Structural contribution to the roughness of supersmooth crystal surface

Technological advances in processing crystals (Si, sapphire α-Al₂O₃, SiC, GaN, LiNbO₃, SrTiO₃, etc.) of substrate materials and X-ray optics elements make it possible to obtain supersmooth surfaces with a periodicity characteristic of the crystal structure. These periodic structures are formed by atomically smooth terraces and steps of nano- and subnanometer sizes, respectively. A model surface with such nanostructures is proposed, and the relations between its roughness parameters and the height of atomic steps are determined. The roughness parameters calculated from these relations almost coincide with the experimental atomic force microscopy (AFM) data obtained from 1 × 1 and 10 × 10 μm areas on the surface of sapphire plates with steps. The minimum roughness parameters for vicinal crystal surfaces, which are due to the structural contribution, are calculated based on the approach proposed. A comparative analysis of the relief and roughness parameters of sapphire plate surfaces with different degrees of polishing is performed. A size effect is established: the relief height distribution changes from stochastic to regular with a decrease in the surface roughness.