Sep. 30, 2003Agrawal: ITC'031 Fault Collapsing Via Functional Dominance Vishwani D. Agrawal Rutgers University, ECE Dept., Piscataway, NJ 08854, USA

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Sep. 30, 2003Agrawal: ITC'031 Fault Collapsing Via Functional Dominance Vishwani D. Agrawal Rutgers University, ECE Dept., Piscataway, NJ 08854, USA A. V. S. S. Prasad and Madhusudan V. Atre Agere Systems, Bangalore , India International Test Conference – ITC’03 Charlotte, NC, Sep Oct. 2, 2003

Sep. 30, 2003Agrawal: ITC'032 Talk Outline Problem statement Introduction to fault collapsing Functional dominance Hierarchical fault collapsing –An example with functional dominance Larger examples –Fault collapsing –ATPG Conclusion

Sep. 30, 2003Agrawal: ITC'033 Problem Statement Reduce the collapsed fault set below 40-60% level – to about 25%. Outline of method: –Use hierarchical fault collapsing (ITC’02) –Use functional dominance

Sep. 30, 2003Agrawal: ITC'034 Role of Fault Collapsing DUT Generate fault list Collapse fault list Generate test vectors Fault Model Required fault coverage

Sep. 30, 2003Agrawal: ITC'035 Definitions Given –T1 is set of all tests for fault F1 –T2 is set of all tests for fault F2 F1 dominates F2 F1 and F2 are equivalent T1 T2 T1=T2

Sep. 30, 2003Agrawal: ITC'036 Structural Equ. and Dom. Structural Equivalence Structural Dominance a b c a 0 a 1 b0b1b0b1 c 0 c 1 a b c a 0 a 1 b0b1b0b1 c 0 c 1

Sep. 30, 2003Agrawal: ITC'037 ISCAS’85 Circuits Circuit name Total faults Collapsed faults (collapse ratio) Equivalence*Dominance** C (0.65)16 (0.47) C (0.61)449 (0.52) C (0.76)706 (0.71) C (0.58)1210 (0.45) C (0.49)1566 (0.41) C (0.52)2318 (0.44) C (0.48)2794 (0.39) C (0.50)4500 (0.42) C (0.62)5824 (0.46) C (0.50)6134 (0.41) * Fastest, Gentest, Hitec, TetraMax **Fastest

Sep. 30, 2003Agrawal: ITC'038 Functional Dominance f1f1 f0f0 f2f2 Always 0 f 1 f 2 f 0 + f 1 f 2 f 0 = 0 T1 T2

Sep. 30, 2003Agrawal: ITC'039 Hierarchical Collapsing a e c a 0 a 1 b0 b1b0 b1 c0 c1c0 c1 d f d 0 d 1 f0 f1f0 f1 e0e1e0e1 b Total faults = 12 Structural Equivalence collapsed faults = 8 Structural Dominance collapsed faults = 6 Three tests, {00,01,10}, cover all faults

Sep. 30, 2003Agrawal: ITC'0310 AND Gate a b c a 0 a 1 b 0 b 1 c 0 c 1 a0a0 b0b0 c0c0 a1a1 b1b1 c1c1 a0a1b0b1c0c1a0a1b0b1c0c1 a0111a0111 a11a11 b0111b0111 b11b11 c0111c0111 c1111c1111 Dominance graph Dominance matrix

Sep. 30, 2003Agrawal: ITC'0311 OR Gate c0c0 d0d0 f0f0 c1c1 d1d1 f1f1 c0c1d0d1f0f1c0c1d0d1f0f1 c01c01 c1111c1111 d01d01 d1111d1111 f0111f0111 f1111f1111 Dominance graph Dominance matrix c d f c 0 c 1 d 0 d 1 f 0 f 1

Sep. 30, 2003Agrawal: ITC'0312 Fanout a e c a 0 a 1 b0 b1b0 b1 c 0 c 1 d f d0 d1d0 d1 f 0 f 1 e0e1e0e1 b b0b0 d0d0 e0e0 b1b1 d1d1 e1e1 e0e1b0b1d0d1e0e1b0b1d0d1 e01e01 e11e11 b01b01 b11b11 d01d01 d11d11 Dominance graph Dominance matrix

Sep. 30, 2003Agrawal: ITC'0313 Functional Dominances e0e1b0b1c0c1d0d1f0f1e0e1b0b1c0c1d0d1f0f1 e011e011 e11111e11111 f111f111 f01f01 d111d111 f i f k f + f i f k f = 0 a 0 a 1 b 0 b 1 c 0 c 1 d 0 d 1 f 0 f 1 e 0 e 1 c11c11

Sep. 30, 2003Agrawal: ITC'0314 Dominance matrix of Circuit a0a1b0b1c0c1a0a1b0b1c0c1 a0111a0111 a11a11 b0111b0111 b11b11 c0111c0111 c1111c1111 d0d1f0f1d0d1f0f d01d01 d111111d f01111f01111 f111111f e0e1e0e1 e0111e0111 e111111e Entries in purple obtained from functional dominance expression.

Sep. 30, 2003Agrawal: ITC'0315 Transitive Closure of Dominance matrix a0a1b0b1c0c1a0a1b0b1c0c1 a0111a0111 a11a11 b0111b0111 b11b11 c0111c0111 c1111c1111 d0d1f0f1d0d1f0f d01d01 d d f f f f e0e1e0e1 e e e e Entries in orange are added in transitive closure.

Sep. 30, 2003Agrawal: ITC'0316 Dominance Fault Collapsing a0a1b0b1c0c1a0a1b0b1c0c1 a0111a0111 a11a11 b0111b0111 b11b11 c0111c0111 c1111c1111 d0d1f0f1d0d1f0f d01d01 d d f f f f e0e1e0e1 e e e e

Sep. 30, 2003Agrawal: ITC'0317 Dominance Collapsed Set a e c a 0 a 1 b0 b1b0 b1 c0 c1c0 c1 d f d0 d1d0 d1 f0 f1f0 f1 e0e1e0e1 b Total faults = 12 Structural Equivalence collapsed faults = 8 Structural Dominance collapsed faults = 6 Functional dominance collapsed faults = 4 Two tests, {01,10}, cover all faults

Sep. 30, 2003Agrawal: ITC' bit Ripple Carry Adder (RCA)

Sep. 30, 2003Agrawal: ITC'0319 XOR Cell a b c d e f g h i j k m c 0 c 1 d0d1d0d1 Functional Dom. examples: d 0 j 0, k 1 g 0

Sep. 30, 2003Agrawal: ITC'0320 Collapsed Dominance Matrix of XOR Cell a0a1b0b1c0c1d0d1m0m1a0a1b0b1c0c1d0d1m0m1 a0111a0111 a1111a1111 b0111b0111 b1111b1111 c01c01 c11c11 d01d01 d11d11 m0111m0111 m1111m x24 matrix is reduced to a 10x10 matrix. Inputs Output Collapsed faults

Sep. 30, 2003Agrawal: ITC'0321 Fault Collapsing Using Functional Dominance Circuit name All faults Number of collapsed faults Structural equivalence Functional dominance xor cell2416 (0.67)4 (0.17) Full-adder6038 (0.63)14 (0.23) 8-bit adder (0.62)112 (0.24) C499exp* (0.58)586 (0.22) * C499exp implements C1355 with XOR cells.

Sep. 30, 2003Agrawal: ITC'0322 ATPG for 8-Bit Adder Fill mode 100% coverage ATPG* vectors 290-fault struc. equ. set 112-fault func. dom. set Don’t care6549 0s3531 1s3227 Random1613 * Gentest

Sep. 30, 2003Agrawal: ITC'0323 Conclusion Functional dominances can be found for small cells and then applied via hierarchical collapsing to large circuits. With functional dominances, the number of faults for ATPG reduces to about 25%; usually gives smaller test set. Caution: fault coverage may not be correct when the collapsed fault set contains redundant faults; coverage may be evaluated for equivalence collapsed set. Reference: Prasad et al., Proc. ITC’02, pp