APPLICATION NOTE
Using Multivariate Models for Practical Applications
INTRODUCTION

Figure 1 PLS model comparing voltage and current®

FabGuard Integrated Process Monitor (IPM) has
supported Multivariate Analysis (MVA) techniques for anumber of years. While MVA use in the semiconductor
industry has been experimental at best, there is anever increasing desire to be able to predict metrology
and other tool values accurately enough to detectexcursions and possibly remove in situ metrology
measurements. Under controlled environments, MVA
methods such as Principal Components Analysis(PCA) and Partial Least Squares (PLS) have shownpromising results for detecting excursions andpredicting metrology.

USING PLS TO PREDICTELECTROPLATE BATH CURRENT
Given constant bath chemistry, there should be an
approximate linear relationship between applied
voltage and the delivered current in an electroplatebath. For given bath conditions a PLS model canapproximate the current given a voltage. This simple
linear approximation can be used to compare against
the actual current measured during the process todetect for changes in the bath properties or in comingsubstrates.
Significant differences between the predicted current
and the measured current can highlight excursions orchanges in the bath chemistry that require
investigation. A report on the model residuals is used
to make sure the voltage and current are both alignedwith the expected resistance. (See Figure 1.) Deviationfrom the expected linear relationship may indicate anissue.

USING PLS TO PREDICT IMPLANTANALYZER MAGNET PERFOR MANCEThe analyzer magnets in an ion implanter are used toseparate out the desired charged species from an ion
beam. A specific current is applied to the analyzer
magnet to filter for specific masses. There is a linear
relationship between the analyzer magnet current andthe extraction voltage used for a specific mass andcharge.
For each implanter a linear model can be built that will
help predict the analyzer magnet current from theextraction voltage, mass, and charge. (See Figure 2.)
This model can be used to determine if the implanter ishaving a tuning issue or a systematic issue/failure withthe analyzer magnet. (See Figure 3.)

1 of 2

Using Multivariate Models for Practical Applications

Figure 2 PLS model for predicting implanter analyzer
magnet current

2 of 2Models must be made for each implanter individually.
This is due to differences in the analyzer magnet
assembly and physical differences in the equipment.
While this may appear like a lot of models, each tool
only requires a single model and those models cover
all the species processed through that analyzer
magnet.

CONCLUSION

Figure 3 Resulting control chart showing deviation
between predicted and measured magnet current

For the two applications discussed here, MVA methodshave been shown to be effective for detecting
excursions and predicting metrology. In particular, asingle Implant Analyzer Magnet model is capable ofproviding fault detection across all operating regions of
the equipment. In a typical fab, this model often
provides subsystem monitoring for thousands ofprocess recipes. Without MVA techniques, each recipe
would have to be monitored independently for analyzer
magnet excursions. Univariate techniques in this casewould be impractical to configure and manage,
resulting in increased risk to product.

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