Elsevier

Ultramicroscopy

Volume 102, Issue 4, March 2005, Pages 317-326
Ultramicroscopy

The spatial resolution of imaging using core-loss spectroscopy in the scanning transmission electron microscope

https://doi.org/10.1016/j.ultramic.2004.11.001Get rights and content

Abstract

The ‘delocalization’ of inelastic scattering is an important issue for the ultimate spatial resolution of core-loss spectroscopy in the electron microscope. This paper investigates the resolution of scanning transmission electron microscopy images for single, isolated atoms. Images are simulated from first principles using a nonlocal model for electron core-loss spectroscopy. The role of the width of the probe relative to the delocalization of the underlying ionization interaction is considered.

Introduction

In recent years, atomic resolution microscopy has become an essential tool in areas such as nanotechnology [1] and bioengineering. Its uses include the investigation of the properties of materials containing dopants and the characterization of biological samples [2]. The scanning transmission electron microscope (STEM) is able to provide images at atomic resolution, the more so if fitted with a field emission gun (FEG) and a spherical aberration corrector.

The advent of aberration correctors for STEM probe forming optics allows third-order spherical aberration as well as defocus to be varied [3], [4]. These aberrations can then be used to offset the effect of fifth-order spherical aberration in order to obtain an aberration balanced probe which approximates an aberration free probe. The reduction in coherent aberrations allows the aperture of the probe forming optics to be increased in size, resulting in a smaller probe [5]. The availability of aberration correctors has led to a rapid increase in resolution in electron microscopy, as manifested, for example, in the UK SuperSTEM and the Department of Energy transmission electron aberration-corrected microscope (TEAM) projects [6], [7]. Aberration corrected STEMs operating at 100 keV can routinely produce STEM probes of approximately 1 Å in size. Small probe sizes have led to successful detection of single atoms on the surface or within bulk samples [8], [9]. Increasing the energy of electrons within the probe to 300 keV leads to a reduced wavelength and the possibility of forming even finer probes, such as in the VG Microscopes HB603U STEM at Oak Ridge National Laboratory (fitted with a NION aberration corrector). All calculations in this paper are done assuming 300 keV incident electrons.

Annular dark field (ADF) images are produced by electrons which have undergone thermal diffuse scattering (TDS). The intensity of these incoherent images varies approximately as the square of the atomic number Z2 and hence is known as Z-contrast imaging. Strong signals are obtained for heavier elements whereas lighter elements, such as O and N, may not be detected in some cases. It also becomes difficult to distinguish between elements in the image which have similar atomic numbers. However, ADF signals are highly localized at atomic positions, making them excellent indicators of atomic locations with sub-Ångström information transfer, as shown by Nellist and Pennycook [10], [11].

Unambiguous identification of the atoms within an ADF image may be performed by electron energy loss spectroscopy (EELS). This detects electrons which have undergone an energy loss associated with a given inelastic scattering event and scattered through a range of angles determined by the detector geometry. To measure a particular atomic ‘signature’ an energy window is set about the threshold energy of a specific ionization event. Unlike ADF, EELS works well for light elements, where the energy losses of the scattered electrons are small. Since the maximum energy loss measurable by an EELS detector is a few keV, measurements are made for relatively loosely bound inner-shell electrons, which means that EELS signals are not as localized at the atomic positions as corresponding ADF signals.

Full structural and elemental composition information of the sample is acquired by correlating spectroscopic information (an EELS map) with a local structure measurement (the ADF image). However, the delocalization of the inner-shell ionization interaction can make direct correlation of the EELS signal with the probe position difficult. One aim of combining EELS data with ADF images is to investigate crystal structure via column-by-column spectroscopy [12]. This requires that the EELS signal is essentially localized to the column in question. As has recently been shown, the spreading of the probe in the crystal coupled with the delocalization of the ionization interaction, leads to EELS signals originating from neighbouring columns in addition to the column of interest [13]. Allen et al. have also shown that a similar ‘cross-talk’ occurs in ADF imaging [14]. Thus a probe used in column-by-column spectroscopy must produce sufficiently resolved results in both the ADF image and EELS spectra if the technique is to be feasible. It is therefore important to correctly model both the probe propagation in the sample and the underlying delocalized ionization interaction, in order to elucidate achievable resolutions in EELS spectroscopy. Simulations are required for the correct interpretation of experimental results and for the improvement of experimental procedures.

This paper discusses the extent to which the width of the probe and the detector size determines the resolution of images based on inner-shell ionization. There has been some robust debate within the field as to the extent of the delocalization of the interaction. Previous quantum mechanical descriptions have predicted both definite localization [12] and significant delocalization [15]. The results presented here are closer to those in Ref. [15]. The calculations in Ref. [12] have an incorrect modulus sign on F(1s,1s) in their Eq. (3), leading to results which are significantly too localized. The effective inelastic scattering potential for core-loss spectroscopy is nonlocal as a consequence of the use of the mixed dynamic form factor formulation and direct interpretation is complicated. If the effective scattering potential can be approximated in a suitable local form, then it can be represented in real space. The localization is then just a measure of the peak widths. Extensive work, however, has shown the importance of the nonlocal form of the interaction and the local, or object function, approximations are not always adequate [16], [17], [18], [19]. However, this form of scattering potential cannot be as easily visualized. In the case of zone-axis illumination, it is a function of four variables and not possible to plot or simply determine localization of the interaction by measuring the width of the potential. In order to avoid this difficulty, this paper will use the full-width at half-maximum (FWHM) of the STEM EELS images as a measure of the delocalization of the EELS interaction.

The modelling of single, isolated atoms provides an environment in which to investigate the spatial resolution for EELS imaging in STEM in a generic way, ignoring sample-dependent effects such as multiple scattering and channelling of the probe, as we have done previously [9], [14], [20], [21]. In addition, it has been assumed that there is no thermal motion of the isolated atom, providing the optimal measure of the STEM image width, without the additional smearing due to thermal motion. However, ignoring these effects, we still expect to obtain a good qualitative feel for what one might expect for EELS imaging of a particular element, irrespective of the local environment in which it resides. The primary limitation on the width of single atom features for EELS is the width of the probe achievable in current machines [21]. This paper investigates the resolution achievable by aberration free probes, both as a function of the probe size and delocalization of the EELS interaction.

Section snippets

STEM probe formation

In momentum space the wave function of a coherent STEM probe is simply the transfer function of the probe forming optics,T(p)=O(p)exp[-iχ(p)],where p is a transverse momentum component in the incident probe and O(p) is the probe forming aperture pupil function. The coherent aberrations of the probe are characterized by χ(p),χ(p)=πΔfλp2+π2Csλ3p4+π3C5λ5p6,where p|p| and λ1/k is the wavelength of the incident electrons, k being the magnitude of the corresponding wave vector. The aberrations

Single atom STEM EELS imaging

Simulated STEM images were made for single, isolated atoms using an incident probe energy of 300 keV, assuming an aberration free probe. The EELS detector has a collection semi-angle β=20mrad and an energy window ΔE=40eV above the threshold energy for ionization. In order to quantify the resolution obtainable with the simulated probe, the FWHM of the STEM images were calculated.

Typical images are shown in Fig. 2(a) for K-shell ionization of carbon, magnesium and calcium where a probe forming

Resolvability

Consider the case of the silicon dumbells as seen under 110 zone axis conditions. The atomic columns in this case are separated by 1.36 Å. Shown in Fig. 6 are the STEM core-loss images that would result from two silicon atoms separated by this distance for α=20mrad and the parameters used in Fig. 3. The images of individual atoms are shown by the dotted lines and the sum of these images shown by the solid line. Fig. 6(a) shows the silicon K-shell images. The individual images have a FWHM of

Conclusion

This paper investigated the resolution of STEM imaging, based on core-loss spectroscopy. The ‘delocalization’ of inelastic scattering is seen to be a crucial issue for the ultimate spatial resolution of core-loss spectroscopy in the electron microscope. Images for single atoms were simulated from first principles using a nonlocal model for electron core-loss spectroscopy. The role of the width of the probe, relative to the delocalization of the underlying ionization interaction has been

Acknowledgements

The authors acknowledge fruitful discussions with Scott Findlay. M.P. Oxley and L.J. Allen acknowledge support by the Australian Research Council. S.J. Pennycook acknowledges support by the Laboratory Directed Research and Development Program of ORNL, managed by UT-Battelle, LLC, for the US Department of Energy under Contract no. DE-AC05-00OR22725.

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