Geometric phase analysis (GPA), a fast and simple Fourier space method for strain analysis, can give useful information on accumulated strain and defect propagation in multiple layers of semiconductors, including quantum dot materials. In this work, GPA has been applied to high resolution Z-contrast scanning transmission electron microscopy (STEM) images. Strain maps determined from different g vectors of these images are compared to each other, in order to analyze and assess the GPA technique in terms of accuracy. The SmartAlign tool has been used to improve the STEM image quality getting more reliable results. Strain maps from template matching as a real space approach are compared with strain maps from GPA, and it is discussed that a real space analysis is a better approach than GPA for aberration corrected STEM images

Holmestad, Randi

Nord, Magnus

Reenaas, Turid W.

Vatanparast, Maryam

Vullum, Per Erik

Zuo, Jian-Min

Journal of Physics : Conference Series

English

Enlighten

Journal of Physics: Conference SeriesPAPER • OPEN ACCESSStrategy for reliable strain measurement inInAs/GaAs materials from high-resolution Z-contrast STEM imagesTo cite this article: Maryam Vatanparast et al 2017 J. Phys.: Conf. Ser. 902 012021 View the article online for updates and enhancements.Related contentOptical strain measurementsE Marom and R K Mueller-Exploring semiconductor quantum dotsand wires by high resolution electronmicroscopyS I Molina, P L Galindo, L Gonzalez et al.-Dislocation-free axial InAs-on-GaAsnanowires on siliconDaria V Beznasyuk, Eric Robin, MartienDen Hertog et al.-This content was downloaded from IP address 130.209.115.202 on 27/11/2017 at 12:171Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distributionof this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.Published under licence by IOP Publishing Ltd1234567890Electron Microscopy and Analysis Group Conference 2017 (EMAG2017) IOP PublishingIOP Conf. Series: Journal of Physics: Conf. Series 902 (2017) 012021  doi :10.1088/1742-6596/902/1/012021      Strategy for reliable strain measurement in InAs/GaAs materials from high-resolution Z-contrast STEM images  Maryam Vatanparast1, Per Erik Vullum1, 2, Magnus Nord3, Jian-Min Zuo4, Turid W. Reenaas1 and Randi Holmestad1 1 Department of Physics, Norwegian University of Science and Technology - NTNU, 7491, Trondheim, Norway 2 SINTEF Materials and Chemistry, 7465, Trondheim, Norway 3 SUPA, School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom 4 Dept. of Materials Science and Engineering, University of Illinois, Urbana, 61801, USA                               Email: maryam.vatanparast@ntnu.no Abstract. Geometric phase analysis (GPA), a fast and simple Fourier space method for strain analysis, can give useful information on accumulated strain and defect propagation in multiple layers of semiconductors, including quantum dot materials. In this work, GPA has been applied to high resolution Z-contrast scanning transmission electron microscopy (STEM) images. Strain maps determined from different g vectors of these images are compared to each other, in order to analyze and assess the GPA technique in terms of accuracy. The SmartAlign tool has been used to improve the STEM image quality getting more reliable results. Strain maps from template matching as a real space approach are compared with strain maps from GPA, and it is discussed that a real space analysis is a better approach than GPA for aberration corrected STEM images. 1.  Introduction GPA is a novel and widely applied technique that can be used for quantitative measurements of lattice strains in both high-resolution transmission electron microscopy (HRTEM) and atomic resolution high angular annular dark field (HAADF) STEM images. The method is based on the assumption that there exists a constant spatial relationship between the intensity maxima and the location of lattice planes in the studied material [1]. This relationship appears in the form of a spatial shift of the intensity maxima positions with respect to the lattice. With the development of probe aberration correctors in STEM, sub-Ångström resolution now can be achieved with relatively uniform contrast, providing precise atomic-column positions and clear contrast to map the strain field. Nevertheless, additional precautions must be taken in experimental images to avoid unwanted effects from the microscope or the specimen that can produce incorrect strains. Questions also remain on the best strategy for strain mapping, and in GPA also to which two g vectors should be chosen in the Fourier transform to create the strain maps [2]. 2.  Experimental Details In the present work, the GPA technique is applied to experimental HRSTEM images of InAs/GaAs quantum dot (QD) based intermediate band solar cell (IBSC) materials. The aim is to study strain relaxation mechanisms during the growth process of III–V semiconductors. The IBSC utilizes multiple band gaps in order to increase the efficiency beyond the Shockley-Queisser limit [3]. A necessary but challenging step towards fabricating high efficiency QD based IBSCs is to precisely control the QD structures, including strain, which requires accurate structure information. The InAs/GaAs QD materials studied here were grown by molecular beam epitaxy (MBE), in the Stranski-Krastanov (SK) growth mode on [001] GaAs substrates. The lattice mismatch between two materials in SK growth is used to create the QDs. For pure InAs grown epitaxially on GaAs, the mismatch is 7.2%, and the mismatch is smaller when there is a mixing between In and Ga. Thus, the maximum strain is expected at 7.2%. This 21234567890Electron Microscopy and Analysis Group Conference 2017 (EMAG2017) IOP PublishingIOP Conf. Series: Journal of Physics: Conf. Series 902 (2017) 012021  doi :10.1088/1742-6596/902/1/012021      strain can be a problem when growing multiple layers of QDs, due to formation of defects, which might act as recombination centers. To compensate for the inherent strain, one can introduce nitrogen in the spacer layers. The small N atoms are supposed to cancel out the strain introduced by the large In atoms. The experimental HAADF-STEM images in Figs. 1 and 4 were taken using a double Cs-corrected, JEOL ARM-200CF microscope, at 200 kV, and the HAADF-STEM image in Fig. 2 was acquired using a 300kV FEI Titan with a Cs probe corrector. All images were taken with the electron beam parallel to the crystallographic [110] direction. 3.  Results and discussion  A major issue in using HAADF-STEM images for strain mapping is the scan noise due to the flyback errors in the STEM scanning coils. A strategy to reduce the scan noise, and also to improve the quality of HAADF-STEM images, is to use multiple images recorded with a short scan dwell time and at 0° and 90 scan directions. Fig. 1 compares the effectiveness of this strategy by comparing the yy map obtained from a single HAADF-STEM image and the scan noise corrected HAADF-STEM image using the SmartAlign tool [4]. We have used a very short dwell time of 2 s, and recorded up to 40 frames at 0 and 90̊ rotations. The SmartAlign tool [4] superposes this image stack into a single image. Much of the noise and horizontal, artificial strain lines seen in the strain map from a single STEM image acquired with the pixel time of 38.8 s are removed in the strain map of the HAADF-STEM image after applying SmartAlign with 90 ̊ rotation between every image in the stack that is shown in Fig.1 (b). We observe in Fig. 1 (d) that the systematic lines are removed from the strain map.              The GPA requires two independent Bragg spots as a pair in the Fourier spectrum. The choice of the pair could have a large impact on the GPA results. In Fig. 3, GPA has been applied on different pairs in the fast Fourier transform (FFT) of the single HAADF-STEM image in Fig. 2. Strain maps obtained from (004)/(220), (002)/(220) and {111} pairs (a-c) using GPA show that in case of (004)/(220) the noise is doubled compared with {111}, and that {111} reflections give the best result from GPA in this case. The (002)/(220) pair gives a somewhat different strain map. The (002) reflection in InGaAs/GaAs is composition sensitive, while the (004) reflection is strain sensitive. In principle, the (004)/(220) pair is a good choice since these two reflections are orthogonal to each other and thus provide the most Figure 1. HAADF-STEM image of InAs/GaAs QD, before (a) and and after (b) applying the SmartAlign with 90̊ rotation, (c) yy strain measured from (a), (d) yy strain measured from (b). The Bragg spots highlighted in the inset FFT in (c) areused to create strain maps.   31234567890Electron Microscopy and Analysis Group Conference 2017 (EMAG2017) IOP PublishingIOP Conf. Series: Journal of Physics: Conf. Series 902 (2017) 012021  doi :10.1088/1742-6596/902/1/012021      information. However, the problem with the use of (004)/(220) in the case of Fig. 2 is noise. A single STEM image is too noisy for the low intensity reflections, such as (004). The scanning noise is a kind of high frequency noise and (004) is also affected. So, the overall noise of (004) in a single HAADF-STEM image is high.    An atomic resolution image contains multiple reflections or spatial frequencies, and GPA only uses two frequencies to calculate strain, as Fig. 3 demonstrates. While the  approach used by GPA is advantageous for the analysis of HRTEM images of limited spatial resolution, ideally, the analysis of aberration Figure 2. High resolution HAADF STEM image of InAs/GaAs QD. Figure 3. (d-f) yy strain measured from Fig. 2 using the Bragg spots highlighted in the (a-c) FFTs. Figure 4. (a) HAADF STEM image of InAs/GaAs wetting layer after applying the SmartAlign, (b and c) xx strain maps for strain parallel to thecrystallographic [001] direction from (a) using the Bragg spots {111} and (004)/(220), respectively in the FFTs. (d) xx strain map from TeMA, (e) The strain profile along a line crossing through the wetting layers shown with dashed lines in (b and c), (f) The strain profile along a line crossing through the wetting layers shown with dashed lines in (d). 41234567890Electron Microscopy and Analysis Group Conference 2017 (EMAG2017) IOP PublishingIOP Conf. Series: Journal of Physics: Conf. Series 902 (2017) 012021  doi :10.1088/1742-6596/902/1/012021      corrected STEM images should take the advantages of all frequencies, and this can be achieved using real space based methods based on atomic peak finding or template matching (TeMA) [5, 6]. In these methods, the position of the atomic columns is determined by the intensity distribution, which utilizes all information recorded in the image. Fig. 4a shows a HAADF STEM image a GaAs/InAs wetting layer after applying the SmartAlign algorithm. GPA and TeMA have been used to measure the strain in this image. Fig. 4 (b and c) show the strain map from {111} and (004)/(220) reflections, respectively, and Fig. 4 (d) is the strain map from TeMA. The profiles in Fig.4 (e and f) that are taken from Fig. 4(b-d) show that (004)/(220) is in closer agreement with the real space approach (TeMA), and {111} gives systematic noise and interfacial features that are not seen in (004)/(220). This could be a Fourier termination effect due to the stronger background in the FFT spectrum near the {111} reflections.   Finally, thin foil relaxation effects are not taken into account in the strain measurements since the dimensions of the QDs are small and the sample is not extremely thin. Together, we expect the relaxation happens mostly on the same surfaces [7].  4.  Conclusions In conclusion, we have demonstrated several strategies for improving the results of strain analysis by GPA of the InAs/GaAs quantum dot (QD) material, including 1) The image quality can be significantly improved by performing multiple scans with 0° and 90° rotations and by using SmartAlign to reduce noise and scan errors. 2) The choice of g vectors in the GPA procedure can have a large impact on the strain mapping results. The use of {111} reflections are the most effective in case of a single HAADF-STEM image. However, the same {111} pair applied to the improved HAADF-STEM image revealed artefacts at the wetting layer interface. 3) By using SmartAlign for a series of images to improve the signals at high frequencies, and as it is shown in Fig. 4c, the (004)/(220) reflections gave the best results when using GPA for strain measurements. The data in this paper also shows that GPA analysis using only one pair of reflections has its limitations since it does not take advantage of all information recorded at atomic resolution. For GPA, the challenge is how to combine information obtained by using different Fourier pairs in order to obtain true strain information. With aberration corrected microscopes the resolution is much higher, and by using SmartAlign we get better atomic resolution images, which definitely improves the GPA analysis. However, still additional information can be picked up with real space approaches which use information from all frequencies and would be a better approach than GPA.  Acknowledgments The Norwegian Research Council is acknowledged for funding the HighQ-IB project under contract no. 10415201. The (S)TEM work was carried out on the NORTEM infrastructure at the TEM Gemini Centre, NTNU, Norway. JMZ is supported by Onsager Professorship of NTNU. References [1] Hÿtch M J, Snoeck E and Kilaas R 1998 Ultramicroscopy 74 131-146 [2] Peters J J P et al. 2015 Ultramicroscopy 157 91-97 [3] Shockley W and Queisser H J 1961 Journal of Applied Physics 32 510 [4] Jones L and Yang H 2015 Advanced Structural and Chemical Imaging 1 1-16 [5] Kim H, Meng Y, Rouviére J L and Zuo J M 2017 Micron 92 6-12 [6] Nord M, Vullum P E, MacLaren I, Tybell T and Holmestad R 2017 Advanced Structural and                    Chemical Imaging 3 9 [7]     Treacy, M. M. J. and J. M. Gibson 1986  Journal of Vacuum Science & Technology B 4, 1458-1466. 

Strategy for reliable strain measurement in InAs/GaAs materials from high-resolution Z-contrast STEM images

Nord, Magnus Kristofer

Zuo, Jian Min

Reenaas, Turid Worren

NORA - Norwegian Open Research Archives

Enlighten: Publications

Journal of Physics: Conference Series
PAPER • OPEN ACCESS
Strategy for reliable strain measurement in
InAs/GaAs materials from high-resolution Z-
contrast STEM images
To cite this article: Maryam Vatanparast et al 2017 J. Phys.: Conf. Ser. 902 012021
 
View the article online for updates and enhancements.
Related content
Optical strain measurements
E Marom and R K Mueller
-
Exploring semiconductor quantum dots
and wires by high resolution electron
microscopy
S I Molina, P L Galindo, L Gonzalez et al.
-
Dislocation-free axial InAs-on-GaAs
nanowires on silicon
Daria V Beznasyuk, Eric Robin, Martien
Den Hertog et al.
-
This content was downloaded from IP address 130.209.115.202 on 27/11/2017 at 12:17
1Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution
of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Published under licence by IOP Publishing Ltd
1234567890
Electron Microscopy and Analysis Group Conference 2017 (EMAG2017) IOP Publishing
IOP Conf. Series: Journal of Physics: Conf. Series 902 (2017) 012021  doi :10.1088/1742-6596/902/1/012021
 
 
 
 
 
 
Strategy for reliable strain measurement in InAs/GaAs 
materials from high-resolution Z-contrast STEM images 
 
Maryam Vatanparast1, Per Erik Vullum1, 2, Magnus Nord3, Jian-Min Zuo4, Turid 
W. Reenaas1 and Randi Holmestad1 
1 Department of Physics, Norwegian University of Science and Technology - NTNU, 
7491, Trondheim, Norway 
2 SINTEF Materials and Chemistry, 7465, Trondheim, Norway 
3 SUPA, School of Physics and Astronomy, University of Glasgow, Glasgow, United 
Kingdom 
4 Dept. of Materials Science and Engineering, University of Illinois, Urbana, 61801, 
USA 
 
                             Email: maryam.vatanparast@ntnu.no 
Abstract. Geometric phase analysis (GPA), a fast and simple Fourier space method for strain 
analysis, can give useful information on accumulated strain and defect propagation in multiple 
layers of semiconductors, including quantum dot materials. In this work, GPA has been applied 
to high resolution Z-contrast scanning transmission electron microscopy (STEM) images. Strain 
maps determined from different g vectors of these images are compared to each other, in order 
to analyze and assess the GPA technique in terms of accuracy. The SmartAlign tool has been 
used to improve the STEM image quality getting more reliable results. Strain maps from template 
matching as a real space approach are compared with strain maps from GPA, and it is discussed 
that a real space analysis is a better approach than GPA for aberration corrected STEM images. 
1.  Introduction 
GPA is a novel and widely applied technique that can be used for quantitative measurements of lattice 
strains in both high-resolution transmission electron microscopy (HRTEM) and atomic resolution high 
angular annular dark field (HAADF) STEM images. The method is based on the assumption that there 
exists a constant spatial relationship between the intensity maxima and the location of lattice planes in 
the studied material [1]. This relationship appears in the form of a spatial shift of the intensity maxima 
positions with respect to the lattice. With the development of probe aberration correctors in STEM, sub-
Ångström resolution now can be achieved with relatively uniform contrast, providing precise atomic-
column positions and clear contrast to map the strain field. Nevertheless, additional precautions must be 
taken in experimental images to avoid unwanted effects from the microscope or the specimen that can 
produce incorrect strains. Questions also remain on the best strategy for strain mapping, and in GPA 
also to which two g vectors should be chosen in the Fourier transform to create the strain maps [2]. 
2.  Experimental Details 
In the present work, the GPA technique is applied to experimental HRSTEM images of InAs/GaAs 
quantum dot (QD) based intermediate band solar cell (IBSC) materials. The aim is to study strain 
relaxation mechanisms during the growth process of III–V semiconductors. The IBSC utilizes multiple 
band gaps in order to increase the efficiency beyond the Shockley-Queisser limit [3]. A necessary but 
challenging step towards fabricating high efficiency QD based IBSCs is to precisely control the QD 
structures, including strain, which requires accurate structure information. The InAs/GaAs QD materials 
studied here were grown by molecular beam epitaxy (MBE), in the Stranski-Krastanov (SK) growth 
mode on [001] GaAs substrates. The lattice mismatch between two materials in SK growth is used to 
create the QDs. For pure InAs grown epitaxially on GaAs, the mismatch is 7.2%, and the mismatch is 
smaller when there is a mixing between In and Ga. Thus, the maximum strain is expected at 7.2%. This 
21234567890
Electron Microscopy and Analysis Group Conference 2017 (EMAG2017) IOP Publishing
IOP Conf. Series: Journal of Physics: Conf. Series 902 (2017) 012021  doi :10.1088/1742-6596/902/1/012021
 
 
 
 
 
 
strain can be a problem when growing multiple layers of QDs, due to formation of defects, which might 
act as recombination centers. To compensate for the inherent strain, one can introduce nitrogen in the 
spacer layers. The small N atoms are supposed to cancel out the strain introduced by the large In atoms. 
The experimental HAADF-STEM images in Figs. 1 and 4 were taken using a double Cs-corrected, JEOL 
ARM-200CF microscope, at 200 kV, and the HAADF-STEM image in Fig. 2 was acquired using a 
300kV FEI Titan with a Cs probe corrector. All images were taken with the electron beam parallel to 
the crystallographic [110] direction. 
3.  Results and discussion  
A major issue in using HAADF-STEM images for strain mapping is the scan noise due to the flyback 
errors in the STEM scanning coils. A strategy to reduce the scan noise, and also to improve the quality 
of HAADF-STEM images, is to use multiple images recorded with a short scan dwell time and at 0° and 
90 scan directions. Fig. 1 compares the effectiveness of this strategy by comparing the yy map obtained 
from a single HAADF-STEM image and the scan noise corrected HAADF-STEM image using the 
SmartAlign tool [4]. We have used a very short dwell time of 2 s, and recorded up to 40 frames at 0 
and 90̊ rotations. The SmartAlign tool [4] superposes this image stack into a single image. Much of the 
noise and horizontal, artificial strain lines seen in the strain map from a single STEM image acquired 
with the pixel time of 38.8 s are removed in the strain map of the HAADF-STEM image after applying 
SmartAlign with 90 ̊ rotation between every image in the stack that is shown in Fig.1 (b). We observe in 
Fig. 1 (d) that the systematic lines are removed from the strain map.  
 
 
 
 
 
 
 
 
 
 
 
 
The GPA requires two independent Bragg spots as a pair in the Fourier spectrum. The choice of the pair 
could have a large impact on the GPA results. In Fig. 3, GPA has been applied on different pairs in the 
fast Fourier transform (FFT) of the single HAADF-STEM image in Fig. 2. Strain maps obtained from 
(004)/(220), (002)/(220) and {111} pairs (a-c) using GPA show that in case of (004)/(220) the noise is 
doubled compared with {111}, and that {111} reflections give the best result from GPA in this case. 
The (002)/(220) pair gives a somewhat different strain map. The (002) reflection in InGaAs/GaAs is 
composition sensitive, while the (004) reflection is strain sensitive. In principle, the (004)/(220) pair is 
a good choice since these two reflections are orthogonal to each other and thus provide the most 
Figure 1. HAADF-STEM image of InAs/GaAs QD, before (a) and and after (b) applying the SmartAlign with 90̊ rotation, 
(c) yy strain measured from (a), (d) yy strain measured from (b). The Bragg spots highlighted in the inset FFT in (c) are
used to create strain maps.   
31234567890
Electron Microscopy and Analysis Group Conference 2017 (EMAG2017) IOP Publishing
IOP Conf. Series: Journal of Physics: Conf. Series 902 (2017) 012021  doi :10.1088/1742-6596/902/1/012021
 
 
 
 
 
 
information. However, the problem with the use of (004)/(220) in the case of Fig. 2 is noise. A single 
STEM image is too noisy for the low intensity reflections, such as (004). The scanning noise is a kind 
of high frequency noise and (004) is also affected. So, the overall noise of (004) in a single HAADF-
STEM image is high. 
 
 
 
An atomic resolution image contains multiple reflections or spatial frequencies, and GPA only uses two 
frequencies to calculate strain, as Fig. 3 demonstrates. While the  approach used by GPA is advantageous 
for the analysis of HRTEM images of limited spatial resolution, ideally, the analysis of aberration 
Figure 2. High resolution HAADF STEM 
image of InAs/GaAs QD. 
Figure 3. (d-f) yy strain measured from Fig. 2 using the Bragg spots highlighted in the 
(a-c) FFTs. 
Figure 4. (a) HAADF STEM image of InAs/GaAs wetting layer after applying the SmartAlign, (b and c) xx strain maps for strain parallel to the
crystallographic [001] direction from (a) using the Bragg spots {111} and (004)/(220), respectively in the FFTs. (d) xx strain map from TeMA, (e) The 
strain profile along a line crossing through the wetting layers shown with dashed lines in (b and c), (f) The strain profile along a line crossing through 
the wetting layers shown with dashed lines in (d). 
41234567890
Electron Microscopy and Analysis Group Conference 2017 (EMAG2017) IOP Publishing
IOP Conf. Series: Journal of Physics: Conf. Series 902 (2017) 012021  doi :10.1088/1742-6596/902/1/012021
 
 
 
 
 
 
corrected STEM images should take the advantages of all frequencies, and this can be achieved using 
real space based methods based on atomic peak finding or template matching (TeMA) [5, 6]. In these 
methods, the position of the atomic columns is determined by the intensity distribution, which utilizes 
all information recorded in the image. Fig. 4a shows a HAADF STEM image a GaAs/InAs wetting layer 
after applying the SmartAlign algorithm. GPA and TeMA have been used to measure the strain in this 
image. Fig. 4 (b and c) show the strain map from {111} and (004)/(220) reflections, respectively, and 
Fig. 4 (d) is the strain map from TeMA. The profiles in Fig.4 (e and f) that are taken from Fig. 4(b-d) 
show that (004)/(220) is in closer agreement with the real space approach (TeMA), and {111} gives 
systematic noise and interfacial features that are not seen in (004)/(220). This could be a Fourier 
termination effect due to the stronger background in the FFT spectrum near the {111} reflections.  
 
Finally, thin foil relaxation effects are not taken into account in the strain measurements since the 
dimensions of the QDs are small and the sample is not extremely thin. Together, we expect the relaxation 
happens mostly on the same surfaces [7]. 
 
4.  Conclusions 
In conclusion, we have demonstrated several strategies for improving the results of strain analysis by 
GPA of the InAs/GaAs quantum dot (QD) material, including 
1) The image quality can be significantly improved by performing multiple scans with 0° and 90° 
rotations and by using SmartAlign to reduce noise and scan errors. 
2) The choice of g vectors in the GPA procedure can have a large impact on the strain mapping 
results. The use of {111} reflections are the most effective in case of a single HAADF-STEM 
image. However, the same {111} pair applied to the improved HAADF-STEM image revealed 
artefacts at the wetting layer interface. 
3) By using SmartAlign for a series of images to improve the signals at high frequencies, and as it 
is shown in Fig. 4c, the (004)/(220) reflections gave the best results when using GPA for strain 
measurements. 
The data in this paper also shows that GPA analysis using only one pair of reflections has its limitations 
since it does not take advantage of all information recorded at atomic resolution. For GPA, the challenge 
is how to combine information obtained by using different Fourier pairs in order to obtain true strain 
information. With aberration corrected microscopes the resolution is much higher, and by using 
SmartAlign we get better atomic resolution images, which definitely improves the GPA analysis. 
However, still additional information can be picked up with real space approaches which use 
information from all frequencies and would be a better approach than GPA. 
 
Acknowledgments 
The Norwegian Research Council is acknowledged for funding the HighQ-IB project under contract no. 
10415201. The (S)TEM work was carried out on the NORTEM infrastructure at the TEM Gemini 
Centre, NTNU, Norway. JMZ is supported by Onsager Professorship of NTNU. 
References 
[1] Hÿtch M J, Snoeck E and Kilaas R 1998 Ultramicroscopy 74 131-146 
[2] Peters J J P et al. 2015 Ultramicroscopy 157 91-97 
[3] Shockley W and Queisser H J 1961 Journal of Applied Physics 32 510 
[4] Jones L and Yang H 2015 Advanced Structural and Chemical Imaging 1 1-16 
[5] Kim H, Meng Y, Rouviére J L and Zuo J M 2017 Micron 92 6-12 
[6] Nord M, Vullum P E, MacLaren I, Tybell T and Holmestad R 2017 Advanced Structural and       
             Chemical Imaging 3 9 
[7]     Treacy, M. M. J. and J. M. Gibson 1986  Journal of Vacuum Science & Technology B 4, 1458-
1466. 


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Strategy for reliable strain measurement in InAs/GaAs materials from high-resolution Z-contrast STEM images

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