Power spectral density-based fractal analysis of annealing effect in low cost solution-processed Al-doped ZnO thin films

Abstract

Thin films of aluminium-doped zinc oxide (Al:ZnO) have been deposited using the sol-gel spin coating method and annealed at 300 °C, 400 °C, and 500 °C. The structural phase purity of the annealed films has been confirmed by the glancing angle x-ray diffraction patterns. The average microcrystalline size and residual microcrystalline stress have been calculated from it. It is observed that the average microcrystalline size increases and the residual microcrystalline compressive stress first increases and then decreases with increasing annealing temperature from 300 °C to 500 °C. The conventional surface roughness calculations and the power spectral density (PSD)-based fractal computations of the AFM micrographs have been carried out. The values of the power-law exponent demonstrate the underlying mechanism of the films' residual surface growth. All the annealed films have a combined surface transport mechanism of viscous flow and evaporation-condensation. However, evaporation-condensation becomes dominant at the higher annealing temperatures of 400 °C and 500 °C. The spatial and vertical anisotropy of thin film surface topography has been quantified in a scale-invariant and generalized manner with the help of fractal geometrical analysis. The values of the fractal dimensions and Hurst exponents indicate that the vertical roughness of the films increases and the spatial self-similarity decreases with increasing annealing temperature. It is noteworthy that the Hurst exponent can alone depict the complexity of a thin film surface, whereas in conventional techniques at least three parameters are necessary for this. The fractal dimension increases with increasing average grain size and annealing temperature. Consequently, overall surface complexity increases with increasing annealing temperature. Thus, the fractal analysis can find its application in the predictability and assessment of surface topography. Also, various physical properties of films may be correlated with the fractal parameter of thin film surfaces in future works for micro and nano device fabrications.

Fractal Theory in Thin Films: Literature Review and Bibliometric Evidence on Applications and Trends

“…The fractal dimension was used as the most effective quantitative descriptor of self-affine/similar surfaces of thin film surfaces [44]. Hurst exponent, which relates to autocorrelations of the time series in surface roughness of thin film structures, has also been used as a quantitative measure of fractal properties [45,46]. As seen in Figure 6, fractal dimension and Hurst exponent are strongly related to surface roughness and microstructural features of thin films.…”