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May 17, 2007North Atlantic Test Workshop (NATW) 2007, May 16-18, Boxborough, Massachusetts 1 Nitin Yogi and Vishwani D. Agrawal Auburn University Department of ECE Auburn, AL 36849, USA Optimizing Tests for Multiple Fault Models
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May 17, 2007North Atlantic Test Workshop (NATW) 2007, May 16-18, Boxborough, Massachusetts 2 Outline Multiple fault models Importance Minimization problem Multiple Fault Model Test Minimization Minimization of total number of vectors Minimizing I DDQ measurements Results Combined ILP model Results Hybrid LP-ILP method Results Conclusion
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May 17, 2007North Atlantic Test Workshop (NATW) 2007, May 16-18, Boxborough, Massachusetts 3 Multiple Fault Models Importance Each fault model targets specific defects Sematech study (Nigh et. al. VTS’97) 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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May 17, 2007North Atlantic Test Workshop (NATW) 2007, May 16-18, Boxborough, Massachusetts 4 Conventional Test Vector Minimization (one fault model at a time) CircuitType of vecs Mentor Fastscan vectors Fault Cov. (%) Un-minimizedMinimized c3540 Stuck-at 16713096.00 I DDQ (pseudo stuck-at) 534599.09 Transition 29922996.55 Total 519404- s5378 Stuck-at 15014599.30 I DDQ (pseudo stuck-at) 717085.75 LOS 31929398.31 LOC 25624290.05 Total 796750-
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May 17, 2007North Atlantic Test Workshop (NATW) 2007, May 16-18, Boxborough, Massachusetts 5 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 { t j } – one for each vector t j = 0: drop vector ; t j = 1: select vector Set of constraints { c k } – one for each fault Example: for k th fault detected by vectors u, v and w c k : t u + t v + t w ≥ 1 Objective function Minimize ∑ t j ; j = 1 to N
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May 17, 2007North Atlantic Test Workshop (NATW) 2007, May 16-18, Boxborough, Massachusetts 6 Finding vectors for I DDQ measurements Given minimized set of ‘n’ vectors, define: Integer [0,1] variables { t j } – one for each vector t j = 0 : drop vector j ; t j = 1 : select vector j Constraints { c k } – one for each I DDQ fault Example: for k th I DDQ fault detected by vectors u, v and w c k : t u + t v + t w ≥ 1 Objective function Minimize ∑ t j ; j = 1 to n
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May 17, 2007North Atlantic Test Workshop (NATW) 2007, May 16-18, Boxborough, Massachusetts 7 Multiple fault model test minimization Circuit No. of vectors / I DDQ meas. Mentor FastscanILP OriginalOptimized Vecs / I DDQ CPU $ (s) Vecs / I DDQ c3540 Vectors51940422541 I DDQ 534539694 s5378 Vectors796750320148 I DDQ 71708414 * CPU time limit of 5000 exceeded $ SUN Sparc Ultra 10, four CPU machine with 4.0 GB shared RAM Need to further reduce I DDQ meas.
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May 17, 2007North Atlantic Test Workshop (NATW) 2007, May 16-18, Boxborough, Massachusetts 8 Combined ILP Define two integer [0, 1] variables: { t j, i j } – one for each vector ; j = 1 to N t j = 0 : drop vector j t j = 1 : select vector j i j = 0 : no I DDQ measurement for vector j i j = 1 : measure I DDQ for vector j
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May 17, 2007North Atlantic Test Workshop (NATW) 2007, May 16-18, Boxborough, Massachusetts 9 Combined ILP (cont.) Constraints {c k } For k th fault detected by vectors u, v and w c k : t u + t v + t w ≥ 1 i u + i v + i w ≥ 1 t u ≥ i u t v ≥ i v t w ≥ i w Only if j th fault is an I DDQ fault
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May 17, 2007North Atlantic Test Workshop (NATW) 2007, May 16-18, Boxborough, Massachusetts 10 Combined ILP (cont.) Objective function Minimize { ∑ t j + W × ∑ i j } N : total number of vectors t j : variables to select vectors (I DDQ or non-I DDQ ) i j : variables to select I DDQ measurements W : weighting factor How strongly to minimize I DDQ vectors j = 1 N N
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May 17, 2007North Atlantic Test Workshop (NATW) 2007, May 16-18, Boxborough, Massachusetts 11 Results – Combined ILP Ckt No. of vecs. / I DDQ meas. Two-step ILPCombined ILP Vecs / I DDQ CPU $ (s) W = 0.1W = 1W = 10 Vecs / I DDQ CPU $ (s) Vecs / I DDQ CPU $ (s) Vecs / I DDQ CPU $ (s) c3540 Vecs22541225 5044* 226 5047* 247 5047* I DDQ 39694404137 s5378 Vecs320148320 2314 326 5154* 353 5161* I DDQ 8414787364 * CPU time limit of 5000 exceeded $ SUN Sparc Ultra 10, four CPU machine with 4.0 GB shared RAM Need for reducing CPU time
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May 17, 2007North Atlantic Test Workshop (NATW) 2007, May 16-18, Boxborough, Massachusetts 12 Hybrid LP – ILP Approximate solution to ILP Algorithm: 1.All variables redefined as real [0,1] real variables (LP model) 2.Loop : 1.Solve LP 2.Round variables {t j }, {i j } to add constraints 1.Round to 0 if ( 0.0 < variables ≤ 0.1) 2.Round to 1 if ( 0.9 ≤ variables < 1.0) 3.Exit loop if no variables are rounded 3.Reconvert variables to [0,1] integers and solve ILP
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May 17, 2007North Atlantic Test Workshop (NATW) 2007, May 16-18, Boxborough, Massachusetts 13 Results - Hybrid LP - ILP minimization Ckt. No. of vecs. / I DDQ meas. Combined ILP model ILP solutionHybrid LP – ILP solution W = 0.1W = 1W = 10W = 0.1W = 1W = 10 Vecs / I DDQ CPU $ (s.) Vecs / I DDQ CPU $ (s.) Vecs / I DDQ CPU $ (s.) Vecs / I DDQ CPU $ (s.) Vecs / I DDQ CPU $ (s.) Vecs / I DDQ CPU $ (s.) c3540 Vecs 225 5044* 226 5047* 247 5047* 225 167 226 189 248 516 I DDQ 404137413934 s5378 Vecs 320 2314 326 5154* 353 5161* 320 529 326 617 353 793 I DDQ 787364807263 * CPU time limit of 5000 exceeded $ SUN Sparc Ultra 10, four CPU machine with 4.0 GB RAM shared among 4 CPUs Order of magnitude reduction in CPU time
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May 17, 2007North Atlantic Test Workshop (NATW) 2007, May 16-18, Boxborough, Massachusetts 14 How good is Hybrid Optimization? CircuitWeight (W) Minimized (vectors + W x IDDQ measurements) Lower BoundILPHybrid LP – ILP c35400.1227.94229*229.1 1257.82267*265 10499.97617*588 s53780.1326.76327.8328 1392.28399*398 10910.68993*983 * CPU time limit of 5000 exceeded
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May 17, 2007North Atlantic Test Workshop (NATW) 2007, May 16-18, Boxborough, Massachusetts 15 Conclusion Proposed technique Minimizes test vectors for multiple fault models Minimizes I DDQ measurements. Cost Trade-off Vector Length and I DDQ measurements Hybrid LP – ILP procedure reduces time complexity of the solution
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May 17, 2007North Atlantic Test Workshop (NATW) 2007, May 16-18, Boxborough, Massachusetts 16 Thank You! Any questions please ?
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