Aberration-Corrected TEM
largest phase shiſt in the EW phase map. Te atomic locations marked “A” and “B” in Figure 6b are clearly distinguished by different peak values in the EW phase map, and these peaks represent the location of single carbon atoms in either the top or bottom graphene. Te average value of the EW phase of the carbon atoms in the “A” indexed locations is 9.5 percent larger than the phase shiſt value at the “B” indexed locations. Tis is clearly above the 2.3 percent noise level estimated from shot noise considerations calculated from the experimental dose rate. Further, the line scan in Figure 6e shows that a typical difference in phase between atomic peaks in the single- layer area, due to uncorrected residual aberrations, is significantly smaller (0.002 radians = noise level) than the phase difference between carbon atoms belonging to the two different layers (top versus bottom) in the double-layer region (average signal = 0.010 radians). Te fundamental measurement units of the EW phase are given as an angle measured in radians. Tis can be understood as one full cycle of an electron spatial wavelength representing 360 degrees or 2π radians because the relativistic electron wavelength at the chosen accelerating voltage is the “measuring stick” we are using on the atomic structure. So a noise level of 0.002 radians means that we are measuring with an uncertainty of only ~0.1 degrees in the wavelength’s angular cycle! As a further comparison between theory and experiment, line scan analyses (indicated in Figure 6f) on the simulated model structure predict that there is a 0.014-radian phase difference between the single-C-atom “columns” depending on whether they are in the top layer or the bottom sheet (marked “A” or “B” respectively in the line scan data in Figure 6g). Te difference in height in the beam direction of these two atomic positions is 3.5 Angstroms. Finally, the simulation was run with a defocus change of both +3 Å and –3 Å. In the single- layer area, the line scan in Figure 6h shows that the predicted simulated phase change for this focus change (equivalent to moving a carbon atom by the same amount) is +0.010 rad (for +3 Å defocus) and –0.014 rad (for –3 Å defocus). Tis verifies that the measurable phase difference between “A” and “B” in the experimental data is caused by the difference in upper/lower sheet position in the double-layer area.
Conclusion and Future Prospects Tis graphene study [4] has shown two steps of results:
First, by applying FSR to HR-TEM images obtained with a aberration-corrected TEM, and taking advantage of the improved low energy-spread of a monochromated source, we are able to obtain the fundamental experimental quantity known as the EW phase for a sample containing both single- and double-layer graphene structure. As a second step, the small residual microscope aberrations were inferred and numerically removed from this EW phase, resulting in unprecedented imaging of the same structure. Te final result demonstrates an ability to numerically verify the positions of the atoms in all three dimensions, even in the vertical direction differentiating 3A height differences with high signal fidelity. In this study, it was possible to obtain the residual
aberrations using single-layer graphene as a known “calibration structure,” but for many samples this would not be possible. Terefore, it would be desirable to have a procedure to measure the residual aberrations of the Cs aberration corrector at a given
14
time. Te aberrations could then be directly subtracted (or deconvolved) from the EW phase function, allowing the level of imaging quality in this study to be repeated on a wider range of samples and structures, including wholly unknown structures without the equivalent of a graphene “single-layer calibration.” Methods for measuring with high accuracy the corrector’s residual aberrations via soſtware are under development. Soon it should be possible to use these methods via automated algorithms to measure the actual residual aberrations of the corrected microscope [13]. Tis will allow residual aberrations to be directly measured and numerically deconvolved for a greater range of samples and experimental conditions. For example, recent studies of graphene with nitrogen doping provide evidence that HR-TEM studies can record changes in electron density due to chemical bonding [14], and it may be possible that the techniques described in this review could enable experimental studies that would further shed light on this exciting new topic, just to give one example of potential future directions of investigation.
Acknowledgments Te authors would like to thank Edgar Voelkl for helpful
comments on this article.
References [1] “Tere’s Plenty of Room at the Bottom,” a speech given by physicist R.P. Feynman at a meeting of the American Physical Society at California Institute of Technology, December 29, 1959.
[2] W Coene, A Tust, M Op de Beeck, and D Van Dyck, Ultramicroscopy 64 (1996) 109–35; and A Tust, WMJ Coene, M Op de Beek, and D van Dyck, Ultramicroscopy 64 (1996) 211–30.
[3] M Haider, S Uhlemann, E Schwan, H Rose, B Kabius, and K Urban, Nature 392 (1998) 768–69.
[4] JR Jinschek, E Yucelen, HA Calderon, and B Freitag, Carbon 49 (2011) 556–62.
[5] A Tust, Microsc Microanal 11 (Suppl 2) (2005) 602–03. [6] DB Williams and CB Carter, Transmission Electron Microscopy—A Textbook for Materials Science, Plenum Press, New York, 1996, p. 461.
[7] L Reimer and H Kohl, Transmission Electron Microscopy: Physics of Image Formation, 5th ed., Springer Science, New York, 2005.
[8] P Schlossmacher, Ch Kuebel, B Freitag, D Hubert, and R Perquin, Microsc Microanal 13 (Suppl 2) (2007) 1170–71.
[9] E Voelkl, B Jiang, ZR Dai, and JP Bradley, Microscopy Today 16(6) (2008) 36–38.
[10] C-L Jia, M Lentzen, K Urban, Microsc Microanal 10 (2004) 174–84.
[11] J Barthel and A Tust, Phys Rev Lett 101(20) (2008) 200801.
[12] R Kilaas, “HREM image simulation” in Proceeding of 49th EMSA Meeting, ed. G W Bailey, San Francisco Press, San Francisco, 1991, p. 528–29.
[13] J Barthel and A Tust, Ultramicroscopy 111 (2010) 27–46.
[14] JC Meyer et al., Nature Mater 10 (2011) 209–15.
www.microscopy-today.com • 2011 May
Page 1 |
Page 2 |
Page 3 |
Page 4 |
Page 5 |
Page 6 |
Page 7 |
Page 8 |
Page 9 |
Page 10 |
Page 11 |
Page 12 |
Page 13 |
Page 14 |
Page 15 |
Page 16 |
Page 17 |
Page 18 |
Page 19 |
Page 20 |
Page 21 |
Page 22 |
Page 23 |
Page 24 |
Page 25 |
Page 26 |
Page 27 |
Page 28 |
Page 29 |
Page 30 |
Page 31 |
Page 32 |
Page 33 |
Page 34 |
Page 35 |
Page 36 |
Page 37 |
Page 38 |
Page 39 |
Page 40 |
Page 41 |
Page 42 |
Page 43 |
Page 44 |
Page 45 |
Page 46 |
Page 47 |
Page 48 |
Page 49 |
Page 50 |
Page 51 |
Page 52 |
Page 53 |
Page 54 |
Page 55 |
Page 56 |
Page 57 |
Page 58 |
Page 59 |
Page 60 |
Page 61 |
Page 62 |
Page 63 |
Page 64 |
Page 65 |
Page 66 |
Page 67 |
Page 68 |
Page 69 |
Page 70 |
Page 71 |
Page 72 |
Page 73 |
Page 74 |
Page 75 |
Page 76