Correlating the Nonlinear Roughening and Optical Properties of Anatase Thin Films—A Fractal Geometric Approach

Abstract The anatase phase of TiO 2 is highly suitable for photocatalytic application consequently, prerequisite an unpretentious scale‐independent understanding of its roughening‐facilitated surface topography dynamics. Herein, the nonlinear roughening in anatase thin films and its correlation with the nonlinear trend of optical properties in the framework of fractal geometry are investigated. The self‐affine nature of analyzed surfaces is confirmed from the autocorrelation function. The dynamic scaling exponents indicate the existence of Kardar–Parisi–Zhang scaling in surface growth. In addition, the trend of generalized Hurst exponent and mass exponent indicates insignificant multifractal characteristics in the analyzed surfaces. Moreover, fractal analysis explains and aids to description of roughening trend from stereometric and Minkowski functionals analysis. Furthermore, the significance of fractal dimension for probing the surface roughening is validated from the principal component analysis. Consequently, variation in optical bandgap and linear refractive index are investigated in regards to the fractal dimension and root mean‐squared surface slope and regression equations are proposed for tuning of bandgap.