Determination of the power spectral density functions of differently rough boundaries of thin films using multi-wavelength angle-resolved scattering, spectroscopic ellipsometry, and spectroscopic reflectometry

The power spectral density functions of the differently rough boundaries of non-absorbing SiO2 thin film are determined using the combined optical method as a function of spatial frequency. This method is based on measuring and processing angle-resolved scattering of these films at three wavelengths. The Rayleigh–Rice theory is used to express these functions that are modeled as exponentials of quadratic splines. However, the power spectral density functions can be determined only when the spectral dependencies of the film refractive index are evaluated independently. These spectral dependencies are determined using variable-angle spectroscopic ellipsometry and spectroscopic reflectometry applied in near-infrared, visible, and near-ultraviolet ranges. It is shown that the ellipsometric parameters are consistent with the Rayleigh–Rice theory within the entire spectral range. The coherent reflectance must be processed using a combination of the Rayleigh–Rice and scalar diffraction theories across the entire spectral range. The incoherent reflectance is processed by the scalar diffraction theory in the part of the spectral range in which the scattering of light is realized. The Sellmeier dispersion model is used to describe the spectral dependency of the refractive index of the thin film. Using ellipsometry and reflectometry, the mean thickness and roughness parameters are determined. The power spectral density function of the upper boundary is smaller than that of the lower boundary. This implies that the upper boundary is slightly smoothed during film deposition. The power spectral density functions and roughness parameters are confirmed using atomic force microscopy.