Neural network analysis of neutron and x-ray reflectivity data: pathological cases, performance and perspectives

Alessandro Greco,Vladimir Starostin,Maximilian W A Skoda,Alexander Gerlach,Frank Schreiber,Stefan Kowarik,Alexander Hinderhofer

doi:10.1088/2632-2153/abf9b1

Abstract

Neutron and x-ray reflectometry (NR and XRR) are powerful techniques to investigate the structural, morphological and even magnetic properties of solid and liquid thin films. While neutrons and x-rays behave similarly in many ways and can be described by the same general theory, they fundamentally differ in certain specific aspects. These aspects can be exploited to investigate different properties of a system, depending on which particular questions need to be answered. Having demonstrated the general applicability of neural networks to analyze XRR and NR data before (Greco et al 2019 J. Appl. Cryst. 52 1342), this study discusses challenges arising from certain pathological cases as well as performance issues and perspectives. These cases include a low signal-to-noise ratio, a high background signal (e.g. from incoherent scattering), as well as a potential lack of a total reflection edge (TRE). By dynamically modifying the training data after every mini batch, a fully-connected neural network was trained to determine thin film parameters from reflectivity curves. We show that noise and background intensity pose no significant problem as long as they do not affect the TRE. However, for curves without strong features the prediction accuracy is diminished. Furthermore, we compare the prediction accuracy for different scattering length density combinations. The results are demonstrated using simulated data of a single-layer system while also discussing challenges for multi-component systems.

Highlights

To investigate the structural, morphological or magnetic properties of surfaces and layered structures, such as solid and liquid thin films [1,2,3,4,5,6,7,8], x-ray and neutron reflectometry (XRR and NR) are often employed due to an array of benefits
Definition of the prediction accuracy The performance of the trained neural network was tested using 10 000 simulated reflectivity curves that were generated within the same ranges as the training data, excluding cases with low scattering length density (SLD) contrast
In order to better quantify the performance of the neural network predictions, we separated all predictions into two classes: those that are near the ground truth were classified as ‘correct’ whereas all others were classified as ‘incorrect’

Summary

Introduction

Morphological or magnetic properties of surfaces and layered structures, such as solid and liquid thin films [1,2,3,4,5,6,7,8], x-ray and neutron reflectometry (XRR and NR) are often employed due to an array of benefits. While x-rays interact with electrons, neutrons mainly interact with the nuclei (except for magnetic effects, which we neglect here), which allows them to be employed as probes for different types of samples, and answer different questions in a complementary manner [11]. These differences are reflected in the data the two methods produce and they must be taken into account during data analysis in order to extract the correct information from a given measurement [12].

Methods

Results

Conclusion