Design of Virtual Metrology Models by
Machine Learning : A Matlab Prototype
A.
1Ecole
1
Ferreira ,
G.
1
Pages ,
Y.
2
Oussar
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
Ranking and selection variables
Case Study
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:
STMicroelectronics Rousset site
Prediction of Overlay of Photolithography process
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).
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
43 variables out of 169 have been selected