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X-Alignment Techniques for Improving the Observ-

ability ofResponse Compactors

Ozgur Sinanoglu Sobeeh Almukhaizim†Math & Computer Science Department Computer Engineering Department

Kuwait University Kuwait Universityozgur@sci.kuniv.edu.kw sobeeh@eng.kuniv.edu.kw

2010 년 10 월 16 일김인수

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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.

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Properties of X-alignment tech-niques

• X-alignment hardware is fixed for a given de-sign 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 con-junction with any response compactor to ma-nipulate x-distribution in favor of the compactor

• X-alignment hardware has a small area over-head and its insertion can be seamlessly inte-grated into the conventional design flow.

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Response compaction tech-niques

Vertical Compaction Methods

Horizontal Compaction Methods

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XOR-based V-compaction

• XOR-based compaction with two parity trees

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XOR-based V-compaction with V-align

• Delaying shift-out operations in two scan chains for aligning x’s

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• Vertical Align block

ΔMAX (maximum allowable delay) = 3

XOR-based V-compaction with V-align

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Vertical Alignment of X’s

the transformation of the scan response into a map of known and un-known bits.T(c, δ) := 1 if(δ − 1)th cell of cth chain = x,

0 otherwise 0 ≤ c < num_chains, 1 ≤ δ ≤ depth

the definition of the solution variables.

dc := 1 if cth chain is delayed, 0 otherwise 0 ≤ c < num_chains

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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 = 0s1 = s4 = 1, s0 = s2 = s3 = 0

Vertical Alignment of X’s

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XOR-based H-compaction with H-align

• Horizontal Align block

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Horizontal Alignment of X’s

the rotation of scan slices into a map of known and unknown bits.

T(c, δ) := 1 if δth cell of cth chain = x, 0 otherwise 0 ≤ c < num_chains, 0 ≤ δ ≤ depth

the definition of the rotation variables.

rδ := 1 if δth chain is rotated, 0 otherwise 0 ≤ δ ≤ depth

does not increase the scan depth

rotate direction : upward

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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 ∧ r3r1 = 1, r0 = r2 = r3 = 0c1 = c3 = 1, c0 = c2 = 0

Chains:

Horizontal Alignment of X’s

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2D-alignment

• Vertical Alignment

• Horizontal Alignment

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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

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• A clear advantage of aligning x’s in both directions (regardless of the or-der) 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.

2D-alignment

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Response Shaper

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X-Alignment: Random Responses

Px : unknown probability

# of observable scan cells

ΔMAX = 1

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A, B : two industrial circuits(provided by Cadence)80X196 : 80 scan chains with a scan depth of 196

# of observable scan cells

ΔMAX = 1

X-Alignment: Industrial Responses

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COST COMPARISONS ON ISCAS89 CIR-CUITS

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