Nanotube abundance from non-negative matrix factorization of Raman spectra as an example of chemical purity from open source machine learning

The chemical purity of materials is important for semiconductors, including the carbon nanotube material system, which is emerging in semiconductor applications. One approach to get statistically meaningful abundances and/or concentrations is to measure a large number of small samples. Automated multivariate classification algorithms can be used to draw conclusions from such large data sets. Here, we use spatially-mapped Raman spectra of mixtures of chirality-sorted single walled carbon nanotubes dispersed sparsely on flat silicon/silicon oxide substrates. We use non-negative matrix factorization (NMF) decomposition in scikit-learn, an open-source, python language “machine learning” package, to extract spectral components and derive weighting factors. We extract the abundance of minority species (7,5) nanotubes in mixtures by testing both synthetic data, and real samples prepared by dilution. We show how noise limits the purity level that can be evaluated. We determine real situations where this approach works well, and identify situations where it fails.