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

Abstract 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  μ m to 7.5  μ 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.