Improving STEM scale calibration reliability with scanning noise correction and image registration

doi:10.21203/rs.3.rs-2130064/v1

Download PDF

Technical Report

Improving STEM scale calibration reliability with scanning noise correction and image registration

https://doi.org/10.21203/rs.3.rs-2130064/v1

This work is licensed under a CC BY 4.0 License

You are reading this latest preprint version

In conventional scanning transmission electron microscopy (STEM) calibration, an image of a known specimen is taken and, the length is determined based on the known spacing appearing in the image. However, in high-magnification images, the accuracy of scale calibration decreases as the effect of scanning noise, which can be caused by the vibration of equipment, the instability of AC power and temperature, etc., increases. In this report, we introduce a calibration method for STEM, including scanning noise correction and image registration using a Si single-crystal image. The validity of the calibration method was confirmed by verifying the lattice parameter of an example sample of Cu₃Al. The validation results show that the calibration can be more reliable by reducing the influence of scanning noise, allowing the lattice parameters to be accurately measured with a relative error of less than 3%.

scanning transmission electron microscopy

calibration

scanning noise

signal-to-noise ratio

image registration

Scanning transmission electron microscopy (STEM) is a microscopic technique that directly observes atoms through raster scanning of the electron beam over the sample and can be used to determine the distance between atoms or the structure of molecules. Therefore, accurate scale information is essential for reliable STEM analysis. Generally, in transmission electron microscopy (TEM) and STEM, scale calibration is performed by taking an image of well characterized standard specimens and then adjusting the length based on the intervals of a specific pattern that appeared in the image. Well-known and widely used standard specimens include multilayer Si-Ge/Si (McCaffrey and Baribeau 1995) and monodisperse gold nanoparticles (Zhao and Yang 2010). Filippov et al. proposed various materials that can be used as standard samples (Filippov et al. 2011). Laak et al. performed calibration using the Fourier transform of a replica image (van der Laak et al. 2006). However, even with this method, a microscopic error of several angstroms may occur in STEM when an image is formed through scanning.

As referred to above, unlike TEM, STEM imaging is performed by pixel-by-pixel scanning process using a focused electron beam. Therefore, image formation takes a certain amount of time and the serial imaging process of STEM is inevitably vulnerable to artifacts that are a function of time, such as drift. When high-magnification images are taken in STEM, the effects of scanning noise caused by the vibration of equipment, the instability of AC power and temperature, etc. can be much more pronounced (Muller et al. 2006). There are several types of such scanning noise, including nonlinear and linear drift, and random noise, (Ophus et al. 2016) which causes image distortion and a significant error in the distance represented as the lattice parameter and the interplanar spacing. To overcome this problem, several studies have been attempted to correct the scanning noise (Braidy et al. 2012; Jones and Nellist 2013; Sang and LeBeau 2014; Ophus et al. 2016; Wang et al. 2018; Fujinaka et al. 2020).

In this study, scale calibration was performed by correcting the scanning noise for a high-magnification STEM image of Si single crystal and measuring the distance between pixels formed in the image using the Si dumbbell as a reference. We then validated this method by using the calibrated scale to determine the lattice constants for different materials.

Random noise and linear and nonlinear drifts can be removed using the method proposed by Ophus et al. (Ophus et al. 2016). The fast scan direction has an incomparably smaller effect on scanning noise than the slow scan direction, so the scan noise in the fast scan direction is negligible. Therefore, in this study, as shown in Fig. 1, scanning noise was corrected by matching the original image with the image obtained by rotating the scan direction 90° so that the fast scan direction and the slow scan direction are swapped while leaving the specimen intact. In addition, the Poisson noise was minimized by increasing the signal-to-noise ratio (SNR) using the method of lattice vector translation proposed by Lu et al. (Lu et al. 2016). This can be achieved faster and more accurately by utilizing an iterative periodicity vector retrieval method described in Kang et al. (Kang et al., 2022).

A thin foil of the single-crystal Si sample used as a reference for a STEM scale calibration was prepared by mechanical polishing followed by Ar + ion milling using a precision ion polishing system (691 PIPS, Gatan, Inc.). The images of the Si reference sample along [110] zone axis were obtained using a spherical aberration (Cs) corrected STEM (ARM-200F, JEOL Ltd.) operated at 200 kV.

As shown in Fig. 2, the two periodicity vectors (vector 1 and 2) are searched using the iterative periodicity vector retrieval method. These vectors were used for image registration after dividing the original image into unit tiles to obtain a high-SNR unit image. The high-SNR processed unit image can be rearranged according to the periodicity vectors to form a reference with the same resolution as the original image.

A STEM scale calibration was performed by comparing the number of pixels (101 pixels) between Si dumbbells and the corresponding {110} interplanar spacing (0.384 nm) of the Si reference data to calculate the dimension of a single pixel (0.0038 nm) of the image taken at 50 million times magnification. Detailed calculation results are shown in Table 1.

Table 1

Scale of pixels for each magnification in Fig. 2.
	ⓐ Length of 101 pixels at 50 Mx	ⓑ Length of 1 pixel at 50 Mx (ⓐ/101)	ⓒ Length of 1 pixel at 20 Mx (2.5×ⓑ)
Value	0.384 nm (Si {110} interplanar distance)	0.0038 nm	0.0095 nm

Table 2

The detailed lattice parameter calculated by only linear drift corrected image and high SNR processed image.
< 110 > zone axis	① Ratio to lattice parameter	Image with linear drift correction only (at 20 Mx)			Image with high SNR processing (at 20 Mx)
< 110 > zone axis	① Ratio to lattice parameter	② Interplanar distance (pixels)	③ Interplanar distance (nm) (②×ⓒ)	④ Calculated lattice parameter (③/①)	⑤ Interplanar distance (pixels)	⑥ Interplanar distance (nm) (⑤×ⓒ)	⑦ Calculated lattice parameter (⑥/①)
Cu₃Al\(\left(1\overline{1}0\right)\)	\(1/\sqrt{2}\)	221 / 9	0.233 nm	0.330 nm	241 / 9	0.254 nm	0.359 nm
Cu₃Al\(\left(1\overline{1}1\right)\)	\(\sqrt{6}/4\)	212 / 9	0.224 nm	0.365 nm	208 / 9	0.220 nm	0.359 nm
Cu₃Al\(\left(1\overline{1}\overline{1}\right)\)	\(\sqrt{6}/4\)	219 / 9	0.231 nm	0.377 nm	207 / 9	0.219 nm	0.358 nm

As shown in Fig. 3 and Table 2, the lattice parameter was measured in the high magnification (20 Mx) image of the example specimen (Cu₃Al [110]) using this calibrated scale to validate the method. At the 20 Mx, the length of a single pixel is 0.0095 nm as shown in Table 1 ⓒ. The measured lattice parameters after performing only linear drift correction on the sample image show a relatively large deviation as seen in Table 2 ④. On the other hand, when the lattice parameter is measured with a high SNR processed image, an almost constant value of approximately 0.359 nm can be obtained as shown in Table 2 ⑦, which is close to the theoretically calculated and experimentally measured values of 0.3607 nm to 0.369 nm. (Yang et al. 2011; Dong et al. 2012)

In addition, for the three previously measured lattice planes, the lattice constant values calculated by averaging the distances between 100 planes by increasing the number from 9 planes in the images before and after image registration are 0.346 nm and 0.358 nm, respectively, showing no significant difference. However, the difference in standard deviation between the registration image (0.0066 nm) and the original image (0.0346 nm) is still considerably large. Based on this, it can be confirmed that, when the scale calibration is performed without image registration, a relatively accurate scale can be obtained only by including a large amount of data. In other words, if the method through image registration proposed in this study is used, reliable results can be obtained without comparing large amounts of data.

In summary, this study described a series of processes for removing noise due to linear drift and low precision and calibrating the scale of STEM images. Scale calibration was performed using the denoised reference Si image. To ensure correct calibration, this method was used to measure the lattice parameters of Cu₃Al sample. As a result, the scale calibration was successful and the lattice parameters are accurately measured with a relative error of less than 3%.

STEM

Scanning transmission electron microscopy

TEM

Transmission electron microscopy

Alternating current

SNR

Signal-to-noise ratio

Availability of data and materials

All data generated or analyzed during this study are included in this published article.

Competing interests

The authors declare that they have no competing interests.

Funding

This work was supported by the National Research Foundation of Korea (NRF) grants funded by the Korean government (MSIT) under contract NRF-2022R1A2C1005507

Authors' contributions

M.-C. K. and C.-W. Y. conceived of the presented idea and wrote the manuscript. M.-C. K. and J. P. developed the theory and performed the computations. M.-C. K., K.-J. J. and J. H. L. contributed to the sample preparation and electron microscopy. C.-W. Y. supervised this work. All authors read and approved the final manuscript.

Acknowledgements

The authors are grateful for the support from the Cooperative Center for Research Facilities (CCRF) at Sungkyunkwan University.

Braidy N, le Bouar Y, Lazar S, Ricolleau C (2012) Correcting scanning instabilities from images of periodic structures. Ultramicroscopy 118:67–76. https://doi.org/10.1016/j.ultramic.2012.04.001
Dong L-M, Han Z-D, Wang Y-L, Li W, Zhang X-Y (2012) Theoretical investigation on electronic structure and mechanical properties of cubic crystallographic structures with point defects in Al-based alloys. Solid State Communications 152:1263–1269. https://doi.org/10.1016/j.ssc.2012.03.037
Filippov MN, Gavrilenko VP, Kovalchuk MV, Mityukhlyaev VB, Ozerin YV, Rakov AV, Roddatis VV, Todua PA, Vasiliev AL (2011) Reference material for transmission electron microscope calibration. Measurement Science and Technology 22: 094014. https://doi.org/10.1088/0957-0233/22/9/094014
Fujinaka S, Sato Y, Teranishi R, Kaneko K (2020) Understanding of scanning-system distortions of atomic-scale scanning transmission electron microscopy images for accurate lattice parameter measurements. Journal of Materials Science 55:8123–8133. https://doi.org/10.1007/s10853-020-04602-w
Jones L, Nellist PD (2013) Identifying and correcting scan noise and drift in the scanning transmission electron microscope. In: Microscopy and Microanalysis 19:1050–1060. https://doi.org/10.1017/S1431927613001402
Kang M-C, Oh J-S, Jo K-J, Kim T-H, Yang C-W (2022) Nonlinear drift/random noise correction using high signal to noise ratio reference generated by image registration. In preparation
Lu P, Yuan RL, Ihlefeld JF, Spoerke ED, Pan W, Zuo JM (2016) Fast Atomic-Scale Chemical Imaging of Crystalline Materials and Dynamic Phase Transformations. Nano Letters 16:2728–2733. https://doi.org/10.1021/acs.nanolett.6b00401
McCaffrey JP, Baribeau J-M (1995) A transmission electron microscope (TEM) calibration standard sample for all magnification, camera constant, and image/diffraction pattern rotation calibrations. Microsc Research and Technique 32:449–454. https://doi.org/10.1002/jemt.1070320507
Muller DA, Kirkland EJ, Thomas MG, Grazul JL, Fitting L, Weyland M (2006) Room design for high-performance electron microscopy. Ultramicroscopy 106:1033–1040. https://doi.org/10.1016/j.ultramic.2006.04.017
Ophus C, Ciston J, Nelson CT (2016) Correcting nonlinear drift distortion of scanning probe and scanning transmission electron microscopies from image pairs with orthogonal scan directions. Ultramicroscopy 162:1–9. https://doi.org/10.1016/j.ultramic.2015.12.002
Sang X, LeBeau JM (2014) Revolving scanning transmission electron microscopy: Correcting sample drift distortion without prior knowledge. Ultramicroscopy 138:28–35. https://doi.org/10.1016/j.ultramic.2013.12.004
van der Laak JAWM, Dijkman HBPM, Pahlplatz MMM (2006) Automated magnification calibration in transmission electron microscopy using Fourier analysis of replica images. Ultramicroscopy 106:255–260
Wang Y, Eren SY, Salzberger U, Hahn K, Srot V, Sigle W, van Aken PA (2018) Correcting the linear and nonlinear distortions for atomically resolved STEM spectrum and diffraction imaging. Microscopy 67:i114–i122. https://doi.org/10.1093/jmicro/dfy002
Yang CD, Li W, Zhi W (2011) Study on mechanical behavior and electronic structures of Al-Cu intermetallic compounds based on first-principles calculations. Solid State Communications 151:1270–1274. https://doi.org/10.1016/j.ssc.2011.05.040
Zhao F, Yang Y (2010) Use of monodisperse gold nanoparticles for transmission electron microscope high magnification calibration. Colloid Journal 72:346–352. https://doi.org/10.1134/S1061933X10030087

Download PDF

Editorial decision: Minor revision
28 Nov, 2022
Reviewers agreed at journal
24 Oct, 2022
Editor invited by journal
10 Oct, 2022
Reviewers invited by journal
10 Oct, 2022
Editor assigned by journal
10 Oct, 2022
Submission checks completed at journal
09 Oct, 2022
First submitted to journal
06 Oct, 2022

You are reading this latest preprint version

Improving STEM scale calibration reliability with scanning noise correction and image registration

Status:

Version 1

Abstract

Figures

Introduction

Scale Calibration Procedure

Validation Of The Proposed Method

Conclusion

Abbreviations

Declarations

References

Status:

Version 1