Analysis of the Spatial-Frequency Characteristics of the Photo-Assisted Method of a Quartz Rough Surface Nano-Polishing

The relationship between the spatial-frequency parameters of a rough surface with a random profile, which has a Gaussian form of the correlation function, and the amplitude-frequency characteristics of the electric field created by this surface is determined. The numerical determination of the evanescent field optimal configuration formed near the quartz rough surface in the gaseous medium saturated with chlorine molecules when illuminated from the quartz side has been considered. The finite-element approach is used to solve the Helmholtz two-dimensional vector equation. It was found that at the initial stage of photochemical polishing different electrodynamic conditions are created for the etching process depending on the profile height standard deviation value. In particular, when the standard deviation is less than 1 nm, all surface protrusions, for which the spatial spectrum harmonics of the profile are located in the region of the maximum slope of the spectral function, are most actively etched. This leads to a decrease in the effective width of the spatial spectrum of a rough quartz surface and an increase in its correlation length. Therefore, simultaneously with decreasing the height of the protrusions, the surface becomes flatter. The paper shows the different character of quartz surface nano-polishing process conditions depending on the initial standard deviation of the profile height.