The dependence of fractal dimension on measuring conditions of scanning probe microscopy

Abstract

The fractal dimension of sputtered thin film surfaces was determined. Topography was measured using scanning tunneling microscopy (STM) and atomic force microscopy (AFM). It can be shown that measuring conditions have an important influence on the topographic data and the obtained fractal dimension. This influence was investigated systematically. The results of STM- and AFM-measurements have been compared. The results for surfaces imaged with AFM give lower values for the fractal dimension than with STM. Measurements were carried out with a standard cantilever and so the data have been filtered. Dynamic behavior of the measuring system is influenced by scanning speed and loop gain factor. During measurement of topographic signal high scanning speed and low loop gain factor produce a low pass behavior and the fractal dimension will be varied. If there is a disturbance in addition to the topographic signal (e.g. a noise) we found power spectra with more than one linear part. The calculated fractal dimension especially depended on the density of measuring points in the profile. The experimental results were verified by calculated Weierstrass-Mandelbrot functions.