Specific Features of Surface Research of ZnO–SiO2 Films by Multifractal Analysis
DOI:
https://doi.org/10.15407/ujpe68.12.822Keywords:
nanorelief, multifractal analysis, determination errors of R´enyi numbers, sol-gel technology, nanolayer surfaceAbstract
On the example of the multifractal (MF) analysis of the images obtained for the surfaces of nanofilms synthesized in the ZnO–SiO2 system using the sol-gel technology, the specific features of this method relevant for measuring the quantitative surface characteristics have been discussed. As the input information for the implementation of this approach to the description of the surface state, Secondary-Electron Microscopy (SEM) images of the surfaces of specimens synthesized under given conditions are used. Numerical calculations of the generalized partition functions for the area and volume of spatial nanoforms show the linear dependences of those nano-geometric parameters of the surface on spatial dimensions, which is the main proof of their self-similarity and fractal symmetry. The necessity to enhance the reliability of determining the parameters of MF spectra is emphasized, and the factors responsible for the accuracy of the calculated absolute values of the R´enyi numbers are analyzed. Recommendations have been made to minimize errors in order to obtain the most reliable data for the MF surface parameters. The dependences of the R´enyi numbers on the temperature of the sol-gel synthesis of ZnO–SiO2 layers are presented. For the further implementation of the multifractal analysis (MFA) results in physical calculations, the attention is attracted to the necessity of a correct choice of those R´enyi numbers that include the required information about the simulated fractal parameter. The physical origins for the appearance of a relation between, on the one hand, the parameters of MF spectra for the surface area and the volume of nanoforms formed on the film surface and, on the other hand, the conditions of their synthesis have been discussed.
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