A I Kirkland is Professor of Materials at Oxford University and the author of over 170 refereed papers. He was awarded “best materials paper” of 2005 by the Microscopy Society of America. Since 2000 he has also been involved in the characterisation of CCD cameras for TEM. His most recent work involves the development of approaches to complex phase extension and diffractive imaging to further improve resolution. J Hutchinson is a Reader in Materials at Oxford University and has published over 300 refereed papers during his career.. He is currently Vice-President of the Royal Microscopical Society (President 2002-2004), and from 2000-2004 was also a member of the Executive Board of the European Microscopy Society. He has also been involved in the development of the world’s first double-aberration-corrected electron microscope.

Nanocharacterisation

By Augus I Kirkland, John L Hutchison

The Royal Society of Chemistry

Copyright © 2007 The Royal Society of Chemistry
All rights reserved.
ISBN: 978-0-85404-241-8

Contents

Chapter 1 Characterisation of Nanomaterials Using Transmission Electron Microscopy D. J. Smith,
Chapter 2 Scanning Transmission Electron Microscopy A. R. Lupini, S. N. Rashkeev, M. Varela, A. Y. Borisevich, M. P. Oxley, K. van Benthem, Y. Peng, N. de Jonge, G. M. Veith, S. T. Pantelides, M. F. Chisholm and S. J. Pennycook,
Chapter 3 Scanning Tunneling Microscopy of Surfaces and Nanostructures M. R. Castell,
Chapter 4 Electron Energy-loss Spectroscopy and Energy Dispersive X-Ray Analysis R. Brydson,
Chapter 5 Electron Holography of Nanostructured Materials R. E. Dunin-Borkowski, T. Kasama and R. J. Harrison,
Chapter 6 Electron Tomography M. Weyland and P. A. Midgley,
Chapter 7 In-situ Environmental Transmission Electron Microscopy P. L. Gai,
Subject Index, 291,

CHAPTER 1

Characterisation of Nanomaterials Using Transmission Electron Microscopy

D. J. SMITH

Department of Physics, Arizona State University, Tempe, AZ 85287 USA

1.1 Introduction

The Transmission Electron Microscope (TEM) has evolved over many years into a highly sophisticated instrument that has found widespread application across the scientific disciplines. Because the TEM has an unparalleled ability to provide structural and chemical information over a range of length scales down to the level of atomic dimensions, it has developed into an indispensable tool for scientists who are interested in understanding the properties of nanostructured materials and in manipulating their behaviour.

The resolution of the optical microscope is restricted by the wavelength of visible light, which thus precludes atomic-scale imaging. In contrast, an energetic electron has a wavelength of much less than 1 Å (where 1 Å = 10-10 m), so that an enormous improvement in resolution can be achieved, at least in principle, by using a beam of fast electrons for imaging. A suitable combination of (magnetic) electron lenses is required, both for focusing the electron beam onto the object and also for providing an enlarged image. Maximum magnifications at the microscope are typically close to or exceed one million times, so that details of the nanoscale object are clearly visible on the final viewing screen or recording medium.

Image formation in the TEM is more complicated in practice than is the case for the optical microscope. Strong magnetic fields are needed for focusing the electron beam, and these cause electrons to take a spiral trajectory through the lens field. In addition, a major restriction on ultimate microscope performance results from unavoidable aberrations of round electron lenses. Primarily, due to the need for a compromise between small-angle diffraction effects and wide-angle spherical-aberration limits, the resolution, d can be roughly expressed by an equation of the form

d = A C1/4sλ3/4 (1.1)

where CS is the spherical aberration coefficient of the objective lens, λ is the electron wavelength, and A is a constant with a value ranging from 0.43 to 0.7 depending on the type of imaging (coherent, incoherent, or phase contrast). Values of d typically range from about 3.0 Å down to 1.0 Å as electron energies are increased from 100 to 1250 keV. Modern-day TEMs operating at 200 or 300 keV have resolution limits well below 2.0 Å, which is comparable to the spacing between atoms. Individual columns of atoms can thus be resolved in crystalline materials, which must first, however, be oriented so that the incident electron beam is aligned along some major crystallographic zone axis of the sample.

The power of the technique is illustrated by the example in Figure 1.1, which shows the boundary region between two Al crystals, both of which are oriented so that the electron beam is parallel with the [001]-type zone axis. Each black spot in the image marks the position of a column of Al metal atoms viewed in an end-on geometry. It is obviously straightforward to visualise the periodic array of misfit dislocations (arrowed) that accommodate the angular misfit of 6° 1 between the two crystals, and further analysis would enable the detailed atomic structure around the dislocation core to be determined.

This chapter begins by providing a brief introduction to the TEM and some of the key aspects of high-resolution imaging. Applications to nanostructured materials are then described in greater detail, and some emerging trends and unresolved issues are briefly discussed. For further information about microscope operation and more details about applications to a broader range of materials, the interested reader is referred to the review articles and monographs listed at the end of the chapter.

1.2 Imaging

1.2.1 Transmission Electron Microscopy

In the standard TEM operating mode, which is commonly referred to as amplitude or diffraction contrast imaging, only a fraction of those electrons that have passed through the sample are used to form the highly magnified final image. Most of the scattered (or diffracted) electrons are prevented from reaching the image plane by positioning a small objective aperture located in the back focal plane of the objective lens. This aperture thus serves to determine the image contrast. For the case of crystalline samples, the electron diffraction pattern (EDP) is used to ensure that the orientation of the specimen relative to the direction of the incident electron beam will satisfy a strongly diffracting condition. Many common structural defects have a highly characteristic appearance under such diffraction contrast conditions. The spacings and angles between crystal lattice planes can also be determined if the EDP is first calibrated using a known material. In addition, the availability of a crystalline substrate or support can provide a convenient method for sample orientation during observation. By using the substrate EDP for reference purposes, internal interfaces can be aligned perpendicular to the electron-beam direction so that any changes in the microstructure of thin films and multilayers can then be determined as a function of film thickness. As an example, Figure 1.2 shows a multilayered Magnetic Tunneling Transistor (MTT) deposited directly on the native oxide of a Si substrate. The individual layers of the MTT can be clearly recognised, and their thickness uniformity is easily confirmed. Finally, it should be appreciated by the reader that examination of such complex samples with the TEM can represent a serious challenge to the electron microscopist. Because of considerable differences in thinning rates, it will often be difficult to prepare samples that are electron transparent across the entire region of interest simultaneously. Descriptions of different approaches for preparing electron-transparent specimens can be found elsewhere.

1.2.2 High-Resolution Electron Microscopy

In the technique of High-Resolution Electron Microscopy (HREM), a much larger objective aperture (or sometimes none at all) is used. The directly transmitted beam can then interfere with one or more diffracted beams, and the contrast across the image will depend on the relative phases of the various beams. This imaging mode is thus often referred to as phase contrast imaging. When the microscope imaging conditions are properly adjusted (lens defocus, image astigmatism, incident beam alignment) it is possible to interpret phase-contrast images in terms of the projected crystal potential provided that the specimen thickness is not too great (less than 10 nm preferred). Indeed, individual atomic columns can be separately resolved in many crystalline inorganic materials using the latest generations of HREM instruments. High electron doses, typically ~ 500–2000 electrons per square Å, are required to record such images, which means that specimens intended for high-resolution studies must be relatively resistant to electron-irradiation effects. It is impossible to examine most organic materials and polymers directly under such intense imaging conditions. By using a specimen-heating holder, and by adding a TV rate image pickup system to the base of the electron microscope lens column, dynamic events can be followed in real time without significant loss of spatial resolution.

Over the past 40 years, HREM has been used to characterise a wide range of inorganic materials. Important applications include determining the micro-structure of crystalline defects, interfaces and grain boundaries, investigating nanocrystalline features in amorphous films, and studying small particles in heterogeneous catalysts. The characterisation of magnetic thin films and multi-layers, for example, continues to be very important, since layer continuity and defect microstructure are crucial to the viability of recording media. High resolution images are able to provide specific details that are usually unavailable using other techniques. As an illustration, Figure 1.3(a) and (b) compare two high-resolution electron micrographs that reveal the amorphous or polycrys-talline nature of the barrier layers in simple magnetic tunnel junctions grown by dc reactive sputtering. The layer sequences in the images are: (a) Co (50 nm)/ HfO2 (10 nm)/Fe (50 nm), and (b) Co (50 nm)/CoO (10 nm)/Fe (50 nm). Further high resolution images of nanomaterials are presented in later sections.

1.2.3 Basis of High-Resolution Imaging

Image formation in the electron microscope occurs in two stages. Electrons of the incident beam interact with the specimen, undergoing both elastic and inelastic scattering. The electron wavefunction emerging from the exit surface of the specimen passes through the objective lens and additional magnifying lenses are used to form the final image. Electrons that are elastically scattered mainly contribute to the high-resolution bright-field image. Note that the inelastically scattered electrons can provide valuable information about sample composition via the technique of Electron Energy-Loss Spectroscopy (EELS), while electrons scattered to very large angles can be used for Z-contrast Annular Dark-Field (ADF) imaging in the Scanning Transmission Electron Microscope (STEM). These possibilities are described in other chapters.

Unlike X-ray or neutron scattering, electron scattering is strongly dynamical, meaning that the kinematical scattering approximation will be inadequate for understanding image formation except for the very thinnest of samples. Multiple electron scattering with large phase changes is far more typical, so that knowledge about the relative heights and locations of different atoms in the specimen becomes important for quantitative interpretation of image features. Indeed, image simulations are considered as essential for extracting detailed information about atomic arrangements at dislocations and interfaces. Several approaches to image simulation have been developed over the years, with the most widespread, commonly known as the multislice method, being based on an n-beam dynamical theory of electron scattering. In this approach, atoms in the specimen are considered as being located on narrowly separated planes (or slices), normal to the beam direction. The electron wavefunction is then propagated slice-by-slice through the sample to eventually form the exit-surface wavefunction. This iterative process lends itself to convenient computer algorithms that enable rapid computations to be carried out, and these simulations are especially useful during the refinement of unknown defect structures. Further information about different but equivalent theories of electron scattering can be found in the monograph by Cowley.

The electron wavefunction at the exit surface of the specimen must still be transferred to the final viewing screen or recording medium. This process is determined primarily by the properties of the objective lens. The effect of this lens can be conveniently understood by reference to what is termed the Phase-Contrast Transfer Function (PCTF), as described by Hanszen. The basic form of the PCTF is independent of both specimen and microscope so that a single set of universal curves can be used to describe the transfer characteristics of all objective lenses. Electron microscopes with different objective lenses, or operating at different electron energies, are then easily compared by using suitable scaling factors. Figure 1.4 shows PCTFs for the optimum defocus of the objective lens of a typical 400 kV HREM. The two curves correspond to: (a) coherent, and (b) partially coherent, incident electron illumination.

It is important to appreciate that the PCTF has an oscillatory nature, as visible in Figure 1.4, which means that electrons scattered to different angles undergo reversals in phase. These phase oscillations will thus cause artefactual detail in the final image that may be misinterpreted. The PCTF is also focus dependent, meaning that further phase changes occur when the focus is changed, and these will also affect the appearance of the image. Thus, much of the detail visible in the recorded micrograph could be uninterpretable unless the lens defocus is accurately known. Also note that the incident electron beam is ideally a coherent, monochromatic plane wave, whereas in practice some loss of coherence results from focal spread (temporal coherence) and finite beam divergence (spatial coherence). These effects of partial coherence are conveniently represented by envelope functions that cause dampening of the PCTF at larger scattering angles. Specimen information scattered to higher spatial frequencies, equivalent to higher image resolution, is therefore lost. These incoherent effects are illustrated by the curve labeled (b) in Figure 1.4, where it should also be noted that the positions of the PCTF zeroes are not affected by the envelopes. Finally, note that additional specimen information may become available through the use of the highly coherent Field- Emission electron Gun (FEG).

1.2.4 Resolution Limits

The resolution of any imaging system is closely coupled to the illumination wavelength. Thus, resolution limits on the picometre scale might reasonably be expected for high-energy electrons. As mentioned earlier, the compromise between diffraction and spherical aberration gives an approximate estimate of the image resolution. In practice, high-resolution imaging is considerably more complicated, and there are several alternative definitions that are applicable depending on the sample and the microscope operating conditions. These resolution limits are most easily understood by considering the PCTF of the objective lens.

The interpretable image resolution, which is sometimes referred to as the structural or point resolution, is defined only at the optimum or Scherzer defocus, where the PCTF has the largest possible band of spatial frequencies without any phase reversal. The corresponding first zero crossover, as indicated by the arrow in Figure 1.4, gives the interpretable resolution. Cs values increase slightly at higher electron energies. However, because of the reduction in λ improvements in theoretical resolution limits are obtained. Typical interpretable resolutions are in the range of 2.5 Å down to 1.2 Å for corresponding accelerating voltages of 200 kV up to 1000 kV. The size and cost of higher-voltage electron microscopes, as well as the increasing likelihood of electron irradiation damage for higher-energy electrons, are further practical factors that need to be taken into account. Intermediate-voltage HREMs, operating in the 200 to 400 kV range, have become widespread because of these considerations.

The envelope functions define the instrumental resolution or information limit of the HREM. A value of roughly 15% [i.e. exp(-2)] is usually taken as the resolution cutoff since this level is commonly regarded as the minimum acceptable for image-processing requirements. This resolution limit can extend well beyond the interpretable resolution for 200 or 300 kV HREMs equipped with an FEG electron source, as illustrated in Figure 1.5. Very fine detail is thus often present but it is not easily related to specimen features because of the PCTF oscillations mentioned earlier. An objective aperture of suitable diameter can be used to prevent beams with inverted phase from contributing to the image. Alternatively, the phase modulations caused by the PCTF can be removed by a posteriori image processing when the defocus and Cs values are known well enough. Improved image resolution can then be achieved, as demonstrated by the pioneering studies of Coene et al. who were able to resolve columns of oxygen atoms in a high-temperature superconductor for the first time using an approach based on focal-series reconstruction.

The expression lattice-fringe resolution refers to the very finest spacings that can be obtained as a result of interference between two or more diffracted beams. Here, the instrumental stability of the HREM is critical, as well as freedom of the microscope environment from adverse external factors such as acoustic noise, mechanical vibrations, and stray magnetic fields. The lattice-fringe resolution was formerly regarded as an important figure of merit for comparing microscope performance but the interpretable and instrumental resolution limits are nowadays considered more relevant. Note that very fine lattice fringes do not usually contain any useful local information about atomic structure. The interfering diffracted beams can originate from comparatively large specimen areas, and the lattice-fringe images may be recorded at significant underfocus conditions when there are many PCTF oscillations.

(Continues…)Excerpted from Nanocharacterisation by Augus I Kirkland, John L Hutchison. Copyright © 2007 The Royal Society of Chemistry. Excerpted by permission of The Royal Society of Chemistry.
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