Quick Analysis and Adaptive Mapping of Micro-Beam X-Ray Diffraction Through Machine Learning

X-ray diffraction is one of the crucial characterization methods for the materials. The measured data of X-ray diffraction patterns recently have become highly complicated, and the number and size of datasets have increased thanks to the technological developments of optical systems and detectors. The analysis of such complex ‘big data’ is not always straightforward.<br/><br/>In this study, we first employed unsupervised machine learning to analyze numerous complex X-ray diffraction patterns using feature patterns derived from the data. Our study focused on a crystalline SiGe film on a Si substrate with spatial variations in both composition and crystal orientation, resulting in intricate multipeak diffraction patterns. Non-negative Matrix Factorization (NMF), a method in unsupervised machine learning, was applied to 961 patterns obtained via spatial mapping from micro-beam X-ray diffraction measurements. NMF provided four feature patterns that corresponded to typical SiGe film diffraction patterns, capturing variations in Si composition and crystal orientations. Using the four feature patterns, the relative Si composition and crystal orientation were evaluated in less than 1 s without time-consuming numerical fittings.<br/><br/>In the second step, we implemented Bayesian optimization (BO) and active learning (AL) for level set estimation (LSE) to the spatial mapping of micro-beam X-ray diffraction with NMF analysis. The BO found characteristic points with large crystallographic inclinations, and the AL-LSE revealed the spatial size and shape complexity of the fluctuation. These results demonstrate that the mapping system and algorithms work as designed. The performance of the BO and AL-LSE was evaluated and compared to conventional mesh grid mapping. The results show that both methods are effective in reducing the number of measurement points<br/><br/>The combination of NMF for the feature pattern extraction and BO and AL-LSE for the adaptive mapping showcased in this study promises efficient analysis of numerous X-ray diffraction patterns exhibiting extensive and intricate fluctuations.