pubs.acs.org/NanoLett
Standardless Atom Counting in Scanning Transmission Electron Microscopy James M. LeBeau,*,† Scott D. Findlay,‡ Leslie J. Allen,§ and Susanne Stemmer*,† †
Materials Department, University of California, Santa Barbara, California 93106-5050, United States, ‡ Institute of Engineering Innovation, School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan, and § School of Physics, University of Melbourne, Victoria 3010, Australia ABSTRACT We demonstrate that high-angle annular dark-field imaging in scanning transmission electron microscopy allows for quantification of the number and location of all atoms in a three-dimensional, crystalline, arbitrarily shaped specimen without the need for a calibration standard. We show that the method also provides for an approach to directly measure the finite effective source size of a scanning transmission electron microscope. KEYWORDS Scanning transmission electron microscopy (STEM), gold, nanoscale characterization
T
he properties of nanostructures are determined by their size and shape, requiring methods for their characterization that should be capable of precisely quantifying the position, type, and number of all atoms in an arbitrarily shaped sample. Scanning transmission electron microscopy (STEM) holds great promise as a truly quantitative, atomic-resolution characterization tool: it provides directly interpretable atomic resolution images that are highly sensitive to the type1 and number of atoms.2,3 Prior attempts to quantify the number of atoms in nanoparticles and clusters have relied on calibration standards,4,5 only applicable to the particular specimen under investigation. Applicability of calibration standards is further limited by the nonintuitive scaling of image intensities with thickness and an image contrast that depends on sample orientation or phase (i.e., amorphous vs crystalline, polymorph, etc.).6-8 Other, semiquantitative methods that rely on comparisons of relative contrast3,9,10 preclude the determination of absolute atom counts. In this letter, we demonstrate that a truly quantitative approach to atomic resolution STEM, in which experimental images are directly compared with theory,7,11 provides highly accurate, column-by-column counts of atoms in a three-dimensional volume of a sample without the need for a calibration standard or any a priori knowledge of sample shape or thickness. The sample investigated here was a wedge-shaped gold foil deposited on a NaCl single crystal and thinned to electron transparency. To obtain well-defined (111) facets, the sample was annealed in situ, using a parallel electron beam in transmission electron microscopy (TEM) mode.12 A FEI Titan 80-300 TEM/STEM (Cs ≈ 1.2 mm) operating at 300 kV and equipped with an annular dark-field detector (Fischione
Model 3000) was used for high-angle annular dark-field (HAADF) STEM imaging. The convergence semiangle was 9.6 mrad and the inner detector semiangle was 65 mrad. The focus (53 nm underfocus) was determined using comparisons with simulations. The method to obtain images on an absolute intensity scale relative to the incident beam for direct comparison with simulations has been described elsewhere.11 To determine the local sample thickness and ensure accurate tilt, position averaged convergent beam electron diffraction (PACBED) patterns were acquired.13 The frozen phonon multislice method,14 which accurately predicts image intensities over a wide thickness range,7,8 was used to simulate image intensities using a 2.855 nm × 2.884 nm supercell sampled on a 2048 × 2048 grid and averaged over 20 phonon configurations. The Debye-Waller factor for Au was 0.000079 nm2 (ref 15). The effective source size was estimated as a Gaussian envelope function with a full width at half-maximum of 0.110 nm.16 Image analysis made use of MATLAB and the Image Processing Toolbox. The positions of all atom columns in the experimental images were determined by normalized crosscorrelation17 after applying a Wiener filter to the image to reduce noise,17 which improved the accuracy of column finding. The cross-correlation operation applied a twodimensional Gaussian template with a standard deviation of 0.113 nm. The signal at each atom column was extracted from the unfiltered, original image by averaging the intensities about each atom position within a small disk of radius 0.023 nm. Because of the “tearing” noise typical for unfiltered STEM images, which can reduce the intensity at the centroid position, the column intensity was defined as the maximum average intensity found within (5 pixels or 0.04 nm. Similarly, the signal of the simulated atom column was extracted by averaging about the same circular region. Comparison between experimental and simulated atom column intensities was then used to determine the number
* To whom correspondence should be addressed. E-mail: (J.M.L) jmlebeau@ ncsu.edu; (S.S.)
[email protected]. Received for review: 06/7/2010 Published on Web: 10/14/2010 © 2010 American Chemical Society
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FIGURE 1. HAADF-STEM image of a wedge-shaped gold film viewed along 〈110〉. The intensity maxima correspond to gold atom columns and the white labels near the lower right of each atom column indicate the number of atoms contained in that column. The black box outlines the region from which the PACBED pattern shown in Figure 3 was obtained. The image intensities are shown on an absolute scale relative to the incident beam intensity (see scale bar).
of atoms in each column via linear interpolation and rounding to the nearest integer value. Figure 1 shows an experimental HAADF-STEM image of the gold foil observed along 〈110〉. The labels in Figure 1 indicate the number of gold atoms in each column obtained from the comparison. In the thicker region of the sample, the number of atoms in adjacent planes increases smoothly with thickness, generally by one atom. An apparent steplike decrease by more than one atom occurs for the two layers nearest to the sample edge. Simulations suggest that beam broadening into the vacuum cannot account for the intensity step. Thus these outermost layers either contain vacancies or have a larger Debye-Waller factor, as expected near surfaces.18,19 Both effects would serve to reduce the intensity of the column.8 To illustrate the accuracy of the column atom counts, Figure 2a shows a histogram containing all the atom columns in Figure 1, binned according to the number of atoms they contain. The histogram shows that the atom columns in each bin are all self-similar, indicating precise counting. Visual inspection would have already allowed sorting the columns with a precision of (1 atom. For example, the atom column intensities in the bin of columns containing 24 atoms are distinct from those of bins 22 or 26. For a comparison with theory, an average was taken of the atom columns in each bin (Figure 2b). Near perfect agreement is obtained between simulation and experiment for all atom counts. For a more quantitative assessment of the method, an independent measure of the local specimen thickness and © 2010 American Chemical Society
FIGURE 2. (a) Histogram of all the columns in Figure 1 binned by the number of atoms they contain. (b) Atom column images extracted from simulations (top) and experiments (bottom) after averaging all the experimental columns in each bin shown in (a). 4406
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column intensity and is thus not suitable for accurate and precise atom counting. However, both signals (mean and maximum intensities) must match simulations simultaneously. Using this requirement, confidence bands are obtained in Figure 4, which represent errors of (1 atom and (2 atoms, respectively. In other words, columns within the light-shaded band in Figure 4 do not have a counting error greater than 1 atom (as can be seen by shifting one of the data points parallel to the x-axis by two counts). The two bands contain 86 and 99% of the atom columns, respectively. Finally, summing all the atoms in the image shown in Figure 1 yields 10 674 ( 300 atoms, or 3.5 ( 0.1 attograms, within the image. The error represents the maximum possible error (worst case scenario) by assuming that all columns in the (1 atom and (2 atom confidence bands indeed have an error of (1 atom and (2 atoms, respectively. The quantitative analysis of atom column counts in a gold sample also suggests a method for calibrating the finite effective source size of the microscope, a parameter that has been difficult to measure in nonaberration corrected STEM.20 For example, if the source size used in the simulations would have been changed by a mere 4.5% (i.e., a fwhm of 0.105 nm), then only 67% of the columns would have been contained in the (1 atom confidence band. In summary, we have demonstrated that the absolute number of atoms across an entire image can be quantified on a column-by-column basis with single atom sensitivity in atomic resolution STEM. No experimental, empirical calibration standards are required. We note that the method is not limited to Au foils, as quantitative agreement between images and simulations has been shown for a wide range of atomic numbers.7,8 Although contamination layers can reduce the contrast of atom columns, the effect is not significant if reasonable care is taken in the sample preparation process.21 The method is entirely general and can be applied to any arbitrarily shaped sample, such as nanoparticles, nanowires, or thin foils. Since the image simulations accurately describe the experimental image contrast for at least up to 100 nm thick specimens,7,8 a similar analysis can be performed for thicker specimens, at least within the dechanneling length or depth of focus.22 Simultaneously, the method also provides a measurement of the finite effective source size, leaving no experimental sample or microscope parameter undetermined. Combined with already available methods such as atomic resolution electron energyloss spectroscopy23-25 and energy dispersive X-ray spectroscopy,26 this approach opens the path to determining the position, type, and number of all atoms in the material.
FIGURE 3. Experimental (left) and simulated (right) PACBED patterns. The experimental pattern was obtained from the boxed region in Figure 1. The simulation is an average of all the thicknesses corresponding to the experimental atom counts in the boxed region.
FIGURE 4. Comparison of the mean atom column intensity from experiment (circles) and simulations (shaded regions) as a function of number of atoms in the column. The triangles show the experimental, average mean intensities. The light-shaded region represents the (1 atom confidence interval from simulations and the dark band represents the (2 atom confidence interval. The intervals are obtained from the simulated mean intensities for column atom counts that are (1 atom and (2 atoms different compared to what is stated on the x-axis. For example, for the 10-atom-column the borders of the light-shaded region are the simulated mean intensities for 9 and 11 atoms in the column, respectively.
a measure for the error in the atom count were also obtained. One measure of the accuracy of the column atom count can be obtained from comparison with PACBED patterns (Figure 3). PACBED patterns were simulated by averaging patterns corresponding to the range of thicknesses obtained by the atom count in the region from which the experimental PACBED pattern was obtained (boxed region in Figure 1). Within the accuracy of the PACBED method ((1 nm13), excellent agreement between the experimental and simulated PACBED pattern is observed, confirming the accuracy of the atom count. A measure of the error in the total atom count can be obtained from Figure 4, which shows the mean intensity of each atom column (from a region 0.223 × 0.223 nm2 centered about the column) as a function of the estimated number of atoms in that column obtained from the maximum intensity, as described above. The mean intensity varies more slowly with thickness than the maximum © 2010 American Chemical Society
Acknowledgment. The authors thank Junwoo Son for the deposition of the gold films. The research at UCSB was supported by the U.S. National Science Foundation (Grant DMR-0804631). J.M.L. also thanks the U.S. Department of Education for a grant under the GAANN program (Grant P200A07044). The work made use of the UCSB MRL Central 4407
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facilities supported by the MRSEC Program of the National Science Foundation under award No. DMR-0520415. L.J.A. acknowledges support by the Australian Research Council.
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