Influences of planarization modification and morphological filtering by AFM probe-tip on the evaluation accuracy of fractal dimension

The scaling characteristic of surface roughness could reveal the fractal property of a surface, which is common for the thin films fabricated via physical vapor deposition. In our previous study, a roughness scaling extraction (RSE) method was proposed to accurately calculate the fractal dimension (D), which is an effective parameter to represent the irregularity and fragmental property of a fractal surface. RSE method was based on a single morphological image of the concerned surface, and was much more accurate than the traditional methods with a low mean relative error of 0.64%. In this study, RSE method was firstly optimized by using the planarization modification on the morphological images of artificial surfaces with ideal dimensions (D-i) ranging from 2.1 to 2.9, which were generated through Weierstrass-Mandelbrot (W-M) function. The calculation accuracy of RSE method could be enhanced by using the second order planarization modification, with a lowest mean relative error of only 0.42% between D-i and the calculated dimensions (D-c). Secondly, artificial surfaces with high resolution and D-i from 2.2 to 2.8 were utilized to investigate the influence of atomic force microscopy (AFM) probe-tip geometry on the calculation accuracy. A typical geometry with a probe-tip radius (r) of 10 nm was employed to carry out the simulation of morphological filtering for the surface images, and the filtered images with various scales (L) from 0.5 mu m to 7.5 mu m were generated. RSE method was found to be robust only when the ratio of L/r was above 400, while a significant deviation occurred at lower ratio values, which would be instructive for the fractal analysis on the AFM images of various surface morphologies.