X-Alignment Techniques for Improving the Observability of Response Compactors Ozgur Sinanoglu Sobeeh Almukhaizim† Math & Computer Science Department Computer Engineering Department Kuwait University 년 10 월 16 일 김인수 1

Purposes of this paper Improving the observability of response compactors. Enhancing fault detection per test pattern. Making room for more test patterns in the tester memory. –Propose X-Align technique. 2

Properties of X-alignment techniques X-alignment hardware is fixed for a given design and is independent of any test set and any fault model. X-alignment hardware can be reconfigured based on any given set of test responses. X-alignment techniques can be utilized in conjunction with any response compactor to manipulate x-distribution in favor of the compactor X-alignment hardware has a small area overhead and its insertion can be seamlessly integrated into the conventional design flow. 3

Response compaction techniques 4 Vertical Compaction Methods Horizontal Compaction Methods

XOR-based V-compaction XOR-based compaction with two parity trees 5

XOR-based V-compaction with V-align Delaying shift-out operations in two scan chains for aligning x’s 6

Vertical Align block 7 Δ MAX (maximum allowable delay) = 3 XOR-based V-compaction with V-align

Vertical Alignment of X’s 8 the transformation of the scan response into a map of known and unknown bits. T(c, δ) := 1 if(δ − 1) th cell of c th chain = x, 0 otherwise 0 ≤ c < num_chains, 1 ≤ δ ≤ depth the definition of the solution variables. dc := 1 if c th chain is delayed, 0 otherwise 0 ≤ c < num_chains

9 if the scan slice i is observable: s0 = (d0 + d0) ∧ (d1 + d1) ∧ (0 + d2) ∧ (d3 + d3) = d2 : AND clause s1 = d1 ∧ d2 ∧ d3 s2 = d0 ∧ d1 ∧ d2 ∧ d3 s3 = 0 s4 = d0 Slices : d0 = d2 = 1, d1 = d3 = 0 s1 = s4 = 1, s0 = s2 = s3 = 0 Vertical Alignment of X’s

XOR-based H-compaction with H-align Horizontal Align block 10

Horizontal Alignment of X’s 11 the rotation of scan slices into a map of known and unknown bits. T(c, δ) := 1 if δ th cell of c th chain = x, 0 otherwise 0 ≤ c < num_chains, 0 ≤ δ ≤ depth the definition of the rotation variables. rδ := 1 if δ th chain is rotated, 0 otherwise 0 ≤ δ ≤ depth does not increase the scan depth rotate direction : upward

12 if the scan chain i is observable: c0 = (r0 + r0) ∧ (r1) ∧ (r2) ∧ (r3) = r1 ∧ r2 ∧ r3 : AND clause c1 = r0 ∧ r1 ∧ r2 c2 = r0 ∧ r1 ∧ r2 c3 = r1 ∧ r2 ∧ r3 r1 = 1, r0 = r2 = r3 = 0 c1 = c3 = 1, c0 = c2 = 0 Chains: Horizontal Alignment of X’s

2D-alignment Vertical Alignment Horizontal Alignment 13

14 Without Alignment (Obs = 0) With h-align Only (Obs = 8) With v-align Only (Obs = 6) With v-align After h-Align (Obs = 10) 2D-alignment

A clear advantage of aligning x’s in both directions (regardless of the order) is that the observability level of the 2D-alignment is guaranteed to surpass, or be equal to, that when x’s are aligned in one direction only. 15 2D-alignment

Response Shaper 16

X-Alignment: Random Responses 17 Px : unknown probability # of observable scan cells Δ MAX = 1

18 A, B : two industrial circuits(provided by Cadence) 80X196 : 80 scan chains with a scan depth of 196 # of observable scan cells Δ MAX = 1 X-Alignment: Industrial Responses

COST COMPARISONS ON ISCAS89 CIRCUITS 19 TDV : Test data volume of the base case includes those of uncompressed stimuli and uncompacted responses. The reported area costs for x-align and response shaper do not include the cost of the XOR tree. 20 CHAINS, SINGLE XOR TREE