Analyzing the surface dynamics of titanium thin films using fractal and multifractal geometry

Abstract

Titanium thin films are prepared by DC magnetron sputtering on the glass substrate with varying sputtering power. The nanoscale surface morphology and nanotexture are captured via atomic force microscopy (AFM). The value of average roughness and interface width show the increasing trend with sputtering power. The autocorrelation and height-height correlation function are applied to characterize the formation of the self-affine and mounded surfaces. The roughness (or Hurst) exponent and fractal dimension are estimated by height-height correlation function while lateral correlation length is measured by autocorrelation. It is found that the surface complexity is affected with various sputtering power. The value of Hurst exponent of the topography greater than 0.5 indicates a persistent behavior and such system shows memory effect. The fractal lacunarity, succolarity and surface entropy is used for investigating the surface microtexture and percolation. The 2D Multifractal Detrended Fluctuation Analysis (2D MFDFA) method is used to study the multifractal nature of thin-film surfaces. Computed Δα and Δf show an increase with sputtering power indicating a surface with many characteristic scale patterns. Furthermore, the thin film deposited with the highest sputtering power has greater topographic uniformity, lower surface percolation and greater homogeneity of the surface microtexture.