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 Functional Memory Testing Coverage Measures Needed
A multitude of fault models and test schemes proposed.
Quality of fault coverage difficult to assess.
Coverage Measures Needed
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. Functional Fault Behavior
Sensitized/desensitized by write operations.
Detected by read operations.
write
Unsensitized
Sensitized
read
Detected
1 / 0
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. Fault Model Specification
Fault models are specified as inputs, not hard-coded.
Example
Format 1
sensitization
< write op. >
< mem. pattern >
< write op. > .
< mem. pattern > .
desensitization
< write op. >
< mem. pattern >
< write op. > .
< mem. pattern > .
sensitized fault
mem. pattern
write op. 1

8. Ex.: 2-cell OR-type Bridging Fault
Operation a b
sensitization
write-1, a
write-1, b 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
write-0, b 1
write-1, a 1
write-1, b 1

9. Coverage Analysis
Simulation performed for arbitrary test sequences.
write-1,
< add. >
case: write
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. Sensitization & Desensitization
A write operation can sensitize/desensitize several faults.
Example
faults in cells y , y , y , y sensitized by write operation 1 2 3 4
active NPSF x p 2 1 4 y 1 2 3 4 3 3
transition in nbh. pattern
p , p , p , p sensitizes fault 1 2 3 4

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

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

13. 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 A B C 1 1 1 1 1 1 1 1 1 1 1 1 1 1 A C A C A C 1 1 1 1 1 1 1 1 B B B 
the pattern surrounding cell C is all 1’s
a sleeping-sickness fault is sensitized

14. Complexity NPSFs k-cell coupling faults
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. Examples of Test Algorithms
March X
March C- 1
GALPAT

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

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

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

19. Trace of Simulation for ANPSF Test
(local)

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.