1. Combinatorial Group Testing Methods for the BIST Diagnosis Problem Andrew B. KahngSherief Reda CSE & ECE Departments University of CA, San Diego La Jolla, CA 92093 abk@cs.ucsd.edu CSE Department University of CA, San Diego La Jolla, CA 92093 sreda@cs.ucsd.edu Presented by Prof. C. K. Cheng CSE Department University of CA, San Diego La Jolla, CA 92093 kuan@cs.ucsd.edu UCSD VLSI CAD Laboratory, http://vlsicad.ucsd.edu

2. 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

3. Diagnosis in BIST Environments Scan Chain Circuit Under Test Compactor Generator 1 0 0 0 1 1 0 1 0 1 1 0 0 1 1 0 0 0 1 1 0 1 0 0 0 1 1 1 1 1 0 0 0 Signature A test session applies a number of test patterns

4. Scan Chain Circuit Under Test Compactor Generator 1 0 0 0 1 1 0 1 0 1 1 0 0 1 1 0 0 0 1 1 0 1 0 0 0 1 1 1 1 0 1 0 0 fault 0 1 Signature A test session applies a number of test patterns Diagnosis in BIST Environments

5. Problem: Given a faulty BIST environment, identify faulty scan cells (= subset of scan cells receiving faulty responses) in the minimum amount of time. Abstractly: Given a set of items (scan cells), some of which are faulty (faulty scan cells), identify the subset of faulty items using a tester (compactor) that gives only a Yes/No response. Diagnosis in BIST Environments

6. → Combinatorial Group Testing (CGT) → New Diagnosis Techniques: ─ Digging ─ Multi-Stage Batching ─ Doubling and Jumping ─ Hybrid Techniques: Batched Binary Search → Experimental Results and Conclusions Outline

7. Combinatorial Group Testing (CGT)  CGT tests groups of items instead of individual items. A group tests positive (faulty) when at least one item in the group tests positive.  CGT = Generic class of algorithms applied when many individuals or items are subjected to same test.  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.

8. 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 Outline

9. New Diagnosis Techniques: Digging  Saves lots of diagnosis time with small number of faulty cells 1 27 12345678 3 9 8 6 10 11 54 345678 6 8 7 10 9 Binary SearchDigging  Example: Digging saves one test session over Binary Search Faulty Signature Fault-Free Signature

10. New Diagnosis Techniques: Multi-Stage Batching 12345678910111213141516 12 3 45678910111213141516 STAGE 1 5678 13141516 8 1314 567 1516 STAGE 2 8 1314 8 13 14 STAGE 3 8 13 8 STAGE 4 Cell status undetermined Faulty Cell Fault-Free cell  Saves lots of diagnosis time with large number of faulty cells  Divide scan cells under test into groups of size = square root of total.

11. New Diagnosis Techniques: Doubling  The number of faults is unknown Cell status undetermined Faulty cell Fault-Free cell 123456789101112131415 112323 ` 4567 ` 4567 ` 891011 ` 12131415 ` 891011 ` 12131415 Identify faulty cells using binary search 1113

12. New Diagnosis Techniques: Hybrid Techniques 13141516 Phase 2: Binary Search or Digging 5678 8 13 12345678910111213141516 12 3 456789101112 Phase 1: Batching 13141516

13. 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 Outline

14. Experimental Results FaultsDiagnosis LiteratureProposed from CGT Newly Proposed ABCDEFGHI 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 A Rajski’s Random Partitioning B Bayraktaroglu’s deterministic partitioning C Touba’s binary search D Touba’s linear partitioning E Digging F Multi-Stage Batching G Doubling H Hybrid: Batched-BS I Hybrid: Batched Dig  Diagnosis time for scan chain of length 961

15. Experimental Results Batched Digging Binary Search Doubling Multi-Stage Batching  Techniques that excel for small values of faults perform poorly for large values of faults and vice versa

16. 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)