austriamicrosystems status, discussion Poster

1
Design of Virtual Metrology Models by Machine
Learning A Matlab Prototype A. Ferreira1, G.
Pages1, Y. Oussar2 1Ecole Nat. Sup. des Mines de
Saint-Etienne, 2 ESPCI Paristech
Motivation
Matlab Prototype
We propose a methodology for building VM models
using machine learning techniques. After a
standard data pre-processing, a variable ranking
and selection procedure is applied to determine
the most relevant variables for predicting the
metrology variables. Different techniques coming
from the statistical learning theory such as PLS
regression and Least Squares Support Vector
Machine LS-SVM regression are implemented. For
each technique, the model parameters are
estimated using a training algorithm. A k-fold
cross-validation (or leave-one-out) procedure is
used to select the model that exhibits the best
generalization capabilities. Its performance is
then estimated using a test dataset. The EMSE-CMP
methodology was implemented in a Matlab Prototype
dedicated to Virtual Metrology Models design.
Basic Diagram for the Design of VM Models based
on Machine Learning Techniques
Case Study
Ranking and selection variables The main
scientific contributions of EMSE-CMP are the
development of filter and wrapper methods to
ranking and selection variables. Some
manufacturing processes have a very large number
of input variables. The result is complex
predictive models with poor generalization
capabilities The confidence level of a model is
even larger when it uses a small number of
adjusted parameters. In addition, taking into
account irrelevant variables leads to introducing
noisy data that yields to overfitting and then
poor generalization capabilities. The goal of
variable ranking and selection is to determine
the smallest subset of variables, carrying as
much information as possible, to explain the
dependent variable, while discarding both
redundant and/or irrelevant variables (i.e.,
poorly informative). EMSE-CMP has two main
contributions in ranking and variable
selection 1)Contribution to filter method
Mutual Information-based Variable Selection using
a Probe Feature. 2)Contribution to wrapper
method Wrapper with a meta-heuristic approach,
namely a Tabu search algorithm (TabuWrap).
STMicroelectronics Rousset site Prediction of
Overlay of Photolithography process
43 variables out of 169 have been selected
Filter and Wrappers Approaches
Approach Pros Cons
Filter Model free Low computational cost Fairly irregular May degrade performances
Wrapper Consistent High accuracy Improves performances Computational burden

• Conclusion
• Two EMSE-CMP original contributions in variable
  ranking and selection were implemented with the
  LS-SVM regression method in a Matlab Prototype
  for the design of VM models. The Matlab Prototype
  was validated using real data from two case
  studies
• Austriamicrosystems Prediction of PECVD (Plasma
  Enhanced Chemical Vapor Deposition) oxide
  thickness for an Inter Metal Dielectric (IMD)
  layers.
• STMicroelectronics Rousset case Prediction of
  Overlay of Photolithography process