Fractal dimension of heights facilitates mesoscopic mechanical properties in ternary hard film surfaces

Abstract

Hardness of thin films is a noteworthy property in the electronic and mechanical industry and is generally observed to be dependent on the degree of roughening facilitated from surface heights' surface spatial heterogeneity at the mesoscopic observation scale. Nonetheless, owing to enhanced scale fluctuations and higher-order central moments, conventional parameters provide limitations and errors in capturing the spatial heterogeneity of surfaces. Herein, we have utilized scale-independent fractal parameters to analyze the spatial heterogeneity of surface heights in Ti1−xSixN ternary hard films deposited with varying Si doping concentrations using sputtering technique. The fractal dimension, lacunarity coefficient, Moran index, surface entropy, Otsu's separability, and fractal succolarity were computed to provide an overarching understanding of the surface heights' spatial heterogeneity. Principal component analysis was employed on the data sets to identify the parameter(s) accounting for the maximum variance and accordingly, the structure–property relation between spatial heterogeneity of surface and hardness is analyzed and discussed in the context of the fractal dimension of surface heights. The results indicate the possibility of mesoscopic surface engineering and, consequently, tuning of hardness and modulus of elasticity in Ti1−xSixN hard films by mere changing of surface spatial heterogeneity facilitated by the fractal dimension of surface heights.