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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DOI: 10.1021/nl102025s | Nano Lett. 2010, 10, 4405–4408
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).
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DOI: 10.1021/nl102025s | Nano Lett. 2010, 10, 4405-–4408
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
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DOI: 10.1021/nl102025s | Nano Lett. 2010, 10, 4405-–4408
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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DOI: 10.1021/nl102025s | Nano Lett. 2010, 10, 4405-–4408