Convolutional neural network analysis of x-ray diffraction data: strain profile retrieval in ion beam modified materials

This work describes a proof of concept demonstrating that convolutional neural networks (CNNs) can be used to invert x-ray diffraction (XRD) data, so as to, for instance, retrieve depth-resolved strain profiles. The determination of strain distributions in disordered materials is critical in several technological domains, such as the semiconductor industry for instance. Using numerically generated data, a dedicated CNN has been developed, optimized, and trained, with the ultimate objective of inferring spatial strain profiles on the sole basis of XRD data, without the need of a priori knowledge or human intervention. With the example ZrO2 single crystals, in which atomic disorder and strain are introduced by means of ion irradiation, we investigate the physical parameters of the disordered material that condition the performances of the CNN. Simple descriptors of the strain distribution, such as the maximum strain and the strained depth, are predicted with accuracies of 94% and 91%, respectively. The exact shape of the strain distribution is predicted with a 82% accuracy, and 76% for strain levels <2% where the amount of meaningful information in the XRD data is significantly decreased. The robustness of the CNN against the number of predicted parameters and the size of the training dataset, as well as the uniqueness of the solution in some challenging cases, are critically discussed. Finally, the potential of the CNN has been tested on real, experimental, data. Interestingly, while the CNN has not been trained to operate on experimental data, it still shows promising performances with predictions achieved in a few seconds and corresponding root-mean-square errors in the 0.12–0.17 range for a fully automated approach, vs. a 0.06–0.12 range for a classical, human-based, approach that, in turn, requires several tens of minutes to optimize the solution. While the overall accuracy of the CNN has to be improved, these results pave the way for a fully automated XRD data analysis.