An empirical X-ray K-Ratio framework for thickness measurement of 2D Si and SiO₂ thin films and SiO₂ layer on Si...

The quantitative determination of thin film thickness using X-ray emission analysis provides an accurate, non-destructive alternative to conventional characterisation methods. This study established empirical relationships among the X-ray k-ratio, backscattering electron coefficient (η), and film thickness for two-dimensional (2D) silicon (Si) and silicon dioxide (SiO₂) films, and a silicon dioxide (SiO₂) layer on a Si substrate. Monte Carlo simulations using the McXRayLite to model the electron-solid interactions at primary beam energies of 3-10 keV and film thicknesses of 2-10 nm. The Si Kα₁ signal intensity was used to compute the k-ratios for unsupported Si and SiO₂ films, whereas both Si Kα₁ and O₂ Kα₁ intensities were used for SiO₂/Si. For the Si Kα₁ signal used, a strong linear correlation was obtained between the k-ratio and the thickness of the 2D Si and SiO₂ films, where an inverse linear relationship was observed for the SiO₂/Si sample. For the O₂ Kα₁ signal used, a strong linear correlation between the k-ratio and top-film SiO₂ thickness on the Si substrate was observed. The k-ratio also exhibited a consistent dependence on the backscattering coefficient (η), confirming the influence of backscattered electrons on X-ray generation. Empirical equations were derived to predict the film thickness with uncertainties below 4%, demonstrating that the k-ratio method is a reliable and accurate tool for nanoscale thin film measurements.