Matrices of Multiple Weights
for Test Response Compaction
with Unknown Values

Overview
 Introduction to test response compaction.
 Motivation.
 Compaction technique.

 Problem caused by unknown values.
 Impact on current compaction technique.

Thomas Clouqueur
COE Technical presentation
January 27 2005

 New scheme:
 Main idea.
 Properties and evaluation.

 Conclusion and Future work.

2

Need for compaction

Compaction techniqueUbiquitous Networked Media Computing: need for circuits
for intensive computation and with high reliability.
 Our focus: test VLSI circuits (processor, ASIC…)

 Example: parity check.

Complexity, desired reliability.
 Economics: fast test required (cost=1yen/sec).
Inputs:
Test stimuli

100+Testing scheme: scan.

001+011011

111

 In general, compactor characteristics are:Compactor

Real circuit during test

Circuit simulation
010

Chip

 Compaction ratio.

Outputs:
Test response Error detection capabilities.

34

Linear compactors

Unknown values

 Compactors implemented with xor trees and Unknown values (X) are circuit responses

that cannot be determined duringsimulation.

represented by matrices.

n inputs

⎛1⎜
⎜1
⎜0
⎜
⎜0
⎜1
⎜
⎜0
⎜
⎜1
⎜0
⎝

0 0 0⎞⎟
1 0 1⎟
1 0 0⎟⎟
1 1 1⎟
1 1 0 ⎟⎟0 1 0⎟⎟
0 1 1⎟
0 0 1 ⎟⎠m outputs

Scan out 1

 Sources: bus contention, unmodeled memory…

Scan out 2
Scan out 3

 Impact on compactor:

Scan out 4
Scan out 5
Scan out 6

 Masking of values fromother cells.

Circuit simulation

Scan out 70

Scan out 8Out
1

Out
2

Out
3+Out
4X

 Matrices correspond to check matrices of errorcorrecting codes.

5X

 In practice, 1% of scancells with Xs can mask
remaining 99% of scancells for compaction
ratio of 100.

61

Main idea

Properties of multiple weight matrices.

 Goal: reduce X-masking.

 In absence of Xs: same property as single weightmatrices.

 Scheme: modify the compactor matrix.
 Previously proposed matrices: single weight,

000
00
1
11

 If all the rows arei.e. every row has same number of ones.
 Observations:nonzero, different and all
the weights are odd, thenthere is guarantee ofdetection of 1,2,3 or any
odd number of errors.

 A row with small weight propagates to few outputs.
 Some scan chains produce more Xs than others.

 Idea: use multiple weights to build thecompactor matrix.

100

0

78

Properties of multiple weight matrices.

Evaluation

 In presence of Xs: different properties from Percentage of scan cells masked

single weight matrices.

 Compactor with 1600 inputs, 16 outputs.

 In presence of one X

occurring at a row with smallweight, it is guaranteed todetect one error anywhere.
 Also, if 2*weight_low <weight_high: in presence of 2Xs occurring at rows of small
weight, it is guaranteed todetect one error occurring at
row of high weight.

 90% of Xs are produced by 10% of scan

00
000
X
1
X

chains.

% of scan cells producing X values

10X

X

0.01

0.02

0.05

0.1

0.25

0.50

1.00

Single weight (7)

0.067

0.26

1.9

7.9

4283

99

Multiple weight(3,7)

0.027

0.066

0.29

1.1

8.6

36

82

910Compaction ratio

Conclusion and future work Using multiple weights can also increase the Multiple weight matrices can:compaction ratio.
 Maximum number of inputs for a given number ofoutputs:

6810

 Increase the compaction ratio.

 Future work: Evaluate the error-masking performance of

Number of outputs
4 Reduce X-masking.

12

multiple weight matrices.

14Single weight

4

20

56

252

792

3432

Multiple weight

832

128

512

2048

8192

 Evaluate the combination of error and X-masking with industrial circuits.

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