Energy dispersive X-ray analysis on an absolute scale in scanning transmission electron microscopy
Introduction
Analytical electron microscopy has long been able to determine elemental concentration ratios with a sensitivity of a few atomic percent in microanalysis via energy dispersive X-ray spectroscopy (EDX). This is done via EDX signal ratios and comparison with reference specimens to minimize the effect of uncertainties in factors such as thickness, ionization cross-section, fluorescence yield and detector geometry [1], [2]. However, in principle, absolute-scale comparison with ionization cross-section calculations is possible. Recent developments in aberration-corrected electron optics and X-ray detector design [3], [4] have facilitated scanning transmission electron microscopy (STEM) EDX mapping at atomic resolution [5], [6], [7], [8], [9], [10], [11], [12], and on this length scale absolute elemental concentrations will often be more useful than relative concentrations. For instance, in nanoparticles, nanoprecipitates, or dopant segregation at interfaces, the absolute number of atoms of a given species contains critical information about their structural arrangement and distribution.
In this paper, we show that absolute-scale agreement between experiment and simulations, which has recently been achieved in high-angle annular dark field (HAADF) imaging [13], [14], [15] and electron energy loss spectroscopy [16], [17], is also possible in STEM EDX. We emphasize that, in on-axis conditions, quantitative agreement requires accounting for dynamical electron scattering, also called “channelling”, even for very thin specimens.
Section snippets
Absolute-scale EDX
EDX measurements were taken using an aberration-corrected FEI Titan3 electron microscope operating at 302 kV. Experiments were carried out for a range of thicknesses in a SrTiO3 crystal viewed along the zone axis. The sample was prepared by cross-sectional tripod/wedge polishing, with final thinning by Ar-ion milling [18]. Two different probe-forming aperture semi-angles were used, 15.2 and 21.5 mrad, both of which produce an atomically fine probe. However, the modest effective collection
Thickness determination
For absolute-scale comparison of the experimental STEM EDX data against simulation, independent measurement of sample thickness is necessary. Our primary method of thickness determination is position averaged convergent beam electron diffraction (PACBED). Some authors successfully apply PACBED with the same convergence angle used for imaging [37], but we obtain better thickness sensitivity for smaller probe-forming aperture angles [19], [38]. Therefore, PACBED patterns were recorded with a 9.2
Effects of channelling
In Fig. 1 the effect of channelling, not hitherto included in quantitative STEM EDX measurements [2], is clearly large, even though the position-averaged signal approach is believed to reduce the severity of channelling effects [20], [41]. From Eq. (2), neglecting X-ray absorption for simplicity, the probe-position averaged signal is given bywheregives the probability density of the fast electron projected across the specimen
Conclusion
We have demonstrated agreement between experiment and simulations incorporating dynamical electron scattering on an absolute-scale in STEM EDX imaging without any free adjustable parameters. Absolute chemical specific atom counting by STEM-EDX analysis with atomic resolution is now clearly in prospect.
Acknowledgements
The authors gratefully acknowledge Dr. Y. Zhu for the sample and Drs. N.R. Lugg and J.M. LeBeau for helpful discussions. We are especially grateful to Dr. N.J. Zaluzec (Argonne National Laboratory) and Alan Sandborg (EDAX Inc.) for assistance with the geometry of our EDX detector. We thank FEI for the measurements of the Be double tilt holder. This research was supported under the Australian Research Councils Discovery Projects funding scheme (Projects no. DP110102228 and DP140102538), its
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These authors contributed equally to this work.