Uncertainty modeling in nanoscale scanning probe microscopy measurements of fullerene C60

Abstract

Nanoscale dimensional measurements are very often focused on small objects formed by only a few atomic layers in one or more dimensions. The classical convolution approach to tip–sample artifacts cannot be, on its own, sufficient for these specimens due to their quantum-mechanical nature. With growing resolution of specialized metrology scanning probe microscopes and increasing requirements of exact measurements in nanoscale range, it is necessary to make a transition from the classical picture to a quantum approach on the field of uncertainty analysis. In this paper, sources of uncertainty connected with tip–sample relaxation at the atomic level are discussed. Results of density functional theory modeling (using the tight-binding approximation software FIREBALL) of AFM scans on fullerenes are presented. In our approach we model the tip apex and the sample as systems of individual atoms. As interatomic forces act on the sample and the tip of the microscope, the atoms of both relax in order to reach equilibrium positions. This leads to changes in those quantities that are finally interpreted as the ‘atomic force microscope (AFM) tip position’ and influences the resultant dimensional measurements. The results from modeling are compared to the experimental results found in the literature.