Combinatorial Group Testing Methods for the BIST Diagnosis Problem

1. Combinatorial Group Testing Methods for the BIST Diagnosis Problem Andrew B. Kahng Sherief 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. 0 1 1 0 1 0 1 1 0 0 1 0 0 1 1 0 0 1 0 1 1 1 0 1 1 0 0 1 1 0 0 0 0 Diagnosis in BIST Environments A test session applies a number of test patterns Circuit Under Test Generator Scan Chain Signature Compactor

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

5. 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 Problem: Given a faulty BIST environment, identify faulty scan cells (= subset of scan cells receiving faulty responses) in the minimum amount of time.

6. 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

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

9. 6 1 2 3 4 5 6 7 8 7 8 9 10 3 4 5 6 7 8 Fault-Free Signature Faulty Signature New Diagnosis Techniques: Digging Binary Search Digging 1 2 7 9 8 3 6 11 4 5 10 • Example: Digging saves one test session over Binary Search • Saves lots of diagnosis time with small number of faulty cells

10. STAGE 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 4 5 6 7 8 9 10 11 12 13 14 15 16 3 1 2 STAGE 2 13 14 15 16 5 6 7 8 15 16 13 14 5 6 7 8 STAGE 3 8 13 14 Cell status undetermined 13 14 8 STAGE 4 Fault-Free cell 13 8 Faulty Cell 8 13 New Diagnosis Techniques: Multi-Stage Batching • Divide scan cells under test into groups of size = square root of total. • Saves lots of diagnosis time with large number of faulty cells

11. ` ` ` ` ` ` 13 14 15 7 11 4 3 2 12 2 1 1 5 3 11 13 9 6 4 5 6 7 8 9 10 10 11 12 13 14 15 8 Identify faulty cells using binary search Cell status undetermined Fault-Free cell Faulty cell New Diagnosis Techniques: Doubling • The number of faults is unknown 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

12. Phase 1: Batching 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 4 5 5 6 6 7 7 8 8 9 10 11 12 13 13 14 14 15 15 16 16 3 1 2 Phase 2: Binary Search or Digging 8 13 New Diagnosis Techniques: Hybrid Techniques

13. 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

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

15. Experimental Results Batched Digging Doubling Binary Search 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)