Aberration-Corrected TEM
model
the double-layer graphene:
two hexagonal graphene
sheets are overlaid in a so-called Bernal-stacked alignment. Figure 5b shows the EW phase for the simulation result, which is modeled with zero noise and zero aberrations. Te simulated single-layer graphene looks perfectly like its known hexagonal model structure, with bright spots representing single carbon atoms. Te experimentally reconstructed EW phase image in figure 4c strongly resembles the simulation; thus, the FSR has allowed us to clearly identify areas of single and double sheets and to confirm the type of stacking alignment. Te apparent visible structure in Figure 4c at the boundary between vacuum and the single layer is an artifact due to atomic-level motion or evolution of individual edge atoms during the focal series. Because the edge is not a topic of study, this does not affect the results in this review. In figure 6, we provide a more detailed comparison between the simulated model and the experimental results. Te application of FSR discussed above provides an
unscrambled, experimental EW phase function that can be directly compared with theoretical structural studies calculated from Equation (1), such as those calculated in Figure 5b. However, the initially reconstructed EW phase obtained by FSR in Figure 4b contained blur attributable to residual aberrations. In this study, we have taken an important further step by numerically deconvolving the small residual aberrations
that remained aſter aberration correction. Having obtained by FSR the EW phase function experimentally, this further deconvolution was an “easy” subsequent task (mathematically complex, yet straightforward), but we needed to know precisely the actual residual experimental aberrations, either by (a) direct measurement or by (b) some kind of inference. Tere are direct measurement schemes for obtaining residual aberrations that we discuss below, but first we describe how the residual aberrations were inferred in the present experiment with graphene by using the known structure of the single-layer graphene essentially as a calibration standard. Te experimental residual aberrations of the microscope
for this focal series were found by adjusting the aberration coefficients up to third order in the TrueImage soſtware [8] and then using the soſtware to numerically “subtract” these aberrations from the experimental EW phase. Te coefficients were adjusted using a best-fit iterative approach until the new corrected experimental result closely matched the calculated image in Figure 5b for the theoretical EW phase of graphene in the single-layer region. Figure 4c shows the resulting experimental EW phase aſter
this numerical subtraction of residual aberrations. Te single- layer graphene area has converged (because of the aberration coefficient best fit) to an almost noise-free representation of the graphene hexagonal lattice. Te match between the EW phase of the numerically simulated model structure (calculated by a multi-slice implementation [13] of Equation (1) using the detailed model input structure shown as a caricature in Fig- ure 5a) and the experimental EW phase results of Figure 4c is quite remarkable. Tis con- firms that the actual sample structure in the double-layer area is in fact the Bernal- stacking alignment that was programmed into the model simulation as input on the structure.
The Final Result: Extracting Quantitative 3-D Information at the Atomic Scale Figure
6a shows
the
same EW phase experimental result as
in Figure 4c, but
Figure 6: (a) Experimental EW phase images of graphene sheets—the same as Figure 4c (right side). (b and d) Higher magnification in RGB color scale: (b) from the double-layer area; (d) from the single-layer area, indicated by ‘‘h’’ in (a). (c and e) Line scans of experimental phase image: (c) from the double-layer area; (e) from the single-layer area. (f) Simulated EW phase image of graphene sheet(s)—the same as Figure 5b. (g and h) Line scans (as indicated in (f) in ‘‘double layer’’ and ‘‘single layer’’ region) on EW phase images propagated by a defocus of +3 Å and –3 Å [4].
2011 May •
www.microscopy-today.com
with additional quantitative analysis [4]. Te two square sample areas marked in Figure 6a are shown in the color maps in figures 6b and 6d. Te brightest orange spots in Figure 6b represent the two-carbon-atom atomic columns in the double- layer graphene structure and therefore represent the
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