Multivariate Statistical Multivariate Statistical Process Control for Fault Process Control for Fault Detection using Principal Detection using Principal

Component AnalysisComponent Analysis..

APACT Conference ’04APACT Conference ’04

BathBath

PersonnelPersonnel

Richard Southern, Richard Southern, MSc.MSc.

Trinity College Trinity College Dublin,Dublin,

Ireland.Ireland.

Craig Meskell, PhD.Craig Meskell, PhD. Trinity College Trinity College Dublin,Dublin,

Ireland.Ireland.

Peter Twigg, PhD.Peter Twigg, PhD. Manchester Manchester Metropolitan Metropolitan University, Uk.University, Uk.

Ernst-Michael Ernst-Michael Bohne, PhD.Bohne, PhD.

IBM Microelectronics IBM Microelectronics Division, Ireland.Division, Ireland.

OutlineOutline

Process Monitoring and Fault Detection Process Monitoring and Fault Detection and Isolation.and Isolation.

Implement Statistical Quality Control Implement Statistical Quality Control prog.prog.

Maximise Yield through Statistical Data Maximise Yield through Statistical Data AnalysisAnalysis

Application of RWMApplication of RWM Development of NOC modelDevelopment of NOC model Inference and ConclusionsInference and Conclusions

Real World Real World MethodologiesMethodologies

Statistical Process / Quality Control Statistical Process / Quality Control (SP/QC)(SP/QC)

Statistical process monitoring (uni & multivariate)Statistical process monitoring (uni & multivariate)

Fault Detection & Isolation (FDI)Fault Detection & Isolation (FDI) Principal Component Analysis (PCA)Principal Component Analysis (PCA)

Latent structures modelling (PLS)Latent structures modelling (PLS)

Exponentially Weighted Moving Average Exponentially Weighted Moving Average (EWMA)(EWMA) and MEWMA and MEWMA

Batchwise or Run2Run strategies (R2R)Batchwise or Run2Run strategies (R2R)

Statistical ControlStatistical Control

The objective of SPC is to minimise The objective of SPC is to minimise variation and aim to run in a ‘state of variation and aim to run in a ‘state of statistical control’.statistical control’.

Distinction between common cause (stochastic) Distinction between common cause (stochastic) variations and assignable causevariations and assignable cause

Where process is operating efficientlyWhere process is operating efficiently When product is yielding sufficientlyWhen product is yielding sufficiently

MSPC more realistic representation but MSPC more realistic representation but more complexmore complex

Performance enhancementPerformance enhancement MonitoringMonitoring ImprovementImprovement

FDIFDI

Distinguish between Distinguish between productproduct and and testtest Consistently high quality product/process Consistently high quality product/process

is a challengeis a challenge FDI schemeFDI scheme: a specific application of SPC, : a specific application of SPC,

where a distinction needs to be made where a distinction needs to be made between normal process operation and between normal process operation and faulty operation. i.e. faulty operation. i.e. bullet pt. 1bullet pt. 1

Key pointsKey points Process knowledgeProcess knowledge Fault classificationFault classification

Plant OverviewPlant Overview

IBM Microelectronics DivisionIBM Microelectronics Division Testing vendor supplied Testing vendor supplied μμchipschips Many combinations (product & process)Many combinations (product & process)

(wafer/lot/batch/tester/handler)(wafer/lot/batch/tester/handler) Large data sets (inherent redundancy)Large data sets (inherent redundancy)

This leads to the following pertinent This leads to the following pertinent question:question: Chip faultChip fault or evolving or evolving test unittest unit malfunction?? malfunction??

Batch ProcessBatch Process

Finite durationFinite duration non-linear behaviour & system dependentnon-linear behaviour & system dependent

‘‘Open loop’ wrt to product qualityOpen loop’ wrt to product quality no feedback is applied to the process to reduce error no feedback is applied to the process to reduce error

through batch runthrough batch run

3-way data structure (batch x var x time)3-way data structure (batch x var x time) Parametric and non-std data formatsParametric and non-std data formats Differing test timesDiffering test times Yield is calculated as a % of starts/goodsYield is calculated as a % of starts/goods Yield is a logical AND of test metricsYield is a logical AND of test metrics

Test MatrixTest Matrix

GOOD

GOOD

BAD

BAD

PROCESS

PR

OD

UC

TFalse Fail

Genuine Fails

Pass

Data StructureData Structure

Unusual data set, complex in natureUnusual data set, complex in nature Different data structures (HP, Different data structures (HP,

Teradyne)Teradyne) Large data matrix (avg. batch ≈ 7-10K Large data matrix (avg. batch ≈ 7-10K

cycles)cycles) ≈ ≈ 180 metrics/180 metrics/μμchip/cycle (MS/RF) chip/cycle (MS/RF)

Correlation/redundancyCorrelation/redundancy Analogue and Digital test vectorsAnalogue and Digital test vectors

PCA TheoryPCA Theory Rank reduction or data compression methodRank reduction or data compression method Singular Value Decomposition (SVD) Singular Value Decomposition (SVD) variance-covariance matrixvariance-covariance matrix

Variance - eigenvalues (Variance - eigenvalues (λλ)) Loadings - eigenvectors (PC’s) Loadings - eigenvectors (PC’s)

Linear transform equation yields scoresLinear transform equation yields scores 11stst PC has largest PC has largest λλ, sub. smaller, sub. smaller How many components? How many components? Subjective processSubjective process

Disregard Disregard λλ < 1 < 1 Scree plotsScree plots [too many = over parameterise, [too many = over parameterise,

noise]noise] 70 – 90 % var70 – 90 % var [too few = poor model, incomplete][too few = poor model, incomplete]

PCA PCA flowchartflowchart DB link

data set X (n x m)

normalisation

cov matrix

SVD

pre-processing

model eig%

score & loading vector

T2 & Q stat

MEWMA

Fault Detection

NOC ModelNOC Model Pre-process the dataPre-process the data

normalise normalise NN~(0,1)~(0,1) apply limit files (separate components)apply limit files (separate components) partition data and work with subset of known partition data and work with subset of known

goods goods SVD on subsetSVD on subset eigenvalue contribution to model eigenvalue contribution to model (≈70%)(≈70%)

Post-multiply PC’s with normal batch dataPost-multiply PC’s with normal batch data batch data normalised with model statistics batch data normalised with model statistics ((µ,µ,σσ)) model results can be used to identify shift from model results can be used to identify shift from

normalnormal

-15 -10 -5 0 5 10 15-15

-10

-5

0

5

10

Principal Component 1

Prin

cipa

l Com

pone

nt 2

NOC PC Score plot

HP Data 0905 Yield=91.65%

NOC scores

Pass Data Only

-500 0 500 1000 1500 2000 2500 3000 3500-300

-200

-100

0

100

200

300

400

Principal Component 1

Prin

cipa

l Com

pone

nt 2

Monitoring PC Score plot

HP Data 0905 Yield=91.65%

230

5106

1421

3181

4984

NOCBatch 0905

-100 -50 0 50 100

-20

-15

-10

-5

0

5

10

15

20

Principal Component 1

Prin

cipa

l Com

pone

nt 2

Monitoring PC Score plot

HP Data 0905 Yield=91.65%

4363

4874

NOCBatch 0905

Zoom of scores cluster

-50

510

-10

-5

0

5

-5

0

5

10

Principal Component 1

NOC PC Score plot

Principal Component 2

Prin

cipa

l Com

pone

nt 3

NOC

HP 1836 data NOC Model scores cluster

-3000-2000

-10000

1000

-500

0

500

1000

1500-400

-200

0

200

400

600

Principal Component 1

Monitoring PC Score plot

Principal Component 2

Prin

cipa

l Com

pone

nt 3

NOCBatch 1836

HP 1836 data NOC & Batch 1836 scores cluster

HP 1836 data NOC & Batch 1836 scores cluster

(Close Up)

t2036 statisticst2036 statistics

75% eigenvalue 75% eigenvalue contribution (14 contribution (14 PC’s)PC’s)

no. faults = 117 no. faults = 117 Batch size = 2135Batch size = 2135 NOC model shows NOC model shows

fault clustersfault clusters

1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

70

80

90

0%

11%

22%

33%

44%

55%

66%

77%

88%

99%Eigenvalue Pareto

-150 -100 -50 0 50 100 150 200-150

-100

-50

0

50

100

150

200

250NOC Scores

PC Score 1

PC

Sco

re 2

-100-50

050

100150

-100

0

100

200

-300

-200

-100

0

PC Score 1

PC Monitoring Score Chart

PC Score 2

PC

Sco

re 3

-150 -100 -50 0 50 100 150 200-150

-100

-50

0

50

100

150

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250NOC Scores

PC Score 1

PC

Sco

re 2

This fault cluster represent the same fault (8)

MEWMAMEWMA

Rational Rational The PCA is used for a preconditioning, The PCA is used for a preconditioning,

data reduction tooldata reduction tool The scores (subjective level) are used as The scores (subjective level) are used as

input to a MEWMA schemeinput to a MEWMA scheme Create single multivariate chart Create single multivariate chart Weighted average nature is sensitive to Weighted average nature is sensitive to

subtle faultssubtle faults Robust to auto correlated data, Non-Robust to auto correlated data, Non-

normal data normal data

SchematicSchematic

Product Handler TesterProductionData

DUT

DIB Test prog

DB

Yield calc

Summary Stats

Supervisory Scheme

Loop ntimes

SPCPCAMEWMA

Batch loop

ConclusionsConclusions

Process at ‘cell level’Process at ‘cell level’ Reduction of large data setsReduction of large data sets Generation of NOC modelGeneration of NOC model

Tester specific NOC modelTester specific NOC model Product specific NOC modelProduct specific NOC model

Tested with production batch dataTested with production batch data MEWMA method under developmentMEWMA method under development Single fault statistic to max. DUT FPYSingle fault statistic to max. DUT FPY

AcknowledgementsAcknowledgements

IBM Microelectronics Division, IBM Microelectronics Division, IrelandIreland

Trinity College Dublin, IrelandTrinity College Dublin, Ireland APACT 04, Bath.APACT 04, Bath.