Anomalies in nanostructure size measurements by AFM

Anomalies in atomic force microscopy (AFM) based size determination of nanoparticles were studied via comparative analysis of experiments and numerical calculations. Single tungsten oxide nanoparticles with a mean diameter of $3\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ were deposited on mica and graphite substrates and were characterised by AFM. The size (height) of the nanoparticles, measured by tapping mode AFM, was found to be sensitive to the free amplitude of the oscillating tip, thus indicating that the images were not purely topographical. By comparing the experimental results to model calculations, we demonstrate that the dependence of the nanoparticle size on the oscillation amplitude of the tip is an inherent characteristic of the tapping mode AFM; it is also a function of physical properties such as elasticity and surface energy of the nanoparticle and the sample surface, and it depends on the radius of curvature of the tip. We show that good approximation of the real size can easily be obtained from plots of particle height vs free amplitude of the oscillating tip, although errors might persist for individual experiments. The results are valid for size (height) determination of any nanometer-sized objects imaged by tapping mode AFM.