Transcript An Application of Principal Components Analysis to MS/RF

Multivariate Statistical Process
Control for Fault Detection using
Principal Component Analysis.
APACT Conference ’04
Bath
Personnel
Richard Southern, MSc.
Trinity College Dublin,
Ireland.
Craig Meskell, PhD.
Trinity College Dublin,
Ireland.
Peter Twigg, PhD.
Manchester Metropolitan
University, Uk.
Ernst-Michael Bohne, PhD. IBM Microelectronics
Division, Ireland.
Outline
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Process Monitoring and Fault Detection and
Isolation.
Implement Statistical Quality Control prog.
Maximise Yield through Statistical Data Analysis
Application of RWM
Development of NOC model
Inference and Conclusions
Real World Methodologies
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Statistical Process / Quality Control (SP/QC)
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Fault Detection & Isolation (FDI)
Principal Component Analysis (PCA)
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Statistical process monitoring (uni & multivariate)
Latent structures modelling (PLS)
Exponentially Weighted Moving Average
(EWMA) and MEWMA
Batchwise or Run2Run strategies (R2R)
Statistical Control
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The objective of SPC is to minimise variation and aim
to run in a ‘state of statistical control’.
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Distinction between common cause (stochastic) variations and
assignable cause
Where process is operating efficiently
When product is yielding sufficiently
MSPC more realistic representation but more complex
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Performance enhancement
Monitoring
Improvement
FDI
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Distinguish between product and test
Consistently high quality product/process is a challenge
FDI scheme: a specific application of SPC, where a
distinction needs to be made between normal process
operation and faulty operation. i.e. bullet pt. 1
Key points
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Process knowledge
Fault classification
Plant Overview
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IBM Microelectronics Division
Testing vendor supplied μchips
Many combinations (product & process)
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(wafer/lot/batch/tester/handler)
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Large data sets (inherent redundancy)
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This leads to the following pertinent question:
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Chip fault or evolving test unit malfunction??
Batch Process
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Finite duration
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‘Open loop’ wrt to product quality
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non-linear behaviour & system dependent
no feedback is applied to the process to reduce error through batch
run
3-way data structure (batch x var x time)
Parametric and non-std data formats
Differing test times
Yield is calculated as a % of starts/goods
Yield is a logical AND of test metrics
Test Matrix
PROCESS
Pass
PRODUCT
GOOD
GOOD
BAD
Genuine Fails
BAD
False Fail
Data Structure
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Unusual data set, complex in nature
Different data structures (HP, Teradyne)
 Large data matrix (avg. batch ≈ 7-10K cycles)
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≈ 180 metrics/μchip/cycle (MS/RF)
Correlation/redundancy
 Analogue and Digital test vectors
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PCA Theory
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Rank reduction or data compression method
Singular Value Decomposition (SVD)
variance-covariance matrix
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Variance - eigenvalues (λ)
Loadings - eigenvectors (PC’s)
Linear transform equation yields scores
1st PC has largest λ, sub. smaller
How many components? Subjective process
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Disregard λ < 1
Scree plots
70 – 90 % var
[too many = over parameterise, noise]
[too few = poor model, incomplete]
PCA flowchart
DB link
pre-processing
data set X (n x m)
normalisation
cov matrix
SVD
model eig%
score & loading vector
T2 & Q stat
MEWMA
Fault Detection
NOC Model
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Pre-process the data
normalise N~(0,1)
 apply limit files (separate components)
 partition data and work with subset of known goods
 SVD on subset
 eigenvalue contribution to model (≈70%)
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Post-multiply PC’s with normal batch data
batch data normalised with model statistics (µ,σ)
 model results can be used to identify shift from normal
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NOC PC Score plot
10
NOC scores
Principal Component 2
5
0
-5
-10
HP Data 0905 Yield=91.65%
-15
-15
-10
-5
Pass Data Only
0
5
Principal Component 1
10
15
Monitoring PC Score plot
400
300
NOC
Batch 0905
4984
1421
Principal Component 2
200
100
0
HP Data 0905 Yield=91.65%
-100
230
3181
-200
5106
-300
-500
0
500
1000
1500
2000
Principal Component 1
2500
3000
3500
Monitoring PC Score plot
20
NOC
Batch 0905
15
Zoom of scores cluster
Principal Component 2
10
5
4363
0
4874
-5
-10
-15
-20
-100
-50
0
50
Principal Component 1
100
NOC PC Score plot
NOC
Principal Component 3
10
5
HP 1836 data
NOC Model
scores cluster
0
-5
5
10
0
5
-5
Principal Component 2
0
-10
-5
Principal Component 1
Monitoring PC Score plot
NOC
Batch 1836
Principal Component 3
600
400
200
HP 1836 data
NOC &
Batch 1836
scores cluster
0
-200
-400
1500
1000
1000
0
500
-1000
0
Principal Component 2
-2000
-500
-3000
Principal Component 1
HP 1836 data
NOC &
Batch 1836
scores cluster
(Close Up)
t2036 statistics
Eigenvalue Pareto
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90
99%
80
75% eigenvalue
70
contribution (14 PC’s)
60
no. faults = 117
50
Batch size = 2135
40
NOC model shows fault 30
clusters
20
88%
10
11%
0
77%
66%
55%
44%
33%
22%
1
2
3
4
5
6
7
8
9
10
0%
NOC Scores
250
200
150
PC Score 2
100
50
0
-50
-100
-150
-150
-100
-50
0
50
PC Score 1
100
150
200
PC Monitoring Score Chart
PC Score 3
0
-100
-200
-300
200
150
100
50
0
PC Score 2
-100
-50
-100
0
PC Score 1
100
NOC Scores
250
This fault cluster
represent the
same fault (8)
200
150
PC Score 2
100
50
0
-50
-100
-150
-150
-100
-50
0
50
PC Score 1
100
150
200
MEWMA
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Rational
The PCA is used for a preconditioning, data
reduction tool
 The scores (subjective level) are used as input to a
MEWMA scheme
 Create single multivariate chart
 Weighted average nature is sensitive to subtle faults
 Robust to auto correlated data, Non-normal data
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Schematic
SPC
PCA
MEWMA
Supervisory Scheme
DUT
Batch loop
DIB
Test prog
Product
Handler
Tester
Loop
times n
Yield calc
Production
Data
DB
Summary
Stats
Conclusions
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Process at ‘cell level’
Reduction of large data sets
Generation of NOC model
Tester specific NOC model
 Product specific NOC model
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Tested with production batch data
MEWMA method under development
Single fault statistic to max. DUT FPY
Acknowledgements
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IBM Microelectronics Division, Ireland
Trinity College Dublin, Ireland
APACT 04, Bath.