Depth-resolved dielectric function analysis of oxygen-deficient WO3-x thin films via graded ellipsometric modeling

This work presents an investigation of the complex dielectric function of oxygen-deficient WO3-x thin films prepared by non-reactive radio-frequency sputtering and its evolution upon post-deposition annealing in air, using Variable-Angle Spectroscopic Ellipsometry. A depth-dependent graded optical model was developed to resolve spatial variations in the dielectric response arising from oxidation-induced compositional gradients. This approach provides a more accurate physical representation than conventional models, which assume a uniform dielectric function throughout the film. The as-deposited films exhibit strong sub-bandgap absorption, likely attributable to defect states associated with oxygen vacancies. Annealing at 400–500 °C facilitates oxygen incorporation that progressively suppresses the defect-related optical loss near the film surface. Transparency in the visible and near-infrared ranges is achieved within a depth of ∼70 nm, resulting in a homogeneous optical response. In thicker films, deeper regions remain oxygen-deficient due to the limited oxygen diffusion length, resulting in a continuous depth-dependent gradient of the dielectric function that is captured by the fitting model presently developed. The graded model can be used as a quality control tool for the fine-tuning of post-deposition annealing processes, and it provides a robust and physically grounded framework for describing the optical response of oxide thin films with spatially varying defect distributions.