Power spectral density-based fractal analyses of sputtered yttria-stabilized zirconia thin films

Abstract

This study provides information about the surface morphology of sputtered yttria-stabilized zirconia (YSZ) thin films from the atomic force microscope (AFM) spectral analyses using the power spectral density (PSD) function at varying annealing temperatures. Applying fractal and k-correlation fitting models to the PSD data, fractal dimension, Hurst exponent, correlation length, and equivalent root mean square roughness are quantified. The PSDs of the films exhibit an inverse power-law variation at high spatial frequency, which points to the existence of the fractal components in the film’s surface. The annealing temperatures up to 900 ∘C decreased fractal dimension from 2.60 to 2. The surface roughness increased from 0.10 to 13.92 nm and from 0.04 to 3.95 nm, obtained from the statistical analyses of AFM images and the k-correlation model. The films annealed from 500 ∘C to 800 ∘C showed fine grain size morphology with Hurst exponent values from 0.40 to 0.53, indicating a homogeneous spatial roughness distribution. While the film annealed at 900 ∘C exhibited large aggregate grains morphology. The growth of a sample annealed at the temperature of 900 ∘C is more likely to be ruled by the step-edge barrier-induced mound growth and inhomogeneous spatial distribution of roughness. In contrast, normal self-affine behaviour is observed at lower annealing temperatures.