3D electron microscopy in the physical sciences: the development of Z-contrast and EFTEM tomography
Introduction
The ability of modern high-resolution electron microscopes to produce images at near atomic resolution has led to tremendous progress in many fields of biological and materials research. However, the vast majority of images are simply two-dimensional projections of a three-dimensional structure. Of course, for transmission electron microscopy, the sample must be necessarily thin and as such, the projection will be through a relatively small slice of the three-dimensional structure. This has enabled microscopists in many circumstances to regard the third dimension as constant and interpret the image accordingly. Where this third dimension has been seen to be important, for example in looking at dislocation structures, then stereo pairs have been used to give the impression of a third dimension, but in reality reveals very little 3D information.
In biology, the need for true three-dimensional imaging has been apparent for a number of decades. Biological structures, such as viruses or macromolecular assemblies, need to be determined in all three dimensions and particularly where, as is the case for most structures of this type, the topology is crucial to the chemical or physical properties of the complex. Electron tomography is a means by which a three-dimensional structure can be reconstructed from a series of images or projections, taken at regular tilt intervals. As will be discussed in more detail later, these projections allow the three-dimensional structure to be determined with remarkable accuracy and there are now many examples of this in the molecular biology literature [1].
In materials science and engineering, X-ray tomography has been used to reconstruct relatively large three-dimensional structures [2]. However, the wavelength of X-rays, coupled with the poor quality of X-ray lenses, is such that a resolution of no better than 2 μm has ever been achieved and often it is considerably worse than this. At the opposite end of the resolution scale, the atom probe field ion microscope (APFIM) has been developed over the last decade or so to allow atom probe tomography to be undertaken with true atomic scale accuracy [3]. The atom probe technique is the only one which allows single atom counting of a three-dimensional structure and as such it is remarkably powerful. However, this sensitivity is also a limitation in that such a technique can never examine a sample a few hundred nanometres in dimension: even a 100 nm cube of say Si contains 5×107 atoms! More problematic is the need for the sample to be conducting and withstand high field stresses exerted at the tip of the needle-shaped sample needed for APFIM.
Thus there seems to be a need for another technique to fill this middle ground. Such a need is driven by the progress of nanotechnology in the physical sciences and in materials sciences in particular. As structures designed and grown for modern devices become ever smaller, and the lateral dimension of a feature approaches the size of its third dimension, there is a pressing need to examine materials in all three dimensions to gain a full picture of the device structure. This is beginning to happen in the microelectronics industry where the three-dimensionality of vias, dopant profiles, etc. becomes increasingly critical to the performance of the semiconductor. In the magnetic recording industry the small magnetic elements are again approaching ever smaller dimensions and there is a growing need to examine the three-dimensional composition and magnetic microstructure. The latter requires measurement of the magnetic induction of the sample and this can be achieved with electron holography [4]. However, in order to correctly describe a three-dimensional vector field then in principle three tilt series are required with mutually perpendicular tilt axes. However, in the case of magnetic fields, the absence of magnetic monopoles leads to having a requirement for only two tilt series with the third component of the vector field determined uniquely by the other two.
Three-dimensional analysis will also become increasingly important not only for functional materials but also for structural and engineering materials. The design of high temperature, high strength superalloys often requires microstructure to be optimised in all three dimensions, perhaps with a 3D dispersion of hard material within a more ductile matrix. A similar microstructure is found in many composites. Some are already studied with X-ray tomography but new fine scale metal-ceramic composites (cermets) require far higher resolution. The same could be said of metallic foams. In the catalysis industry, heterogeneous catalysts [5] are being designed with nanometre sized active particles distributed in three dimensions on or within a support structure as will be explored later in the paper.
Section snippets
Tomography
It is perhaps worth spending some time reviewing the origins of tomography, and electron tomography in particular, before discussing some of the more detailed aspects and how these are important to the study of specimens found in materials research.
The need to obtain higher dimensionality ‘structures’ using lower dimensionality data is present in many different fields of physical and life sciences. The first real application of this however, was in the field of astronomy when Bracewell [6]
The Radon transform
Although the first practical formulation of tomography was achieved by Bracewell in 1956, in fact it was Radon who first outlined the mathematical principles behind the technique in 1917 [19]. The paper defines the Radon transform, R, as the mapping of a function f(x,y), describing a real space object D, by the projection, or line integral, through f along all possible lines L with unit length ds:The geometry of the transform is illustrated in Fig. 1. A discrete sampling of the
The central slice theorem and Fourier space reconstruction
In practice reconstruction from projections is aided by an understanding of the relationship between a projection in real space and Fourier space. The ‘central slice theorem’ or the ‘projection-slice theorem’ states that a projection at a given angle is a central section through the Fourier transform of that object. This is of course exactly the theorem used for the ‘projection approximation’ relating the intensity of zero order Laue zone (ZOLZ) reflections to the crystal potential projected in
Back-projection: real space reconstruction
The theory of back-projection relies on simple reasoning: a point in space may be uniquely described by any three ‘rays’ passing through that point. If the object is increased in complexity more ‘rays’ are then required to describe it uniquely. In essence a projection of an object is an inverse of such a ‘ray’, and will describe some of the complexity of that object. Therefore inverting the projection, smearing out the projection into an object space at the angle of projection, generates a
Acquisition geometry and anisotropic resolution
For unique (non-repeating) structures, images (projections) must be acquired at regular angular increments by tilting the specimen using the microscope goniometer. Usually ‘single-axis tilting’ is used in which the specimen is tilted about the eucentric axis of the specimen holder rod, from one extreme of the tilt range to the other and Fourier space is sampled by planes whose normals are perpendicular to the tilt axis. Alternatively, a ‘conical tilting’ approach can be used, made possible by
Alignment
In the biological sciences, tomographic alignment of a tilt series is achieved by tracking the movement of fiducial markers (typically gold particles) [36]. However this means that a selection of an area for tomographic reconstruction is limited only to those areas that have sufficient markers for alignment. This is acceptable for a specimen showing many structures dispersed on a carbon film but for specimens that have a small number of areas suitable for analysis, such as is typical in
The projection requirement
To be suitable for tomographic reconstruction a transmitted signal must meet several assumptions of which ‘the most crucial is the belief that what is detected is some kind of projection through the structure. This ‘projection’ need not be a sum or integral through the structure of some physical property of the latter; in principle a monotonically varying function would be acceptable’ [41]. This is known as the projection requirement. Nearly all published electron tomography results use
STEM HAADF (-contrast) tomography
Electrons scattered to low angles are predominantly coherent in nature and as such conventional BF and DF images are prone to contrast reversals with changes in specimen thickness, orientation or defocus. However, electrons scattered to high angles are predominantly incoherent, and images formed using a high-angle annular dark field (HAADF) detector do not show the contrast changes associated with coherent scattering [44]. Such high angle scattering is associated with electron interaction close
EFTEM tomography
Energy-filtered transmission electron microscopy (EFTEM) allows rapid quantitative mapping of elemental species over wide fields of view with a spatial resolutions of ∼1 nm [56], [57], [58]. In the biological sciences zero-loss images are taken routinely for both conventional imaging and electron tomography. In this case an energy filter removes those electrons that have undergone inelastic scattering of greater than about 5 eV, improving the contrast of BF images, particularly for thick
Conclusions
It is now clear that electron tomography offers a means to determine the three-dimensional structure and composition of many different materials at the nanometre level. In general, tomography using BF TEM for materials science applications will not yield true reconstructions because of the coherent nature of the scattering process seen in such images. BF images contain contrast that does not satisfy the projection requirement for tomography. Incoherent signals, such as those used to form STEM
Acknowledgements
The authors would like to acknowledge the contributions of Prof. Sir John Meurig Thomas and Drs Chris Boothroyd, Rafal Dunin-Borkowski and Ron Broom to this research. We thank Profs Peter Buseck and Richard Frankel for the provision of the magnetotactic bacterium sample. We would also thank the EPSRC, FEI and the Royal Commission for the Exhibition of 1851 for their financial support.
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