Reference-free combined analysis GIXRF-XRR for the characterization of thin film materials and uncertainties calculation

The characterization of thin films and multilayered materials is crucial in advanced material science and its applications. In this thesis we introduce a reference-free method for the characterization of thin lm materials by combining X-ray Reflectivity (XRR) and Grazing Incidence X-ray Fluorescence (GIXRF) techniques. XRR is a sensitive technique to the electronic density, allowing for determination of the density, thickness and roughness of thin layers. On the other hand, GIXRF is sensitive to the elemental density, providing information on the elemental depth distribution. The combination of these techniques removes ambiguous results for the characterization of nanometer layers, as well as nanometer depth profiles, resulting in a more accurate sample characterization. The reference-free method is based on the physics of ionization and absorption and requires knowledge of the atomic fundamental parameters rather than the use of reference materials or calibration standards. However, the combined analysis of GIXRF and XRR is a challenging task due to the high number of fitting parameters and to the different dynamic ranges of these two techniques; since XRR exhibits a normalized signal from 0 to 1, whereas a GIXRF spectrum is a histogram presenting peaks of which areas ranging from hundreds to millions of counts.

To address these challenges, we propose in this thesis a recursive method for estimating uncertainties in combined GIXRF-XRR analysis based on the Bootstrap statistical method. This method involves generating random weights to be multiplied by the cost function data points. The application of these weights results in new set of optimized thin film values that differs from the original ones. By repeating the process, a set of optimized structures are calculated, of which statistics can be performed to deduce the uncertainties on the optimized parameters of the sample structure. An additional problem in the reference-free combined GIXRF-XRR analysis is the consideration of uncertainties in the fundamental parameters and the solid angle of detection. We therefore introduce a Monte Carlo-based approach to calculate the uncertainty on the solid angle of detection and the fundamental parameters which are included in the combined analysis. The measurement of several selected samples using GIXRF and XRR were carried out in the CASTOR goniometer on the MÉTROLOGIE beamline of the SOLEIL synchrotron facility. XRR data were initially analyzed to estimate structural composition with IMD software, followed by the fitting XRF spectra using COLEGRAM to derive the intensity of fluorescence X-ray emission lines. The combined GIXRF-XRR analysis was afterwards performed using ELIXIR, in-house software, to derive the sample structure and the associated uncertainties were calculated by a Mathematica program. This methodology was applied to amorphous and crystalline chalcogenides GexSbyTez with different (x, y, z) compositions and on tantalum-based thin films, doped with different elements. The derived uncertainties on the sample structure, fundamental parameters, and solid angle were analyzed. Furthermore, some fundamental parameters, namely mass attenuation coefficients, fluorescence yields and photoelectric absorption coefficients for iron and yttrium were measured and their uncertainties were estimated using different methods. Finally, to improve the resolution of the fluorescence detection, we developed a prototype of a wavelength dispersive spectrometer (WDS) based on Bragg's diffraction, which includes a crystal and a high-resolution CCD sensor, achieving a resolution of 2eV at 8048eV.

X-ray spectrometry, metrology, X-ray fluorescence, material sciences, thin layers

Full document (EN) : https://theses.hal.science/tel-04412121