Mixed-Mode BIST for combinational circuits Main algorithms are described here

1. Survey of the Algorithms in the Column-Matching BIST MethodPetr Fišer, Hana KubátováDepartment of Computer Science and EngineeringCzech Technical UniversityKarlovo nam. 13, 121 35 Prague 2e-mail: fiserp@fel.cvut.cz, kubatova@fel.cvut.cz • Mixed-Mode BIST for combinational circuits • Main algorithms are described here • Mixed-Mode Structure • Two separate test phases: • Pseudorandom – cover the easy-to-detect faults by pseudorandom patterns produced by LFSR (unmodified) • Deterministic – generate deterministic patterns computed by ATPG. These are produced by a transformation of the LFSR vectors • Mixed-Mode BIST Design Phases • Simulate first n LFSR patterns • Determine undetected faults • Compute a test for them (APTG) • Make a decoder producing test from LFSR patterns following those n

2. Column - Matching • The Decoder = purely combinational circuit • It is being designed using the Column-Matching Algorithm • Input: • The C-Matrix = the LFSR code words • The T-Matrix = the deterministic test patterns • Output: • The Decoder logic transforming some of the C-Matrix rows to all T-Matrix rows – makes an assignment of rows • Principles of the Method • We try to implement as many Decoder outputs as simple wires - without any combinational logic • If we reorder the T-matrix vectors so that some test columns are equal to the LFSR columns, the outputs of the decoder described by these columns will be implemented as wires (we call itmatches) • No output decoder is needed for matched columns • Remaining outputs must be synthesized by some Boolean minimizer (ESPRESSO, BOOM) • Direct Matches • If i-th C-Matrix column is matched with j-th T-Matrix column, no decoder logic is needed, however, the MUX has to be present in the Switch • But - if i-th C-Matrix column is matched with i-th T-Matrix column, no MUX is needed – really just a wire! – we call it adirect match • Negative Matches • If i-th C-Matrix column is matched with j-th T-Matrix column, but having opposite values, no decoder is needed, switch = MUX+NOT • If i-th C-Matrix column is matched with i-th T-Matrix column, but having opposite values, no decoder is needed, switch = XOR • Negative (direct) matches

3. How to Do It? • How to select the columns to be matched? • It is of a key importance. But NP-hard  some heuristic needed • In fact – when # of C-Matrix columns >> # of T-matrix columns, almost any match is possible, until some threshold  we do it at random • What to do after a match is found? • The possible assignments of the rows have to be restricted. Two methods: • Decomposition into Set Systems • Initially, each of the test vectors might be assigned to any of the LFSR vectors. When an i­th T-matrix column is matched with j-th C-matrix column, all the values in these columns have to be equal. Thus, both sets of the test and LFSR vectors have to be divided into halves – the halves with the “1” and “0” values in the matched columns. Vectors belonging to the sets with equal values can be matched with each other, the others not  each match = one division, until one set is empty. Then the matching ends. • The final assignment of rows is easy – to each T-matrix row select one at random. • Blocking Matrix • Set system approach is not suitable for tests with don’t cares – the divided matrices must be repeatedly duplicated here – slow • Blocking matrix B = binary matrix, B[r, s] = 1 when r-th C-Matrix row can be assigned to the s-th T-Matrix row • Initially, all cells contain “1”s • After each match, the B matrix is “pruned” • The final assignment is not easy – NP-hard. If c1 is assigned to t1 – OK But if c1 is assigned to t4 – no solution

4. B-Matrix Assignment Algorithms Note: All the T-Matrix rows have to be assigned to some C-Matrix rows all B-Matrix columns have to be covered by rows Not a standard CP! One row covers only one column! Methods • Random Randomly select one column, then randomly select one row – just for comparison • LCLR (Least Column - Least Row) heuristic Select column with the least number of “1”s (i.e., with a small chance to be covered) and select an appropriate row with a least number of 1s to it (i.e., for other columns the most “useless” one) • Scoring matrix based heuristic Like LCLR, however more sophisticated – computes scoring matrix based on those two frequencies of 1s. Good, but slow. Comparison with Other Methods Acknowledgement This research was supported by a grant GA 102/03/0672 and MSM 212300014