Statistical and fractal features of nanocrystalline AZO thin films

In this paper, We investigate the morphology effect of Aluminum-doped zinc oxide (AZO) thin films on the physical properties such as conductivity and grain size. The AZO thin films are prepared by spray pyrolysis at different thicknesses in the range 100-400 nm. Height fluctuations obtained from atomic force microscopy (AFM) analysis are applied to the statistical and fractal analysis of thin films. We show that the conductivity of thin films is proportional to the roughness parameter as σ∼Wm which m=6.42±0.50. Calculating the nonlinear measures (skewness and kurtosis) of height fluctuations demonstrates the isotropic nature of AZO rough surfaces. Fractal analysis of the mentioned thin films using two dimensional multifractal detrended fluctuation analysis illustrates the multifractality scaling and the strength of multifractality increases with thickness. Our results show that the reason for the multi-affinity is the existence of different correlations in the height fluctuations of the thin films. Calculating the contour loops features of the height fluctuations reveals that the radius, length, and area of loops increase with thickness enhancement and the radius of contour loops is introduced as a new statistical parameter which is linearly related to the grain size and could be useful to calculate it.