Atom counting based on Voronoi averaged STEM intensities using a crosstalk correction scheme

Abstract

If quantitative scanning transmission electron microscopy is used for very precise thickness measurements with atomic resolution, it is commonly referred to as »atom counting«. Due to scattering and the finite probe extent the signal recorded in one atomic column is dependent not only on its own height but also on the height of its neighbours. Especially for thicker specimens this crosstalk effect can have significant impact on the measured intensity. If it is not appropriately accounted for in the evaluation, it can result in a deterioration of accuracy that impedes the possibility of actual atom counting. However, as the number of possible neighbour configurations can be excessively large, a comprehensive consideration of all in the evaluation reference is neigh impossible. This work proposes a method that allows for the a-posteriori reduction of crosstalk during the evaluation by algebraic means. Based on a parametric model, which is described in detail in the article, the crosstalk is expressed by an invertible matrix. Applying the inverted matrix to the measurement yields crosstalk corrected intensity values with very little computational effort. These can subsequently be evaluated by direct comparison to simple reference data. The working principle of the method is presented on the example of crystalline gold. The crosstalk parametrisation is found by fitting a model to sets of specifically created multislice simulations. The parameters are given for both aberration corrected and uncorrected STEM. Subsequently the abilities and potential of the technique are assessed in simulative studies on multiple model systems including gold nanoparticles. Overall a significant and robust improvement of the attainable precision can be demonstrated making the proposed method a promising tool for reference-based atom counting.