Feature extraction and spatial imaging of synchrotron radiation X-ray diffraction patterns using unsupervised machine learning

We analyzed a number of complicated X-ray diffraction patterns using feature patterns obtained through unsupervised machine learning. A crystalline SiGe film on a Si substrate with a spatial fluctuation in both composition and crystal orientation was tested as a model sample having complicated X-ray diffraction patterns with multipeaks. Non-negative matrix factorization (NMF), an unsupervised machine learning method, was performed on 961 patterns obtained by spatial mapping of micro-beam X-ray diffraction measurements. Among the tested number of the feature patterns from 1 to 10, four feature patterns were the most useful for extracting the information about the composition and crystal orientation because they correspond to the diffraction patterns of typical SiGe films with high and low Si fraction, and right- and left-tilted orientation. Reasonable spatial maps of composition and crystal orientation were visualized using coefficients of the four feature patterns. Furthermore, the spatial constraint was tested for NMF using 225 diffraction patterns which were down-sized from 33 x 33 to 16 x 16 pixels due to the high computational cost of simple implementation without techniques to reduce the cost. Four feature patterns similar to those of the simple NMF without the constraints and the more reasonable distribution reflecting the SiGe spatial domain structure were obtained. The feature pattern extraction by NMF and interpretation by experts demonstrated in this study will be useful for quick analysis of a number of X-ray diffraction patterns with large and complicated fluctuations.