Investigation of Substrate-effect on BaF₂ Thin Films: A Study of Fractal Nature

BaF2 thin films of thickness 20 nm are prepared using the electron beam evaporation technique (at room temperature) on glass, silicon (Si) as well as aluminum (Al) substrate, respectively. These substrates play a crucial role in the evolution of thin film surface morphology. The thin films grown far from equilibrium have self-affine nature which is reminiscent of fractal behaviour. The surface morphology of films is recorded by atomic force microscopy (AFM). Scaling law analysis is performed on AFM images to confirm that the thin film surfaces under investigation have self-affine nature. The concept of fractal geometry is applied to explore-how different substrates affect the surface morphology of films. The fractal dimension of horizontal as well as vertical sections of AFM images are extracted by applying Higuchi’s algorithm. Value of Hurst exponent (H) for each sample is estimated from fractal dimension. It is found to be greater than 0.5 for Al as well as glass substrates, indicating that the height fluctuations at neighboring pixels are correlated positively. However, for Si substrate, its value is less than 0.5 which suggests that the height fluctuations at neighboring pixels are not positively correlated.

Keywords: BaF2 thin film, Atomic force microscopy (AFM), Self-affine, Hurst exponent, fractal dimension.