Towards atomic column-by-column spectroscopy

Abstract

The optical arrangement of the scanning transmission electron microscope (STEM) is ideally suited for performing analysis of individual atomic columns in materials. Using the incoherent Z-contrast image as a reference, and arranging incoherent conditions also for the spectroscopy, a precise correspondence is ensured between features in the inelastic image and elastic signals. In this way the exact probe position needed to maximise the inelastic signal from a selected column can be located and monitored during the analysis using the much higher intensity elastic signal. Although object functions for EELS are typically less than 1 Å full-width at half-maximum, this is still an order of magnitude larger than the corresponding object functions for elastic (or diffuse) scattering used to form the Z-contrast image. Therefore, the analysis is performed with an effective probe that is significantly broader than that used for the reference Z-contrast image. For a 2.2 Å probe the effective probe is of the order of 2.5 Å, while for a 1.3 Å probe the effective probe is 1.6 Å. Such increases in effective probe size can significantly reduce or even eliminate contrast between atomic columns that are visible in the image. However, this is only true if we consider circular collector apertures. Calculations based upon the theory of Maslen and Rossouw [Maslen and Rossouw, Philos. Mag. 49 (6) (1984) 735–742; Rossouw and Maslen, Philos. Mag. 49 (6) (1984) 743–757] show that employing an annular collector aperture can reduce the FWHM of the inelastic object function down to values close 0.1 Å. With practical collector aperture sizes it should be possible to achieve this increased spatial resolution without losing too much signal.

Introduction

Internal interfaces are known to dominate the structure–property relationships of many materials and devices. Thus, the ultimate goal of all atomic or near atomic resolution analysis techniques is to determine both the physical and electronic structure of defects, such as a dislocation core or an interface, within a crystalline matrix with atomic column sensitivity. The optical arrangement in the HB603U STEM is ideally suited for performing analysis of individual atomic columns in materials. The major strength of this instrument is that with incoherent Z-contrast imaging it is possible to obtain direct structure images of the atomic configuration of the specimen. One can directly image defects within a sample and determine the physical structure of the sample on-line without having to rely on any post acquisition image processing techniques. Using the incoherent Z-contrast image as a reference, and arranging incoherent conditions for the spectroscopy, a precise correspondence is ensured between features in the inelastic and elastic signals. In this way the exact probe position needed to maximise the inelastic signal from a selected column can be located and monitored during the analysis using the much higher intensity elastic scattering. Electron energy loss spectroscopy (EELS) analysis offers many advantages over X-ray spectroscopy, such as high collection efficiency and the ability to analyse near edge fine structure. Thus, integrating the HB603U with a dedicated McMullan-type PEELS system will spawn an instrument with unique performance [1].

Defining incoherent imaging conditions for the EELS means that the probe can be separated out of the expression for the inelastic intensity, and the real space distribution of scattering power is then referred to as the object function. The inelastic image is then given by the convolution of the probe intensity profile with the object function. As these functions are similar to Gaussians in many cases, the best single measure of resolution is the FWHM, as convoluting two Gaussians leads to a Gaussian with FWHM equal to the individual two summed in quadrature. However, although object functions for EELS are typically less than 1 Å FWHM, this is still an order of magnitude larger than the corresponding object functions for elastic (diffuse) scattering used to form the Z-contrast image. Therefore, the analysis is performed with an effective probe that is significantly broader than that used for the reference Z-contrast image. For a 2.2 Å probe the effective probe is of the order 2.5 Å, while for a 1.3 Å probe the effective probe is 1.6 Å. Such increases in the effective probe size can significantly reduce or even eliminate the contrast between atomic columns that are visible in the image. A sub-angstrom probe is thus more essential for atomic resolution analysis than it is for imaging. It may be possible to avoid this larger effective probe size if we could set up the experimental conditions to produce an object function with a smaller FWHM. A possible method to achieve this was indicated by Kohl and Rose [2] and explicitly outlined by Ritchie and Howie [3].

The calculations presented by Kohl and Rose illustrated an increase in the localisation of the inelastic signal with the use of a larger collection aperture, while Ritchie and Howie suggested that the use of an off-axis collector aperture would increase the spatial resolution of the inelastic signal. By removing the low angle inelastic scattering events from the electrons forming the spectrum or inelastic image it should be possible to reduce the size of the effective probe used for the analysis. This can be achieved experimentally by using an annular collector aperture. Here we present calculations of the inelastic object function for K-shell ionisation based upon the non-relativistic theory of Maslen and Rossouw [4], [5], [6] for both circular and annular collector apertures. Although we have a 300 kV beam and are using a non-relativistic theory we feel that the results will provide a qualitative idea of the various effects discussed. One of the main differences between this approach and previous object function (actually response function) calculations is that we include the full quantum mechanical nature of the matrix elements describing the transitions. In other calculations [2], [7] these matrix elements have been replaced by some approximation that removes their structure at higher scattering angles; in reality, the matrix elements are not constant over all scattering angles. We briefly discuss the methodology of this theory, point out some of its limitations and how it could be extended to include effects such as multiple scattering. The Z-dependence of the FWHM of the object functions and how this relationship changes with collector aperture geometry will be presented as will the beam energy dependence of the object functions. The practical limitations to the use of annular collector apertures such as the physical limitations to the aperture sizes within the HB603U and the potential loss of signal will also be outlined. This last point will also be discussed in the context of high angle plasmon imaging. Firstly, we shall outline the ideas of incoherent Z-contrast imaging to show how we can relate the elastic signal to the inelastic signal by the use of an effective probe.