Three Approaches for Representing the Statistical Uncertainty on Atom-Counting Results in Quantitative ADF STEM

A decade ago, a statistics-based method was introduced to count the number of atoms from annular dark-field scanning transmission electron microscopy (ADF STEM) images. In the past years, this method was successfully applied to nanocrystals of arbitrary shape, size, and composition (and its high accuracy and precision has been demonstrated). However, the counting results obtained from this statistical framework are so far presented without a visualization of the actual uncertainty about this estimate. In this paper, we present three approaches that can be used to represent counting results together with their statistical error, and discuss which approach is most suited for further use based on simulations and an experimental ADF STEM image. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 770887 and No. 823717 ESTEEM3). The authors acknowledge financial support from the Research Foundation Flanders (FWO, Belgium) through grants to A.D.w. and A.D.B. and projects G.0502.18N, G.0267.18N, and EOS 30489208. S.V.A. acknowledges TOP BOF funding from the University of Antwerp. The authors are grateful to L.M. Liz-Marzán (CIC biomaGUNE and Ikerbasque) for providing the samples.