Fractal and multifractal analysis of In-doped ZnO thin films deposited on glass, ITO, and silicon substrates

Abstract

Indium-doped zinc oxide (IZO) thin films have been deposited on glass (IZO/glass), ITO (IZO/ITO), and silicon (IZO/Si) substrates using sol–gel spin coating method. Glancing angle X-ray diffraction has been used to verify phase purity, average grain size, and microcrystalline stress of the annealed films. Effect of substrates on surface morphology is explicitly investigated using the conventional statistical techniques along with nonlinear fractal and multifractal geometrical analysis. The root-mean-square surface roughness value is the lowest in IZO/glass films and increases in IZO/ITO films and the highest in IZO/Si films. Fractal and multifractal formalism acts as a scale-independent microscopic analytical tool for surface analysis. All IZO films show fractal and multifractal behaviour. The fractal parameters such as fractal dimensions and Hurst exponents are different for films deposited on different substrates and, thus, able to characterize surface morphology precisely. Hurst exponent values of IZO films indicate that although IZO/Si films have highest vertical roughness, it has strongly correlated (highest self-similarity) surface morphology than other two films deposited on glass and ITO substrates. Inhomogeneity in scaling exponents could be better understood with the help of multifractal formalism. The difference of fractal dimensions in all IZO films deposited on glass, ITO, and Si substrates is very small (almost close to zero). Therefore, there is very little multifractality exist in those film surfaces. Width of multifractal spectrum is the largest in IZO/Si and the smallest (also similar) in IZO/ITO and IZO/glass films, indicating that multifractallity in IZO/Si film is more prominent. A quantitative information about the surface morphology has been provided by inferring multifractal parameters. Detailed fractal and multifractal formalism of surface morphology may find its importance in understanding various surface-based device fabrication and performances.