1. Pseudorandom Testability – Study of the Effect of the Generator Type Petr Fišer, Hana Kubátová Czech Technical University in Prague Dept. of Computer Science & Engineering Karlovo nám. 13, CZ-121 35, Prague 2, Czech Rep. E-mail: fiserp@fel.cvut.cz, kubatova@fel.cvut.cz

2. Outline Introduction Introduction LFSR Structure LFSR Structure Fault Coverage Statistics Fault Coverage Statistics Influence of LFSR Influence of LFSR Mixed-Mode BIST Mixed-Mode BIST Column-Matching Column-Matching BIST Design Results BIST Design Results Conclusions Conclusions

3. Introduction Most of BIST methods are based on LFSR Most of BIST methods are based on LFSR Fault coverage strictly depends on the LFSR type Fault coverage strictly depends on the LFSR type

4. LFSR Parameters: Generating polynomial Seed

5. Fault Coverage Statistics  Pseudo-Random Testability Depends on the number of hard-to-detect faults Depends on the number of hard-to-detect faults The number of pseudo-random test patterns strictly depends on the LFSR polynomial & seed The number of pseudo-random test patterns strictly depends on the LFSR polynomial & seed This number notably varies This number notably varies

6. Fault Coverage Statistics – complete fault coverage

7. Fault Coverage Statistics – non-complete fault coverage

8. Influence of the LFSR type

9. Important observation – the fault coverage capabilities are steadily distributed Important observation – the fault coverage capabilities are steadily distributed Primitive polynomials are not needed (if the period is satisfied) Primitive polynomials are not needed (if the period is satisfied) Best poly: one-tap Best poly: one-tap

10. Mixed-Mode BIST The test is divided into two phases Pseudo-Random – try to detect easy-to-detect faults Pseudo-Random – try to detect easy-to-detect faults Deterministic – generate deteterministic patterms Deterministic – generate deteterministic patterms

11. Column-Matching LFSR produces code words LFSR produces code words These have to be transformed into deterministic patterns (APTG) These have to be transformed into deterministic patterns (APTG) => Output Decoder

12. Column-Matching Mixed-Mode BIST Simulate first n LFSR patterns Determine undetected faults Compute a test for them (APTG) Make a decoder producing test from LFSR patterns > n

13. Influence of the test length benchrand / det.ud.vct.GEs c19081000 / 1000463046.5 2000 / 100019107.5 c35401000 / 1000332215 2000 / 1000887.5 5000 / 1000336 s526500 / 500211730.5 1000 / 100012114.5 2000 / 1000764.5 s8201000 / 1000702863 5000 / 500034140

14. Influence of LFSR ud.vct.GEsud.vct.GEs 19107.5331537 21919.5341633 241323.5361838 261528372040.5 261325392253 281537.5442640 281422.5462242.5 301436482444 321631522863.5 331727.5623469

15. Conclusions The effect of the LFSR type on the fault coverage was studied The effect of the LFSR type on the fault coverage was studied FC strictly depends on LFSR poly & seed FC strictly depends on LFSR poly & seed But cannot be computed But cannot be computed Primitive polynomial is not necessary Primitive polynomial is not necessary The best poly is one-tap The best poly is one-tap Shown in praxis – Column-Matching BIST Shown in praxis – Column-Matching BIST