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Fault Coverage Analysis of RAM Test Algorithms. Marc Riedel McGill University, Montreal, Canada Janusz Rajski Mentor Graphics, Wilsonville, Oregon. Outline. Motivation Fault Models Methodology and Complexity Fault Simulation Results Conclusions. Motivation.

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Fault coverage analysis of ram test algorithms l.jpg
Fault Coverage Analysis of RAM Test Algorithms

Marc Riedel

McGill University, Montreal, Canada

Janusz Rajski

Mentor Graphics, Wilsonville, Oregon


Outline l.jpg
Outline

  • Motivation

  • Fault Models

  • Methodology and Complexity

  • Fault Simulation Results

  • Conclusions


Motivation l.jpg
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).


Functional cell array model l.jpg

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Functional Cell Array Model

Bit-addressable 2-D array of binary storage elements:

...

Operations: read, write-0, write-1.


Functional fault behavior l.jpg

1 / 0

Functional Fault Behavior

  • Sensitized/desensitized by write operations.

  • Detected by read operations.

write

Unsensitized

Sensitized

read

Detected

0 / 1

write


Cell array fault models l.jpg
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


Fault model specification l.jpg

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sensitized fault

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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 >


Ex 2 cell or type bridging fault l.jpg
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


Coverage analysis l.jpg
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.

.


Sensitization desensitization l.jpg

faults in cells y , y , y , y sensitized by write operation

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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


Delayed state transitions l.jpg

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:


Multiple faults l.jpg

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


Multiple faults cont l.jpg

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1

1

0

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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


Complexity l.jpg
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.


Examples of test algorithms l.jpg

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Examples of Test Algorithms

March X

March C-

GALPAT


Slide16 l.jpg

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)


Slide17 l.jpg

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)


Simulation results for galpat l.jpg

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)


Trace of simulation for anpsf test l.jpg

(local)

(local)

Trace of Simulation for ANPSF Test


Conclusions l.jpg
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.


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