiport, FIFO).

4. ... . . . . . . . . . . . . ... Functional Cell Array Model Bit-addressable 2-D array of binary storage elements: ... Operations: read, write-0, write-1.

5. 1 / 0 Functional Fault Behavior • Sensitized/desensitized by write operations. • Detected by read operations. write Unsensitized Sensitized read Detected 0 / 1 write

6. Cell Array Fault Models Single Cell stuck-at, transition, stuck-open, data-retention idempotent, inversion, state, dynamic (2-cell and 3-cell versions) Coupling AND-type, OR-type (2-cell and 3-cell versions) Bridging active, passive, static (type I and type II neighborhoods) Neighborhood Pattern Sensitive

7. 1 0 0 1 0 1 . . . . . . 0 1 1 . . . . 0 1 sensitized fault . . mem. pattern write op. Fault Model Specification Fault models are specified as inputs, not hard-coded. Example Format sensitization < write op. > < mem. pattern > < write op. > < mem. pattern > desensitization < write op. > < mem. pattern > < write op. > < mem. pattern >

8. Ex.: 2-cell OR-type Bridging Fault Operation a b sensitization write-1, a 0 0 write-1, b 0 0 a b write-0, a 1 1 write-0, b 1 1 read to either cell returns OR(a,b) desensitization write-0, a 1 0 write-0, b 0 1 write-1, a 0 1 write-1, b 1 0

9. Coverage Analysis Simulation performed for arbitrary test sequences. case: write write-1, < add. > read, < add. > Determine which faults are sensitized or desensitized. write-0, < add. > write-1, < add. > case: read read, < add. > . . Classify all sensitized faults as covered. .

10. faults in cells y , y , y , y sensitized by write operation 1 2 3 4 p 1 x p p y 1 4 2 p y y 2 4 y 3 transition in nbh. pattern p , p , p , p sensitizes fault 4 3 1 2 Sensitization & Desensitization A write operation can sensitize/desensitize several faults. Example active NPSF 3 3

11. t . D t 1 1 1 1 1 1 D 1 0 1 1 1 1 1 1 1 1 1 1 Delayed State Transitions Sensitization/desensitization occur after a time delay Used to model retention faults, e.g., "sleeping-sickness" failures in DRAMS:

12. CFid(x and z 0 0 1 x y z CFid(y and z 1 0 1 x y z CFid(x and y 0 1 CFid(y and z x y z Multiple Faults Error masking Multiple sensitizations

13. 1 1 1 0 1 0 A C 1 1 0 B Multiple Faults (cont.) • Sensitized faults change the memory pattern. • This affects the sequence of sensitization/desensitization of other faults. Example no faults sensitized fault A sensitized fault B sensitized faults A and B sensitized 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 1 0 A C A C A C 1 1 1 1 1 1 1 1 0 B B B  the pattern surrounding cell C is all 1’s a sleeping-sickness fault is sensitized

14. Complexity with respect to the test sequence length t NPSFs with respect to the neighborhood size k k-cell coupling faults with respect to the memory size n & number of coupled cells k NPSFs: cells in physical proximity. Coupling faults:cells located anywhere in memory array.

15. 1 0 0 0 0 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 Examples of Test Algorithms March X March C- GALPAT

16. Fault Class FC (%) Fault Class FC (%) global 2-cell Type I NPSF CFid 50.0 Active 6.25 SCF 75.0 Passive 6.25 ABF 50.0 Static 15.6 local 3-cell Type II NPSF CFid 25.0 Active 0.39 SCF 100 Passive 0.39 ABF 50.0 Static 1.76 Simulation Results for March X 256-bit memory (16 rows x 16 columns)

17. Fault Class FC (%) Fault Class FC (%) global 2-cell Type I NPSF CFid 100 Active 12.5 SCF 100 Passive 12.5 ABF 100 Static 31.2 local 3-cell Type II NPSF CFid 50.0 Active 0.78 SCF 100 Passive 0.78 ABF 100 Static 3.52 Simulation Results for March C- 256-bit memory (16 rows x 16 columns)

18. Fault Class FC (%) Fault Class FC (%) global 2-cell Type I NPSF CFid 99.7 Active 11.7 SCF 100 Passive 15.6 ABF 100 Static 40.6 local 3-cell Type II NPSF CFid 48.2 Active 0.81 SCF 79.9 Passive 0.98 ABF 100 Static 4.10 Simulation Results for GALPAT 256-bit memory (16 rows x 16 columns)

19. (local) (local) Trace of Simulation for ANPSF Test

20. Conclusions • General RAM fault simulation methodology. • Library of over 25 functional fault models. • Coverage statistics for over 40 test algorithms. Application: • Evaluation of arithmetic BIST schemes for memories.