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 Process Monitoring and Fault Detection and Isolation. Process Monitoring and Fault Detection and Isolation. Implement Statistical Quality Control prog. Implement Statistical Quality Control prog. Maximise Yield through Statistical Data Analysis Maximise Yield through Statistical Data Analysis Application of RWM Application of RWM Development of NOC model Development of NOC model Inference and Conclusions Inference and Conclusions

Real World Methodologies Statistical Process / Quality Control (SP/QC) Statistical Process / Quality Control (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 (EWMA) and MEWMA Exponentially Weighted Moving Average (EWMA) and MEWMA Batchwise or Run2Run strategies (R2R) Batchwise or Run2Run strategies (R2R)

Statistical Control The objective of SPC is to minimise variation and aim to run in a ‘state of statistical control’. The objective of SPC is to minimise variation and aim to run in a ‘state of statistical control’. Distinction between common cause (stochastic) variations and assignable cause Distinction between common cause (stochastic) variations and assignable cause Where process is operating efficiently Where process is operating efficiently When product is yielding sufficiently When product is yielding sufficiently MSPC more realistic representation but more complex MSPC more realistic representation but more complex Performance enhancement Performance enhancement Monitoring Monitoring Improvement Improvement

FDI Distinguish between product and test Distinguish between product and test Consistently high quality product/process is a challenge 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 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 Key points Process knowledge Process knowledge Fault classification Fault classification

Plant Overview IBM Microelectronics Division IBM Microelectronics Division Testing vendor supplied μchips Testing vendor supplied μchips 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 question: This leads to the following pertinent question: Chip fault or evolving test unit malfunction?? Chip fault or evolving test unit malfunction??

Batch Process Finite duration Finite duration non-linear behaviour & system dependent non-linear behaviour & system dependent ‘Open loop’ wrt to product quality ‘Open loop’ wrt to product quality no feedback is applied to the process to reduce error through batch run no feedback is applied to the process to reduce error through 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 formats Parametric and non-std data formats Differing test times Differing test times Yield is calculated as a % of starts/goods Yield is calculated as a % of starts/goods Yield is a logical AND of test metrics Yield is a logical AND of test metrics

Test Matrix GOOD BAD PROCESS PRODUCT False Fail Genuine Fails Pass

Data Structure Unusual data set, complex in nature Unusual data set, complex in nature Different data structures (HP, Teradyne) Different data structures (HP, Teradyne) Large data matrix (avg. batch ≈ 7-10K cycles) Large data matrix (avg. batch ≈ 7-10K cycles) ≈ 180 metrics/μchip/cycle (MS/RF) ≈ 180 metrics/μchip/cycle (MS/RF) Correlation/redundancy Correlation/redundancy Analogue and Digital test vectors Analogue and Digital test vectors

PCA Theory Rank reduction or data compression method Rank reduction or data compression method Singular Value Decomposition (SVD) Singular Value Decomposition (SVD) variance-covariance matrix variance-covariance matrix Variance - eigenvalues (λ) Variance - eigenvalues (λ) Loadings - eigenvectors (PC’s) Loadings - eigenvectors (PC’s) Linear transform equation yields scores Linear transform equation yields scores 1 st PC has largest λ, sub. smaller 1 st PC has largest λ, sub. smaller How many components? Subjective process How many components? Subjective process Disregard λ < 1 Disregard λ < 1 Scree plots[too many = over parameterise, noise] Scree plots[too many = over parameterise, noise] 70 – 90 % var[too few = poor model, incomplete] 70 – 90 % var[too few = poor model, incomplete]

PCA flowchart DB link data set X (n x m) normalisation cov matrix SVD pre-processing model eig% score & loading vector T 2 & Q stat MEWMA Fault Detection

NOC Model Pre-process the data Pre-process the data normalise N~(0,1) normalise N~(0,1) apply limit files (separate components) apply limit files (separate components) partition data and work with subset of known goods partition data and work with subset of known goods SVD on subset SVD on subset eigenvalue contribution to model (≈70%) eigenvalue contribution to model (≈70%) Post-multiply PC’s with normal batch data Post-multiply PC’s with normal batch data batch data normalised with model statistics (µ,σ) batch data normalised with model statistics (µ,σ) model results can be used to identify shift from normal model results can be used to identify shift from normal

Pass Data Only

Zoom of scores cluster

HP 1836 data NOC Model scores cluster

HP 1836 data NOC & Batch 1836 scores cluster

(Close Up)

t2036 statistics 75% eigenvalue contribution (14 PC’s) 75% eigenvalue contribution (14 PC’s) no. faults = 117 no. faults = 117 Batch size = 2135 Batch size = 2135 NOC model shows fault clusters NOC model shows fault clusters

This fault cluster represent the same fault (8)

MEWMA Rational Rational The PCA is used for a preconditioning, data reduction tool The PCA is used for a preconditioning, data reduction tool The scores (subjective level) are used as input to a MEWMA scheme The scores (subjective level) are used as input to a MEWMA scheme Create single multivariate chart Create single multivariate chart Weighted average nature is sensitive to subtle faults Weighted average nature is sensitive to subtle faults Robust to auto correlated data, Non-normal data Robust to auto correlated data, Non-normal data

Schematic ProductHandlerTester Production Data DUTDIBTest prog DB Yield calc Summary Stats Supervisory Scheme Loop n times SPC PCA MEWMA Batch loop

Conclusions Process at ‘cell level’ Process at ‘cell level’ Reduction of large data sets Reduction of large data sets Generation of NOC model Generation of NOC model Tester specific NOC model Tester specific NOC model Product specific NOC model Product specific NOC model Tested with production batch data Tested with production batch data MEWMA method under development MEWMA method under development Single fault statistic to max. DUT FPY Single fault statistic to max. DUT FPY

Acknowledgements IBM Microelectronics Division, Ireland IBM Microelectronics Division, Ireland Trinity College Dublin, Ireland Trinity College Dublin, Ireland APACT 04, Bath. APACT 04, Bath.