Preliminary Application of Principal Components Analysis (PCA) to a Microchip Test Process for MS/RF Test Data.

Preliminary Application of Principal Components Analysis (PCA) to a Microchip Test Process for MS/RF Test Data. APACT Conference ’03 York

Personnel

Introduction • Dynamic test process • Batchwise testing • < cycle times • > testers, handlers • Many constituent vars. • Continuous / discrete data • Non-standard formats, dB extraction • Dependencies • Lot, batches, wafer • Platform & tester

Philosophy ‘Real World’ Methodologies: • SPC • FDI • R2R (RbR) • PCA A combination of these can be used to analyse and model a process for the purpose of quality improvement.

Quality Quality can be broken down into: • Product • ‘conformance to requirements’ • Fitness for use • Process • Monitor, control and minimise variation(s) for a given process One is controllable

Variation • Chance • Natural variation inherent in a process. Cumulative effect of many small, unavoidable causes. • Assignable • Variations in raw material, machine tools, mechanical failure and human error. These are accountable circumstances and are normally larger. These both generate process variation.

The Process Microelectronic Division • µelectronic product test facility • Pass or Fail • Yield based on test process & products • Multiple Device Under Test (DUT’s) • Multiple test cells • Large product base

Test Cell • Handler • Device Under Test (DUT) • Device Interface Board (DIB) • DIB Socket • Picker • Tester • Test Program • Pass/Fail is function of imposed limits • Of greater interest is test variation • Common Infrastructure

Data Reduction • Principal Components Analysis (PCA) • Linear data reduction technique • Explain as much variation as possible in as few components • Decorrelate vars. Transforms m correlated vars. Into m new vars. These are uncorrelated Using a matrix of Eigenvectors Transformed vars. are the PC’s of The ith PC is

PCA • Reduction of high volume data sets • Generates combinations that describe the process • 1st Principal Component (PC) accounts for max variance • Succeeding PC’s account for remaining variance • Too few – poor model, incomplete representation of the process • Too many – over parameterised, includes noise

PCA • z -m dimension projected vector • U -PCA projection vectors • x -original, d dimension data vector • m < d, usually m << d

PCA Where R -Correlation matrix  -Eigenvalue I -Identity matrix v -Eigenvector

PCA • Eigenvalues (λ) are variance of the original components • 1st PC has largestλ • 2nd PC has 2nd largest λ etc. • How many components? • Disregard λ < 1 • Scree plots • Subjective process

PCA • Latent vars can sometimes be interpreted as measures of physical characteristics of a process i.e., temp, pressure. • Var reduction can increase the sensitivity of a control scheme to assignable causes • However, PCA as a process monitoring scheme can not always detect process mean shifts

PCA • The application of PCA to SPC / R2R monitoring is increasing • Start with a reference set defining normal operation conditions, look for assignable causes • Generate a set of indicator variables that best describe the dynamics of the process • PCA is sensitive to data types

Results • From a controlled experiment, data were extracted from a MS/RF testing cell • Matlab • Data distributions • Descriptive stats. (mean, std, skew) • Parameter plots • Pass / Fail • Data reduction (PCA)

Results

Results • 178 columns of variables • Approx. 1000 cycles • Dissimilar data • Approx. 50% of variance can be explained through the initial 10 PC’s • Scree-plot showing similar trend throughout

Conclusion • Results suggest possible candidate indicators for process monitoring • Reduction in data volume helps analysis • A robust model is important • A PCA model will be applied to production data in the form of a statistical monitoring scheme, SPC & R2R

Preliminary Application of Principal Components Analysis (PCA) to a Microchip Test Process for MS/RF Test Data.