Towards atom counting from first moment STEM images: methodology and possibilities

TL;DR

This paper introduces a statistical model-based method for atom counting in first moment STEM images, demonstrating improved accuracy over traditional methods and robustness through comparison with bulk crystal simulations.

Contribution

It develops a novel quantification approach using least squares estimation for atom counting in first moment STEM images, enhancing precision and robustness.

Findings

First moment STEM images enable more precise atom counts than HAADF STEM.

The method accurately estimates atomic column potentials from noisy images.

Bulk crystal simulations serve as reliable reference libraries for atom counting.

Abstract

Through a simulation-based study we develop a statistical model-based quantification method for atomic resolution first moment scanning transmission electron microscopy (STEM) images. This method uses the uniformly weighted least squares estimator to determine the unknown structure parameters of the images and to isolate contributions from individual atomic columns. In this way, a quantification of the projected potential per atomic column is achieved. Since the integrated projected potential of an atomic column scales linearly with the number of atoms it contains, it can serve as a basis for atom counting. The performance of atom counting from first moment STEM imaging is compared to that from traditional HAADF STEM in the presence of noise. Through this comparison, we demonstrate the advantage of first moment STEM images to attain more precise atom counts. Finally, we compare the integrated intensities extracted from first-moment images of a wedge-shaped sample to those values from the bulk crystal. The excellent agreement found between these values proves the robustness of using bulk crystal simulations as a reference library. This enables atom counting for samples with different shapes by comparison with these library values.