Development of a self-consistent free-form approach for studying the three-dimensional morphology of a thin film

A method capable of extracting the depth distribution of the dielectric constant of a thin film deposited on a substrate and the three power spectral density (PSD) functions characterizing its roughness is presented. It is based on the concurrent analysis of x-ray reflectivity and scattering measurements obtained at different glancing angle values of the probe beam so that the effect of roughness is taken into account during reconstruction of the dielectric constant profile. Likewise, the latter is taken into account when determining the PSD functions describing the film roughness. This approach is using a numerical computation iterative procedure that demonstrated a rapid convergence for the overall set of data leading to a precise description of the three-dimensional morphology of a film. In the case of a tungsten thin film deposited by dc-magnetron sputtering onto a silicon substrate and characterized under vacuum, the analysis of the x-ray data showed the tungsten density to vary with depth from 95% of the bulk density at the top of the film to about 80% near the substrate, where the presence of an interlayer, estimated to be 0.7 nm thick, was evidenced. The latter may be due to diffusion and/or implantation of tungsten atoms into the silicon substrate. In the reconstruction of the depth profile, the resolution (minimum feature size correctly reconstructed) was estimated to be of the order of 0.4-0.5 nm. The depth distribution of the dielectric constant was shown to affect the roughness conformity coefficient extracted from the measured x-ray scattering distributions, while the deposition process increased the film roughness at high spatial frequency as compared to the virgin substrate. On the contrary, the roughness showed a weak influence on the dielectric constant depth profile extracted, as the sample used in our particular experiment was extremely smooth.