Influence of pixelization on height measurement in atomic force microscopy

Though AFM is capable of obtaining sub-angstrom resolution in z-direction, the accurate height measurement of protruding particles is hindered by raster nature of this technique. In this work using Monte Carlo simulations we have quantified the influence of pixelization on the mean AFM apparent height (h_mean) of spheres and cylinders. We have demonstrated that for a zero size AFM probe h_mean may be increasing, decreasing function of a pixel size, or has more complex character depending on the standard deviation of a particle size. Therefore, AFM pixelization effects may induce both under- and overestimation of the true diameter. The observed complex behavior of h_mean is explained by interplay of two opposing factors: the mismatch of the position of the "highest" pixel to the real topographical maximum and higher registration probabilities of larger particles. Consideration of the AFM probe size results in even bigger pixelization induced drops of h_mean, which may amount to ∼50% of the true value. The obtained results contribute to AFM data interpretation and methodological aspects of AFM operation in many fields of nanoscience. In particular, they may be used for estimation of true height of nanoparticles from their AFM images obtained with different (even low) pixel resolution.