1. Efficient On-Line Testing of FPGAs with Provable Diagnosabilities Vinay Verma (Xilinx Inc. ) Shantanu Dutt (Univ. of Illinois at Chicago) Vishal Suthar (Univ. of Illinois at Chicago)

2. Outline Previous on-line testing methods Roving Tester (ROTE) & Bulilt-in Self Tester (BISTer) Concepts Two new BISTer architectures – –1-diagnosable BISTer-1 – –2-diagnosable BISTer-2 New fast functional testing and diagnosis: FAST- TAD Simulation results (fault coverage and fault latency) Conclusions

3. Previous On-Line Testing Methods On-line testing: Testing a (small) part of the FPGA while a circuit is executing on another part – increases system availability Fault scanning technique of [Shnidman et al., IEEE Tr. VLSI’98] that is applicable to bus-based FPGAs STAR technique of [Abramovici, et al., ITC’99] that uses a roving tester that tests part of the FPGA while the rest executes the application circuit. –Their group have presented several Built-in-Self-Testers (BISTers) with different diagnosabilities and complex adaptive diagnosis; e.g., [Abramovici, et al., ITW’00] – will be discussed later –Have also presented on-line BIST for interconnects [Stroud et al., ITW’01]

4. Roving Tester (ROTE) with Built-in-Self-Testers (BISTers) CIRCUIT ROTE BISTer Two column left spare for ROTE; one for fault reconf. ROTE roves across the FPGA ROTE concept similar to STAR at a high level Differentiation: BIST designs, fault reconfig. & incr. re-routing techniques SPARE COLUMN CIRCUIT SPARE COLUMN TPG - Test Pattern Generator CUT - Cells Under Test ORA - Output Response Anal. TPG CUT ORA BISTer Syndrome

5. Definitions k-diagnosability: A testing technique is said to be k-diagnosable if in the presence of any m ≤ k faulty components it can correctly identify all m faulty components among the n ≥ k components that it tests. Detailed syndrome: The detailed syndrome for a session is the 0/1 bit pattern observed at the ORA output (0 => match, 1 => mismatch) over all the test vectors of the TPG. Gross syndrome: A gross syndrome of a session is the overall pass/fail (indicated as X/√) observation over all modes of operation for that session. In other words, the gross syndrome of a session is a X (fail) if the ORA output is 1 for any input test vector and is a √ (pass), otherwise. TPG CUT ORA BISTer Syndrome

6. TPG - Test Pattern Generator CUT - Cells Under Test ORA - Output Response Analyser BISTer-0 [M. Abramovici et. al., ITC ’99] CUT ORA TPG CUT ORA CUT TPG CUT ORA A B C D A A B B C C D D CUT TPG ORA CUT A D B C (S1) (S2) (S3) (S4) Exhaustive testing of CUTs S1, S2, S3, S4 are four sessions of testing in a BISTer tile

7. S1S2S3S4 ATPGCUTORACUT BCUTTPGCUTORA CORACUTTPGCUT DCUTORACUTTPG Theorem: BISTer-0 is zero-diagnosable. Proof: The same pair of PLBs are configured as CUTs in two different sessions: PLBs A and C in S2 and S4 PLBs B and D in S1 and S3. When either PLB fails, the gross syndrome will be identical in these sessions. E.g. if A fails as a CUT only, then its gross syndrome is identical to the gross syn. of C failing as a CUT only. Hence we cannot distinguish between faulty PLBs A and C.FaultyPLBS1S2S3S4A√X √/ XX C X√X BISTer-0 [M. Abramovici et. al., ITC ’99] Thus has a complex adaptive diagnosis phase

8. Our BISTer-1 Architecture A B C D TPG ORA CUT ORACUT S1S2S3S4 Sess  PLB  TPGCUT ORA B A C D S1S2S3S4Inference √√√√ No faulty PLB X√√√ Fault not in PLB √X√√ √√X√ √√√X XX√√ Faulty C (CUT) √XX√ Faulty D (CUT) √√XX Faulty A (CUT) X√√X Faulty B (CUT) X√X√ Fault not in PLB √X√X XXX√ Faulty D √XXX Faulty A XX√X Faulty C X√XX Faulty B XXXX Fault not in PLB CUT B A C D TPG CUT ORA

9. Our BISTer-1 Architecture S1S2S3S4Inference √√√√ No faulty PLB X√√√ Fault not in PLB √X√√ √√X√ √√√X XX√√ Faulty C (CUT) √XX√ Faulty D (CUT) √√XX Faulty A (CUT) X√√X Faulty B (CUT) X√X√ Fault not in PLB √X√X XXX√ Faulty D √XXX Faulty A XX√X Faulty C X√XX Faulty B XXXX Fault not in PLB A B C D TPG ORA CUT ORACUT S1S2S3S4 Sess  PLB  CUT Theorem: BISTer-1 is 1-diagnosable Each PLB is a CUT in 2 unique sessn’s and a TPG in another unique session – this serves to uniquely identify the faulty PLB which will have a X X √ in these sessions.

10. BISTer-2 Architecture Y2 Y1 D ORA 2 C CUT TPG CUTTPG ORA 1 A B E F Y1 – output of the ORA comparing CUTs Y2 – output of the ORA comparing TPGs Theorem: BISTer-2 is 1-diagnosable Faulty PLB S1S2S3S4S5S6AX √XXXX BXX √XXX CXXX √XX DXXXX √X EXXXXX √ F √XXXXX Gross syndrome corresponding to Y1 Proof: Gross syndrome corresponding to Y1 for each faulty PLB is unique. E.g. Y1 is pass in section 2 only for faulty PLB A and no other PLB. 6 rotations => 6 sessions

11. Theorem: BISTer-2 is 2-diagnosable under the assumptions: 1. No fault masking for all detailed syndromes 2. Faulty PLBs either uniformly all fail or all pass as TPG/ORA Proof: For the case faulty PLBs fail as TPG/ORA also, possible gross syndromes (GS) are: Y1Y2 = X √ and XX Class 1: faulty pairs corresponding to GS= X √. 3 Class 1 pairs: (CUT,CUT) 2, (CUT,OR1) 1 and (OR1,CUT) 1 Class 2 includes remaining faulty pairs (GS=XX). For session S1, Class 1 includes BD 2, BC 1 and CD 1 Y2 Y1 D OR 2 C CUT TPG CUTTPG OR 1 A B E F BISTer-2 Architecture (cont.) (S1) Y2 D TPG C OR1 CUT TPGOR2 CUT A B E F (S2) Y1 Y2 Y1 D TPG C OR2 OR1CUT A B E F (S6) S1: GS = X √ => BC/CD/BD S2: GS = X √ => CD S2: GS = X X => BC/BD S6: GS = X √ => BC S6: GS = X X => BD S1: GS = X X => Class 2 pairs In S1-S6 all the faulty pairs at dist. 1 & 2 will be in Class 1 and hence will be diag. => GS’s are distinct for all dist. 1 & 2 faulty pairs dist. 3 pair dist. 1 pair Class 1 pairs CD only Class 1 pair from S1 BC only Class 1 pair from S1 Class 1 pairs dist. 2 pair

12. The detailed syndrome for a session is the 0/1 bit pattern observed at the ORA output (0 => match, 1 => mismatch) over all the test vectors of the TPG. For faulty pairs at dist. 3, i.e., pairs AD, BE and CF, G.S. of Y1Y2 = XX in all sessions. Hence they don’t fall in Class 1 and hence are not distinguishable among themselves. To distinguish these dist. 3 pairs we compare their detailed syndromes: AD: dS1 = dS3 (T-C in both sess’s), dS4 = dS6 (C-T in both) Similarly, BE: dS1 = dS5, dS2 = dS4 CF: dS2 = dS6, dS3 = dS5 These pairs are uniquely diag. except for the case when dS1 = dS3 = dS5 and dS2 = dS4 = dS6; which is a very low probability event---e.g. requires 4 v. low prob. events of the type ds(CUT, TPG) = ds(TPG, CUT) Thus all faulty pairs are diagnosable with high probability. Y2 Y1 D OR 2 C CUT TPG CUTTPG OR 1 A E F BISTer-2 Architecture (cont.) (S1) Y1 Y2 D CUT C OR1 OR2TPG A B E F (S3) B Three dist. 3 pairs

13. Fast-TAD: A Fast Functional Testing and Diagnosis In this methodology a PLB is tested only for specific functions (called operational functions) it will assume as the ROTE moves across the FPGA. A PLB X is functionally-faulty (f-faulty) if faults in X produce incorrect outputs, when X implements any of its operational functions. Property: While roving the ROTE in an FPGA either without f-faults or with reconfigured f-faults, a PLB X needs to implement at most 2 functions: its original function (when ROTE is in its initial position) and the fn. of the PLB two f-fault-free PLBs to its right. ROTE PLB in column c3 implements functions fx1 and fx3 as the ROTE moves across the FPGA. c3 c4 c5 fx1fx2 fx3fx4 c6 c7 ROTE c1 c2 c5 fx3fx4 c6 c7 fx2fx1 c1 c2 c3 c4 fx3 fx4 c5 c6 c7 ROTE c1 c2 Operational functions of c3 Advantages: Faster T&D >> yield >> availab.

14. Diagnosis in Fast-TAD (overlaid on BISTer-1) SesPLBS1S2S3S4 ATPGORACUTd1,d2CUTa1,a2 BCUTb1,b2TPGORACUTa1,a2 CCUTb1,b2CUTc1,c2TPGORA DORACUTc1,c2CUTd1,d2TPG f-faultyPLBS1S2S3S4A √X/√ X BX√ C X√ D X√ Each PLB is tested in its two operational fn. A f-faulty PLB Q config. as a TPG will have a GS of √ while Q configured as a CUT & performing its oper. functions will have GS of X. In all other cases GS is either a √ or a X √X /√ X X√ In some cases, faults in A and C ( or B and D) may not be distinguishable – a 2 nd test reqd. Require 10.t1 time versus 16.t1 if both CUTs in a session are config. both their oper fns.Ses.PLBS1(C/A)S2(B/D)ATPGCUTb1,b2 BCUTc1,c2CUTb1,b2 CCUTc1,c2ORA DORATPG FaultyPLBS1(C/A)S2(B/D)A√ BX CX D√ Theorem: Fast-TAD using BISTer-1 is 1-diagnosableSesPLBS1S2S3S4ATPGORACUTd1,d2a1,a2CUTa1,a2b1,b2 BCUTb1,b2c1,c2TPGORACUTa1,a2b1,b2 CCUTb1,b2c1,c2CUTc1,c2d1,d2TPGORA DORACUTc1,c2d1,d2CUTd1,d2a1,a2TPG

15. Simulation Environment A 32 x 32 FPGA was simulated with 3-input 1-output PLBs. Fast-TAD with BISTer-1 and STAR BISTer (enhancement of BISTer-0 with 1-diagnosability) techniques were implemented on this FPGA. The adaptive diagnosis phase of the STAR BISTer is very complex; we have simulated only the fault detection and direct diagnosis phase of the STAR BISTer (BISTer-1 has no adaptive diagnosis phase) Two types of faults (with internal fault density up to 25%) were inserted: 1. Randomly distributed faults with external faulty density up to 40% 2. Clustered faults with cluster density up to 3% Prob. of a fault around a “center” fault = k/d (k=const, d=distance) 1 2 Center faulty PLB Correlated faulty PLB Non-faulty PLB Legend:

16. Simulation of 3 x 2 STAR BISTer [M. Abramovici et, al., ITW ’00]TCTO TC TCTO TC 1-diagnosable; it can diagnose 1 fault in a 3 x 2 BISTer area (1 / 6). Each BISTer consists of 3 TPGs, 2 CUTs and 1 ORA – 6 sessions reqd. STAR moves by 2 cols Very complex adaptive diagnosis phase T – TPG, O – ORA, C – CUT BAT CDT BATCDT TBATCD BATCDT TBATCD Version of our 2 x 2 BISTer-1 w/ a 3-PLB TPG # of TPG PLBs = ratio of inps/outps in PLB => 3 TPGs for testing 3-inp 1-outp PLBs 2x3 BISTer-1: 3 TPGs, 2 CUTs & 1 ORA Basically two partially overlapped basic 2x2 BISTer-1’s – 8 sessions reqd. ROTE moves by 2 cols Result: Can diagnose up to 1 fault in every alt. col of a 2-row FPGA subarray – diagnosability is thus 1 / 4 approaching that of ideal Bister-1’s

17. Results: Fault Coverage v/s Fault Density Randomly distributed faults Clustered faults with k = 0.5 in The three values of fault density in the plot correspond to cluster densities of 1%, 2% and 3% respectively.

18. Results: Fault Latency v/s Fault Density

19. Conclusions Developed a 1-diag. (1 of 4) BISTer Developed (for the 1st time) a 2-diag. (2 of 6) – w/ high prob. -- BISTer Developed (for the 1st time) functional T&D: tests PLBs in only 2 funcs that they will perform; prev. methods performed exhaust testing Fast-TAD w/ BISTer-1 has the same diagnosability (1 of 4) for f-faults Our methods do not require adaptive diagnosis; previous techniques have complex adaptive diag. mechanisms Simulation results for Fast-TAD w/ BISTer-1: fault coverages of 96% & 92 % at fault densities of 10% & 20% resp. The previous best STAR-2x3-BISTer (non-adaptive version): coverages of 74% & 46% at these densities Much lower fault latency of Fast-TAD w/ BISTer-1 compared to that of the STAR-3x2-BISter Its high fault coverage at high flt. densities and low fault latency should prove useful for testing and diagnosing emerging tech. FPGAs (<= 90 nm, nanotechnology) that are expected to have high fault densities

21. BISTer-2 architecture Y2 Y1 D ORA 2 C CUT TPG CUTTPG ORA 1 A B E F S1S2S3S4S5S6ATPGOR2TPGCUTOR1CUT BCUTTPGOR2TPGCUTOR1 COR1CUTTPGOR2TPGCUT DCUTOR1CUTTPGOR2TPG ETPGCUTOR1CUTTPGOR2 FOR2TPGCUTOR1CUTTPG OR1 => ORA 1 (Y1) OR2 => ORA 2 (Y2) Y1 – output of the ORA comparing CUTs Y2 – output of the ORA comparing TPGs Theorem: BISTer-2 is 1-diagnosable Proof: Gross syndrome corresponding to Y1 for each faulty PLB is unique. E.g. Y1 is pass in section 2 only for faulty PLB A and no other PLB. Faulty PLB S1S2S3S4S5S6AX √XXXX BXX √XXX CXXX √XX DXXXX √X EXXXXX √ F √XXXXX Gross syndrome corresponding to Y1