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Deterministic BIST

Deterministic BIST

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Deterministic BIST

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  1. Project Presentation for ELE6306 (Test des Circuits Electronics) Deterministic BIST By Amiri Amir Mohammad Professor Dr. Abdelhakim Khouas Ecole Polytechnique

  2. Deterministic BIST • Schemes To Discuss • I.DBIST Schemes Based On Reseeding of LFSR • A. General DBIST Scheme • B. Implicit Encoding (Re-ordering Of Patterns) • C. Implicit Encoding(Reordering 2Of Test cubes+ next-bit) • II.DBIST Schemes Using Internal Patterns • A. Bit-Flipping BIST (BFF) • B. Improved BFF BIST (SMF) • III.Others • SMF with Multiple Scan • DBIST with TPI Ecole Polytechnique

  3. BIST OVERVIEW • PRPG • Random patterns by LFSR with P(x) • Signature Analysis by MISR • Large number of Patterns to achieve FC • Delay & performance issues • Deterministic • Complex Algorithms • Increased Complexity for larger and complex circuits • Many patterns needed to achieve desired FC • Delay and Costly Ecole Polytechnique

  4. Deterministic BIST • What? • Improved BIST scheme • Why? • Increase FC in Scan-Based Design • Improve test application time and performance • How? • Random Patterns + Deterministic • Initiallyrandom patterns • Generated by Internal LFSR • Random resistant faults not detected • Followed by Deterministic Patterns • Generated by ATPG • Tend to detect hard-to-detect faults (random resistant) Ecole Polytechnique

  5. I. DBIST (LFSR Reseeding) • A. General Scheme • k-bit MP-LFSR Programmable • 2k distinct patterns • x primitive polynomials => x different sequences of patterns depending on initial value (seed) • ATPG-generated deterministic pattern encoded into n-bit word • q-bit => Poly. Id (2qPolynomials) • (n- q) bit => LFSR seed • m-bitScan Register Ecole Polytechnique

  6. I. DBIST (LFSR Reseeding) • Behavior • LFSR loaded with seed value • Poly ID identifies FeedBack configuration • LFSR output bits serially shifted into the Scan Register in m-clocks • Generated pattern consistent with encoded deterministic pattern • Original Test Cube - - 0 0 - - - 1 - 0 • Generated pattern 1 1 0 0 101 1 0 0 Ecole Polytechnique

  7. I. DBIST (LFSR Reseeding) • Encoding Of Test Cubes • Size of seed depends on number of carebitsin Test Cube C • carebit=> specified bit either 1 or 0, not‘x’ • A set of test cubesT = { C1, C2,…, Ci } • S(Ci) = { indice of carebits in test cube Ci} • s(Ci) = Number of carebits in test cube Ci • smax(T) = maximum number of specified bits in set T • Example: T={ C1 , C2 , C3 } • C1 = x1xx0x11xx , C2 = xxx10xx1xx, C3 = 0x1xxxx0xx • S(C1) = {2 , 3 , 5 , 8} s(C1)=4s(C2)=3 s(C3) = 3smax(T) = 4 • aiconsistentwithci • * ci = ai = (a(0). Mi )1 = (a(0).Mi-k+1 )k • Companion matrixM Ecole Polytechnique

  8. I. DBIST (LFSR Reseeding) • Encoding Of Test Cubes (continued..) • To encode C into a seed a • Solvings(C)system of non-linear equations in terms of seed variables(a0, …, ak-1) & polynomial coefficients (p0,…,pk-1 ), obtained from * • Two way to solve: • 1. Fixing seed variables, and finding the corresponding P(x) • System of non-linear equations (complex to solve) • 2. Fixing P(x), and finding seed variables • Simpler to solve • Less computation time in general • If no solution with P1(x), choose next polynomial • average # of polynomials analyzed slightly greater than one Ecole Polytechnique

  9. I. DBIST (LFSR Reseeding) • (M i-k+1 )kCalculated for each i and k • Subscript k indicates kthposition in the set of seed variablesa(0) • Example:GivenP (x) = x4 + x3 + 1 • p0=1 p1=0 p2=0 p3=1 • C = “x 1xx 0xx 11x” => S(C) = {1,2,5,8} and s(C) = 4. • For each index i in S(C), calculate a(0). Mi Ecole Polytechnique

  10. I. DBIST (LFSR Reseeding) • Only 4-bit encoding for 10 bit test cube • (4 + q)-bit stored in Memory Ecole Polytechnique

  11. I. DBIST (LFSR Reseeding) • General Scheme • Efficient Encoding • Probabilistic Analysis show Very high probability of successfull encoding with s + 4 bits ( 16 polynomial LFSR ) • Area Overhead • N Patterns => N x (s + q) bits of storage • Control Logic For configuration • Optimization possible in terms of storage area Ecole Polytechnique

  12. I. DBIST (LFSR Reseeding) • B. Implicit Encoding Scheme (1) • Modified Reseeding Scheme • Re-ordering of Test Cubes • Reduced Storage Size • No storage for poly id • Periodic Operation • Mod-p counter • p is the period of the sequence of polynomials (p feedback polynomials) • Addition of Random Patterns to complete periods • High Computational Effort Ecole Polytechnique

  13. I. DBIST (LFSR Reseeding) • B. Implicit Encoding Scheme (1) (Continued..) • Periodic Operation Example: • T = {C1, C2, C3, C4} & set of PolynomialsP(C)whereP (Ci)contains all the polynomials that can generateCi • P (C1) = {p1, p4}, P (C2) = P (C3) ={p1, p2, p3, p4} P (C4) ={p2, p3} • p1andp2can generate all the patterns • (C1, C2) by p1 ; (C3, C4) by p2 • Therefore: ( C1, C2, C3, C4 ) Implies Sequence of Polynomials (p1, p1, p2, p2) • Re-ordering : (p1, p2, p1, p2) => ( C1, C3, C2, C4 ) minimum period2 • adding random patternsto make perfect ordering not necessary (i.e counter can be stopped in last period at any time) • Can insert more polynomial from P(Ci) at the expense of AREA Ecole Polytechnique

  14. I. DBIST (LFSR Reseeding) • B. Implicit Encoding Scheme (1) (Continued..) • Issue: • achieve a re-ordering of the polynomials such that all the test cubes are covered, and so by having a sequence of polynomials with minimum period • Therefore: Need An Algorithm to reduce the list of test cubes generated by each polynomial and hence reduce period • TestCubeCompaction • To improve time of test application and the efficiency of encoding • Techniques • Simplification : Removal of Ci from T if Ci is a subsets of Cj • Merging : consistent test cubes combined such that s(mrg(C1C2…Ci))≤ s(T) is met. • Concatenation : Ci&Cj&…&Cz if s(concat(..))≤ s(T) Ecole Polytechnique

  15. I. DBIST (LFSR Reseeding) Ecole Polytechnique • B. Implicit Encoding Scheme (1) (Continued..) • TestCube Compaction (Example): • Simplification And Merging

  16. I. DBIST (LFSR Reseeding) • Only 3 encoding needed as opposed to 4. • Therefore, Reduced Encoding and consequently improved time of test application can be obtained Ecole Polytechnique • B. Implicit Encoding Scheme (1) (Continued..) • TestCube Compaction (Example..): • Concatenation

  17. I. DBIST (LFSR Reseeding) • B. Implicit Encoding Scheme (2) • Modified Reseeding Scheme • Re-ordering of Test Cubes • Reduced Storage Size • Seed grouping • Storage required for Next-bit • q-bit counter • Each state of Counter correponds to a feedback configuration • No Balancing needed in the number of seeds • (smax + 1) x N storage for N patterns Ecole Polytechnique

  18. II. DBIST Scheme Using Internal Patterns • A. Bit Flipping BIST (BFF) (Continued..) • Pattern mapping • Useless random patterns converted intodeterministic • BFF block is combinational and responsible to flip an output bit of LFSR at particular states of LFSR Ecole Polytechnique

  19. II. DBIST Scheme Using Internal Patterns • A. Bit Flipping BIST (BFF) (Continued..) • Efficient Mapping • Pr and Pd with minimumhumming distance • Minimumcost (least number of minterms) • Random PatternPr • Pr = f ( LFSR states) • On-set(Pr): Modifiable bits • Off-set(Pr): fixed bits (consistent with Pd ) • Fix-set: • On-, Off-, Fix-setscontainLFSR states • {s0, s1, …, s k-1} Ecole Polytechnique

  20. II. DBIST Scheme Using Internal Patterns • A. Bit Flipping BIST (BFF) (Continued..) • BFFfunction • Constructed iteratively starting with BFF0 ending with BFFR in R iterations • At each iterationr (0 ≤ r ≤ R ) • New Pd embeded in BFF • More Hard-to-detect faults coverd • New set of Hard-to-detect faults F identified • Final BFFR covers all faults • Fix0set of LFSR states, whose random patterns detect some faults Ecole Polytechnique

  21. II. DBIST Scheme Using Internal Patterns • A. Bit Flipping BIST (BFF) (Continued..) • Example: 3-bit LFSR, 5-bit Scan Register, F = {f1, f2, f3, f4, f5}, primitiveP (x) generating s0-s6 as below. • Assume P1 = 11xxx and P2 = 0xx1x Covering f1, f2, f3 • Fix1={s5, s6}Fix2={s3, s6}and Fix0 = Union(Fix1, Fix2} = {s3 , s5 , s6 } • BFF0 = Ø and Fix0 = {s3 , s5 , s6 } • A determinstic pattern Pd = 11 x 01 covering f4, f5 • Hence, need to mapPdonto a Pr in the list Ecole Polytechnique

  22. II. DBIST Scheme Using Internal Patterns • A. Bit Flipping BIST (BFF) (Continued..) • Example (cont..): • on-set and off-set for all Pr w.r.t (Pd = 11 x 01) • Candidates for mapping Pd:P1, P2, P4. Why notP3, P5? P1 chosen, because minimumcost (humming distance + least # of minterms ) • NewBFF= Union {BFF0, on-set (Pd, P1)} = { s0 } • NewFIX = FIX1 = Union {FIX0, on-set (Pd , P1), off-set (Pd , P1)} = {s0, s1, s3, s4, s5, s6} Ecole Polytechnique

  23. II. DBIST Scheme Using Internal Patterns • A. Bit Flipping BIST (BFF) (Continued..) • MinimizingBFF by considering s0 (on-set elements) only • New LFSR patterns => • Pd = 11 x 01 • P1=11xxxP2=0xx1x • Randomly modified Ecole Polytechnique

  24. II. DBIST Scheme Using Internal Patterns • B. Improved BFF (SMF) • Extension of BFF • Improves Area Overhead • Autocorrelation between random patterns • 1111- 0111-1011-1101-1110 • SMF = f ( LFSR states, Bit-counter bits, Pattern-counter bits) • Same procedure as BFF to get SMF function, exceptstate variables are different Ecole Polytechnique

  25. II. DBIST Scheme Using Internal Patterns • B. Improved BFF (SMF) (continued..) • Example: Given 2-bit LFSR with P(x) with states as below, test length 6, 5-bit Scan Register, and need to generate • Pd1 = “00010 , Pd2 = “00011 • Looking at the table • Minimum of 2 bits need to be modified for a chosen Pr Ecole Polytechnique

  26. II. DBIST Scheme Using Internal Patterns • B. Improved BFF (SMF) (continued..) • Example(continued.. ) • Pd1, Pd2 are similar • Pd1 maps onto P1(minimum cost) • On1 ( Pd1 , P1 )= { 000 000 01, 010 000 01} • Off1 ( Pd1 ,P1 )={ 001 000 10, 011 000 01, 100 000 10} • logic minimization similar to BFF • SMF1= {xx0 xxx x1} • covering all terms of On1 ( Pd1 , P1 )but none of Off1 ( Pd1 ,P1 ) • Fix1=Union{ On1 ( Pd1 , P1 ), Off1 ( Pd1 ,P1 )} • To map Pd2, repeated P1 (P4) is the candidate Ecole Polytechnique

  27. II. DBIST Scheme Using Internal Patterns • B. Improved BFF (SMF) (continued..) • SMF1: • With the new table, only 1-bit modification possible for mapping Pd2 • On2( Pd2 , P4)= {100 011 10} • Off 2(Pd2 , P4) = {000 011 01, 001 01110, 010 011 11, 011 011 01}and FIX2 = Union { Fix1, Off 2(Pd2 , P4), On2( Pd2 , P4)} • SMF2= {xx0 xxx x1, xx0 xx1 xx}=b0. (p0 + t0) Ecole Polytechnique

  28. II. DBIST Scheme Using Internal Patterns • B. Improved BFF (SMF) (continued..) • SMF2: • Pd1and Pd2 mapped efficiently with only two minterms Ecole Polytechnique

  29. II. DBIST Scheme Using Internal Patterns • B. Improved BFF (SMF) (continued..) • Efficiency of the SMF over PRPG • High FC compared to PRPG for • Less Area than the 32-bit register used for PRPG for the same FC • Less Area than BOTH (BFF and General) Ecole Polytechnique

  30. III. OthersSchemes • SMF with Multiple Scan • Improvement over single-scan SMF • Breaking one large scan register into several scan registers • Reduced time of test application (less FFs) • Similar Synthesis process as single scan SMF , except at logic minimization step • Patterns feed several scan paths • Pd can map onto any path Ecole Polytechnique

  31. III. OthersSchemes • DBIST Schemes • DBIST with TPI • BFFcombined with TPI (Test point insertion) • Improves • Random testability • Controllability and Observability • 100% FC achieved with less area Ecole Polytechnique

  32. VI. Conclusion • DBIST Schemes • Reseeding of LFSR • General DBIST Scheme • High FC • Efficient Encoding ( Less computational effort for encoding of seeds) • Storage Area Overhead (seed + poly id ) • Implicit Encoding (1) • High FC • Less Storage Area ; mod-p counter needed • More Computational effort needed for encoding of seeds • Re-ordering needed + added Random Patterns for balancing • Implicit Encoding (2) • High FC • next-bit + p-bit counter (for p polynomials of LFSR) • No balancing problem, hence no random patterns need to be added Ecole Polytechnique

  33. VI. Conclusion • DBIST Schemes • Internal Pattern Generation • BFF • High FC • Pattern Mapping • Less Area Overhead (No Storage required) • Synthesis process • SMF (single scan design) • High FC • Pattern Mapping • Furthre improve BFF for area overhead ( reduced-size LFSR ) • Synthesis Process • SMF with Multiple Scan Register • improved time of test Application Ecole Polytechnique

  34. Questions? Ecole Polytechnique