Single Atom Detection from Low Contrast-to-Noise Ratio Electron Microscopy Images

Single atom detection is of key importance to solving a wide range of scientific and technological problems. The strong interaction of electrons with matter makes transmission electron microscopy one of the most promising techniques. In particular, aberration correction using scanning transmission electron microscopy has made a significant step forward toward detecting single atoms. However, to overcome radiation damage, related to the use of high-energy electrons, the incoming electron dose should be kept low enough. This results in images exhibiting a low signal-to-noise ratio and extremely weak contrast, especially for light-element nanomaterials. To overcome this problem, a combination of physics-based model fitting and the use of a model-order selection method is proposed, enabling one to detect single atoms with high reliability.

Figure 1

(a) HAADF image of ${\mathrm{SrTiO}}_3$ [100] with an incoming electron dose of $(9.1\pm 0.4)\times {10}^5{e}^{-}/{\AA }^2$ and a minimum column CNR of 71.6. The region indicated by the square has been magnified in the inset, where Sr columns and Ti-O columns are indicated in red and green, respectively. (b) Noisier counterpart of the inset in (a) with an incoming electron dose of $(1.08\pm 0.05)\times {10}^4{e}^{-}/{\AA }^2$ and a minimum column CNR of 5.2. (c) MAP probability rule evaluated for the experimental data shown in (b). Refined models with optimized parameters are shown in the inset, taking into account 12, 13, and 14 atomic columns, where the most probable parametric model is the one containing 13 atomic columns, as indicated by the MAP probability rule. (d) Synthetic ADF image of graphene obtained from an experimental 4D STEM data set with an incoming electron dose of around $3\times {10}^5{e}^{-}/{\AA }^2$ and a minimum column CNR of around 6.1. (e) MAP probability rule evaluated for the experimental data shown in (d). (f) Most probable parametric model of the experimental data in (d) as indicated by the MAP probability rule in (e).

Figure 2

(a) Experimental HAADF image of a Au nanorod with an incoming electron dose of around $2\times {10}^5{e}^{-}/{\AA }^2$ and a minimum column CNR of around 11.1. (b) Most probable atomic columns detected from (a) by a combination of an ordinary peak-finding routine and the MAP probability rule near the edge of the rod, where columns in red have been detected by the ordinary peak-finding routine, columns in yellow by both the ordinary peak-finding routine and the MAP probability rule, and columns in green by the MAP probability rule only. (c) Simulated HAADF image of a Au nanorod with the presence of Poisson noise with an incoming electron dose of $5000e^{-}/{\AA }^2$ and a minimum column CNR of 8.9. (d) Most probable atomic columns detected from (c), where the arrow indicates an atom detected at a position where no atom was present.

Figure 3

(a),(c),(e) Sequence of HAADF STEM images of a Ge cluster with an incoming electron dose of around $6.8\times {10}^4{e}^{-}/{\AA }^2$ and a minimum column CNR of around 21.0. (b),(d),(e) Most probable parametric model of the experimental data in (a),(c),(e) indicated by the MAP probability rule with atom-counting results added in which green, red, and blue dots correspond to 1, 2, or 3 atoms, respectively.