Nitin Yogi and Vishwani D. Agrawal

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Optimizing Tests for Multiple Fault Models

• Nitin Yogi and Vishwani D. Agrawal
• Auburn University
• Department of ECE
• Auburn, AL 36849, USA

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Outline

• Multiple fault models
• Importance
• Minimization problem
• Multiple Fault Model Test Minimization
• Minimization of total number of vectors
• Minimizing IDDQ measurements
• Results
• Combined ILP model
• Results
• Hybrid LP-ILP method
• Results
• Conclusion

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Multiple Fault Models

• Importance
• Each fault model targets specific defects
• Sematech study (Nigh et. al. VTS97) concluded
• To detect most defects, tests for all fault
  models need to included
• Combine test sets covering different fault models
• Concatenating test sets - number of vectors grows
  rapidly
• Minimization problem
• Obtain minimized test set for considered fault
  models
• Take advantage of vectors detecting faults in
  multiple fault models
• Fault simulator/ATPG handles only one fault model
  at a time
• Need for a new minimization approach

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Conventional Test Vector Minimization (one fault
model at a time)
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Multiple Fault Model Test Minimization

• Obtain fault dictionary by fault simulations
• Determine faults detected by each vector
• F faults for all considered fault models
• N vectors generated for all considered fault
  models
• ILP test minimization
• Set of integer 0,1 variables tj one for
  each vector
• tj 0 drop vector tj 1 select vector
• Set of constraints ck one for each fault
• Example for kth fault detected by vectors u, v
  and w ck tu tv tw 1
• Objective function
• Minimize ? tj j 1 to N

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Finding vectors for IDDQ measurements

• Given minimized set of n vectors, define
• Integer 0,1 variables tj one for each
  vector
• tj 0 drop vector j tj 1 select vector j
• Constraints ck one for each IDDQ fault
• Example for kth IDDQ fault detected by vectors
  u, v and w ck tu tv tw 1
• Objective function
• Minimize ? tj j 1 to n

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Multiple fault model test minimization
CPU time limit of 5000 exceeded
Need to further reduce IDDQ meas.
SUN Sparc Ultra 10, four CPU machine with 4.0
GB shared RAM
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Combined ILP

• Define two integer 0, 1 variables
• tj , ij one for each vector j 1 to N
• tj 0 drop vector j
• tj 1 select vector j
• ij 0 no IDDQ measurement for vector j
• ij 1 measure IDDQ for vector j

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Combined ILP (cont.)

• Constraints ck
• For kth fault detected by vectors u, v and w
  ck tu tv tw 1
• iu iv iw 1 tu iu
  tv iv tw iw

Only if jth fault is an IDDQ fault
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Combined ILP (cont.)

• Objective function
• Minimize ? tj W ? ij
• N total number of vectors
• tj variables to select vectors (IDDQ or
  non-IDDQ)
• ij variables to select IDDQ measurements
• W weighting factor
• How strongly to minimize IDDQ vectors

N
N
j 1
j 1
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Results Combined ILP
CPU time limit of 5000 exceeded
Need for reducing CPU time
SUN Sparc Ultra 10, four CPU machine with 4.0
GB shared RAM
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Hybrid LP ILP

• Approximate solution to ILP
• Algorithm
• All variables redefined as real 0,1 real
  variables (LP model)
• Loop
• Solve LP
• Round variables tj , ij to add constraints
• Round to 0 if ( 0.0 lt variables 0.1)
• Round to 1 if ( 0.9 variables lt 1.0)
• Exit loop if no variables are rounded
• Reconvert variables to 0,1 integers and solve
  ILP

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Results - Hybrid LP - ILP minimization
CPU time limit of 5000 exceeded
Order of magnitude reduction in CPU time
SUN Sparc Ultra 10, four CPU machine with 4.0
GB RAM shared among 4 CPUs
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How good is Hybrid Optimization?
CPU time limit of 5000 exceeded
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Conclusion

• Proposed technique
• Minimizes test vectors for multiple fault models
• Minimizes IDDQ measurements.
• Cost Trade-off
• Vector Length and IDDQ measurements
• Hybrid LP ILP procedure reduces time complexity
  of the solution

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• Thank You!
• Any questions please ?