Assessment of fractal and multifractal features of sol-gel spin coated ZnO thin film surface

Abstract

Scaling property of the atomic force microscopic (AFM) images of the annealed sol-gel spin coated ZnO thin film at different scales along with the glass substrate has been studied explicitly using fractal and multifractal formalism. Accordingly, the thin film surface growth and roughening are discussed. Polycrystalline Hexagonal wurtzite structure with preferential c-axis orientation and very little microcrystalline stress have been found from the glancing angle x-ray diffraction (GAXRD) pattern analysis of the annealed ZnO film on Glass substrate. Presence of statistical self-similarity in the surface micrographs is realized. Consequently, the fractal dimensions and Hurst exponents have been computed using the Higuchi’s algorithm and the correlation properties of the surfaces are quantified by these parameters. Values of the Hurst exponent indicate that the nature of overall surface growth is anti-correlated or anti-persistent, and while zoomed first it appears random or Brownian, having no ultimate correlation then seems to be positively correlated while further zoomed. The height and width of the singularity spectrum computed using box-counting multifractal formalism can quantify surface complexity both vertically and spatially. The multifractal analysis illustrates that the larger scan sized images have less overall surface complexity. Also, the multifractal parameters are found to be more universal than any other surface complexity measuring parameters. The fractal and multifractal behavior of both the glass substrate and the ZnO film on it reveal that the surface complexity of the ZnO thin film is originated from the complexity of the glass substrate. Furthermore, it has been understood that the proper choice of scan size is necessary to assess the actual complexity of a rough surface. Further investigation of the fractal and multifractal character of residual surface micrographs by varying various deposition conditions in sol-gel derived films could depict film growth and roughening mechanism in a scale-independent, precise, complete and generalized manner by avoiding an excessive number of parameters in conventional roughness and symmetry analysis methods.