test pattern generator is bist scan chains testgenerator compacompaccttoorrcompacompaccttoorrctor...

Test pattern generator is BISTTest pattern generator is BIST

scan chainsscan chains

TTEESSTT

GGEENNEERRAATTOORR

CCOOMMPPAACCTTOORR

ControlControl

Generators Generators

Capable of generating “good” pseudorandom test patterns• Long aperiodic sequences• No structural dependencies• Low linear dependencies

Capable of driving large number of scan chains Very simple hardware, small area Fast operational speed Easy to synthesize and analyze

Linear feedback shift registersLinear feedback shift registers A series connection of delay elements (D flip-flops)A series connection of delay elements (D flip-flops) All feedback provided by means of XOR gatesAll feedback provided by means of XOR gates The characteristic polynomial: The characteristic polynomial: xx1616 + + xx1010 + + xx77 + + xx44 + 1 + 1 Two implementationsTwo implementations

Larger fanout but smaller delayLarger fanout but smaller delay

1515 1414 1313 1212 1111 1010 99 88 77 66 55 44 33 22 11 00

00 11 22 33 44 55 66 77 88 99 1010 1111 1212 1313 1414 1515

CheckingCheckingCheckingChecking

Primitive polynomialPrimitive polynomial

11 00 00 00

An n-bit LFSR with nonzero seed generates An n-bit LFSR with nonzero seed generates m-sequencem-sequence (maximum length sequence) with period 2(maximum length sequence) with period 2nn-1-1

1 3 7 15 14 13 10 5 11 6 12 9 2 4 81 3 7 15 14 13 10 5 11 6 12 9 2 4 8

1 1 1 1 0 1 0 1 1 0 0 1 0 0 01 1 1 1 0 1 0 1 1 0 0 1 0 0 0

AbsoluteAbsoluteAbsoluteAbsolute

PrimesPrimesPrimesPrimes

Properties of m-sequenceProperties of m-sequence It consists of 2It consists of 2n-1 n-1 1s and (21s and (2n-1n-1 - 1) 0s - 1) 0s There is one pattern of n consecutive 1s and one pattern of n - 1 There is one pattern of n consecutive 1s and one pattern of n - 1

consecutive 0sconsecutive 0s Any pair comprising an m-sequence and its circularly shifted version Any pair comprising an m-sequence and its circularly shifted version

isis identical identical in 2 in 2n-1n-1 - 1 positions and - 1 positions and differdiffer in 2 in 2n-1n-1 positions positions A sum of an m-sequence and its circularly shifted version is another A sum of an m-sequence and its circularly shifted version is another

shifted version of that m-sequenceshifted version of that m-sequence

000000110000111100110011111111

00001111001100111111110000 0011

00111111110000001100001111 0011

Shifted by 8 bitsShifted by 8 bits

Shifted by 2 bitsShifted by 2 bits

Linear dependenciesLinear dependencies

a a d d

a a c c d d

a a b b c c d d

b b c c d d

a a b b c c

b b d d

a a c c

a a b b d d

c c d d

b b c c

a a b b

dd

cc

bb

aa

Cannot generatetest 111 !

1111

00

1100

11

0011

11

0000

00Only these 4Only these 4combinationscombinationsare possibleare possible

dd cc bb aa

!

Probability of linear dependencyProbability of linear dependency

Gaussian elimination can be used to determine Gaussian elimination can be used to determine linear dependencieslinear dependencies

Probability of k-bit linear dependency in m-Probability of k-bit linear dependency in m-sequence generated by an n-bit LFSR with sequence generated by an n-bit LFSR with primitive polynomialprimitive polynomial

For smaller sequences the probability may be For smaller sequences the probability may be much highermuch higher

Trinomials are particularly sensitiveTrinomials are particularly sensitive

11

00 1122222211)),,((

kk

iinn

iinn

iikknnpp

Probability of linear dependencyProbability of linear dependency

0.000001

0.00001

0.0001

0.001

0.01

0.1

1

12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 k

n = 30n = 30

......

22nn - 1 - 1nn

LFSRLFSR

Selection of polynomialSelection of polynomial

Degree: Degree: • Large enough so the states will not repeat Large enough so the states will not repeat • Large enough to reduce linear dependenciesLarge enough to reduce linear dependencies

TypeType• PrimitivePrimitive• Avoid trinomials (increased linear dependencies)Avoid trinomials (increased linear dependencies)• Use at least pentanomials or septanomialsUse at least pentanomials or septanomials

Seed valueSeed value• Selected through fault simulationSelected through fault simulation• Selected intelligently through reseedingSelected intelligently through reseeding

Two-dimensional generatorsTwo-dimensional generators

StructuralStructural

dependenciesdependencies

0011

2233

4455

6677

8899

1010

1111

......

Two-dimensional generatorsTwo-dimensional generators

PPHHAASSEE

SSHHIIFFTTEERR

PPHHAASSEE

SSHHIIFFTTEERR

0011

2233

4455

6677

8899

1010

1111

Find XOR network Find XOR network which guarantees which guarantees minimum channel minimum channel separationseparation

XOR taps selectionXOR taps selection

Determine a dual LFSRDetermine a dual LFSR Initialize it to Initialize it to 10 ... 010 ... 0 pattern pattern Run it for 2Run it for 2nn - 1 - k cycles - 1 - k cycles Read the resulting content of the dual LFSRRead the resulting content of the dual LFSR

Locations of 1s point out positions that should be included in a phase shifter to obtain a sequence shifted by k bits

!

Application of LFSR dualityApplication of LFSR duality

11 00 00 0011 00 00 00

1 0 0 11 0 0 11 1 0 11 1 0 11 1 1 11 1 1 11 1 1 01 1 1 00 1 1 10 1 1 11 0 1 01 0 1 00 1 0 10 1 0 11 0 1 11 0 1 11 1 0 01 1 0 0

ShiftShift 55 66 77 8 8 991010111112121313

11DualDualDualDual

PRPG with phase shifterPRPG with phase shifter

0011

2233

4455

6677

8899

1010

1111

............

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 20 40 60 80 100

theoretical limit

scan size

Impact on linear dependencyImpact on linear dependency

16-bit type I LFRS 16-bit type I LFRS 13 polynomials 13 polynomials 15 specified bits15 specified bits

No PSNo PS

scan: 16 50

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1 10 100 1000 10000

separation

theoretical limit

With PSWith PS

Extra fault coverageExtra fault coverage

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

s923

4

s923

4.1

s537

8

s385

84.1

s384

17

s359

32

s158

50.1

s142

3

s132

07

s132

07.1

s385

84

s158

50

No phase shifterNo phase shifter

With phaseWith phaseshiftersshifters

54 polynomials, 16-, 24- and 32-bit type I LFRSs54 polynomials, 16-, 24- and 32-bit type I LFRSs0 0 the lowest fault coverage recorded the lowest fault coverage recorded

maxmax

avg.avg.

minmin

Cellular automataCellular automata

11 11 00 11 00 11 00 11

00

00

Capable of generating m-sequences with primitive polynomials

Improved modularity (compared to LFSRs) Reduced need for phase shifters May exhibit some structural dependencies

LFSRsLFSRs

External feedback External feedback LFSLFSRRExternal feedback External feedback LFSLFSRR

Internal feedback Internal feedback LFLFSRSRInternal feedback Internal feedback LFLFSRSR

- - many levels of many levels of logiclogic - - many levels of many levels of logiclogic

- big - big fan-outfan-out - big - big fan-outfan-out

- - large gate large gate countcount - - large gate large gate countcount

Hybrid LFSR and cellular automatonHybrid LFSR and cellular automaton

Hybrid LFHybrid LFSRSRHybrid LFHybrid LFSRSR

Cellular Cellular automatonautomatonCellular Cellular automatonautomaton

- - delay and fan-outdelay and fan-out- - delay and fan-outdelay and fan-out

Ring architectureRing architecture

One sources per one destination Fast

11 + + xx44 + + xx88 + + xx1212 + + xx1717 + + xx2020 + + xx2323 + + xx2288 ++ x x3232

282828282323232320202020171717171212121288884444

Modular PRPG

SynthesisSynthesis

1 + 1 + xx1212 + + xx1414 + + xx2727 + + x x3232

1515 1414 1313 1212 1111 66991010 88 55 44 3377 22 11 00

1616 1717 1818 1919 2020 2121 2222 2323 2424 2525 2626 2727 2828 2929 3030 3131

1010

2222

1010 +12+12 == 2222 (32-12)/2(32-12)/2 ==

1010

99

2323

99 +14+14 == 2323 99 +14+14 == 2323 (32-14)/2(32-14)/2 = = 99 (32-14)/2(32-14)/2 = = 99

22

2929

22 +27+27 == 2929 22 +27+27 == 2929 (32-27)/2(32-27)/2 = = 22 (32-27)/2(32-27)/2 = = 22

Comparison summaryComparison summary

H LFSRH LFSRIF LFSRIF LFSREF LFSREF LFSR CACA RingRing

2 k + 1k + 1 (2, k +1)(2, k +1)22 33 22

loglog22kk 11 (1, log(1, log22k)k) 22 11

k k 2n - 22n - 2(k +1) / 2kk kk kk(k +1) / 2(k +1) / 2

h(x) = x n + x i + ... + x j + 1k

only for some polynomials

Fan-outFan-out

Levels of logicLevels of logic

XOR gatesXOR gates

ModularityModularity k k ****(k +1) / 2** ** ********

Reseeding of LFSRsReseeding of LFSRs

LFSRLFSRLFSRLFSR Scan chainScan chainScan chainScan chain

SeedSeedSeedSeed Test cubeTest cubeTest cubeTest cube

Identification of random Identification of random pattern resistant faults by pattern resistant faults by fault simulation of pseudo-fault simulation of pseudo-random patternsrandom patterns

Final fault grading of the test Final fault grading of the test vectors obtained from the vectors obtained from the seeds by fault simulation of seeds by fault simulation of decompressed patternsdecompressed patterns

Generation of test cubes for Generation of test cubes for random pattern resistant faults random pattern resistant faults using ATPG with dynamic using ATPG with dynamic compression, targeting several compression, targeting several faults and leaving many “don’t faults and leaving many “don’t care” inputscare” inputs

Computation of seeds by Computation of seeds by solving systems of linear solving systems of linear equations through equations through Gaussian eliminationGaussian elimination

Weighted random patternsWeighted random patterns

00 11 22 33 44 55 66 77 88 99 1010 1111

The average number of patterns The average number of patterns to detect s-a-0:to detect s-a-0:

Pseudo-random: Pseudo-random: 1/0.51/0.5-9-9 = 512 = 512

Weighted PS: 1/(1 - 2Weighted PS: 1/(1 - 2-7-7))-9-9 1.07 1.07

Placement of compactorPlacement of compactor


TTEESSTT

GGEENNEERRAATTOORR

CCOOMMPPAACCTTOORR

Requirements for Logic BISTRequirements for Logic BIST

ObjectiveObjective: reduce the volume of test data and still be able to : reduce the volume of test data and still be able to determine if the response was correctdetermine if the response was correct

simple hardware and small area tested as part of the embedded test circuitry simple software compute the signature at the speed of the test perform logarithmic compaction of data no aliasing

No scheme meets all criteria, but some come close!

Properties of ideal compactors:Properties of ideal compactors:

Requirements for deterministic testRequirements for deterministic test

Dramatically reduce volume of output test data Maintain high test quality Minimize impact on design and flow Provide in-production diagnosis

MotivationMotivation

DDeeccoommpprreessssoorr

99.99%99.99%99.99%99.99%99.99%99.99%

XXXX

XXXX

> 1> 1> 1> 1----

DiagnosisDiagnosis

>100x>100xQualityQuality

X toleranceX tolerance

QualityQuality


99.99%99.99%99.99%99.99%99.99%99.99%

QualityQuality

CompactionCompaction


> 1> 1> 1> 1----

>100x>100x



XXXX

XXXX


MotivationMotivation


DiagnosisDiagnosis

Compaction schemesCompaction schemes

Time compactors• polynomial division - signature analysis• arithmetic accumulation• various forms of counting

Space compactors• XOR trees

Finite memory compactors• Convolutional compactors• Block-based compactors

Error models and aliasingError models and aliasing

Single-bit and burst errorsSingle-bit and burst errors Equally likely errorsEqually likely errors Stationary and non-stationary independent errorsStationary and non-stationary independent errors Asymmetric errorsAsymmetric errors

Aliasing or error maskingAliasing or error masking - signature obtained from a - signature obtained from a faulty circuit is the same as that of the fault-free circuitfaulty circuit is the same as that of the fault-free circuit

00 11 22 33 44 55 66 77 88 99 1010 1111OK 0OK 0

Fault detected 1Fault detected 1

LFSR and Markov modelLFSR and Markov model

010010

011011

110110

101101

001001

100100

111111

111111 00 00 00

000000

1111

000000

100100

110110

011011

001001

100100

010010

001001

000000

00 00 0011 00 0011 11 0000 11 1100 00 1111 00 0000 11 0000 00 1100 00 00

TransientTransient

0

0.5

10 20 30 40 50

Number of patterns

Alia

sin

g p

roba

bilit

y

(primitive polynomial)p = 0.9

p = 0.8

p = 0.2

p = 0.1

h(x) = x3 + x2 + 10.4

0.3

0.2

0.1

Aliasing probabilityAliasing probability

How likely is it that a fault will generate a signature How likely is it that a fault will generate a signature identical to a fault-free signature? identical to a fault-free signature?

The Markov chain representing the compaction The Markov chain representing the compaction performed by n-bit LFSR is performed by n-bit LFSR is irreducible, aperiodicirreducible, aperiodic, and , and its transition matrix is its transition matrix is doubly stochasticdoubly stochastic. Thus the . Thus the probability that it enters any state is probability that it enters any state is

provided that a steady state has been reached.provided that a steady state has been reached.

For n = 20, p For n = 20, p 10 10-6-6 and n = 30, p and n = 30, p 10 10-9-9

2-n

Multiple Input Signature RegisterMultiple Input Signature Register

Parallel data acquisition from multiple scan chains Multiple error injections High compaction speed Simple hardware

Parallel data acquisition from multiple scan chains Multiple error injections High compaction speed Simple hardware

1515 1414 1313 1212 1111 1010 99 88 77 66 55 44 33 22 11 00

Time compactorsTime compactors

MISR – infinite memory MISR – infinite memory compactorcompactorMISR – infinite memory MISR – infinite memory compactorcompactor

Compaction ratios 108 x Unable to handle unknown states Multiple-pass complicated fault diagnosis

Space compactorsSpace compactors

Smaller compaction than time compactors Handling of unknown states

XOR XOR treetreeXOR XOR treetree


Certain minimum number of outputs required Improved diagnostic capabilities


Balanced tree is preferable


Fault cancellationFault cancellation

scanscan

scanscan

Unknown statesUnknown states

scanscan

scanscan

XXXX

XXXX

Selective space compactorsSelective space compactors

Deterministic compaction control

...

...

decoderdecoder

control

scanscan

scanscan

scanscan

scanscan

Convolutional compactor 10:1Convolutional compactor 10:1

Polynomials 3/6Polynomials 3/6

Architecture of convolutional compactor Architecture of convolutional compactor ...

...

Injector networkInjector network

Observable scan chainsObservable scan chains

2020 171171 324324 580580 920920 11361136

1212 5555 100100 164164 216216

88 2121 3636 5252 5656

sizesize 11 22 44 88 1616

66 1010 1616 2020

1010 3636 6464 100100 120120

1616 105105 196196 340340 504504 560560

3232 465465 900900 16841684 29362936 44004400

2424 253253 484484 884884 14641464 19681968

2828 351351 676676 12521252 21362136 30563056

outputsoutputs

3/M3/Mpolynomials

polynomials

3/M3/Mpolynomials

polynomials

Error maskingError masking

0.00.0 0.00.0 0.00.0 0.00.0 0.00.0

Error masking - no X statesError masking - no X states

0.00.0

44 33

0.0 + 0.0 + 11

0.0 + 0.0 + 22

……Error multiplicityError multiplicity

2i+12i+12i2i22 33 44 55 66 77 8811

……Error time spanError time span

00 11 22 33 44

……Compactor sizeCompactor size

1616 3232

Probability of 4-error maskingProbability of 4-error masking

1.00E-07

1.00E-06

1.00E-05

1.00E-04

1.00E-03

16 20 24 28 32 36 40 44 48

100x compaction100x compaction3/M polynomials3/M polynomialsError time span = 0Error time span = 0 1 output1 output 2 outputs2 outputs 4 outputs4 outputs 8 outputs8 outputs 16 outputs16 outputs 32 outputs32 outputs

Compactor sizeCompactor size

Unknown statesUnknown states

XX

Single error detected in the Single error detected in the

presence of a single X statepresence of a single X state

Diagnostic resolutionDiagnostic resolution

Errors identified by unique syndroms

Diagnostic resolution (%)Diagnostic resolution (%)

0

20

40

60

80

100

1 2 3 4 5 6

MM == 88

MM == 1212

MM == 1616

MM == 2020

MM == 2424

MM == 2828

MM == 3232MM == 4040

Error multiplicityError multiplicity

Same time injectionSame time injectionSame time injectionSame time injection

Convolutional MISRConvolutional MISR

………………

……………………

…………

Diagnostic modeDiagnostic modeDiagnostic modeDiagnostic mode0011

Go / No go testGo / No go testGo / No go testGo / No go test

ExampleExample

... Injector networkInjector network

474474

88

UnobservedUnobserved37.28%37.28%

UnobservedUnobserved37.28%37.28%

X X 0.39% 0.39%X X 0.39% 0.39%

2.5M gates2.5M gates

57K scan cells57K scan cells2.5M gates2.5M gates

57K scan cells57K scan cells......

......

......

......

Distribution of X statesDistribution of X states

...

112233445566778899

1010

474474

Majority of unknown values produced by small fraction of scan chains

5050 1001002525 7575

D.2 (2.1%)D.2 (2.1%)D.2 (2.1%)D.2 (2.1%)

95.595.5

Selective convolutional compactorSelective convolutional compactor

ConvolutionalConvolutional

compactorcompactor

...

Disabling of defective scan chains

Experimental resultsExperimental results

GatesGates

Scan cellsScan cells

Scan chainsScan chains

Unknown states (%)Unknown states (%)

No. outputsNo. outputs

DesignDesign

Compaction ratioCompaction ratio

Compactor sizeCompactor size

Unobserved cells (%) …Unobserved cells (%) …

… … with scan masking (%)with scan masking (%)

Maximum masked chainsMaximum masked chains

D.1D.1

1.6M1.6M

45K45K

9696

0.72 0.72

4 4

2424

3636

16.9616.96

4.324.32

22

2.5M2.5M

57K57K

474474

0.390.39

4 4

118.5118.5

3232

37.2837.28

1.761.76

99

D.2D.2

2.7M2.7M

138K138K

457457

0.090.09

44

114.3114.3

3232

8.518.51

5.125.12

66

D.3D.3

ConclusionsConclusions

New class of finite memory compaction schemes Dramatic compaction of test responses (100x) Flexible number of outputs (1) Good observability in presence of X states ( 95%) Direct diagnosis from compacted responses

test pattern generator is bist scan chains testgenerator compacompaccttoorrcompacompaccttoorrctor...

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