Matrix Factorisation Techniques for Endpoint Detection in Plasma Etching

Advanced data mining techniques such as variable selection through matrix factorization have been intensively applied in the last ten years in the area of plasma-etch point detection using optimal emission spectroscopy (OES). OES data sets are enormous, consisting of measurements of over 2000 wavelength recorded at sample rates of 1 - 3 Hertz, and consequently, these techniques are needed in order to generate compact representations of the relevant process characteristics. To date, the main technique employed in this regard has been PCA (principal components analysis), a matrix factorisation technique which generates linear combinations of the original variables that best capture the information in the data (in terms of variance explained). Recently, an alternative matrix factorisation technique, non- negative matrix factorisation (NMF), has been gaining increasing attention in the fields of image feature extraction and blind source separation due to its tendency to yield sparse representations of data. The aim of this work is to introduce non-negative matrix factorisation to the semiconductor research community and to provide a comparison with PCA in order to highlight its properties.