Improvement of the Fault Coverage of the PseudoRandom Phase inColumnMatching BIST

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Improvement of the Fault Coverage of the
Pseudo-Random Phase in Column-Matching BIST

• Petr Fier, Hana Kubátová
• Department of Computer Science and Engineering
• Czech Technical University

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Outline

• Mixed-Mode BIST
• Pseudo-Random Fault Coverage
• Weighted Pattern Testing
• Column-Matching BIST
• Enhancing the Fault Coverage
• Conclusions

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Mixed-Mode BIST

• Generate test patterns
• Apply the patterns to the circuit
• Evaluate the response

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Mixed-Mode BIST

• Combination of pseudo-random and deterministic
  testing
• Two disjoint phases

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Pseudo-Random Fault Coverage

• The aim to cover maximum faults in the
  pseudo-random phase
• Experiments performed
• Difference between LFSR and CA
• Influence of the LFSR generating polynomial
• Influence of the LFSR generating seed

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Pseudo-Random Fault Coverage

• Influence of the LFSR Generating Polynomial on
  Fault Coverage

• Questions
• Should we use primitive polynomials?
• Does the polynomial significantly influence the
  fault coverage?
• Whats the simplest way?

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Pseudo-Random Fault Coverage

• Influence of the LFSR Generating Polynomial on
  Fault Coverage

• Answers
• Should we use primitive polynomials? No.
• Does the polynomial significantly influence the
  fault coverage? No.
• Whats the simplest way? One-tap poly.

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Pseudo-Random Fault Coverage

• Influence of the LFSR Generating Polynomial on
  Fault Coverage

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Pseudo-Random Fault Coverage

• Fault Coverage Probability

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Pseudo-Random Fault Coverage

• Fault Coverage Probability

• Conclusions
• For a low number of patterns many faults are left
  undetected, while also their number varies a lot
• When increasing the number of test patterns, the
  number of undetected faults rapidly decreases,
  while the standard deviation of this number
  decreases as well
• Good choice of a PRPG becomes very important when
  the number of the applied patterns is low

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Pseudo-Random Fault Coverage

• Cellular Automata vs. LFSRs

• Questions
• What is better?
• Is there any difference indeed?
• People say that CA are better. Really? And in
  what sense?

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Pseudo-Random Fault Coverage

• Cellular Automata vs. LFSRs

• Answers
• What is better? Hard to say
• Is there any difference indeed? Definitely.
• People say that CA are better. Really?And in
  what sense? ---gt

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Pseudo-Random Fault Coverage

• Cellular Automata vs. LFSRs

CA rule 60
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Pseudo-Random Fault Coverage

• Cellular Automata vs. LFSRs

• Mean value of the number of undetected faults is
  the same
• Standard deviation is decreased !

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Pseudo-Random Fault Coverage

• Influence of the Seed (for LFSRs and CA)

• Questions
• How important is the seed selection?

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Pseudo-Random Fault Coverage

• Influence of the Seed (for LFSRs and CA)

• Answers
• How important is the seed selection?
• VERY important. Sometimes

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Pseudo-Random Fault Coverage

• Influence of the Seed (for LFSRs and CA)

• Four experiments
• LFSR with balanced seed (random distribution of
  1s and 0s)
• CA with balanced seed
• LFSR with unbalanced seed, only one 1 value
• CA with unbalanced seed

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Pseudo-Random Fault Coverage

• Influence of the Seed (for LFSRs and CA)

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Pseudo-Random Fault Coverage

• Influence of the Seed (for LFSRs and CA)

• Conclusions
• Balanced seed almost eliminates differences
  between LFSRs and CA
• Using unbalanced seeds for LFSRs is BAD.
• Using unbalanced seeds for CA can be bad, but
  also very good, if a proper seed is selected

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Weighted Pattern Testing

• Main idea it can be advantageous in
  pseudo-random testing, when some CUT inputs have
  a certain frequency of 1s(and 0s)
• Thus we somehow modify the PRPG patterns, to
  increase/decrease the probability of occurrence
  of 1s at some outputs

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Weighted Pattern Testing

• Distribution of weights

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Column-Matching
Example
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Enhancing Pseudo-Random Fault Coverage

• Four Methods
• Repetitive Balanced LFSR Reseeding
• Repetitive Unbalanced CA Reseeding
• Test Weight-Based Wire Reordering
• Weighted Random Pattern Testing

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Enhancing Pseudo-Random Fault Coverage

• Repetitive Balanced LFSR Reseeding
• Select LFSR polynomial
• Randomly generate the seed
• Simulate fault coverage of the LFSR
• Repeat several times 2 and 3, until
• Take the best seed

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Enhancing Pseudo-Random Fault Coverage

• Repetitive Unbalanced CA Reseeding
• Select CA type
• Randomly place one 1 into all-zero seed
• Simulate fault coverage of the CA
• Repeat several times 2 and 3, until
• Take the best seed

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Enhancing Pseudo-Random Fault Coverage

• Test Weight-Based Wire Reordering
• Select CA type
• Randomly place one 1 into all-zero seed
• Compute test weights, sort them
• Compute CA weights, sort them
• Assign the CA outputs to CUT inputs, by the order
  of their weights

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Enhancing Pseudo-Random Fault Coverage

• Weighted Random Pattern Testing
• Select LFSR polynomial
• Randomly generate the seed (balanced)
• Compute test weights
• Add weight-modification logic to LFSR outputs
  (ANDs, ORs)

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Enhancing Pseudo-Random Fault Coverage

• Comparison

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Conclusions

• When LFSR is used, the one-tap one is OK
• The pseudo-random phase should be altered, so
  that maximum of faults are detected
• Four methods were examined
• But no universal method can be found