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Background: In order to improve the reliability of the electron tomography (ET) technique, which reveals three- dimensional information of nanostructured materials from a series of tilted two-dimensional images, it is essential that the mechanical tilt angle be accurately measured by the transmission electron microscopy (TEM) goniometer. Findings: In this study, a calibration specimen was fabricated by nanohole patterning using a focused ion beam in order to determine mechanical tilt angles. The TEM goniometer tilt-angle accuracies were directly confirmed by measuring the changing areas of the projected nanosized hole. New calibration equations were developed and applied for the accurate determination of tilt angle. Conclusion: We expect that the calibration specimen will effectively determine and correct the mechanical tilt angles in TEM goniometers leading to improvements in the ET technique. Keywords: Electron tomography, Calibration specimen, Goniometer, Nanohole patterning, Focused ion beam Introduction of angles, are required in order to reconstruct a high- Transmission electron microscopy (TEM) is an essential quality 3D image. The exact alignment of a series of tool for the quantitative structural analysis of nanostruc- tilted 2D images prior to the construction of the 3D tured materials, due to its ability to directly visualize in- image in a manner that avoids image distortion is also dividual nanosized objects. In particular, structural important for improving 3D information. Furthermore, information such as specimen shape, size, and distribu- an accurate TEM goniometer is required for the acquisi- tion can be analyzed from the directly obtained images tion of the tilted 2D images in order to prevent image (Mühlfeld et al. 2007). However, projected two- misalignment (Hayashida et al. 2014). However, errors dimensional (2D) images acquired from three- between the actual and TEM goniometer-displayed tilt dimensional (3D) nanostructured materials can provide angles may occur due to mechanical imperfections. For limited information, and sometimes, information is this reason, it is necessary to accurately measure and missing; the development of nanotechnology requires correct the tilt angles measured by the TEM goniometer the relationship between the 3D structure and properties (Hayashida et al. 2011). Although monocrystalline dif- of the material to be characterized on the nanometer fraction patterns or Kikuchi diffraction patterns have scale (Ercius et al. 2015). In order to overcome the lack been used to measure mechanical tilt angles in a previ- of information provided by 2D images, the electron tom- ous report (Shaw and Hills 1981), the method is not ap- ography (ED) technique has been employed to produce plicable to all types of TEM specimens and currently reconstructed 3D images. In this technique, multiple 2D manufactured transmission electron microscopes. There- images (normally 50–150 images), acquired by tilting the fore, an advanced method for the measurement of the nanosized object in 1° or 2° intervals over a wide range actual tilt angle by a TEM goniometer is required. In this study, we report the development of a new method for the direct and accurate determination of tilt angles by a * Correspondence: email@example.com TEM goniometer. Electron Microscopy Research Center, Korea Basic Science Institute (KBSI), 169-148 Gwahak-ro, Yuseong-gu, Daejeon 34133, South Korea © The Author(s). 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Lee et al. Journal of Analytical Science and Technology (2018) 9:6 Page 2 of 5 Experimental developed protocol is presented in Fig. 1. When the inci- Fabrication of nanohole patterns dent beam is perpendicular to plane A, the tilt angle be- A nanohole with a diameter of 500 nm was fabricated tween thenanoholeand planeAis θ. The area of the on a SiN membrane TEM window grid (SN100-A50Q10, nanohole projected by the transmitted beam (A )isequal SiMPore Inc.) using a focused ion beam (FIB) (Quanta to the overlap area between the red and blue circles multi- 3D FEG, FEI) at an accelerating voltage of 30 kV, ion plied by cos θ,as shown in Fig. 1b, where the overlap area, current of 10 pA, and dwell time of 15 μs. Prior to nano- A ,isdefined as hole patterning, the SiN membrane was coated with a A ¼ 2 ðÞ A −A ¼ rðÞ 2α− sin2α ð2Þ O C IT several-nm-thick Au layer using a sputter coater (SCD 055, BAL-TEC) to reduce the effect of charging caused and A and θ are derived as shown below: by the insulating SiN film. A ¼ A cosθ ¼ rðÞ 2α− sin2α cosθ ð3Þ T O Nanohole pattern imaging A A π T T −1 −1 The nanosized hole was analyzed by Cs-corrected TEM θ ¼ cos ¼ cos ð4Þ rðÞ 2α− sin2α AðÞ 2α− sin2α (Libra 200 HT Mc, Carl Zeiss). A series of tilted 2D im- ages of the nanosized hole was obtained over the − 50° to + 50° range in 2° increments. In each 2D image, the In Eq. (2), A is the area of the yellow sector, A and C IT projected area of the nanosized hole was measured using α are the area and vertex angle of the green isosceles tri- the particle analysis tool available in the DigitalMicro- angle, respectively, and r is the radius of the hole. Angle graph (DM) software package (Gatan Inc.). α is obtained by introducing the additional variables dis- played in Fig. 1a as follows: Results and discussion t tanθ Establishment of the calibration equation x ¼ Tilt angle can simply be determined from the projected ð5Þ t tanθ −1 area of the hole using the following equation: α ¼ cos 2r where t is the thickness of the nanohole. −1 θ ¼ cos ð1Þ If the nanohole is very thin (r > > t), then Eq. (4) col- lapses to Eq. (1) as expected. From Eqs. (4) and (5), we where θ is the tilt angle, A is the projected area of the see that θ is a function of A , t, and r. Since t and r are T O nanohole tilted at angle θ,and A is the initial area of the known variables determined from the features of the nanohole. However, this equation is only applicable when nanohole, we only need to consider the projected area of the nanohole is very thin. Indeed, the nanohole pattern the tilted nanohole in order to calculate the tilt angle. that we used was 50 nm thick (the thickness of the SiN To verify the reliability of this equation, tilt angles membrane). Therefore, we modified the formula to take were calculated using a simulated 3D model with an as- into account the thickness of the nanohole through simple pect ratio of 0.1 between diameter and thickness. geometrical calculations. A schematic diagram of the Figure 2a shows the representative 3D model images Fig. 1 a Schematic diagram of the tilted hole. b The projected object for the calculation of the projection area Lee et al. Journal of Analytical Science and Technology (2018) 9:6 Page 3 of 5 Fig. 2 a 3D–simulated images at different tilt angles. b Selected hole area. c Corresponding histogram. d Calculated vs. actual angles obtained at different tilt angles in which the models were formed by hair masking the Au coating to form guidelines tilted in 2° increments over the − 50° to + 50° range. The for the location of the nanohole pattern in the center of projected area of the nanohole was measured by count- the window (red square). For tilt-angle measurements, we ing the number pixels above the threshold intensity of fabricated a 500-nm-diameter nanohole in a 50-nm-thick the brightest region using the DM software, as shown in SiN membrane, as shown in Fig. 3b. Fig. 2b, c. Finally, the numerical tilt-angle solution was determined from the acquired projected area by com- puter calculation. Figure 2d displays the calculated tilt Analysis of the fabricated nanosized hole by TEM angle as a function of actual tilt angle. All calculated an- During the TEM analysis of the nanohole, both bright- gles corresponded to the actual angle to within an error field TEM (BF-TEM) images in conventional TEM mode (2σ) of 0.6%; the R value of the linear fit was unity, were acquired, as shown in Fig. 4a, b, as well as high- which means that a well-defined nanohole device will angle annular dark field images in scanning TEM mode lead to the correct goniometer tilt angle from the pro- (HAADF-STEM), as shown in Fig. 4d, e, in order to jected area fraction without the need for any external compare the measurement accuracies. Figure 4c, f device for measuring tilt angle. displays the BF-TEM and HAADF-STEM image histograms, respectively, which reveal that the HAADF- Fabrication of the nanohole pattern STEM images display more distinct edge contrast be- To fabricate a well-defined nanohole, we used the FIB pat- tween the nanohole and the amorphous thin film and, terning technique. Figure 3a shows an SEM image that consequently, the hole area was more accurately selected displays the morphology of the entire SiN membrane of for measurement. Based on the analyzed results, the the TEM window grid. The dark line in the blue square is measurement error is significantly reduced in HAADF- an array of 200-nm-diameter holes (inset, Fig. 3a) that was STEM mode. Fig. 3 a SEM image of the SiN membrane TEM window grid (the inset shows the guide-hole array). b An individual nanohole fabricated by FIB patterning Lee et al. Journal of Analytical Science and Technology (2018) 9:6 Page 4 of 5 Fig. 4 The determination of projected area. a The BF-TEM image. b The selected hole area. c The corresponding TEM histogram. d The HAADF- STEM image. e The selected hole area. f The corresponding STEM histogram. b–c The selected hole area was highlighted in green color The fabricated nanosized hole was applied in a prac- Conclusions tical setting for the actual measurement of tilt angles by A 500-nm-diameter nanosized hole was fabricated in a the TEM goniometer. The 500-nm nanosized hole was SiN membrane TEM window grid by FIB patterning. used to acquire a series of tilted 2D images. The pro- The ion beam milling conditions were optimized in jected area of the nanosized hole was determined in each order to produce the desired shape and size of the nano- 2D image, and the changes in tilt angle were calculated sized hole. In this technical note, we address a newly de- by computer using the equations discussed in the previ- veloped method for the measurement of the tilt angle in ous section. Figure 5 displays the calculated angle as a a TEM goniometer using a fabricated nanohole, and a function of the nominal angle displayed by the goniom- simple equation that considers the nanohole geometry is eter. The average differences between the two angles in introduced to accurately calculate tilt angles in a TEM the 0 to + 50° and 0 to − 50° ranges were 1.09° and 2.18°, goniometer. By applying this advanced method, the arti- respectively. The errors determined by computer calcu- ficial nanohole can be as a calibration specimen to cor- lation appear to be quite high when compared to the rect the mechanical tilt angles provided by a TEM value of ± 0.02° provided by the TEM manufacturer. goniometer. We expect that this method will increase However, since we formulated Eq. (4) assuming an ideal the reliability of the ET technique for the structural ana- nanohole geometry, this observed difference is possibly lysis of nanosized objects without the need for expensive due to the gentle slope of the nanohole wall. devices, although further development of the FIB tech- nique is needed in order to improve sharp-edge control, to reduce the influence of film thickness, and to improve angular-measurement accuracies. Abbreviations BF: Bright field; ET: Electron tomography; FIB: Focused ion beam; HAAFD: High-angle annular dark field; STEM: Scanning transmission electron microscopy; TEM: Transmission electron microscopy Acknowledgements This work was supported by a Korea Basic Science Institute grant (D38612). Authors’ contributions JGK designed and coordinated the study. JHL and SGL carried out the experiments and image processing. HS and SJY refined the data and drafted the manuscript. All authors have read and approved the final manuscript. Fig. 5 Calculated angle as a function of nominal angle displayed by Competing interests the TEM goniometer The authors declare that they have no competing interests. Lee et al. Journal of Analytical Science and Technology (2018) 9:6 Page 5 of 5 Publisher’sNote Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Received: 13 November 2017 Accepted: 22 January 2018 References Ercius P, Alaidi O, Rames MJ, Ren G. Electron tomography: a three-dimensional analytic tool for hard and soft materials research. Adv Mater. 2015;27:5638–63. Hayashida M, Malac M, Bergen M, Egerton RF, Li P. Accurate measurement of relative tilt and azimuth angles in electron tomography: a comparison of fiducial marker method with electron diffraction. Rev Sci Instrum. 2014;85:083704. Hayashida M, Terauchi S, Fujimoto T. Calibration method of tilt and azimuth angles for alignment of TEM tomographic tilt series. Rev Sci Instrum. 2011;82:103706. Mühlfeld C, Rothen-Rutishauser B, Vanhecke D, Blank F, Gehr P, Ochs M. Visualization and quantitative analysis of nanoparticles in the respiratory tract by transmission electron microscopy. Part Fibre Toxicol. 2007;4:11. Shaw PJ, Hills GJ. Tilted specimen in the electron microscope: a simple specimen holder and the calculation of tilt angles for crystalline specimens. Micron. 1981;12:279–82.
"Journal of Analytical Science and Technology" – Springer Journals
Published: Dec 1, 2018
Keywords: Analytical Chemistry; Characterization and Evaluation of Materials; Monitoring/Environmental Analysis
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