Combinatorial Group Testing Methods for the BIST Diagnosis Problem

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Combinatorial Group Testing Methods for the BIST
Diagnosis Problem
Andrew B. Kahng
Sherief Reda
CSE ECE Departments University of CA, San
Diego La Jolla, CA 92093 abk_at_cs.ucsd.edu
CSE Department University of CA, San Diego La
Jolla, CA 92093 sreda_at_cs.ucsd.edu
Presented by Prof. C. K. Cheng
CSE Department University of CA, San Diego La
Jolla, CA 92093 kuan_at_cs.ucsd.edu
UCSD VLSI CAD Laboratory, http//vlsicad.ucsd.edu
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Outline

• Diagnosis in BIST Environments

• Combinatorial Group Testing (CGT)

• New Diagnosis Techniques

• Digging

• Multi-Stage Batching

• Doubling and Jumping

• Hybrid Techniques Batched Binary Search

• Experimental Results and Conclusions

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Diagnosis in BIST Environments
A test session applies a number of test patterns
Circuit Under Test
Generator
Scan Chain
Signature
Compactor
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Diagnosis in BIST Environments
A test session applies a number of test patterns
Circuit Under Test
fault
Generator
Scan Chain
Compactor
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Diagnosis in BIST Environments
Problem Given a faulty BIST environment,
identify faulty scan cells ( subset of scan
cells receiving faulty responses) in the minimum
amount of time.
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Outline

• Diagnosis in BIST Environments

• Combinatorial Group Testing (CGT)

• New Diagnosis Techniques

• Digging

• Multi-Stage Batching

• Doubling and Jumping

• Hybrid Techniques Batched Binary Search

• Experimental Results and Conclusions

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Combinatorial Group Testing (CGT)

• CGT Generic class of algorithms applied when
  many individuals or items are subjected to same
  test.

• CGT tests groups of items instead of individual
  items. A group tests positive (faulty) when at
  least one item in the group tests positive.

• A CGT experiment consists of (1) defining the
  groups, and (2) a diagnosis or decoding procedure
  to infer the status of items from the status of
  groups.

• We use CGT methods to improve existing diagnosis
  techniques, and as the basis of new techniques.

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Outline

• Diagnosis in BIST Environments

• Combinatorial Group Testing (CGT)

• New Diagnosis Techniques

• Digging

• Multi-Stage Batching

• Doubling and Jumping

• Hybrid Techniques Batched Binary Search

• Experimental Results and Conclusions

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New Diagnosis Techniques Digging
Binary Search
Digging
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7
9
8
3
6
11
10
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• Example Digging saves one test session over
  Binary Search

• Saves lots of diagnosis time with small number
  of faulty cells

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New Diagnosis Techniques Multi-Stage Batching

• Divide scan cells under test into groups of
  size square root of total.

• Saves lots of diagnosis time with large number
  of faulty cells

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New Diagnosis Techniques Doubling

• The number of faults is unknown

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New Diagnosis Techniques Hybrid Techniques
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Outline

• Diagnosis in BIST Environments

• Combinatorial Group Testing (CGT)

• New Diagnosis Techniques

• Digging

• Multi-Stage Batching

• Doubling and Jumping

• Hybrid Techniques Batched Binary Search

• Experimental Results and Conclusions

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Experimental Results
Rajskis Random Partitioning
A

• Diagnosis time for scan chain of length 961

Bayraktaroglus deterministic partitioning
Faults Diagnosis Literature Diagnosis Literature Diagnosis Literature Diagnosis Literature Proposed from CGT Proposed from CGT Proposed from CGT Newly Proposed Newly Proposed
Faults A B C D E F G H I
1 2 3 4 5 6 7 8 9 10 84 100 113 128 137 152 161 174 183 198 62 90 97 111 122 130 139 146 161 169 15 28 39 50 61 70 80 89 97 107 63 95 122 149 177 201 231 250 277 301 11 22 32 41 51 61 71 80 90 100 45 54 64 75 86 99 111 124 138 152 19 36 51 64 79 92 104 118 128 140 39 47 54 61 69 76 83 90 96 104 37 43 49 55 61 67 73 78 84 90
B
Toubas binary search
C
Toubas linear partitioning
D
E
Digging
Multi-Stage Batching
F
Doubling
G
Hybrid Batched-BS
H
Hybrid Batched Dig
I
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Experimental Results
Batched Digging
Doubling
Binary Search
Multi-Stage Batching

• Techniques that excel for small values of faults
  perform poorly for large values of faults and
  vice versa

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Conclusions

• We show that the BIST diagnosis problem
  corresponds to the established field of
  Combinatorial Group Testing (CGT)

• We improve on existing techniques in CGT
  literature

• We propose and adapt a number of algorithms from
  CGT to the BIST diagnosis problem

Future Work

• Competitive CGT techniques for theoretical
  benchmarking of various diagnosis techniques

• Non-adaptive diagnosis techniques using binary
  superimposed codes

• Diagnosis in the presence of unreliable tests,
  e.g., aliasing effects in compactors like
  Multiple-Input Shift Registers (MISR)