Atom‐counting in a non‐probe corrected
STEM
Authors: Schowalter Marco , Gerken Beeke , Krause Florian Fritz , Grieb Tim , Müller‐Caspary Knut , Mahr Christoph , Mehrtens Thorsten , Özaslan Mehtap , Backer Annick De , Aert Sandra Van , Rosenauer Andreas 
Published: December 2016

In recent years scanning transmission electron microscopy (STEM) has attracted great attention due to its high sensitivity with respect to atomic number and specimen thickness. The great advantage of this technique is to determine the number of atoms in single atomic columns in the specimen [1,2]. For instance, the reconstruction of the atomic structure of Ag nanoparticles was realized by acquiring a small series of high resolution STEM images in different zone axis orientations. Such a reconstruction enables to study facets of nanoparticles.
Basically two different atom counting techniques exist: (1) In simulation‐based techniques typically the mean intensity in a well‐known material within a certain region around each atom column position, such as a Voronoi cell [3] is measured and compared with appropriate simulations. (2) Statistics‐based techniques, as introduced by Van Aert et al. [2] fit a parametric model consisting of Gaussians at the positions of the atom columns to the image intensities. Then volumes below the Gaussians are computed. Gaussian mixture models are fitted to the distribution of the volumes using the expectation maximization algorithm (see e.g. Fig. 1a) as a function of the number of Gaussian components. For each fit an order selection criterion is computed and plotted as shown in Fig. 1b. The minimum of the order selection criterion then determines the number of components in the applicable mixture model [2,4]. Finally, the number of atoms (Fig. 1c) in each column is determined by maximizing the probability that a column's intensity volume belongs to a certain component of the selected mixture model. The component with smallest volume is assumed to belong to a column with one atom.
Usually, atom counting is performed using probe corrected STEM. We performed a simulation test, whether atom counting is possible in a non‐probe corrected STEM on a hypothetical Au wedge used by De Backer et al. [4]. In the respective model the number of atoms increases from 1 to 7 and then decreases again from 7 to one. From Fig. 1 it becomes clear that atoms were correctly counted from the simulated image.
In general it can be expected that the column with mimimum number of atoms in an image does not necessarily contain only one atom. We studied the effect of an offset in the number of atoms on the counting result by adding additional layers of Au on top of the model. In order to account for the offset in the statistics‐based measurement positions of the Gaussian components were linearly fitted and the respective offset was derived from the parameters of the fit. We found that for small offsets the method worked reasonable, however for an offset of 7 atoms the number of atoms was overestimated by one atom, due to small deviations from the linear behaviour of the volumes. For a larger offset of 13 atoms severe errors were observed and a combination with simulations is needed to retrieve the offset value [5].
In a further test we added an amorphous carbon layer to an InAs cleavage wedge (Fig. 2a). Fig. 2b shows that the statistics‐based method well identifies the number of atoms despite the amorphous carbon layer. Errors can be observed for simulation‐based atom counting due to the additional intensity arising in the amorphous carbon layers.
Fig. 3a shows an experimental HRSTEM image of a twinned Pt nanoparticle taken in our non‐probe corrected Titan 80‐300ST. Atoms have been counted in one of the twins using the simulation‐based atom counting technique (Fig 3b). For a statistics‐based atom counting evaluation the same limits have been found. For the evaluations instrumental imperfections such as reported in ref. [6] were taken care.