Optical method for determining the power spectral density function of randomly rough surfaces by simultaneous processing of spectroscopic reflectometry, variable-angle spectroscopic ellipsometry and angle-resolved scattering data

Two samples of silicon-single crystal substrates with randomly rough surfaces covered by native oxide layers are investigated by means of angle-resolved scattering, spectroscopic reflectometry and variable-angle spectroscopic ellipsometry. For each sample, the experimental optical data are processed simultaneously to determine the power spectral density functions, which are modeled by exponentials of quadratic splines. The thicknesses of native oxide layers are also determined. The influence of roughness on the reflectance and ellipsometry is described by the combination of the scalar diffraction theory, which is used for the part of roughness with low spatial frequencies, and the Rayleigh-Rice theory, which is used for the part of roughness with high and moderate spatial frequencies. The separation of the roughness into the parts with low and high/moderate spatial frequencies is performed using a bound dependent on the wavelength of the incident light. The PSDFs determined by the optical method are compared with the PSDFs determined by processing the AFM scans.

Automated summary

Two samples of silicon-single crystal substrates with randomly rough surfaces covered by native oxide layers were studied using angle-resolved scattering, spectroscopic reflectometry, and variable-angle spectroscopic ellipsometry. The power spectral density functions were determined by simultaneously processing the experimental optical data and modeled using exponentials of quadratic splines. The thicknesses of native oxide layers were also determined. The influence of roughness on reflectance and ellipsometry was described using a combination of scalar diffraction theory for low spatial frequencies and Rayleigh-Rice theory for high and moderate spatial frequencies. The roughness was separated into parts using a bound dependent on the wavelength of the incident light. The power spectral density functions determined by the optical method were compared with those determined by processing AFM scans.