1. 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

2. 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

3. 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

4. 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-

5. 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

6. 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

7. 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.

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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

15. 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

16. May 17, 2007North Atlantic Test Workshop (NATW) 2007, May 16-18, Boxborough, Massachusetts 16 Thank You! Any questions please ?