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Abstract
In this work, a new Python-based tool for atomic-scale mapping of high-angle annular dark-field (HAADF) and annular bright-field (ABF) scanning transmission electron microscopy (STEM) images using the Z-contrast method is introduced, aimed to help in the analysis of superlattice layers’ composition, and in the determination of material of interfaces. The operation principle of the program, as well as specific examples of use, are explained in many details. Good customization flexibility using the user-friendly graphical user interface (GUI), allows the processing of a wide range of images, demonstrating a decent accuracy of coordinates extraction and performance.
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1. Introduction
In 1977, Sai-Halasz, Esaki, and Tsu [1] proposed the concept of a new semiconductor superlattice, a periodic structure, which contains thin layers of two different materials, with a conduction band of the first material, located close to the valence band of the second one. It was assumed, that due to the quantum-mechanical effects, by tuning the thickness and mole fractions of the host materials, a “tailor-made” semiconductor with a significantly different energy gap can be received. Nowadays, this concept is known as “band engineering”. To improve optical properties by using ultrathin layers, in 1987 the type-II (staggered band gap alignment) strained InAs/GaSb superlattice was introduced by Smith and Mailhiot [2] as a candidate for infrared (IR) detector.
During the last three decades, there have been numerous studies on type-II superlattice [3], and several typical designs, such as 14/7 monolayers of InAs/GaSb for cut-off wavelength ∼10 µm at 77K have been discussed in numerous papers [3–7]. Also, various simulation approaches to the superlattice band calculation exist, based on k.p [4–7] or tight-binding [8] methods, showing a good agreement with experimental data. Despite an illusion of simplicity, the band calculation depends, not only on the selected method but on the geometry of the superlattice, which could contain uncertainties. It is well-known, that no atom in common InAs/GaSb superlattices, typically can possess the Ga-As or In-Sb atomic formation of the interfaces [9]. The In-Sb formation is more favorable for the tensile strain compensation between InAs layers and the GaSb substrate. By tuning of molecular beam epitaxy (MBE) process [10], a GaAs-like interface is typically replaced by a forced InSb-like interface. It improves the optical properties of the structure, however, also impacts the cut-off wavelength [4–6], [10]. Therefore, the type of the interface shouldn’t be ignored during the modeling stage, in order to obtain a better match between prediction and experimental results.
However, based on our own experience, even using a well-known design of the superlattice as a reference (which eliminates the possibility of calculation errors) it still might happen, that the experimental results won't match the expectations. The potential reasons for this mismatch are:
- • types of interfaces are different from the assumed;
- • the deviations from the designed geometry of host (target) layers, which can lead to significant deviations of the cut-off wavelength (see Fig. 1);
- • the deviations of mole fractions of the ternary and quaternary materials.
Fig. 1. Simulated dependence of the cut-off wavelength of the superlattice from the thickness of InAs and GaSb layers. The model includes forced InSb-like interfaces, equally distributed between host layers. The calculation is performed in Nextnano3 [11], with material parameters taken from [5].
To find the actual reason for the mismatch, and optimize the growth conditions, a proper analysis of the sample should be performed. In this paper, we will provide some useful tips on the analysis of fabricated samples based on Z-contrast imaging [12]. Also, a new tool for automatic processing of STEM images, aimed to simplify and speed up the analysis of the results, will be introduced.
2. Samples analysis
A wide variety of techniques are available for the materials analysis, applicable for superlattice interfaces study: X-Ray diffraction [13], transmission electron microscope (TEM) [14], high-resolution STEM [9,15], cross-sectional scanning tunneling microscopy (XSTM) [16, 17], atom probe tomography (APT) [9,18], and energy dispersive X-ray spectroscopy (EDX/EDS) [19]. Among these techniques, the most accessible yet powerful one is HAADF STEM image analysis, based on Z-contrast imaging, widely used for the atomic-scale mapping of superlattices [9,17], [20,21].
The method is based on the analysis of the intensity (contrast) of the atom associated with its atomic number (Z). Depending on the quality and resolution of STEM images as well as the used materials, the complexity of analysis is different. The analysis can be performed for the individual slices of the image, with their further generalization. Receiving such information for each slice within the image manually is time-consuming and can contain errors done by the operator. Additionally, due to the variable intensity of the atoms within the period, the material determination of the interfacial layers can become problematic. As an alternative, the images can be processed using additional software, such as Atomap [22]: a Python library, which allows the extraction of atomic coordinates, as well as multiple additional parameters, aimed to simplify the analysis. Unlike the bulk layer, showing the relatively uniform spacing between atoms and dumbbells, which can be efficiently processed by Atomap, in superlattice, the fluctuation of properties of dumbbells is larger, which makes the analysis more problematic. It is related to the key coordinates extraction algorithm implemented in the package, which will be simplistically explained further.
To receive the coordinates of the dumbbell lattice, where atomic coordinates are grouped into dumbbells for further analysis, the two values of separation between intensity peaks (Δ1 and Δ2) should be estimated. Δ1 corresponds to the spacing between peaks, such as all atomic positions are roughly found. Δ2 corresponds to the spacing between brighter peaks of dumbbells, such as only one peak per dumbbell is extracted. The dumbbells are formed by combining the coordinates extracted for Δ1 and Δ2, as shown in Fig. 2. The functionality of Atomap aimed to simplify the estimation of Δ1 and Δ2, making it intuitive. However, for actual TEM images, such an estimation can be challenging due to the fluctuations of the vertical positions of the dumbbells within the monolayer, the presence of interfaces, as well as due to the image noise. The last factor can be partially suppressed using optional filtering algorithms, however, the two first factors are essential for superlattice.
Fig. 2. Simplified algorithm of coordinates extraction implemented in the Atomap library. Left parts of images correspond to idealized dumbbell lattice, randomly generated by Atomap. Right parts correspond to the actual TEM images of the same scale.
As shown in Fig. 2, using smaller values of separations (Δ1b and Δ2b) allows the extraction of larger number of intensity peaks, some portion of them is spurious. Using larger values of separation (Δ1a and Δ2a) reduces the number of spurious peaks, as well as peaks that correspond to actual atoms. Therefore, there is a trade-off between the loss of useful information and the number of errors, the program can automatically eliminate. Depending on the image quality and the efficiency of filtering, the complexity of estimation of Δ1 and Δ2 is different. However, typically, the few combinations of separation values should be checked, which is time-consuming. Also, as can be seen from the right part of Fig. 2, the proposed optimal (maximum number of useful information is extracted) combination of separation values (Δ1a and Δ2a), didn’t allow the extraction of positions of all dumbbells. A large number of these dumbbells (except for the edges of the image) are situated at the interface, which is indicated by the inversion of the intensity peaks in the middle image of Fig. 2. Loss of such important information is a significant drawback for superlattice analysis and can be overcome only by using another approach to the coordinates extraction.
Also, extraction of the coordinates and corresponding intensities itself is not sufficient to perform the material identification based on the Z-contrast method, especially at the interfaces, where the intensity of atomic peaks is different from the bulk. To overcome these difficulties, as well as to facilitate the analysis of results, we created a Python-based processing kit – Atomic Mapper, which will be discussed in the following section.
3. Python-based atomic mapper
Atomic Mapper is a standalone program, written in Python language, and designed to facilitate the analysis of STEM images by extracting the positions and corresponding properties of dumbbells and atoms within the whole image during a single calculation run. The visualization of results is performed using dumbbell- and atomic overlays, allowing displaying multiple properties of the material and aimed to reduce the complexity and time to perform material identification, which will be discussed in many details in the next chapter.
Atomic Mapper utilizes multiple open-source packages: NumPy [23], OpenCV [24], SciPy [25], HyperSpy [26], Matplotlib [27], scikit-learn [28]. The program doesn’t use the Atomap library [22] and the coordinates extraction approach is different from it. Also, the interaction with the program is performed using the graphical user interface (GUI), shown in Fig. 3, which is aimed to give good flexibility of customization while remaining user-friendly. In contrast, Atomap requires a Python environment and is optimized for IPython [29], while basic programming skills are required from the user. Atomic Mapper supports a wide variety of graphical images, text files, as well as Digital Micrograph data files, which is the typical format of the TEM analysis. The program is designed for the analysis of superlattices and is optimized for the images that contain dumbbells, and are being received in [110] or [$1\bar{1}0$] directions. However, images received for another crystalline orientation and do not contain dumbbells can be also processed if the atoms are aligned horizontally. Both HAADF and ABF images are supported.
Fig. 3. The graphical user interface of the main tab of Atomic Mapper, showing the main program’s features
The efficiency of the coordinates extraction and further analysis depends on the quality of the input image in terms of resolution (pixels per atom) and the presence of noise. The measurement setup has a significant impact on both of these factors. The minimum resolution, required to extract atomic coordinates, depends on the amount and type of noise. Based on our experience, for the images that don’t contain distortions of the shape, it is about 7∼9 pixels per dumbbell’s length. Also, additional noise can be caused by the human factor. Therefore, the processing of the TEM image starts with optional filtering to reduce the noise while minimizing the loss of useful information. Several filtering options are available to get rid of specific types of noise:
- • Principal component analysis (PCA)-based, reported extremely efficient for the processing of STEM images [30] suppressing various types of noise.
- • Brightness normalization using a mask image received by Gaussian blur.
- • A median filter, a very popular tool for the reduction of salt-and-pepper noise [31].
- • Fast mean denoise as an alternative to median filter.
Fig. 5. The preview window with filtered image. The right side represents the effect of the high-pass filter with the corresponding filtering coefficient.
The schematic of the extraction algorithm of atomic coordinates implemented in Atomic Mapper is shown in Fig. 6. First, a high-pass filter is applied, turning pixels with an intensity less than the cutoff value into zeros, while the remaining pixels are used for further extraction of coordinates. A cutoff value divided by the mean pixel intensity within the whole image was called a filtering coefficient (FC). Depending on the brightness and contrast of the initial image, the optimal filtering coefficient can be different. However, typically, FC lies within the 1.0-1.2 range. The impact of the filtering coefficient is displayed in real-time in the preview windows, as shown in Fig. 5. Additionally, Atomic Mapper allows the extraction of multiple results for the pre-defined range of filtering coefficients during a single calculation run.
Using such a contrast-based method, for each group of non-zero pixels, the extraction of coordinates of centers of dumbbells is performed analytically, using the set of scale settings, calculated based on the number of monolayers per image, which can be estimated automatically. Then, the coordinates of atoms are extracted as two local intensity maxima in opposite directions from the center of the dumbbell. Based on the extracted coordinates, the properties of atoms and dumbbells are estimated, which are used for further analysis, and will be discussed in more detail in the following chapter.
Atomic Mapper is designed to give a user more flexibility while trying to reduce the number of operations necessary to run a single calculation. The settings are aimed to be intuitive, yet the user has access to a wide range of calculation parameters. Additional quality-of-life features are implemented such as a planner, save/load settings, built-in manual, error message boxes, and the option to redraw image overlays with different parameters after the calculation is finished. The demonstration version of Atomic Mapper and discussed in this paper TEM images are available on the website of our center [32].
4. Program operation and results analysis
In this section, we will discuss the practical use of the program and provide an example of results analysis. The investigated sample had target geometry of 14/7 monolayers of InAs/GaSb which is the typical type-II superlattice absorber structure for the longwave infrared (LWIR) detector. STEM image, shown in Fig. 7 (left), was received by JEOL JEM-ARM200F electron microscope with HAADF detector in [110] direction. The input file was in .dm3 format with a resolution of 512×512 points. No additional filtering algorithms were applied. The image is relatively clear in terms of atomic shape distortions, however, salt-and-pepper noise is present. Based on the image scale and resolution, the PCA-based filtering was applied to reduce the majority of the noise. Then, the median filter with was used to eliminate the residual noise. The effect of the filtering is shown in Fig. 7 (right).
Fig. 7. Full initial STEM image of LWIR’s absorber with target period composition of 14/7 InAs/GaSb monolayers and enlarged cropped area with a demonstration of filtering using PCA-based and median filters.
Figure 8 shows the dumbbell overlay, displaying extracted coordinates of the dumbbell centers. The positions are limited by the blue frame to avoid spurious results, extracted using cropped dumbbells at the edges of the image. Such an image is less informative than the atomic overlay, however, useful information about the structure’s composition can be extracted. Also, for heavily distorted images, the extraction of atomic coordinates can be problematic. To help in the analysis of the results, the color map of the dumbbell centers corresponds to the mean intensity of the dumbbell, divided by the maximum intensity within the image. On the left side of the image, optional information about layers is provided, such as average spacing and average intensity, aimed to help in the analysis of the results.
Fig. 8. Extracted dumbbell overlay of LWIR’s absorber with target period composition of 14/7 InAs/GaSb monolayers with additional information about layers.
To analyze the dumbbell overlay, the atomic numbers of the host layers should be taken into consideration. The dumbbells which contain In (Z = 49) and As (Z = 33) show smaller intensity contrast between atomic peaks compared to ones containing Ga (Z = 31) and Sb (Z = 51) and have inversed positions of the brightest atom within a dumbbell, as shown in Fig. 9. Due to the fact, that atoms with smaller Z show smaller atomic radius, and because of the application of the high-pass filter, turning the edges of atoms with smaller Z into zeros, the position of the center of a dumbbell becomes shifted towards the brightest atom. Therefore, the points of interest are local extrema, which should correspond to the interfaces: local minimum to In-Sb, and local maximum to Ga-As, as shown in see Fig. 9. From Fig. 8 it can be observed, that the local minimum corresponds to the spacing between layers #4 and #5, however, the spacing between the underlying two layers is also reduced, which can be related to the variable position of the interface, or a presence of InSb or GaAs dumbbells. The reduced mean intensity of layers #4-#6 confirms such an assumption about the close position of the interface because the intensity of interfacial layers is smaller than that of bulk [9,17], [20,21]. By comparing the value of local minimum with adjacent layers, we can conclude, that layer #5 is different from layer #4, therefore, roughly can be identified as InAs. Taking into account the reduced spacing of the underlying layers, we can assume, that a certain number of In atoms is replaced by Ga.
Fig. 9. The schematic of the idealized case of InAs/GaAs interfaces: InSb-like (left) and GaAs-like (right). Black crosses represent the extracted positions of dumbbell centers, shifted towards the larger (brighter) atoms, creating a local minimum of spacing at the InSb-like interface, and a local maximum at GaAs-like one.
The local maximum of the spacing corresponds to the distance between layers #18-#19, which is similar to the previous case related to the inversion of the atoms with the largest Z-value within the dumbbell. However, spacing between layers #17 and #18 is also increased, compared to spacing of InAs layers which lay above. Therefore, layer #18 is assumed to be corresponding to a different material. Similar to the previous case, we can assume, that position of the interface is non-constant, or some GaSb dumbbells of layer #18 are replaced by InSb or GaAs. Knowing, the details of the fabrication process (MBE sequence), and based on the reference papers, the proposed material composition can be confirmed. However, to demonstrate the self-sufficiency of our program, as well as to investigate potential anomalies of the structure’s composition, we will continue our analysis using more advanced methods.
For such a purpose, Atomic Mapper provides atomic overlays, visualizing different parameters of the atoms and dumbbells with individual color maps. Using a scaled diverging color map gives a focus on the middle part of the parameter’s distribution, while a sequential color map more efficiently highlights the values, situated at the edges, as it was used in the dumbbell overlay. For the diverging color maps, the divergence point can be selected based on the probability distribution, calculated using kernel density estimation (KDE) method with Gaussian kernel (implemented using scikit-learn [28] package) or taken as a value, situated at the center of the distribution. In contrast, in Atomap only the second option is available, which makes the analysis less intuitive.
The probability-dependent option was created for the cases when parameters of different materials have a different range of deviations. Therefore, for such a case, taking a central value as a divergence point is incorrect. Also, during the program tuning, we noticed, that spurious results typically situated at the edges of parameter distribution, therefore, can have a significant impact on the divergence point, taken as the center of the distribution. The physical meaning of a divergence point is a position of transition from one material to another one.
To determine the material composition of the interfacial layers, we will display the peak intensity of top and bottom atoms on the atomic overlay, as shown in Fig. 10. Scaled diverging color maps with probability-based positions of divergence points are used, while the colormap for the bottom atom has inverted colors, to make analysis more intuitive.
Fig. 10. Atomic overlay of LWIR’s absorber with target period composition of 14/7 InAs/GaSb monolayers, displaying peak intensities for the top and bottom atoms.
Several algorithms for finding the divergence point of the color map are programmed, based on the assumption, that the parameter distribution can be expressed by the Gaussian functions. If the distribution has two distinguishable peaks, the 3σ-based approach is used, where σ is the standard deviation, extracted from the half-width at half maximum (HWHM) towards the opposite direction from the interface, as shown in Fig. 11. The selection of HWHM instead of full width at half maximum (FWHM) is aimed to eliminate the impact of the interfaces on the σ. The values which lay within the 3σ range should correspond to the host material. The values which lay outside can correspond to different materials. In the case of the overlap of 3σ regions corresponding to different peaks, the overlapped region is assumed to have both host materials, while the divergence point corresponds to the value, equally divided between both materials.
The selection of the divergence point is analytical and depends on the image scale, quality, and the number of layers of the host materials. The main algorithm is dividing the region between 3σ positions (independently from the fact of overlap), proportional to the corresponding values of standard deviations. If the distribution minimum lies in the close range from this position, the program uses this minimum as a divergence point, as shown in Fig. 11 (left). Otherwise, the initial position, proportional to σ, is taken, as it is shown in the right histogram. Potentially, the program can be improved by implementing the support-vector machine (SVM) algorithm [33] for the extraction of the divergence point based on the shape of the multi-dimensional hyperplane. However, the following problems must be solved first:
- • selection of training-data points that are not affected by noise to avoid the error of the construction of hyperplane;
- • selection of the kernel and its parameters.
From Fig. 11 we can see that both distributions of the top (Ga-In) and bottom (As-Sb) atoms have overlapped 3σ regions, which makes the analysis not straightforward. However, we can confirm the previous assumption, that proposed interfacial layers, #5 and #18, showing more similar to #6 and #19, rather than to layers lying above. Also, the intensity of the majority of bottom atoms of layer #5 lies outside the overlapped region closer to As distribution peak, while the remaining atoms lay very close to the 3σ position. Therefore, it can be concluded that this atomic layer is As. The top atoms of this layer lie inside the overlapped region, however, closer to the Ga peak, which means that the majority of atoms in this layer should correspond to Ga. For layer #18, the majority of bottom atoms lie outside overlapped 3σ region, close to the Sb peak. For the top peak, the majority of atoms lie within the overlapped region, and similar to a top atom of layer #5, contain Ga and In atoms.
The non-constant brightness of the HAADF image, related to sample thickness variation, has an impact on the extracted values of intensity. Also, due to the small image resolution, the impact of a single very bright pixel per atom can have a significant impact on the filtered image. Therefore, due to salt-and-pepper noise, masking such peak values, the extracted intensity might be inaccurate. To minimize such negative factors, we suggest displaying intensity difference as one of the parameters of the atomic overlay. Unlike individual intensities, the intensity difference is normalized by the maximum value within the dumbbell. It allows compensating for the impact of brightness variation. Such an atomic overlay is shown in Fig. 12, displaying the atomic spacing for the bottom atom, which is recommended default atomic overlay setting. The diverging color map is used for the top atom, with a probability distribution, shown at the right. Unlike the previous atomic overlay, the 3σ region shows no overlap, and the divergence point was selected proportionally to standard deviations. We can notice, that majority of values of layer #18 are situated between the 3σ region of GaSb and a divergence point, while a majority of values of layer #5 lay between 3σ region of InAs and a divergence point. Therefore, we can assume, that the dominant dumbbell type in layer #18 is InSb, while for layer #5 it is GaAs. This assumption can be also confirmed by comparing the spacing between peaks, which is larger for layer #18. Additionally, Atomic Mapper generates the supplementary overlay, fragments of which are shown as insets on the atomic overlay, demonstrating the difference between interfaces. In general, the structure corresponds to a typical case with non-forced interfaces, having mixed InSb-like and GaAs-like interfaces [9]. After the material identification is finished, the information about the thickness of layers can be easily extracted from the output text files, generated by the program.
Fig. 12. Atomic overlay of 14/7 monolayers of InAs/GaSb (left), displaying intensity difference for the top atom and atomic spacing for the bottom atom; intensity difference probability distribution (right).
5. Possible calculation errors and ways to avoid them
Discussed in the previous chapter example demonstrates the general approach to the processing of STEM images. However, to avoid spurious results processing an arbitrary image, we need to discuss some additional details. First, the intensity of the atomic peaks depends on the parameters of the HAADF or ABF sensor, therefore, the same structure might have different intensity distributions, obtained by different microscopes.
Additionally, if the brightness of the image is varying, and the brightness normalization algorithm is activated, the visualization of atomic brightness of individual atoms will have a certain error, related to the subtraction of the Gaussian mask. For such cases, we suggest analyzing intensity difference, as the less sensitive parameter, however, is still affected by this filtering algorithm. Also, we suggest double-checking the assumed material composition using dumbbell- and supplementary overlays.
The errors in the algorithms of estimation of the divergence point of the probability distribution can be related to unequally cropped layer, which leads to the distortions of shape of the Gaussian distribution, and, as a result, incorrect values of standard deviations. In the idealized case, the number of layers per image should be expressed as:
where A and B are target numbers of monolayers of host materials per period, while m and n are integer numbers. If the number of periods per image is large, the impact of m and n is reduced, however, the total accuracy of extracted coordinates is also reduced, due to the decrease of the number in pixels per atom. Also, there is a lower limit of m×A and n×B, which is necessary to form a non-distorted shape of Gaussian. Figure 13 shows combined atomic overlays of 4/10 (A/B) InAs/GaSb superlattice displaying intensity difference and atomic spacing. A larger-scale image contains 19 monolayers and covers only a single period thickness of InAs (m = 1), while having ∼1.5 periods thickness of GaSb (n = 1.5), including 3 interfaces. The corresponding probability distribution showed in Fig. 14 (left). Having m×A = 4 doesn’t allow obtaining a clear shape of the Gaussian, therefore, the extracted position of the peak and standard deviation might be inaccurate. For the GaSb layer, the Gaussian shape looks fine, however, having n = 1.5 extends HWHM as shown by the dashed line, which corresponds to the case with n = 1.Fig. 13. Combined atomic overlays of 4/10 monolayers of InAs/GaSb, displaying intensity difference for the top atom and atomic spacing for the bottom atom.
The right part of the combined image of Fig. 13 has 40 layers and m = n = 3, which is sufficient to form two Gaussians with acceptable shape, shown in Fig. 14 (right). The distribution looks similar to the case, investigated in the previous chapter, showing no overlap between 3σ regions. An insignificant difference between absolute values of the intensities, obtained during different calculation runs is related to a different level of the background noise of initial images. Therefore, extraction of divergence point from one image and applying it to the different one can lead to errors, however, can still be used as an initial position, with further confirmation or modification using additional overlays.
Finally, as it was mentioned before, the incorrect results can be caused by TEM image quality (distortions of the shape, high level of noise, low image resolution, etc). We don’t want to discuss these cases in this paper, assuming that they are abnormal. However, the approaches to the processing of such images, obtained using different microscopes, are provided on the website of our center [32].
6. Comparison of extraction efficiency with Atomap
In this chapter, we would like to compare the performance and extraction efficiency of our program with Atomap, using the image of the previously discussed structure, shown in Fig. 13 (right). To ensure our readers, that the optimal combination of the separation values (Δ1 and Δ2), discussed in chapter 2, was taken, three combinations were used, as shown in Fig. 15. Combinations with smaller values of Δ1 don’t allow forming of the dumbbells due to a large number of spurious peaks. Additionally, the image was filtered using the default algorithm implemented in Atomap, including PCA-based filtering and brightness normalization. The output results were presented as atomic overlays, to make a comparison with our program more intuitive.
Fig. 15. Atomic overlays of 4/10 monolayers of InAs/GaSb, extracted by Atomap with different combinations of peak separations.
The calculation time, necessary to generate one overlay is about 130 seconds, which includes coordinates refinement using 2D Gaussians, necessary for more accurate positions of atoms. This time doesn’t include the time, necessary to estimate the optimal combination of Δ1 and Δ2, which makes the actual calculation time even longer. In contrast, Atomic Mapper generates atomic overlay and all supplementary images and text files in about 50 seconds using the same PC. However, due to the algorithm of the automatic estimation of the scale settings, the preparation time before the launch of the extraction algorithm was negligible.
In terms of the accuracy of extracted results, programs show relatively similar performance in the middle of layers. However, at the interfaces, as it was mentioned before, for the Atomap, there is a trade-off between spurious and lost peaks. Practically, the uncertainties with the material identification won’t allow to build an accurate model of such structure. Also, due to the presense of spurious peaks, Atomap faces the problems of results reproducibility, as shown if Fig. 16, where both of images were calculated using identical code. In contrast, Atomic Mapper extracts overwhelming number of peaks at the interfaces, using automatic scale and filtering settings, while results reproducibility is perfect.
Fig. 16. Atomic overlays of 4/10 monolayers of InAs/GaSb, extracted by Atomap with the same combination of peak spacing to demonstrate the problem of results reproducibility.
Another drawback of Atomap is shown in Fig. 16 (right). The spurious dumbbell at the left corner of the image with a significantly different intensity difference (bottom peak corresponds to the noise) shifted the divergence point of the corresponding color map towards positive values, making the identification of interfacial material confusing. However, the problem is more global, because, for such an approach, the divergence point depends on the values situated at the edges of the parameters’ distribution and can potentially correspond to the improperly extracted data. Probability-dependent color maps, implemented in Atomic Mapper, and discussed in chapters 4 and 5, allow to get rid of this problem because the position of divergence point is calculated based on the positions of distribution peaks rather than the edges.
Finally, we need to mention, that Atomap is a library, and some functionality, such as additional filtering options, analytical algorithms of spurious results elimination, etc., already implemented in Atomic Mapper, can be combined with the Atomap’s functions, which can potentially get rid of specific problems. However, it will also increase the calculation time related to the key algorithms of the coordinates extraction. Also, we need to admit that the functionality of Atomap is generally wider in terms of supported types of TEM images and visualization options. However, the program’s functionality for the dumbbell lattices processing is not optimized for the superlattices due to the essential properties of such images.
7. Conclusions
The properties of the type-II superlattice, widely used as an absorber for the photodetectors, depend on the host materials, period composition, and types of the interfaces. The need to control these parameters is an important issue during the design and fabrication of an actual device. For such a purpose, we introduced the standalone program, Atomic Mapper, written in Python language. The program performs the extraction of dumbbell- and atomic coordinates of STEM images, which are used for the material analysis based on the Z-contrast method. Unlike the existing solution with similar functionality, the Atomap library (requires a Python environment), for actual STEM images of superlattices our program shows better performance, doesn’t require programming skills, and generates results that make the material identification more intuitive. Additionally, Atomic Mapper is designed to be user-friendly, having a wide variety of quality-of-life features, and aimed to reduce the number of operations necessary to run a single calculation. The demonstration version of Atomic Mapper and discussed in this paper TEM images are available on the website of our center [32].
The program might be useful for the researchers, working with superlattices, and not having access to the most advanced imaging techniques, such as APT and EDX/EDS. The extracted results can be used for tuning the MBE process for the desired structure geometry, for the calibration of the models, used for band calculation of the absorber, or the device simulation of the photodetector.
Funding
Civil-Military Technology Cooperation Program (1415170981); Brain Korea 21 Program for Leading Universities & Students; Agency for Defense Development.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are available on the website of our center [32].
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