Effect of Fe Doping on the Surface Morphology and Supercapacitor Properties of Sr(OH)2 Thin Films: A Fractal Approach

Fractal concepts have been employed to explore the morphological evolution of Sr(OH)2 thin films prepared by the successive ionic layer adsorption and reaction (SILAR) method on stainless steel (SS) substrate. The surface morphology of each sample was captured using atomic force microscopy (AFM). Interface width, lateral correlation length, and roughness exponent were computed. Our study reveals that as doping is increased, the roughness exponent decreases and the fractal dimension increases. In all cases, the value of the roughness exponent was found to be greater than 0.5, indicating that the height fluctuations at neighboring pixels are correlated positively and exhibit persistent behavior and memory effect. Advanced fractal parameters such as lacunarity coefficient (σ), Hurst coefficient (HC), fractal succolarity (FS), and surface entropy (SE) are also calculated. Our study reveals that the surface entropy does not show any significant change, indicating a globally uniform surface. Furthermore, the local surface slope is found to play a crucial role in the performance of supercapacitive electrodes. Fractal analysis indicates that electrodes with larger fractal dimension are better for supercapacitor applications. These observations are corroborated with the 0.5 atom % Fe/Sr(OH)2 doped sample. This sample exhibits both the highest fractal dimension and a specific capacity of 776 C g–1 at a scan rate of 5 mV s–1. The materials with higher fractal dimension could thus be a strong candidate for the fabrication of highly efficient supercapacitors.