Optimizing Ultrathin Multilayer Film Thickness Estimation via Angle-Resolved XPS Modeling

The continuous miniaturization of semiconductor-based products, for instance, for the electronic device industry, has increasingly demanded more information about these materials at the nanoscale. These products may consist of ultrathin films, such as SiO₂/Si and Al₂O₃/SiO₂/Si. Different techniques can be employed to characterize these films, including Transmission Electron Microscopy (TEM), Ellipsometry, and Ion Beam Profilometry. However, each technique has its own limitations, and some of them may also be destructive or alter the sample. In this context, Angle-Resolved X-ray Photoelectron Spectroscopy (AR-XPS) emerges as a powerful technique because it is non-destructive and provides information such as the chemical characterization of surfaces and interfaces, film thickness, and, through detailed analysis, the chemical bonding of the constituent elements. In this work, we investigate these ultrathin films and present an approach to measuring the thickness of different film layers. Using the acquired spectra, we perform a mathematical modeling of the signal attenuation as a function of the photoelectron emission angle (from normal emission to grazing emission). We employ classical analytical formulations based on the linearized exponential decay of signal intensities, as well as more sophisticated graphical approaches that account for electron scattering, and nonlinear optimization algorithms for fitting multilayer systems.