Search

The Python package mlreflect is demonstrated, which implements an optimized pipeline for the automated analysis of reflectometry data using machine learning. The package combines several training and data treatment techniques discussed in previous publications. The predictions made by the neural network are accurate and robust enough to serve as good starting parameters for an optional subsequent least-mean-squares (LMS) fit of the data. For a large data set of 242 reflectivity curves of various thin films on silicon substrates, the pipeline reliably finds an LMS minimum very close to a fit produced by a human researcher with the application of physical knowledge and carefully chosen boundary conditions. The differences between simulated and experimental data and their implications for the training and performance of neural networks are discussed. The experimental test set is used to determine the optimal noise level during training. The extremely fast prediction times of the neural network are leveraged to compensate for systematic errors by sampling slight variations in the data.

The Python package

Typically, core–shell–shell semiconductor nanowires (NWs) made from III–V materials with low lattice mismatch grow pseudomorphically along the growth axis, i.e. the axial lattice parameters of the core and shell materials are the same. Therefore, both the structural composition and interface strain of the NWs are encoded along directions perpendicular to the growth axis. Owing to fluctuations in the supplied growth species during molecular beam epitaxy (MBE) growth, structural parameters such as local shell thickness, composition and strain may differ between NWs grown onto the same substrate. This requires structural analysis of single NWs instead of measuring NW ensembles. In this work, the complete structure of single GaAs/(In,Ga)As/GaAs core–shell–shell NW heterostructures is determined by means of X-ray nanodiffraction using synchrotron radiation. The NWs were grown by MBE on a prepatterned silicon (111) substrate with a core diameter of 50 nm and an (In,Ga)As shell thickness of 20 nm with a nominal indium concentration of 15%, capped by a 30 nm GaAs outer shell. In order to access single NWs with the X-ray nanobeam being incident parallel to the surface of the substrate, a single row of holes with a separation of 10 µm was defined by electron-beam lithography to act as nucleation centres for MBE NW growth. These well separated NWs were probed sequentially by X-ray nanodiffraction, recording three-dimensional reciprocal-space maps of Bragg reflections with scattering vectors parallel (out-of-plane) and perpendicular (in-plane) to the NW growth axis. From the out-of-plane 111 Bragg reflection, deviations from hexagonal symmetry were derived, together with the diameters of probed NWs grown under the same conditions. The radial NW composition and interface strain became accessible when measuring the two-dimensional scattering intensity distributions of the in-plane 2{\overline 2}0 and 22{\overline 4} reflections, exhibiting well pronounced thickness fringes perpendicular to the NW side planes (truncation rods, TRs). Quantitative values of thickness, composition and strain acting on the (In,Ga)As and GaAs shells were obtained via finite-element modelling of the core–shell–shell NWs and subsequent Fourier transform, simulating the TRs measured along the three different directions of the hexagonally shaped NWs simultaneously. Considering the experimental constraints of the current experiment, thicknesses and In content have been evaluated with uncertainties of ±2 nm and ±0.01, respectively. Comparing data taken from different single NWs, the shell thicknesses differ from one to another.