Atom column detection from simultaneously acquired ABF and ADF STEM images
Introduction
Due to improvements in aberration correction technology, scanning transmission electron microscopy (STEM) has become a widely used technique to visualize nanomaterials down to sub-angstrom resolution [1], [2]. In particular, annular dark-field (ADF) imaging is a well-established imaging mode in STEM, in which the collection range of the annular detector lies outside of the illumination cone of the focused electron beam [3], [4]. The ADF STEM mode allows to obtain images with atomic resolution and exhibits a strong dependence on atomic number [5], [6]. Yet, merely visually interpreting high-resolution ADF images is insufficient to obtain precise structure information, which is crucial to fully understand the structure-properties relation of nanomaterials, since their physical and chemical properties are strongly dependent on their exact structural and chemical composition. Hence, a quantitative approach is required, which is provided by statistical parameter estimation theory [7], [8], [9], [10], [11], [12]. Recently, it has been shown that the concepts of statistical parameter estimation in STEM can be combined with model-order selection, leading to the so-called maximum a posteriori (MAP) probability rule [13], [14]. This method allows to determine the structure of unknown nanomaterials in an automatic and objective manner and to detect atomic columns and even single atoms from high-resolution ADF STEM images with high reliability. The method is especially useful for the analysis of the structure of beam-sensitive materials. Due to the limited incoming electron dose that should be used to avoid beam damage, images of such materials typically exhibit low signal-to-noise ratio (SNR) and low contrast, and hence low contrast-to-noise ratio (CNR). As a result, a visual determination of the number of atomic columns in such images is unreliable and may lead to biased structure information.
In particular, the visualization of light-element atomic columns from ADF STEM images is challenging since light elements only scatter electrons weakly to high detector angles leading to low intensities in ADF images. As a result, light elements are barely visible and especially difficult to detect in the presence of heavy elements [13], [15], [16]. Interestingly, direct visualization of light elements has been enabled by the annular bright-field (ABF) mode in STEM where an annular detector spanning a range within the illumination cone of the electron beam is used [17], [18]. Due to the fact that ABF image contrast is less dependent on atomic number than ADF contrast [19], [20], light elements can be visualized better in the presence of heavy elements. This reduced dependence on atomic number, though, makes differentiating between atomic columns with close atomic numbers more difficult. In addition, due to dynamical scattering, there is a non-monotonic intensity relationship with atomic number at all thicknesses. As a result, identifying the atom types of columns in an ABF image is not straightforward. Therefore, a simultaneous acquisition of both ABF and ADF STEM images is an interesting option to visualize atoms of a large range of atomic numbers for studying and interpreting materials at the atomic scale consisting of both light and heavy atoms. In case of beam-sensitive materials, the MAP probability rule [13], [14] can be used to determine the number of atomic columns for which there is most evidence in the simultaneously acquired ABF and ADF STEM image data.
Typically, the projected atomic columns in atomic resolution STEM images are modeled as Gaussian peaks superimposed on a constant background [12], [21], [22]. This methodology has been applied predominantly in the analysis of ADF STEM images [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], but it has also been used for obtaining quantitative information from ABF STEM images [34]. In the present paper, alternative parametric models for quantifying simultaneously acquired ABF and ADF STEM images are proposed by extending the commonly used parametric models in STEM. This results in alternative analytical expressions for the recently proposed MAP probability rule. Furthermore, it is shown that the proposed methodology allows to extend the concept of atom detectability [14] to simultaneously acquired ABF and ADF STEM image data. In addition to this, it is shown that the recently introduced ADF image-quality measure, namely the integrated CNR (ICNR) [14], also applies to ABF images and can be extended to simultaneously acquired ABF and ADF images.
This article is organized as follows. In Section 2, the methodology to quantitatively analyze ABF and ADF STEM images simultaneously by the MAP probability rule is described in detail. This is followed in Section 3 by showing that the concepts of atom detectability and ICNR, which were introduced for ADF STEM data, can be extended to simultaneously acquired ABF and ADF images as well. In Section 4, the proposed method is applied to experimental images. Finally, in Section 5, conclusions are drawn.
Section snippets
Model-based parameter estimation
From the viewpoint of statistical parameter estimation theory, STEM images are considered as data planes from which unknown structure parameters need to be estimated. The starting point of this procedure is the construction of a parametric model that describes the expectations of the image pixel values as a function of unknown parameters. Then, quantitative structure information is obtained by fitting the model to the observed experimental data with respect to the unknown parameters using a
Atom detectability, accuracy and precision
Recently, an alternative ADF STEM image-quality measure, ICNR, has been introduced that directly correlates with atom detectability [14]. This means that for increasing ICNR values, the probability of detecting an atom from the image data increases, and vice versa. The ICNR of an individual atomic column in an ADF STEM image is defined as follows [14] where , , and denote the estimated height and width of the column, and the
Experimental examples
In this section, the proposed methodology to detect atomic columns by the MAP probability rule from simultaneously acquired ABF and ADF STEM images is applied to two experimental examples exhibiting low CNR. Hereby, the effect of specimen tilt has been taken into account as small tilts might be present causing a possible shift of the measured atomic column locations in the ABF image as compared to the locations in the ADF image.
Conclusions
In the present paper, a new method for simultaneously analyzing ABF and ADF STEM images using statistical parameter estimation has been introduced. For this, the existing parametric models in STEM have been extended enabling the possibility to simultaneously analyze ABF and ADF image data. Hereby, the effect of specimen tilt, which shifts the ABF peak locations from the true atomic column locations, has been taken into account since small tilts of the electron beam with respect to the crystal
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
The authors acknowledge financial support from the Research Foundation Flanders (FWO, Belgium) through project fundings (No. W.O.010.16N, No. G.0368.15N, No. G.0502.18N, EOS 30489208). 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). The authors acknowledge funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No.
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